Science, Faculty of
Physics and Astronomy, Department of
DSpace
UBCV
Smith, Gareth
Doctor of Philosophy - PhD
University of British Columbia
Antihydrogen, the bound state of an antiproton and a positron, is an ideal system for testing fundamental symmetries between matter and antimatter. The Antihydrogen Laser PHysics Apparatus (ALPHA) at CERN has a proven history of producing and trapping antihydrogen atoms, with many precision tests of charge-parity-time (CPT) symmetry. The new ALPHA-g apparatus extends this program to a test of gravity, directly probing the applicability of the weak equivalence principle (WEP) to an antimatter system for the first time. This dissertation presents the first ALPHA-g results, which confirm that Earth's gravity acts downwards on antimatter. The ratio between the gravitational acceleration of antihydrogen and hydrogen is estimated to be á¸¡/g = 0.75 ± 0.13 (statistical and systematic) ± 0.16 (simulation). This measurement depends on accurately determining the annihilation positions of antihydrogen atoms released from the ALPHA-g magnetic trap, which is accomplished using a time projection chamber (TPC) detector. To reduce the substantial background due to cosmic ray, a time-of-flight barrel scintillator (BSC) detector was also implemented. The author's primary contributions include the commissioning of the BSC, including devising and implementing time-of-flight measurements, leading to a significantly reduced background rate. Additional contributions include improving the TPC tracking algorithms to reach the required annihilation position resolution. This dissertation begins with theoretical motivations for testing the WEP using antihydrogen, followed by an overview of the ALPHA apparatus and antihydrogen production. The TPC and BSC detectors are introduced, including the event reconstruction methods, with care to highlight the author's work. Finally, the gravity measurement methodology and results, as well as future perspectives, are discussed. This first direct test of gravity on antimatter rules out a large difference in the gravitational behaviour of antimatter and matter, furthering our understanding of the fundamental matter-antimatter symmetry, and laying the foundation for future precision WEP tests using antimatter.
Detecting Antihydrogen Annihilations inALPHA-g for Measurement ofGravitational Free FallbyGareth SmithM.Sc., The University of British Columbia, 2021B.Sc., Carleton University, 2019A DISSERTATION SUBMITTED IN PARTIAL FULFILLMENT OFTHE REQUIREMENTS FOR THE DEGREE OFDOCTOR OF PHILOSOPHYinThe Faculty of Graduate and Postdoctoral Studies(Physics)THE UNIVERSITY OF BRITISH COLUMBIA(Vancouver)September 2025© Gareth Smith 2025The following individuals certify that they have read, and recommend to theFaculty of Graduate and Postdoctoral Studies for acceptance, the disserta-tion entitled:Detecting Antihydrogen Annihilations in ALPHA-g for Measure-ment of Gravitational Free Fallsubmitted by Gareth Smith in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in Physics.Examining Committee:Dr. Makoto Fujiwara, Senior Research Scientist, Particle Physics Depart-ment, TRIUMFCo-SupervisorDr. Takamasa Momose, Professor, Department of Chemistry, University ofBritish ColumbiaCo-SupervisorDr. Michael Hasinoff, Professor, Department of Physics and Astronomy,University of British ColumbiaSupervisory Committee MemberDr. Christopher Hearty, Professor, Department of Physics and Astronomy,University of British ColumbiaUniversity ExaminerDr. Andrew MacFarlane, Professor, Department of Chemistry, University ofBritish ColumbiaUniversity ExaminerDr. Michel Lefebvre, Professor, Department of Physics and Astronomy, Uni-versity of VictoriaExternal ExaminerAdditional Supervisory Committee Members:Dr. Mark Halpern, Professor, Department of Physics and Astronomy, Uni-versity of British ColumbiaSupervisory Committee MemberiiAbstractAntihydrogen, the bound state of an antiproton and a positron, is an idealsystem for testing fundamental symmetries between matter and antimat-ter. The Antihydrogen Laser PHysics Apparatus (ALPHA) at CERN has aproven history of producing and trapping antihydrogen atoms, with manyprecision tests of charge-parity-time (CPT) symmetry. The new ALPHA-gapparatus extends this program to a test of gravity, directly probing the ap-plicability of the weak equivalence principle (WEP) to an antimatter systemfor the first time.This dissertation presents the first ALPHA-g results, which confirm thatEarthâs gravity acts downwards on antimatter. The ratio between the grav-itational acceleration of antihydrogen and hydrogen is estimated to be g/g= 0.75 ± 0.13 (statistical and systematic) ± 0.16 (simulation).This measurement depends on accurately determining the annihilationpositions of antihydrogen atoms released from the ALPHA-g magnetic trap,which is accomplished using a time projection chamber (TPC) detector. Toreduce the substantial background due to cosmic rays, a time-of-flight bar-rel scintillator (BSC) detector was also implemented. The authorâs primarycontributions include the commissioning of the BSC, including devising andimplementing time-of-flight measurements, leading to a significantly reducedbackground rate. Additional contributions include improving the TPC track-ing algorithms to reach the required annihilation position resolution.This dissertation begins with theoretical motivations for testing the WEPusing antihydrogen, followed by an overview of the ALPHA apparatus andantihydrogen production. The TPC and BSC detectors are introduced, in-cluding the event reconstruction methods, with care to highlight the authorâswork. Finally, the gravity measurement methodology and results, as well asfuture perspectives, are discussed.This first direct test of gravity on antimatter rules out a large differencein the gravitational behaviour of antimatter and matter, furthering our un-derstanding of the fundamental matter-antimatter symmetry, and laying thefoundation for future precision WEP tests using antimatter.iiiLay summaryThe known universe is almost entirely made of matter â mainly protons,neutrons, and electrons. Each of these particles has an antimatter version, amirror-opposite counterpart. We study these rare particles in the laboratory.The ALPHA collaboration researches the simplest antimatter atom, an-tihydrogen. We recently made headlines by confirming that antihydrogenfalls downwards towards the Earth due to gravity, like normal matter.To do this, ALPHA produces and traps a few hundred antihydrogenatoms, and then releases them so they fall and collide with the apparatus.Each antiatom is destroyed in an annihilation, which we can detect with asophisticated set of particle detectors.In my PhD, I commissioned one of these particle detectors, and developedalgorithms to identify the annihilations. My work contributed directly to themeasurement of gravity, and will enable more precise future measurements.ivPrefaceThis dissertation is based on the ALPHA-g experiment and the work of theALPHA collaboration, an international group of researchers. The apparatus,data collection and analysis is the result of a combined effort from the entirecollaboration. My contributions were made within the context of the ALPHAcollaboration, and would not have been possible without input from manycollaborators. This text is entirely original.The apparatus and techniques described in Chapter 3 reflect individualcontributions from the entire ALPHA collaboration. The ALPHA-g detec-tors described in Chapter 4 were developed and commissioned by M. Fu-jiwara, P-A. Amaudruz, K. Olchanski, A. Capra, L. Martin, I. Carli, N.Massacret, D. Duque, P. Woosaree, R. Henderson, P. Lu, D. Gill, A. Olin,S. Menary, and myself. The TPC reconstruction algorithms described inChapter 5 were primarily developed by A. Capra, K. Olchanski, L. Martin,J. McKenna, and D. Duque, with my own contributions identified throughoutthe chapter. The BSC reconstruction and calibration algorithms presentedin Chapters 6â8 are entirely my own work, and the background rejectionalgorithms were developed by J. McKenna, L. Golino, and myself. The mea-surement procedure described in Chapter 9 is the work of the entire ALPHAcollaboration. The conceptual development was led by J. Fajans, simula-tions led by C. So, magnet design and construction led by W. Bertsche andC. So, ECR development led by T. Friesen and A. Powell, magnetron-metrydevelopment led by A. Christensen, and escape curve analysis led by G.Bonomi, M. Uroni, S. Stracka, J. Fajans, J. Wurtele, and D. Hodgkinson.The discussion of future measurement schemes is my own. For the durationof my time on the ALPHA collaboration, the spokesperson was J. Hangst,co-spokesperson was N. Madsen, and technical coordinator was C. Ã. Ras-mussen.The gravity measurement presented in Chapter 9 is previously publishedin [1], of which I am a coauthor. The BSC calibration methods presented inChapter 7 have been presented at the EXA/LEAP 2024 and PD24 confer-ences, with peer-reviewed conference proceedings in [2] and [3] respectively.The use of Generative AI in this dissertation was limited to editorialvPrefaceand coding purposes. Selected paragraphs were evaluated by ChatGPT-4oto ensure grammatical correctness and good flow. Furthermore, ChatGPT-4o was used for some formatting tasks, such as inputting provided data intoLaTeX tables, or creating BibTeX entries for provided citations. ChatGPT-3was used to generate code which served as a starting point for the neuralnetwork training data pipeline discussed in Section 5.5, quickly introducingme to the syntax for the hdf5 data structure. Finally, ChatGPT-4o was usedto generate code which served as a starting point for some figures includedin this dissertation, specifically Figures 3.2, 3.4, 3.5, 3.11, 3.12, 4.3, 4.6, 4.7,5.16, 8.2, 9.1, 9.8, 9.9, and 9.10. In each case, the generative AI output washeavily altered to create the code which produced the desired figure.viTable of contentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiLay summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ivPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vTable of contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiList of tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiList of figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiiGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviAcknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xx1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42.1 A brief history of antimatter . . . . . . . . . . . . . . . . . . 42.1.1 The discovery of antimatter . . . . . . . . . . . . . . . 42.1.2 Experimental attempts to measure antimatter gravity 62.1.3 Current antimatter experiments . . . . . . . . . . . . 72.2 CPT symmetry . . . . . . . . . . . . . . . . . . . . . . . . . . 82.3 The weak equivalence principle . . . . . . . . . . . . . . . . . 92.4 Motivations for the study of the gravity of antimatter . . . . 102.4.1 The intersection of gravity and CPT symmetry . . . . 102.4.2 The baryon asymmetry of the universe . . . . . . . . 102.4.3 Dark energy . . . . . . . . . . . . . . . . . . . . . . . 112.5 Theoretical considerations on repulsive antimatter gravity . . 122.5.1 Arguments for equal matter-antimatter gravitation . . 132.5.2 Antimatter gravity cosmologies . . . . . . . . . . . . . 142.5.3 Indirect antimatter gravity constraints . . . . . . . . 15viiTable of contents3 Introduction to ALPHA . . . . . . . . . . . . . . . . . . . . . . 173.1 The AD and ELENA . . . . . . . . . . . . . . . . . . . . . . 173.2 Particle trapping . . . . . . . . . . . . . . . . . . . . . . . . . 193.2.1 Charged particle trapping . . . . . . . . . . . . . . . . 203.2.2 Non-neutral plasma trapping . . . . . . . . . . . . . . 233.2.3 Antihydrogen trapping . . . . . . . . . . . . . . . . . 243.3 Annihilation . . . . . . . . . . . . . . . . . . . . . . . . . . . 253.3.1 Positron annihilation . . . . . . . . . . . . . . . . . . 263.3.2 Antiproton annihilation . . . . . . . . . . . . . . . . . 273.3.3 Antihydrogen annihilation . . . . . . . . . . . . . . . 293.4 The ALPHA apparatus . . . . . . . . . . . . . . . . . . . . . 293.4.1 Catching trap . . . . . . . . . . . . . . . . . . . . . . 303.4.2 Positron accumulator . . . . . . . . . . . . . . . . . . 313.4.3 Beamline . . . . . . . . . . . . . . . . . . . . . . . . . 323.4.4 Sticks . . . . . . . . . . . . . . . . . . . . . . . . . . . 333.4.5 Annihilation diagnostics . . . . . . . . . . . . . . . . . 343.4.6 ALPHA-g . . . . . . . . . . . . . . . . . . . . . . . . 353.5 Particle preparation techniques . . . . . . . . . . . . . . . . . 393.5.1 Antiproton preparation . . . . . . . . . . . . . . . . . 393.5.2 Positron preparation . . . . . . . . . . . . . . . . . . . 433.5.3 Antihydrogen formation . . . . . . . . . . . . . . . . . 453.5.4 Antihydrogen cooling . . . . . . . . . . . . . . . . . . 464 The ALPHA-g detectors . . . . . . . . . . . . . . . . . . . . . 504.1 Pion scattering on internal materials . . . . . . . . . . . . . . 524.2 The time projection chamber . . . . . . . . . . . . . . . . . . 534.2.1 Ionization chambers . . . . . . . . . . . . . . . . . . . 534.2.2 The ALPHA-g TPC . . . . . . . . . . . . . . . . . . . 554.3 The barrel scintillator . . . . . . . . . . . . . . . . . . . . . . 574.3.1 Scintillators . . . . . . . . . . . . . . . . . . . . . . . 574.3.2 Photosensors . . . . . . . . . . . . . . . . . . . . . . . 594.3.3 The ALPHA-g barrel scintillator . . . . . . . . . . . . 624.3.4 Detection principles . . . . . . . . . . . . . . . . . . . 644.4 Electronics and data acquisition . . . . . . . . . . . . . . . . 674.4.1 TPC data acquisition . . . . . . . . . . . . . . . . . . 694.4.2 BSC data acquisition . . . . . . . . . . . . . . . . . . 704.4.3 Clock, trigger, and test pulse . . . . . . . . . . . . . . 71viiiTable of contents5 TPC event reconstruction . . . . . . . . . . . . . . . . . . . . 735.1 TPC data processing . . . . . . . . . . . . . . . . . . . . . . 735.2 Event display . . . . . . . . . . . . . . . . . . . . . . . . . . . 745.3 Annihilation position reconstruction . . . . . . . . . . . . . . 785.3.1 Signal deconvolution . . . . . . . . . . . . . . . . . . . 785.3.2 Signal grouping . . . . . . . . . . . . . . . . . . . . . 815.3.3 Spacepoint reconstruction . . . . . . . . . . . . . . . . 825.3.4 Track finding . . . . . . . . . . . . . . . . . . . . . . . 835.3.5 Track fitting . . . . . . . . . . . . . . . . . . . . . . . 885.3.6 Track joining . . . . . . . . . . . . . . . . . . . . . . . 945.3.7 Vertex fitting . . . . . . . . . . . . . . . . . . . . . . . 975.4 Performance improvement results . . . . . . . . . . . . . . . 1005.5 Future work: machine learning vertex finding . . . . . . . . . 1046 Barrel scintillator commissioning and data processing . . . 1076.1 ADC waveform signal processing . . . . . . . . . . . . . . . . 1096.1.1 Hit finding . . . . . . . . . . . . . . . . . . . . . . . . 1096.1.2 Waveform fitting . . . . . . . . . . . . . . . . . . . . . 1126.2 TDC event extraction . . . . . . . . . . . . . . . . . . . . . . 1136.2.1 Fine time using linearity approximation . . . . . . . . 1146.2.2 Fine time using delay element calibration . . . . . . . 1146.2.3 TDC time corrections . . . . . . . . . . . . . . . . . . 1166.2.4 Cable reflections . . . . . . . . . . . . . . . . . . . . . 1176.3 ADC-TDC matching . . . . . . . . . . . . . . . . . . . . . . . 1176.4 Bar end matching . . . . . . . . . . . . . . . . . . . . . . . . 1186.5 Bar hit z calculation . . . . . . . . . . . . . . . . . . . . . . . 1206.6 BSC-TPC matching . . . . . . . . . . . . . . . . . . . . . . . 1216.7 Bar cluster formation . . . . . . . . . . . . . . . . . . . . . . 1226.8 Time-of-flight calculation . . . . . . . . . . . . . . . . . . . . 1256.9 Event display implementation . . . . . . . . . . . . . . . . . 1277 Precision time calibrations . . . . . . . . . . . . . . . . . . . . 1317.1 Issues with traditional methods . . . . . . . . . . . . . . . . . 1337.2 Time walk correction calibration . . . . . . . . . . . . . . . . 1357.2.1 Determining the time walk correction parameters . . 1357.2.2 Determining the direction of cosmic rays . . . . . . . 1377.3 Bar hit z position calibration . . . . . . . . . . . . . . . . . . 1387.3.1 Determining âbot-top and veff . . . . . . . . . . . . . . 1397.3.2 Interplay between time walk correction and hit z po-sition . . . . . . . . . . . . . . . . . . . . . . . . . . . 142ixTable of contents7.3.3 Summary of time walk and hit z position calibrations 1437.4 Bar to bar offsets . . . . . . . . . . . . . . . . . . . . . . . . 1437.4.1 Determining time offsets between pairs of bars . . . . 1447.4.2 Determining time offsets of individual bars . . . . . . 1458 Cosmic ray background rejection . . . . . . . . . . . . . . . . 1478.1 BDT background rejection in ALPHA-2 . . . . . . . . . . . . 1488.2 BDT background rejection in ALPHA-g . . . . . . . . . . . . 1498.3 Inclusion of TOF in background rejection . . . . . . . . . . . 1508.4 Input variables . . . . . . . . . . . . . . . . . . . . . . . . . . 1508.5 Background rejection performance improvement . . . . . . . 1558.6 Background rejection conclusions . . . . . . . . . . . . . . . . 1559 Measuring antihydrogen gravity with ALPHA-g . . . . . . 1589.1 Gravity measurement procedure . . . . . . . . . . . . . . . . 1599.1.1 Measurement technique . . . . . . . . . . . . . . . . . 1599.1.2 Magnetic field measurements . . . . . . . . . . . . . . 1619.1.3 Data collection . . . . . . . . . . . . . . . . . . . . . . 1639.2 Analysis procedure . . . . . . . . . . . . . . . . . . . . . . . . 1649.2.1 Data selection . . . . . . . . . . . . . . . . . . . . . . 1679.2.2 Bayesian analysis . . . . . . . . . . . . . . . . . . . . 1679.2.3 Escape curve simulation . . . . . . . . . . . . . . . . . 1709.3 Measurement uncertainties and systematics . . . . . . . . . . 1719.3.1 Magnetic bias uncertainties . . . . . . . . . . . . . . . 1729.3.2 Annihilation counting uncertainties . . . . . . . . . . 1739.3.3 Simulation uncertainties . . . . . . . . . . . . . . . . . 1739.3.4 Summary of experimental uncertainties . . . . . . . . 1749.4 Future measurements and the impact of this work . . . . . . 1749.4.1 Impact on the gravity paper . . . . . . . . . . . . . . 1769.4.2 Repeated measurements in the same apparatus . . . . 1799.4.3 Measurements using the precision trap region . . . . . 1829.4.4 Alternative measurement schemes . . . . . . . . . . . 18310 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191AppendicesA BSC electronics and DAQ implementation . . . . . . . . . . 205xTable of contentsB BSC quality of data . . . . . . . . . . . . . . . . . . . . . . . . 210C Pileup rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . 213D BSC calibration algorithm implementation . . . . . . . . . . 215xiList of tables3.1 Antiproton-proton and antiproton-neutron branching ratios. . 284.1 A list of symbols used when discussing the data handling ofthe BSC. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655.1 Comparison of track finding methods. . . . . . . . . . . . . . 885.2 Helix selection criteria. . . . . . . . . . . . . . . . . . . . . . . 995.3 Summary of TPC reconstruction improvements. . . . . . . . . 1015.4 Performance comparison of reconstruction improvements splitby dataset. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1066.1 Definition of bar hit types. . . . . . . . . . . . . . . . . . . . . 1196.2 Bar cluster background rejection performance comparison. . . 1247.1 A description of symbols used throughout the BSC calibrationchapter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1328.1 Variables used in ALPHA-2 BDT. . . . . . . . . . . . . . . . 1488.2 Variables used in ALPHA-g BDT training. . . . . . . . . . . . 1529.1 Annihilation counts in each region during gravity measurement.1669.2 Model parameters used in the gravity analysis. . . . . . . . . 1699.3 Summary of gravity measurement uncertainties. . . . . . . . . 1759.4 Derived Pdown uncertainties from degraded detector perfor-mance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179B.1 Description of BSC quality of data plots. . . . . . . . . . . . . 210C.1 Pileup probability rates. . . . . . . . . . . . . . . . . . . . . . 214xiiList of figures3.1 Annotated schematic layout of the AD. . . . . . . . . . . . . . 183.2 Beam momentum during the AD and ELENA cycles. . . . . . 203.3 Electrode layout for Penning and Penning-Malmberg traps. . 213.4 Motion of a charged particle in a Penning-Malmberg trap. . . 233.5 Simplified diagram of an Ioffe-Pritchard trap. . . . . . . . . . 263.6 The ALPHA apparatus. . . . . . . . . . . . . . . . . . . . . . 303.7 Catching trap electrodes and axial catching potential. . . . . 313.8 The positron accumulator. . . . . . . . . . . . . . . . . . . . . 323.9 ALPHA-g full apparatus schematic and trap diagram. . . . . 363.10 ALPHA-g magnet system layout. . . . . . . . . . . . . . . . . 383.11 Evaporative cooling axial potential and energy distribution. . 413.12 Rotating wall electrode diagram and potentials. . . . . . . . . 423.13 Antiproton plasma temperature diagnostic. . . . . . . . . . . 443.14 Electric potentials during antihydrogen formation. . . . . . . 464.1 The ALPHA-2 apparatus, with the three layers of the siliconvertex detector (SVD) shown in blue. Adapted from [4]. . . . 514.2 Diagram of the main components of the ALPHA-g appara-tus inside the time projection chamber detector. Componentsare listed from innermost to outermost with their respectivematerials and thicknesses. . . . . . . . . . . . . . . . . . . . . 524.3 Electron avalanche development in a wire chamber. . . . . . . 544.4 Electron drift in the TPC. . . . . . . . . . . . . . . . . . . . . 564.5 Diagram of a photomultiplier tube. . . . . . . . . . . . . . . . 594.6 Energy levels in doped silicon. . . . . . . . . . . . . . . . . . . 604.7 Charge density, electric field, and potential across a silicondiode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 614.8 Layout of a single photon avalanche detector. . . . . . . . . . 614.9 Photograph and diagram of the barrel scintillator. . . . . . . 634.10 Illustration of the time-of-flight background rejection technique. 684.11 Readout electronics chain for the TPC and the BSC. . . . . . 69xiiiList of figures5.1 The ALPHA-g event display (1). . . . . . . . . . . . . . . . . 755.2 The ALPHA-g event display (2). . . . . . . . . . . . . . . . . 765.3 The ALPHA-g event display TPC waveform viewer. . . . . . 775.4 Stages of the TPC reconstruction. . . . . . . . . . . . . . . . 795.5 Stages of the TPC vertex reconstruction algorithm. . . . . . . 805.6 Anode wire and cathode pad deconvolution. . . . . . . . . . . 815.7 Garfield++ simulation of a charged pion in the TPC. . . . . . 825.8 The adaptive track finder. . . . . . . . . . . . . . . . . . . . . 845.9 The iterative track finder. . . . . . . . . . . . . . . . . . . . . 855.10 The exhaustive track finder. . . . . . . . . . . . . . . . . . . . 875.11 The parametrization of the helix fit function. . . . . . . . . . 905.12 An illustration of cosmic rays in the TPC. . . . . . . . . . . . 945.13 Cyclotron-trapped electrons in the ALPHA-g event display. . 965.14 The original vertex fit method. . . . . . . . . . . . . . . . . . 975.15 The current vertex fit method. . . . . . . . . . . . . . . . . . 985.16 Resolution comparison of reconstruction improvements. . . . . 1025.17 Machine learning vertex finder performance. . . . . . . . . . . 1056.1 Analysis stages for the BSC and TPC data. . . . . . . . . . . 1086.2 Example of an unsaturated ADC waveform. . . . . . . . . . . 1106.3 Example of a saturated ADC waveform. . . . . . . . . . . . . 1106.4 BSC ADC amplitude plot used for calibration. . . . . . . . . 1126.5 TDC fine time counter histogram. . . . . . . . . . . . . . . . . 1156.6 Comparison plot between zADC and zTDC. . . . . . . . . . . . 1216.7 Residuals from BSC matching to TPC. . . . . . . . . . . . . . 1236.8 Number of bar clusters. . . . . . . . . . . . . . . . . . . . . . 1246.9 Measured vs expected TOF in cosmic ray data. . . . . . . . . 1266.10 Residual TOF distribution. . . . . . . . . . . . . . . . . . . . 1276.11 Measured vs expected TOF in antiproton annihilation data. . 1286.12 BSC data in the ALPHA-g event display. . . . . . . . . . . . 1296.13 BSC waveform display in the ALPHA-g event display. . . . . 1307.1 Overview of the BSC calibration algorithm. . . . . . . . . . . 1337.2 Residual TOF distribution between opposite bars, with andwithout time walk correction. . . . . . . . . . . . . . . . . . . 1377.3 Width of residual TOF fits. . . . . . . . . . . . . . . . . . . . 1387.4 Correlation between âz and TOF. . . . . . . . . . . . . . . . 1397.5 TDC time difference between bar ends. . . . . . . . . . . . . . 1407.6 Bar top-bottom time offsets. . . . . . . . . . . . . . . . . . . . 1417.7 Effective speed of photon propagation in each bar. . . . . . . 141xivList of figures7.8 Residual TOF distributions between two bars. . . . . . . . . . 1447.9 Time offsets for each bar. . . . . . . . . . . . . . . . . . . . . 1468.1 BDT classifier output. . . . . . . . . . . . . . . . . . . . . . . 1518.2 Distributions of selected BDT input variables. . . . . . . . . . 1548.3 Signal efficiency and background rate comparison betweenBDT versions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1569.1 On-axis potential in ALPHA-g during gravity measurement. . 1609.2 Frequency spectra from ECR measurement. . . . . . . . . . . 1629.3 Overview of the measurement procedure. . . . . . . . . . . . . 1639.4 Measured annihilation z positions during gravity experiment. 1659.5 The measured escape curve. . . . . . . . . . . . . . . . . . . . 1659.6 Time distribution of annihilations during gravity measurement.1689.7 Simulated escape curves. . . . . . . . . . . . . . . . . . . . . . 1719.8 Simulated annihilations with different detector performanceassumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 1779.9 Pdown from simulated events. . . . . . . . . . . . . . . . . . . 1789.10 Preliminary results showing ongoing improvements. . . . . . . 180A.1 A diagram of the detector electronics and DAQ for the BSC. . 206B.1 Barrel scintillator quality of data plots. . . . . . . . . . . . . . 212D.1 TOF resolution dependence on calibration dataset length. . . 217xvGlossaryg The gravitational acceleration of antihydrogen, analogous to g = 9.81m/s2for matter.AD The Antiproton Decelerator, CERNâs machine which produces a beamof slow antiprotons which is further decelerated by ELENA.ADC Analog-to-Digital Converter, a digitizer which samples an analog sig-nal to store a full waveform.ALPHA The Antihydrogen Laser PHysics Apparatus, the CERN-basedcollaboration of which the author is a member.ALPHA-2 The second-generation ALPHA trap apparatus designed to per-form precision spectroscopy on trapped antihydrogen atoms.ALPHA-g The new ALPHA trap apparatus designed to measure the grav-ity of trapped antihydrogen atoms.alphasoft The reconstruction software developed for the ALPHA detectors.ASD Analog SumDiscriminator board, a custom circuit board which sumstogether the analog signals from multiple SiPMs in the ALPHA-g BSC,and outputs both an analog and a digital discriminated signal.AWB Anode Wire Board, a custom circuit board used to read out theanode wire current of the ALPHA-g TPC.bar One of 64 scintillating bars in the BSC.bar hit A data structure in the BSC reconstruction containing ADC andTDC data from SiPM signals on both ends of a bar.BDT BoostedDescionTrees, a machine learning multivariate analysis method.BSC The Barrel SCintillator, a scintillator-based time-of-flight detector inALPHA-g.xviGlossaryCERN The European Organization for Nuclear Research, the leading globalparticle physics laboratory located in Geneva, Switzerland.cosmic ray A particle originating from outside the Earth, or a secondaryparticle produced by its interaction in the atmosphere. At ground level,these are primarily muons.CPT Charge-Parity-Time, a fundamental symmetry governing the rela-tionship between matter and antimatter.cyclotron motion The fast circular motion of a charged particle in a con-stant magnetic field.DAQ Data AcQuisition.DCCT Direct-Current Current Transformers, an electrical system used tomeasure large currents.ECR Electron Cyclotron Resonance, a technique developed at ALPHA tomeasure magnetic fields using electron plasmas.ELENA The Extra Low ENergy Antiproton ring, which further slows an-tiprotons from the AD and provides them to experiments.end hit A data structure in the BSC reconstruction containing ADC andTDC data from SiPM signals on one end of a bar.FPGA Field Programmable Gate Array, a commercially available repro-grammable integrated circuit.Garfield++ A software toolkit designed for the simulation of gas-basedparticle detectors [5].helix The spiral-shaped function fit to tracks in the TPC reconstruction.Ioffe-Pritchard trap A neutral particle trap which constrains atoms in amagnetic field minima via their magnetic dipole moment. Consists ofan octupole magnet and two solenoidal mirror coils.magnetron motion The slow circular motion of a charged particle due tothe Eâ Ã Bâ drift of non-parallel electric and magnetic fields.xviiGlossarymagnetron-metry A technique developed at ALPHA to measure magneticfields based on the magnetron motion of an electron plasma.MCP MicroChannel Plate, a device used to multiple and accelerate elec-trons. Combined with phosphor screens and CCD cameras to imagecharge particle plasmas in ALPHA.MIDAS Maximum Integrated Data Acquisition System, a data acquisi-tion system developed and TRIUMF and the Paul Scherrer Institute.mirror coil The solenoid magnets of the Ioffe-Pritchard trap responsiblefor the axial confinement of antiatom.Penning-Malmberg trap A trap with cylindrical electrodes which con-strains charged particles using electric fields.PMT PhotoMultiplier Tube, a devide used to detect photons.PWB PadWing Board, a custom circuit board used to read out the cath-ode pads of the ALPHA-g TPC.ROOT A data analysis framework developed at CERN.SDREVC Strong Drive Regime EvaporatiVe Cooling, a plasma manipu-lation technique combining evaporative cooling and the rotating walltechnique. It is used at ALPHA to create reproducible plasmas.SiPM Silicon PhotoMultiplier, a modern silicon-based photon detector.spacepoint A three-dimensional point in the TPC reconstruction corre-sponding to an ionization of the TPC gas.SVD The Silion Vertex Detector, the silicon detector used for track andannihilation vertex reconstruction in ALPHA-2.TDC Time-to-Digital Converter, a digitizer which precisely digitizes thestart time of a signal.time walk The effect where for two signals of the same shape but differentamplitudes, the larger signal will cross a fixed threshold sooner.TOF Time-Of-Flight, a method where particle information is extractedfrom the time between two measurements.xviiiGlossaryTPC The Time Projection Chamber, the drift chamber detector which isused for annihilation track reconstruction in ALPHA-g.track A group of spacepoints in the TPC reconstruction corresponding toa single charged particle.TRIUMF A national physics accelerator laboratory in Vancouver, Canada.vertex The three-dimensional position of an antiproton or antihydrogenannihilation.WEP The Weak Equivalence Principle, the statement that the motionof an object in a gravitational field depends on neither its mass norcomposition.xixAcknowledgementsFirstly, thank you to my supervisor Makoto. Youâve given me both thesupport and feedback I needed to succeed, as well as the freedom and spaceto explore at my pace. I couldnât have asked for a better supervisor. Thankyou as well to the entire ALPHA team at TRIUMF, in particular Andrea,Lars, Konstantin; you helped me hit the ground running at ALPHA.I thoroughly enjoyed my time at CERN, mostly due to the collection ofgenuine, hardworking, and fun people at ALPHA. The sense of communityand collaboration was awesome; I could (and did!) ask questions aboutanything to anyone, and the struggles and efforts were shared. In particular,I want to thank the detector team at CERN: Ina, Joseph, Daniel, Pooja,Lukas â we really made it work.I am incredibly grateful to my parents Rosie and Nigel and my sisterMegan for encouraging me and supporting me throughout my journey. AndI am thankful for the compassionate and inspiring community of friends Ihave met during my graduate studies at UBC, without which I surely wouldhave gone insane in the pandemic.Thank you to Emily for being by my side every step of the way, and forsharing this adventure with me. And of course, to Sally and Charlie.This project was partially funded by the Canadian Institute of NuclearPhysics 2023 Graduate Fellowship. It was partially performed at the TRI-UMF laboratory, which lies on the traditional, ancestral, and unceded terri-tory of the xwm@Tkw@y´@m (Musqueam) People.xxChapter 1IntroductionOur current understanding of the motion and interactions of fundamentalparticles is governed by two theories: Einsteinâs general relativity describingthe force of gravity, and the Standard Model of particle physics describing theweak, strong, and electromagnetic forces. The combination of these theorieshas proven to accurately model the universe around us, despite the fact thatthe two frameworks are fundamentally incompatible, with efforts to create aunified theory of quantum gravity so far unsuccessful.Nevertheless, there are many observations which remain unexplained bythe Standard Model and general relativity, indicating that our understandingof the universe is incomplete and motivating searches for new physics. Onesuch unexplained phenomenon is dark energy, the unknown force which isrequired for general relativity to match our observations of the expansion ofthe universe. Another is the baryon asymmetry problem, the dominance ofmatter over antimatter in our observable universe.The theoretical description of antimatter in the Standard Model is basedon CPT symmetry, an underlying fundamental symmetry between matterand antimatter. However, there is another symmetry between matter andantimatter: their identical gravitational behaviour. This is asserted by theweak equivalence principle (WEP), which is one of the axiomatic assumptionsof general relativity.With unsolved problems indicating that both the Standard Model andgeneral relativity are incomplete, it is important to experimentally verifytheir underlying assumptions. Testing the applicability of the WEP to an-timatter is a natural goal as it lies at the intersection of the two theories,especially since the WEP was formulated before the discovery of antimatter,based solely on observations of matter.Until recently, a direct test of the WEP on antimatter has never beenperformed. Such a test requires using electrically neutral antimatter, as elec-tromagnetic forces would otherwise overwhelm gravity. Excluding antineu-trons, which are prohibitively difficult to trap and manipulate, the simplestviable system is the antihydrogen atom: the bound state of an antiprotonand a positron.1Chapter 1. IntroductionIn pursuit of the goal of verifying the fundamental symmetries betweenmatter and antimatter, the ability to perform measurements on cold trappedantiprotons and antihydrogen atoms has been developed at the AntiprotonDecelerator (AD) at CERN. A wide range of fundamental properties havebeen measured and compared to their matter equivalents, such as the an-tiproton charge-to-mass ratio [6] and magnetic moment [7], the antihydro-gen 1S-2S [8] and 1S-2P [9] transition frequencies, and the antihydrogen finestructure [10] and hyperfine structure [11]. These measurements constitutea series of independent, direct tests of CPT symmetry, and have so far foundno deviation from the predictions of the standard model.Recently, the ALPHA (Antihydrogen Laser PHysics Apparatus) collab-oration at the AD has extended its focus from CPT symmetry to the WEP.This dissertation presents the first direct measurement of the gravitationalfree-fall of the antihydrogen atom, conducted using the new ALPHA-g ap-paratus. Our results [1] are consistent with antihydrogen behaving in accor-dance with the WEP. This is the first direct test of the WEP which has beencarried out on a purely antimatter system in the laboratory, and representsa major milestone towards precision tests.The ALPHA collaboration is a diverse group from a range of disciplinesand with many areas of expertise. During the 15 months I spent at CERN,I took part in the development and data-taking for the ALPHA-g measure-ment, along with various spectroscopy measurements in the ALPHA appa-ratus. I contributed to a variety of tasks through shift work, such as opti-mization and development of particle manipulation techniques, installationof particle detectors and electronics, cryogenic handling, and data analy-sis. I took initiative to improve the particle tracking algorithms used forthe time projection chamber (TPC) detector. I was also responsible for thecommissioning of the barrel scintillator (BSC) detector and the developmentof calibration techniques for this detector, with support from Dr. AndreaCapra and Dr. Ina Carli among others. I was able to successfully imple-ment time-of-flight measurements in this detector for rejecting backgroundevents caused by cosmic rays. I then worked closely with Dr. Lukas Golinoto include these measurements into the machine-learning-based cosmic raybackground rejection algorithm used in ALPHA-g. This led to a factor of10 improvement in background suppression, which will directly enable newmeasurement capabilities in ALPHA-g.Following this introduction, Chapter 2 provides some brief theoreticalbackground on antimatter, CPT symmetry, and the weak equivalence prin-ciple. It also provides some motivation for this study, and reviews contempo-rary experimental efforts towards understanding the gravitational behaviour2Chapter 1. Introductionof antimatter. Chapter 3 describes the apparatus and techniques devel-oped by the ALPHA collaboration to produce and manipulate antihydrogenatoms. Chapter 4 details the particle detector system used to detect andreconstruct the annihilations of antiprotons and antihydrogen atoms. Chap-ter 5 covers the reconstruction algorithms for the main TPC tracking detec-tor. Chapter 6 presents the commissioning and event reconstruction for BSCdetector, Chapter 7 describes the calibration algorithms implemented for thisdetector, and Chapter 8 details the inclusion of this detector into cosmic raybackground rejection algorithms. Chapter 9 reports on the measurement ofthe effect of gravity on antihydrogen, including the techniques, analysis, andthe final results. Finally, Chapter 10 provides concluding remarks.3Chapter 2BackgroundThis chapter presents the theoretical background and context relevant to thestudy of the gravitational interactions of antimatter. We begin by review-ing the historical and current understanding of antimatter. We then explorefundamental symmetries in physics, with particular emphasis on CPT sym-metry and the weak equivalence principle. The question of how antimatterinteracts with gravity is framed within the context of the baryon asymmetryproblem, and as an intersection between the standard model and general rel-ativity. Finally, we summarize the theoretical expectations and experimen-tal constraints on the gravitational behaviour of antimatter, and provide anoverview of ongoing experimental efforts towards its direct measurement.2.1 A brief history of antimatterIn 1915, Einstein published his theory of general relativity [12], describinggravity as the curvature of spacetime induced by mass and energy. We willreturn to this in our discussion of the weak equivalence principle, but itis important to underline that the postulation and discovery of antimatterhappened long after our current understanding of gravity was formulated.Einsteinâs general relativity also serves as a classic success story for theoret-ical prediction in physics; his field equations give rise to the phenomenon ofgravitational waves. Despite Einsteinâs own skepticism regarding their ob-servability [13], the LIGO collaboration in 2015 confirmed the existence ofgravitational waves [14], a century after the theoryâs publication.2.1.1 The discovery of antimatterThe story of antimatter begins with a similar prediction and experimentalverification. In 1928, Paul Dirac published a relativistic equation describingthe electron, reconciling quantum mechanics with Einsteinâs special relativity[15]. Dirac observed that his equation admitted solutions âequally well to anelectron with charge e as to one with charge âeâ [15]. Although he initiallydismissed the negative energy solutions, he later embraced them, identifying42.1. A brief history of antimatterthem in 1931 as âa new kind of particle, unknown to experimental physics,having the same mass and opposite charge to an electron. We may call sucha particle an antielectronâ [16].Dirac was more fortunate than Einstein when it came to experimentalvalidation. Just two years later, in 1933, Carl Anderson observed cosmicray tracks in a cloud chamber under a constant magnetic field [17]. Fromthe curvature of the tracks, he determined the charge-to-mass ratio of eachparticle, identifying fifteen instances of Diracâs antielectron. He named thisparticle the positron.1Dirac predicted the existence of the antiproton during his 1933 Nobellecture [18] following the discovery of the positron. As further particleswere discovered throughout the 1930âs and 1940âs, it was suspected thateach particle might have a corresponding antiparticle. However, antiparticlesbeyond the positron are not observed naturally, and so it was not until theage of high energy collisions that this theory could be verified.The antiproton was discovered in 1955 at the Bevatron, a 6.2GeV protonsynchrotron [19]. Protons were collided with a copper target, and negativelycharged particles with a momentum of 1.19GeV were extracted. Their ve-locity was measured using time-of-flight and Cerenkov counters, confirmingtheir rest mass and hence their identity as antiprotons. The discovery of theantineutron followed a year later in 1956 from a group at the same labora-tory [20]. Antiprotons were passed through a liquid scintillator, which wouldobserve the occasional antineutron produced through a charge exchange in-teraction. The antineutron would then pass undetected through additionalscintillator panels, before annihilating in a Cerenkov detector.As routine production of antiprotons became possible, CERN commis-sioned the Low Energy Antiproton Ring (LEAR) in 1982 [21]. This machinesupplied 100MeV antiprotons to experiments with a broad physics program.These efforts culminated in the 1995 detection of nine antihydrogen atomsin-flight by the PS210 experiment. Antiprotons passing through a xenon tar-get captured positrons pair-produced in an atomâs electric field [22], brieflyproducing an excited state of antihydrogen in flight. LEAR was decommis-sioned in 1996, and repurposed into the Low Energy Ion Ring (LEIR), whichremains an integral part of the LHC heavy ion program.The success of LEAR prompted further investment into the new An-tiproton Decelerator (AD), which began operation in 2000 [23]. Antipro-tons are produced by directing a proton beam into an iridium target, and a1Positron is a contraction of positive electron. He also proposed renaming the electronto the ânegatronâ, a term which regrettably does not see common usage.52.1. A brief history of antimattermagnetic horn focuses antiprotons produced at 3.6GeV into the deceleratorring. These antiproton bunches are slowed to 5.3MeV and delivered to ex-periments such as ATHENA [24], which succeeded in 2002 to produce coldantihydrogen atoms from confined plasmas of antiprotons and positrons. In2010, the ALPHA collaboration became the first to magnetically trap anti-hydrogen [25].2.1.2 Experimental attempts to measure antimatter gravitySince the mass of a particle and corresponding antiparticle are equal, thissuggests that gravity should act equally on both. The work presented inthis dissertation joins a long history of attempts to measure the effect of theEarthâs gravity on a purely antimatter system (hereafter antimatter gravityfor brevity), by observing the gravitational free-fall of an antimatter system.While these methods have only placed loose constraints on antimatter grav-ity, a number of indirect measurements have demonstrated equality betweenmatter and antimatter gravity much more precisely. However, these indirectmethods rely on other underlying assumptions, and will be discussed in Sec-tion 2.5.3. Here, we discuss only direct measurements of antimatter gravity,which involve the observation of the motion of antimatter systems under theinfluence of gravity.In the 1960s, Witteborn and Fairbank sought to compare the Earthâsgravitational pull on positrons and electrons [26]. Their method was to mea-sure the particle time-of-flight in a vertical drift tube, taking care to shieldthe particle from all external electromagnetic fields. However, this proved tobe prohibitively challenging due to a phenomenon known as patch potentials,local variations in the electric potential along the surface of the metal tube.These can be caused by microscopic impurities in the metal tubeâs surfacecausing local charge build up, by grain boundaries, or other effects [27]. Theresulting electrostatic forces dwarfed the expected gravitational effect.2Witteborn and collaborators returned to this problem once slow antipro-tons became available at LEAR [29]. Their idea was that since antiprotonsare much heavier than positrons, they would require less electromagneticshielding to achieve sensitivity to gravity. However, this project faced issuesin trapping and cooling antiprotons while maintaining a sufficiently field-free region for a gravity measurement. The experiment ultimately failed to2Electrons in the conducting walls of the drift tube also experience gravity, forming anelectric potential gradient which counteracts gravity. Witteborn and Fairbank were ableto confirm that the effect of gravity on these electrons is equal to the effect of gravity ona free electron in the drift tube, to within 9% [28].62.1. A brief history of antimatterproduce any results before the shutdown of LEAR [30].This brings us to the present generation of antimatter gravity experi-ments. To avoid electromagnetic interference in a free-fall experiment, onemust use a neutral form of antimatter. Since antineutrons are difficult to trapand manipulate, the best candidate for a direct measurement of gravity on abound antimatter system is the antihydrogen atom. Other experiments havebeen proposed which use an interferometer on a beam of either muonium[31] or positronium [32].A precursor to the 2023 result [1] was published by the ALPHA collab-oration in 2013 [33]. Antihydrogen atoms were released from the ALPHA-2trap, and a search for an asymmetry in the vertical annihilation positionswas performed. An upper limit of 75 was imposed on the ratio of the antihy-drogen gravitational and inertial mass. This study was limited by the smallvertical distance over which the antiatoms could free fall before annihilating;however, its success paved the way for the design of the current ALPHA-gexperiment.2.1.3 Current antimatter experimentsToday, the Extra Low Energy Antiproton ring (ELENA) further deceleratesthe AD antiproton beam to 100 keV [34]. This beam remains the worldâsonly source of low energy antiprotons. It fosters an active community ofunique experiments, including:â¢ BASE [35] â tests CPT symmetry by measuring the antiproton mag-netic moment [7] and charge-to-mass ratio [6].â¢ ASACUSA [36] â aims to create a beam of polarized antihydrogen tostudy the antiproton mass [37] and the zero-field hyperfine splitting.â¢ PUMA [38] â aims to study the surface nucleon density of radioactivenuclei by transporting antiprotons to CERNâs ISOLDE radioactive ionbeam facility.â¢ AEGIS [39] â aims to use a Moire deflectometer to measure Earthâsgravity on a beam of antihydrogen.â¢ GBAR [40] â aims to measure the gravitational free-fall of micro-kelvin antihydrogen, by photo-ionization of positive antihydrogen ions.The ALPHA collaboration also remains active at the AD, having per-formed a wide range of spectroscopic measurements on trapped antihydro-gen with the ALPHA-2 experiment. The new ALPHA-g experiment has also72.2. CPT symmetryyielded recent results in the measurement of gravity acting on antihydrogen,which are presented in this dissertation. A detailed overview of the ALPHAexperiment will be given in Chapter 3.2.2 CPT symmetryThe current generation of AD experiments share a common goal: to studythe fundamental symmetries between matter and antimatter. In physics, asymmetry is synonymous with an invariance. If a theory remains unchangedunder a certain transformation (such as a translation in space), it is said topossess that symmetry or invariance (in this case, translational symmetry).There are three fundamental symmetries that were long believed to beobeyed by all physical processes, corresponding to the following transforma-tions:â¢ Charge conjugation (C): Changes the sign of all charges, effectivelyexchanging a particle with its antiparticle.â¢ Parity inversion (P): Reverses the sign of all three spatial coordinates,equivalent to a mirror reflection along all three spatial axes.â¢ Time reversal (T): Reverses the direction of time.These symmetries were formalized by Wigner [41, 42] and Dirac [16] from1927 to 1933. It came as a surprise when in 1957, Wu demonstrated that theweak interaction violates P symmetry [43]. That same year, Landau pro-posed that the combined CP transformation might still be a true symmetryof nature [44]. This proposal held until 1964, when a group at Brookhavenshowed evidence for CP violation in the decay of neutral kaons [45].Today, only the combined CPT symmetry is thought to hold universally.In 1957, Lüders and Pauli independently proved the CPT theorem, whichstates that any Lorentz-invariant local quantum field theory must be invari-ant under a CPT transformation [46]. The assumptions of Lorentz-invarianceand locality are foundational to both general relativity and quantum fieldtheory; an observation of CPT symmetry violation would indicate physicsbeyond these frameworks.The history of C and CP violation reminds us that even our most deeplyheld theoretical assumptions must be tested. Since CPT symmetry connectsmatter and antimatter, its experimental verification necessarily involves an-timatter systems, as charge conjugation C corresponds to the symmetry82.3. The weak equivalence principlebetween matter and antimatter. Consequently, many of the experiments atthe AD â including the precision spectroscopy program at ALPHA â aredesigned to search for violations of CPT symmetry.2.3 The weak equivalence principleGalileo first formalized the weak equivalence principle (WEP), the statementthat the motion of an object in a gravitational field does not depend on itsmass or composition, around 1590 [47]. Neglecting air resistance, it guaran-tees that an apple and a cannonball will fall at the same rate; a fact he issaid to have demonstrated by dropping such objects from the Leaning Towerof Pisa. An equivalent statement of the WEP is that an objectâs gravita-tional mass (its coupling to gravity) and inertial mass (of Newtonâs secondlaw F = ma) are equal.In 1907, Einstein extended this idea into what is now called the EinsteinEquivalence Principle (EEP) [48], which asserts that the laws of physics areindistinguishable between an accelerated reference frame and one at rest ina gravitational field. These equivalence principles were cornerstones of his1915 theory of general relativity, which has withstood repeated experimentalscrutiny, and remains to this day our most comprehensive theory of gravity.An observation of a violation of the WEP would necessitate a reformula-tion of general relativity, and reshape our understanding of gravity. As such,many generations of experiments have searched for WEP violation using avariety of techniques. Some of the early precision tests were performed byLoránd Eötvös from the 1880s to the 1910s [49], using a torsion balance tocompare the ratio of gravitational to inertial mass across various materials.Variations on this technique were later used to verify the WEP to a precisionof 10â13 [50, 51]. The current best measurement of the WEP was performedby the MICROSCOPE experiment, which achieved a precision of 10â15 usingEarth-orbiting satellites [52].The WEP asserts that two objects of the same mass will experience thesame force of gravity, regardless of their composition; this includes a particleand its antimatter counterpart. Since our understanding of gravity predatesthe prediction and discovery of antimatter, general relativity does not giveany explicit role to antimatter. But we should remember that the WEP wasdevised based on observations of matter-matter interactions, and is taken asa starting point for general relativity. That antimatter should also obey theWEP makes for a very simple and beautiful theory, but as the last hundredyears have demonstrated, it is only by performing experiments that we can92.4. Motivations for the study of the gravity of antimatterverify the laws of nature; beautiful theories do not preclude unexpectedresults.2.4 Motivations for the study of the gravity ofantimatterThe concept of antigravity, or gravitational repulsion, has long been thesubject of science fiction. Beyond pop culture, many theorists have investi-gated the concept, both historically [53] and recently [54]. It is interesting toconsider matter and antimatter which gravitationally repel each other, andwhether such a universe could be consistent with our own.2.4.1 The intersection of gravity and CPT symmetryThere is a solid reason to study the effect of gravity on antimatter from atheoretical perspective. Of the four fundamental forces, the Standard Modeldescribes only three; gravity is left to its own theory, general relativity. De-spite decades of effort, a unified theory that consistently combines the twohas not been found. Antimatter is deeply connected to CPT symmetry,which arises naturally from the principles of Lorentz-invariance and locality,two axioms of the Standard Model. By testing the WEP on antimatter,we are directly testing the compatibility of the foundations of the two theo-ries. The results of such a test will constrain any unified theory of quantumgravity, and perhaps hint towards how the two theories should be united.2.4.2 The baryon asymmetry of the universeThere is another motivation for studying this area, based on an unexplainedobservation. Although the description of antimatter within the standardmodel entirely matches experiment, there is a gap in our understandingknown as the baryon asymmetry problem. As the universe cooled from thevery hot and energetic state immediately following the big bang, elementaryparticles were created via pair production. This mechanism creates particlesin pairs â one particle and one antiparticle â and so the total balance betweenmatter and antimatter in the universe is conserved. The problem is thattodayâs universe is overwhelmingly composed of matter. What mechanismgave rise to this dominance of matter? Was less antimatter created, or didsome unknown process preferentially remove antimatter from the universe?Without violating CPT symmetry, such a mechanism is possible if itobeys the three Sakharov criteria [55]:102.4. Motivations for the study of the gravity of antimatter1. Baryon number violation, i.e. the production of a baryon without thecorresponding antibaryon.2. C and CP symmetry violation.3. Interactions out of thermal equilibrium.Baryon number violation is an obvious requirement to explain the imbal-ance of baryons and antibaryons. However, it has not yet been observed, andis not predicted by the standard model except at very high temperatures [56].The discovery of a process which does not conserve baryon number, such asproton decay, would be a key piece towards understanding the baryon asym-metry problem.C and CP symmetry breaking is a requirement for the development of abaryon asymmetry; if C or CP symmetry held, then any process which cre-ated a baryon would have a C or CP conjugate process creating antibaryonsat the same rate. As we have seen previously, C and CP symmetry break-ing has already been observed. However, the degree of symmetry breakingobserved so far is too small to be solely responsible for the baryon asymme-try of the universe. Searches for further symmetry breaking processes areunderway, for example in the neutrino sector [57].In a thermal equilibrium, the forward and reverse of a process occur at thesame rate; clearly a mechanism to generate a baryon asymmetry must occuroutside of thermal equilibrium. Thus understanding the origin of the baryonasymmetry must go hand in hand with understanding the structure andthermal evolution of the universe; understanding how the universe developswill tell us when conditions out of equilibrium would occur. One of the keyfactors in this development is the gravitational behaviour of the constituentsof the universe, and in this way, understanding the gravitational behaviourof antimatter could give us insight into the origins of the baryon asymmetryproblem.2.4.3 Dark energyThere is a final reason to study the gravity of antimatter: we already haveindications that our understanding of gravity itself is incomplete. In 1917,Einstein amended his theory of general relativity to include a cosmologicalconstant, which was required in order to keep the size of the universe static[58]. This was soon discarded, when Hubble demonstrated in 1929 that theuniverse is expanding [59]. However, the idea of a cosmological constant has112.5. Theoretical considerations on repulsive antimatter gravitybeen revived following observations of the universeâs accelerating expansion[60].The origin of this acceleration is not understood at all, and so has beengiven the mysterious name of dark energy. A cosmological constant is theleading candidate explanation for dark energy, but not the only one.3 It iscommonly identified with the non-zero energy of the quantum-mechanicalvacuum state, which permeates all space. However, the cosmological con-stant has its own problem: quantum field theory predicts a value which is120 orders of magnitude greater than the value which would explain theaccelerated expansion of the universe [62].This non-zero quantum vacuum energy corresponds to the creation andannihilation of pairs of virtual particles and antiparticles which occurs con-tinuously in the vacuum. One highly speculative approach is to consider thegravitational interactions between these virtual particles as it relates to thecosmological constant problem [63].A simpler explanation is that general relativity itself is not correct, anddark energy could arise from a modified theory of gravity. However, inthe absence of experimental results that conflict with general relativity, it isdifficult to predict how and where such a theory should diverge. Thus testinggeneral relativity in new regimes, such as with antimatter, is essential foridentifying possible deviations and guiding modified gravity models.2.5 Theoretical considerations on repulsiveantimatter gravityIt is widely expected among physicists that antimatter should experiencegravity identically to matter. This belief is supported by three classic argu-ments, described by Nieto and Goldman [54], which are frequently cited indiscussions of antimatter gravity. We outline these arguments here, takingcare to highlight their underlying assumptions. We then consider differentantimatter gravity scenarios from a cosmological perspective, and ask if theycould lead to an evolution of the universe which matches our observations.Finally, we examine measurements which indirectly constrain the effect ofgravity on antimatter.3Indeed, recent DESI results [61] are in tension with a cosmological constant solution.122.5. Theoretical considerations on repulsive antimatter gravity2.5.1 Arguments for equal matter-antimatter gravitationThe first argument, proposed by Morrison [64], is based on conservation ofenergy. This argument is stated more simply by Nieto and Goldman [54],whose formulation I describe here. Let us first consider an atom-antiatompair in a universe where the gravitational behaviour of antimatter and matterare identical. Work can be done to raise the pair to a height h above theEarthâs surface, increasing the gravitational potential energy of the pair by2mgh. If the pair then annihilates and the resulting photons fall back to theground, they would be blue-shifted by the Earthâs gravitational field, eachwith energy increased by mgh compared to if they were produced at groundlevel. This corresponds to the work done to raise the atom-antiatom pair,and so energy is conserved.Now suppose antimatter and matter repel gravitationally, so that anantiatom on the Earthâs surface is repelled upwards with gravitational ac-celeration âg. Then an atom-antiatom pair could be raised to a height hat no net energy cost. If the pair annihilates and the resulting photons fallback to the ground, they would still experience the same blue-shift from theEarthâs gravitational field. They would end up with an additional energy of2mgh more than the atom-antiatom pair initially possessed, despite no workbeing done, in violation of the conservation of energy. Thus, Morrison con-cluded that matter and antimatter must experience the same gravitationalacceleration.The second classic argument, due to Schiff [65], draws on the resultsof the Eötvös experiments discussed earlier in the context of WEP tests.The electric field of an atom polarizes the vacuum and generates virtualelectron-positron pairs, which contribute significantly to the mass of theatom as quantum-mechanical loop corrections. Since the magnitude of thiscontribution differs between atoms, any difference in the gravitational massof electrons and positrons would result in composition-dependent variationsin gravitational mass. This would not affect the inertial mass, necessarilyleading to a breaking of the WEP. Such deviations are strongly constrainedby the Eötvös experiments of Section 2.3, leading Schiff to conclude thatantimatter must couple to gravity identically to matter.The third argument, proposed by Good [66], considers neutral kaon os-cillations. A gravitational mass difference between the K0 and K¯0 wouldinduce regeneration of the long-lived KL into the short-lived KS , a CP-violating process. At the time, this was thought to be forbidden. However,CP violation in the neutral kaon system was soon observed experimentally[45], albeit at a smaller magnitude than Good predicted, leaving this argu-132.5. Theoretical considerations on repulsive antimatter gravityment partially undermined but still of interest.These arguments have been scrutinized in the decades since, especiallywith dark energy generating new interest in modified theories of gravity.A recent review by Chardin and Manfredi [67] outlines various theoreticalapproaches that circumvent, dispute, or reinterpret the constraints posedby Morrison, Schiff, and Good. These debates continue, and there is noconsensus as to whether the classical arguments definitively rule out repulsiveantimatter gravity.If these arguments were to be considered indisputable, a direct mea-surement of the gravitational interaction of antimatter could be seen as re-dundant or unnecessary. However, there remains significant interest amongthe community in such a measurement. Each argument relies on underly-ing assumptions, such as the universality of energy conservation in curvedspacetime, or the applicability of general relativity to virtual particles. Thesearguments can then be considered to raise the stakes: a violation of the weakequivalence principle in antimatter systems would force us to reconsider ourunderlying assumptions.2.5.2 Antimatter gravity cosmologiesEven if repulsive gravity between matter and antimatter were not theoreti-cally excluded, it could still be ruled out based on observations of our uni-verse. We must ask whether such a scenario could lead to a universe which isobservationally similar to our own, or whether it is ruled out cosmologically.The study of cosmologies with exotic gravitational behaviour of antimatteris not a mature field, and remains largely speculative.The main cosmology to consider is called the Dirac-Milne universe [68],which contains an equal amount of matter and antimatter, but gives a nega-tive gravitational mass to antimatter. It includes antimatter that is gravita-tionally repelled by both matter and antimatter, violating CPT symmetry.This mutual repulsion between antimatter particles is necessary to addressthe observed baryon asymmetry of the universe: if antimatter was mutuallyrepulsive, antistars and other large antimatter systems would not form, al-lowing it to hide in the cosmic voids. This cosmology can reproduce somecosmological features such as primordial nucleosynthesis rates, but otherssuch as large scale structure have not been reconciled with observations.Such a theory of gravity would be a considerable departure from general rel-ativity, and necessarily violates CPT symmetry, which would have dramaticconsequences.Other more speculative cosmologies with repulsive antimatter gravity142.5. Theoretical considerations on repulsive antimatter gravityhave been proposed which would not require CPT breaking [69]. However,none of these models are compatible with the breadth of our observations ofthe universe, failing to explain features such as baryon acoustic oscillations[70] or the large scale structure of the universe.Should a difference in gravitational behaviour between matter and anti-matter be experimentally confirmed, it would necessitate the developmentof a new cosmological model capable of reproducing our observed universe.The fact that such a model is not currently known does not rule out thepossibility of its existence; rather, it reflects limited theoretical efforts. Theexisting models can be considered starting points for further development, inthe case where experimental results indicate exotic gravitational behaviourof antimatter.2.5.3 Indirect antimatter gravity constraintsWhile a direct free-fall-type WEP test has never been performed on anti-matter, and cosmological models are not sufficiently developed to rule outexotic gravitational behaviour of antimatter, there are a number of indirectlimits on antimatter gravity from other experiments. Here, an indirect limitrefers to a measurement which must be combined with other assumptionsor models in order to constrain antimatter gravity. Such methods are nicelysummarized in [71]. The authors conclude that while indirect reasoning canbe used to rule out WEP violation in antimatter at the 1% level, this anal-ysis relies on models and assumptions which are also worth testing, and soa direct test is still highly valuable.One line of reasoning is that only around 1% of the antiproton mass is dueto the antiquark mass. Most of the remaining mass originates from bindingenergy in the gluon field. If only the antiquark mass is treated gravitationallyas antimatter, then the maximum possible WEP violation in antiprotons is atthe 1% level. A more recent treatment of this logic is presented in [72], whichargues that antiquark kinetic energy should also be treated as antimatter.Based on recent lattice QCD calculations, this brings the total gravitationalantimatter fraction of the antiproton to around 33%. This argument relieson QCD, and so a precise determination of the gravitational acceleration ofantihydrogen could be re-framed in this way as a test of the Standard Model.One indirect constraint can be applied based on the reasoning of Schiffdescribed in Section 2.5.1, which relies on differing fractions of virtual an-tiparticles in the nuclei of different elements. This is estimated to constrainantimatter gravity to be equal to matter gravity to within less than 0.5%[71]. However, this method relies on our understanding of the coupling of152.5. Theoretical considerations on repulsive antimatter gravitygravity to virtual particles, which should itself be called into question.A second category of indirect constraints on antimatter gravity describedin [71] rely on time-scaling effects. Should matter and antimatter experiencedifferent gravitational accelerations, then a matter and antimatter particleheld at the same location will be at different gravitational potentials. As aresult, the antimatter particle will exhibit gravitational time dilation, andthe internal clocks of the matter and antimatter particles will run at differentspeeds.This can result in a number of measurable effects. The first effect is theone proposed by Good (see Section 2.5.1), where the oscillation between kaonstates would be shifted from theoretical expectations. A difference betweenthe gravitational acceleration of matter and antimatter of 0.05% has beenruled out based on these observations. Other measurable effects include adifference in the cyclotron frequency between protons and antiprotons, whichhas been ruled out by the BASE collaboration at the 10â7 level [73], or inneutrino oscillations [74] at the 0.02% level.Whereas gravitational time dilation is usually framed in terms of gravi-tational potential differences, the analysis of each of these time-scaling mea-surements relies on the use of an absolute gravitational potential. Whilethis could be valid in general relativity, since we are interpreting a gravitydifference between matter and antimatter, we have already departed fromthe realm of general relativity; it is questionable whether the notion of anabsolute gravitational potential is justified in this case. Furthermore, it isnot clear which gravitational potential to use; typically the gravitationalpotential of the galaxy or galactic supercluster is used in these calculations.In conclusion, there are many indirect constraints which rule out a de-parture of antimatter from the WEP, at least at the level accessible in theALPHA-g experiment. However, these indirect constraints each rely on as-sumptions which are not fully accepted, or at least merit further testing.As such, there is considerable interest among the antimatter communityin a direct, free-fall type experiment which can be interpreted in a model-independent fashion.16Chapter 3Introduction to ALPHAThe ALPHA collaboration was formed by members of the ATHENA col-laboration, the first group to produce antihydrogen by combining trappedpositrons and antiprotons [24]. The primary physics goal remained: to studythe properties of antihydrogen, in order to verify the fundamental symme-tries between matter and antimatter. In 2010, ALPHA became the firstgroup to trap antihydrogen atoms [25]. This work continues into the presentday with the ALPHA-2 experiment, which has performed a number of spec-troscopic measurements on antihydrogen, such as the 1S-2S transition [8],1S-2P transition [9], fine structure [10], and hyperfine structure [11], amongmany others.Building on these successes, ALPHA has recently turned towards a fur-ther fundamental symmetry between matter and antimatter: the equivalenceof free fall under gravity imposed by the WEP. To this end, the ALPHA-g experiment was commissioned, reusing much of the existing ALPHA in-frastructure and technical knowledge. The first results from ALPHA-g arepublished in [1]; this publication will hereafter be referred to as the gravitypaper. The details of this measurement are included in this dissertation, aswell as in other dissertations [75â78].This chapter will outline the various systems, components, and tech-niques which were used to make these measurements. I will not attemptto provide an exhaustive description of the ALPHA apparatus; instead, Iwill briefly introduce the subsystems and techniques, with a focus on thoseused for the gravity measurement in ALPHA-g. More detailed descriptionsare available in the papers cited above and throughout this chapter. Thischapter will focus on the experimental apparatus and individual techniquesused; the overall measurement procedure for the gravity paper, as well as itslimitations and possible extensions, is described in Chapter 9.3.1 The AD and ELENAAntiproton production at CERN begins with a proton beam. Negative hy-drogen ions are accelerated to an energy of 160MeV by the linear accelerator173.1. The AD and ELENAFigure 3.1: A schematic layout of the AD, adapted from [85]. Additionalred labels: 1. AD target and magnetic horn location. 2. Beam injection andextraction point. 3. RF cavities. 4. Stochastic cooling. 5. Electron cooling.Also visible are the ELENA decelerator and the ALPHA experimental zone.LINAC 4 [79]. The electrons are stripped as the beam passes through a strip-ping foil and into the Proton Synchrotron Booster, an accelerator ring thatfurther accelerates the protons to an energy of 2GeV [80, 81]. They are thenfurther accelerated to 26GeV by the proton synchrotron (PS) [82].This beam is directed into an iridium rod target, where collisions producea plethora of particle types and energies. A magnetic lens, or horn, collectsthe antiprotons produced, guiding those with a momentum of 3.5GeV/c intoa beamline. From here, the antiprotons enter the Antiproton Decelerator(AD) [83, 84], a storage ring where they are slowed to a kinetic energy of5.3MeV. Dipole magnets bend their trajectory into a ring, and quadrupolemagnets focus the beam. The beam deceleration and cooling is facilitatedby a number of systems highlighted in Figure 3.1.183.2. Particle trappingRadiofrequency (RF) cavities lower the momentum of the beam in stepsfrom 3.5GeV/c to 100MeV/c. The bunch arrival time is synchronized withan oscillating electric field. In this way, the field applied to the antiprotonbunches opposes the direction of motion and slows down the bunch.Between each momentum step, cooling techniques are applied to con-trol the spread of particles in position and momentum space, known as thebeam emittance. There are two stochastic cooling stages at 3.5GeV/c and2GeV/c. This process involves using a detector, or âpickupâ, to detect parti-cles deviating from the desired bunch centre. The pickup signal is processedand fed forward to a âkickerâ, which applies a corrective electric field.There are two electron cooling stages at 300MeV/c and 100MeV/c. Anelectron gun is used to create a beam of electrons, and the velocity of thisbeam is matched to the velocity of the antiproton beam. The two beams arethen overlapped. Any antiprotons with higher than average velocity interactwith electrons, transferring their energy via Coulomb scattering, and slowdown towards the average velocity.Following the electron cooling at momentum 100MeV/c, or kinetic en-ergy 5.3MeV, the antiproton beam is injected into a second storage ringcalled the Extra Low ENergy Antiproton Ring (ELENA). In this ring, suc-cessive decelerations using RF cavities are interleaved with electron coolingstages; a similar technique as the AD. The antiproton beam is slowed to akinetic energy of 100 keV. It is extracted at one of two extraction points anddelivered to experiments such as ALPHA, which require such low kineticenergies to efficiently trap the incoming antiprotons.An example of an AD and ELENA cycle, including the deceleration andcooling stages, is shown in Figure 3.2. In typical operation, the cycle lastsapproximately 120 seconds per bunch delivered. The AD team at CERN havealso developed a technique to split each antiproton bunch into four smallersub-bunches, enabling simultaneous delivery to multiple experiments. As aresult, antiprotons were available to ALPHA continuously throughout therun periods.3.2 Particle trappingProduction of antihydrogen in ALPHA begins with the trapping of antipro-tons. A single bunch of antiprotons from ELENA contains approximately7.5Ã106 antiprotons, of which around 5Ã105 are successfully trapped. Sim-ilar numbers of positrons are also generated and captured. These collectionsof charged particles, known as plasmas, have sufficiently high densities that193.2. Particle trappingFigure 3.2: Model of beam momentum over an AD (left) and ELENA (right)cycle. Sloped segments indicate beam momentum adjustments using RF cav-ities. S.C. indicates stochastic cooling periods, and E.C. indicates electroncooling periods. The dashed lines indicate beam injection (green) and ex-traction (black) times.the interactions between particles cannot be neglected. The trapping andmanipulation of these charged particle plasmas is carried out using a numberof Penning-Malmberg traps. The trapping of electrically neutral antihydro-gen atoms requires a different type of trap: ALPHA uses a superimposedmagnetic minimum trap to confine these atoms, relying on the interaction ofthe antihydrogen magnetic moment with inhomogeneous magnetic fields. Inthis section we will discuss the methods used to trap these charged particleplasmas and neutral atoms, both from a theoretical and practical standpoint.3.2.1 Charged particle trappingFirst, let us consider a single charged particle of charge q and mass m, pro-pelled by an electric field Eâ towards a minimum in the electrostatic potentialV . It experiences a force Fâ and subsequent acceleration ¨âx (using the dotnotation for time derivatives) given by:Fâ = m¨âx = qEâ = âqââV (3.2.1)One could trap a charged particle by placing it in a quadratic potentialwell, so that any motion away from the minimum results in a force returningthe particle to the centre. This works well in one dimension; unfortunately,203.2. Particle trappingFigure 3.3: (a.) The hyperbolic electrodes of a Penning trap, from [89]. Auniform magnetic field along the Z axis is applied by solenoid magnet. (b.)The cylindrical electrodes of a Penning-Malmberg trap, from [90].it was proven by Earnshaw in 1842 [86] that no static electric field configu-ration can produce a three-dimensional potential minimum. Today, this isframed in terms of Poissonâs equationââ2V = 0, a consequence of Maxwellâsequations.Since a charged particle cannot be trapped by static electric fields alone,let us consider now the motion of a particle in a constant magnetic field Bâ:Fâ = m¨âx = q Ëâxà Bâ (3.2.2)The particle will experience a force perpendicular to its velocity, resulting incircular motion in the plane perpendicular to the magnetic field, known ascyclotron motion. The frequency of this motion is the cyclotron frequencyÏc = qB/m.The combination of these two ideas led to the development of the Pen-ning trap [87, 88], where a constant magnetic field confines the particle tocircular motion in the radial dimensions, while an electric potential well trapsparticles axially. The electric potential configuration is achieved by two hy-perbolic end caps and a hyperbolic ring electrode, as shown in Figure 3.3.a.The magnetic field is applied by a superimposed solenoid magnet.Achieving a quadratic electrostatic potential on-axis necessarily also cre-ates a radial electrostatic potential. This leads to a Penning trap potentialof the form:V (xâ) =V0R2(2z2 â x2 â y2) (3.2.3)Here, V0 sets the magnitude of the potential, R is a characteristic trap di-mension, and x, y, z are the components of the position xâ. Combining thiselectrostatic potential with a constant magnetic field Bâ = B0zË and solving213.2. Particle trappingthe equations of motion (the sum of equations 3.2.1 and 3.2.2) yields decou-pled axial and radial motions. The axial motion is described by a simpleharmonic motion where Ïz is called the axial bounce frequency:z¨ = â4qV0mR2z = Ï2zz (3.2.4)The radial motion is more complicated; the radial electric field perturbsthe solution from the simple cyclotron motion of a uniform magnetic field.Introducing u(t) = x(t) + iy(t) as a combined spatial coordinate, we canwrite the equation of radial motion as:u¨ = iÏcuËâ 12Ïzu (3.2.5)This has two independent solutions u(t) = u0eâiÏÂ±t. Here Ïc = qB/m isthe classic cyclotron frequency in the absence of the electrostatic field, andÏÂ± =Ïc2± 12âÏ2c â 2Ï2z (3.2.6)The validity of this solution depends on Ï2câ2Ï2z > 0, called the trappingcondition, which requires that the magnetic field be strong compared to theradial electrostatic field in order for the particles to be radially confined.The frequency Ï+ â¼ Ïc is called the modified cyclotron frequency. Thesolution u(t) = u0eâiÏ+t is similar to the motion of a charged particle in aconstant magnetic field, in the absence of electrostatic fields. The frequencyÏâ â¼ Ï2z2Ïcis called the magnetron frequency, and the solution u(t) = u0eâiÏâtis related to the Eâ Ã Bâ drift a charged particle experiences in constantelectrostatic and magnetic fields. The general solution to the radial equationof motion is a linear combination of the two solutions. As a result, themotion of a particle trapped in a Penning trap can be broken down intothree separate components:1. The simple harmonic axial motion with frequency Ïz.2. The slow circular magnetron motion with frequency Ïâ.3. The fast circular cyclotron motion with frequency Ï+.An example of the path traced by a particle in a Penning trap is shownin Figure 3.4.223.2. Particle trappingFigure 3.4: Radial (a.) and three-dimensional (b.) motion of a chargedparticle in a Penning trap. Axes are in arbitrary units; the length scale isset by the strength of the trapping potentials.3.2.2 Non-neutral plasma trappingIn ALPHA and many other practical applications, one would like to simul-taneously trap many charged particles. The hyperbolic geometry of a tra-ditional Penning trap is not well-suited for this, as the electric fields areuniform over only a small spatial volume. Furthermore, the hyperbolic elec-trodes are mechanically cumbersome and offer limited flexibility for particlemanipulation.A Penning-Malmberg trap offers an alternative solution, formed by astack of cylindrical electrodes and a superimposed magnetic solenoid shownin Figure 3.3.b. By applying a voltage to two electrodes separated by sev-eral grounded electrodes, a confining axial electric potential is produced.Combined with a constant axial magnetic field, this configuration confinescharged particles. The electrode cylinder is open at both ends, allowingaccess for particle loading or ejection in either axial direction.The main downside to this cylindrical geometry is that the electric fieldis no longer perfectly quadratic. As a result, the motion of particles in aPenning-Malmberg trap can no longer be described analytically and mustbe modelled by simulation. However, this geometry allows trapping of sig-nificantly larger numbers of particles over an extended axial region. Oncemultiple particles are introduced, the mutual repulsion between them makesdescribing the situation mathematically more complicated. This system ofinteracting particles is referred to as a non-neutral plasma.233.2. Particle trappingA traditional quasi-neutral plasma is a state of matter where the con-stituent particles have enough energy to overcome binding energies betweeneach other, and contains similar numbers of positive and negative particles.These plasmas exhibit collective effects such as Debye screening, where par-ticles on the plasma skin will rearrange themselves to shield the interior ofthe plasma from an electric field. By contrast, a non-neutral plasma is typ-ically composed of charged particles of a single species. As a result, it hasa net charge and generates significant internal electric fields. Confinementrequires a combination of electric and magnetic fields, such as those in aPenning-Malmberg trap, to counteract the internal repulsive forces.The rotational symmetry of the Penning-Malmberg trap leads to a rota-tional invariance, and conservation of the canonical angular momentum L ofthe plasma [91]:L =Nâj=1(mvÎ¸,jrj +qcBrj2rj)= const. (3.2.7)In a sufficiently strong magnetic field, the second term due to the mag-netic field will dominate the first term due to particle angular momentum,and the condition simplifies to a constraint on the mean radius squared ofthe particles:Nâj=1r2j = const. (3.2.8)Given an initially trapped plasma, this leads to an upper bound on thefraction of trapped particles which can reach the trap wall [92]. Typically, aconfined plasma will reach an equilibrium state with a constant r-dependentrotational velocity and density profile.3.2.3 Antihydrogen trappingThe Penning-Malmberg trap relies on particles being charged, allowing themto interact with applied electric and magnetic fields. This trap works wellfor both antiprotons and positrons, but trapping the neutral antihydrogenatom requires a different approach.A neutral atom can still experience a force in a magnetic field due toits magnetic dipole moment. This is a quantum mechanical property whichis a combination of the orbital dipole moment, due to the positron orbitacting as a current loop, and the intrinsic spin dipole moment of the positron243.3. Annihilationand antiproton. The orbital moment is determined by the orbital quantumnumber of the atomic state; this is zero in the ground state, which is byfar the most likely state in a Penning-Malmberg trap. As a result, themagnetic dipole moment is given entirely by the spin dipole moment. Theaxial component of the dipole moment is then µz = âgsµBms, where gsis the spin g-factor, µB is the Bohr magneton, and ms = ±1/2 is the spinquantum number of the state.The Zeeman energy, corresponding to the interaction of the magneticdipole moment with an external magnetic field, is given by:U = âµâ · Bâ (3.2.9)where µâ is the magnetic dipole moment of the antihydrogen atom and Bâ isthe applied magnetic field.The torque resulting from the magnetic field will cause the dipole mo-ment to either align or anti-align with the applied field, and so the potentialexperienced by the antihydrogen atom will either increase or decrease by µB.Those antiatoms which see a decreased potential by µB are known as highfield seekers. Since it is impossible to produce a magnetic field with a lo-cal maximum [93], these antiatoms are deemed untrappable. The antiatomswhich see an increased potential by µB are known as low field seekers. Ifmoved away from the minimum of a magnetic field, they will experience aforce returning them to the minimum.This is the basis of the Ioffe-Pritchard trap [94]. A quadrupole, sex-tupole, or octupole magnet produces a field with strength increasing withradius, which creates radial confinement. A solenoid applies a constant ax-ial magnetic field, which is enhanced at the ends by two small mirror coils,confining the atoms axially. The geometry of a simple Ioffe-Pritchard trapis shown in Figure 3.5.3.3 AnnihilationThe process of annihilation occurs when a particle collides with its antipar-ticle. Both the particle and antiparticle are destroyed, with their mass con-verted to energy following E = mc2. This results in the creation of otherparticles (annihilation products) following the conservation of energy, mo-mentum, spin, charge, and baryon and lepton number.The complexity of annihilation outcomes increases with the energy avail-able in the collision. If either the particle or antiparticle have a large kinetic253.3. AnnihilationFigure 3.5: A simple Ioffe-Pritchard trap. Ioffe bars (red) with alternatingcurrent flow produce a quadrupole magnetic field, while mirror coils (blue)increase the magnetic field at the ends of the trap.energy, then many particles can be created; this is the principle of electron-positron and proton-antiproton colliders. In ALPHA, the highest kineticenergy involved is the 100 keV with which antiprotons are delivered fromELENA. This is far smaller than the 938.8MeV/c2 rest mass of the antipro-ton, and so we will limit our discussion of annihilation to the case whereboth particles are (almost) at rest.3.3.1 Positron annihilationBy far the most probable channels in electron-positron annihilation are theproduction of either two photons e++eâ ââ 2γ or three photons e++eâ ââ3Î³. The electron and positron have a very small rest mass of 511 keV/c2; theonly other particles with low enough rest mass to be created are neutrinos,and these are suppressed by the relative weakness of the weak force.A low-energy positron is typically slowed down and captured by an elec-tron to form positronium. After a short time (either 0.12 ns or 13.6 ns), theelectron and positron annihilate. The lifetime and number of photons pro-duced depends on the alignment of the electron and positron spins. If thespins are anti-aligned (as in para-positronium), conservation of charge parityprohibits the production of an odd number of photons, leading to the dom-inance of 2γ channel. If the electron and positron spins are aligned (as inortho-positronium), the production of an even number of photons is prohib-ited, resulting in primarily 3γ production. It is also possible for a positronto annihilate directly on an electron without forming positronium, in which263.3. Annihilationcase the 2γ production is most probable [95].The relative probability of the 2γ and 3γ annihilations depends on theformation rates of para-positronium and ortho-positronium. With a tripletof three spin configurations, ortho-positronium is approximately three timesmore likely to be formed than para-positronium, which has only one spinconfiguration. However, the exact ratio varies slightly depending on thematerial [96].The single photon channel e++ eâ ââ γ is forbidden by conservation ofmomentum. In the centre of mass frame of reference, in which the electron-positron pair has zero total momentum, the resulting photon must also havezero momentum. Since the photon energy and momentum are related byp = Ec, this photon would have zero energy, which cannot occur.In the two photon case, the same argument can be applied to show thatthe photons must be created back-to-back, with 511 keV of energy each. Thisis incidentally the principle by which positron emission tomography works,and so we can thank conservation of momentum in annihilations for savingcountably many lives.43.3.2 Antiproton annihilationAntiproton annihilation is a much messier affair than electron-positron an-nihilation due to two main factors:1. Protons and antiprotons have a higher rest mass of 938.8MeV/c2, in-creasing the number and types of annihilation products.2. Protons and antiprotons are ensembles of three quarks, and not ele-mentary particles.The proton is composed of two u quarks and one d quark, while theantiproton is composed of two u¯ antiquarks and a d¯ antiquark. Instead of anantiproton annihilation, we should consider the annihilation of an antiquarkwith a quark. An antiquark in an antiproton can also annihilate with aquark in a neutron, and so we should consider both antiproton-proton andantiproton-neutron annihilations.The pion final state branching ratios of these two processes are shownin Table 3.1. Almost all annihilations end in a state with some number ofcharged pions ÏÂ± (the ud¯ and du¯ bound states of a quark and an antiquark)and neutral pions Ï0 (the (uu¯ + dd¯)/â2 bound state). Antiproton-proton4Positron emission tomography is often cited as a practical application of antimatter.273.3. Annihilationannihilation results in an equal number of Ï+ and Ïâ mesons due to conser-vation of charge, while antiproton-neutron annihilation results in one moreÏâ meson.(a) Antiproton-proton (from [38, 97])Pion final state %Ï0Ï0 0.028Ï0Ï0Ï0 0.76Ï0Ï0Ï0Ï0 3.0Ï+Ïâ 0.32Ï+ÏâÏ0 6.9Ï+ÏâÏ0Ï0 9.3Ï+ÏâÏ0Ï0Ï0 23.3Ï+ÏâÏ0Ï0Ï0Ï0 2.8Ï+ÏâÏ+Ïâ 6.9Ï+ÏâÏ+ÏâÏ0 19.6Ï+ÏâÏ+ÏâÏ0Ï0 16.6Ï+ÏâÏ+ÏâÏ0Ï0Ï0 4.2Ï+ÏâÏ+ÏâÏ+Ïâ 2.1Ï+ÏâÏ+ÏâÏ+ÏâÏ0 1.9(b) Antiproton-neutron (from [38, 98])Pion final state %ÏâÏ0 0.75ÏânÏ0 (n > 1) 16.9ÏâÏâÏ+ 0.23ÏâÏâÏ+Ï0 17.0ÏâÏâÏ+nÏ0 (n > 1) 39.7ÏâÏâÏâÏ+Ï+ 4.2ÏâÏâÏâÏ+Ï+Ï0 12.0ÏâÏâÏâÏ+Ï+nÏ0 (n > 1) 6.6ÏâÏâÏâÏâÏ+Ï+Ï+nÏ0(n â¥ 0)0.35Table 3.1: Measured pionic final states and branching ratios for antiproton-proton and antiproton-neutron annihilation. In (b), n refers to the numberof Ï0 mesons. Note that the total adds to 97.7% for each table, since not alldecay channels are shown.The ÏÂ± rest mass is 139.6MeV/c2 and its lifetime at rest is Ï = 26ns[56]. Pions are typically produced with around 100MeV of kinetic energy; acharged pion at this energy has a mean decay length of L = Î³Î²cÏ = 11m,and so they can be considered stable particles over the length scale of theALPHA detectors.The Ï0 has rest mass 135MeV/c2, but its lifetime at rest is much shorterat 8.5 Ã 10â17 s [56]. The same calculation yields a mean decay length of36 nm, and so we should consider the decay of the neutral pion. The domi-nant mode with 99% of the branching ratio is Ï0 ââ 2γ, and most remainingdecays are Ï0 ââ eâ + e+ + γ [56]. These photons further interact via pairproduction γ ââ eâ + e+ in the electromagnetic field of a nucleus, withan attenuation length on the order of 1 cm. The resulting state as observedin the ALPHA particle detectors is N Ï+ mesons, either N or N + 1 Ïâmesons, and some number of eâe+ pairs from displaced photon pair produc-283.4. The ALPHA apparatustion vertices.A further complication arises when we consider than our antiprotonsare not annihilating on free protons and neutrons, but on those containedwithin a nucleus. Some number of produced pions may travel further intothe nucleus and be absorbed, reducing the observed pion multiplicity ofthe annihilation. This may have further effects such as causing a nucleonexcitation and subsequent decay, or producing additional particles througha further pion-nucleon cascade [99, 100].3.3.3 Antihydrogen annihilationThe annihilation of antihydrogen atoms can be thought of as the combinationof the antiproton annihilation and the positron annihilation processes. Whenan antihydrogen atom comes into contact with a regular atom, the antiprotonwill annihilate with a nucleus as discussed in Section 3.3.2 and the positronwill annihilate with an electron as discussed in Section 3.3.1.The positron annihilation contributes only a small fraction of the overallenergy and produces only two or three photons. These are often difficult todetect among the higher multiplicity of secondary particles from the antipro-ton annihilation. In some detection schemes, the back-to-back photon signalof the positron annihilation can be used as a supporting signal to distinguishantihydrogen annihilations. Primarily, however, the signals of the antiprotonannihilation and antihydrogen annihilation are practically identical, and thetwo must be distinguished by a well-designed experimental procedure.3.4 The ALPHA apparatusThe ALPHA experiment is a mature project which has made many distinctmeasurements in the same apparatus. Although they are often said to beseparate experiments, the modular design means much of the apparatus isshared between ALPHA-2 and ALPHA-g. The ALPHA-2 and ALPHA-gatom traps are variations on the same design: a Penning-Malmberg chargedparticle trap and a superimposed Ioffe-Pritchard neutral atom trap. Theentire ALPHA apparatus is shown in Figure 3.6. This section will describethe components of the ALPHA apparatus relevant for gravity experimentsin ALPHA-g: the catching trap, positron accumulator, beamline, beam di-agnostics, annihilation diagnostics, and the ALPHA-g trap.293.4. The ALPHA apparatusFigure 3.6: Cross-section of the full ALPHA apparatus. Adapted from [101].3.4.1 Catching trapThe ALPHA catching trap is a Penning-Malmberg trap designed to receiveand cool bunches of antiprotons from ELENA. A superconducting solenoidprovides a 3T axial magnetic field for radial confinement, while axial confine-ment is provided by a set of 20 cylindrical electrode segments. To facilitatethe superconducting magnet, the apparatus is enclosed by a closed-systemliquid helium cryostat. Scroll pumps, turbo pumps, and ion pumps are usedto create a vacuum of 10â10mbar. This is further enhanced by cryopumpingwhich improves the vacuum to better than 10â13mbar [102].Upon arrival, an antiproton bunch passes through a 1 µm aluminiumdegrader foil, optimized for the 100 keV ELENA ejection energy [103]. Afraction of the bunch will annihilate on the foil, but the remaining antiprotonswill be slowed to even lower energies, facilitating their capture.The catching trap features two specialized high-voltage electrodes whichcan be biased to up to ±5 kV. The downstream electrode is held at â5 kV,and the upstream electrode is ramped to the same voltage immediately afterthe bunch arrival. This confines antiprotons with energy less than 5 keVbetween the two high voltage electrodes, as discussed in Section 3.2.1. Thisprocess is depicted in Figure 3.7, which shows the resulting axial potentialbefore and after the upstream electrode is raised.This process also includes loading an electron plasma into the catching303.4. The ALPHA apparatusFigure 3.7: The catching trap electrodes (top) and axial potential (bottom).The potential is shown before (dashed) and after (solid) HVA is ramped toâ5 kV. Figure from [104].trap prior to the antiproton arrival, to facilitate electron cooling. This andother antiproton plasma preparation techniques will be discussed in Sec-tion 3.5.1. Following this preparation, a potential gradient is applied usingthe electrodes, to kick the antiprotons downstream out of the catching trapand into the beamline.3.4.2 Positron accumulatorThe positrons used in ALPHA are created by the β+ decay of a sodium-22source with a half-life of 2.6 years [105] and an activity of 2.8GBq [106]:2211Naâ2210 Ne+ e+ + νe (3.4.1)They typically have energies on the order of an MeV, too high for trap-ping. To slow down the positrons, a solid Ne moderator is grown on thesurface of the source. While the majority of positrons annihilate within themoderator, a small fraction stop near the surface of the moderator and sur-vive. These positrons are released into the vacuum chamber with an energyof around 50 eV.These moderated positrons are electromagnetically steered into a modi-fied Penning-Malmberg trap known as a Surko trap [107]. A 0.15T magneticfield confines the positrons radially, and seven cylindrical electrodes provideaxial confinement. The diameter of these electrodes increases from 12.7mm313.4. The ALPHA apparatusFigure 3.8: A diagram of the positron accumulator, taken from [106]. Theinlaid diagram shows the axial potential and pressure.for the first two electrodes, to 30.5mm for the third electrode, and finallyto 200.7mm for the last four electrodes. A pressure gradient is establishedby injecting a nitrogen buffer gas near the narrow electrodes and pumpingit away near the wider ones.Both the gas pressure and electric field are highest near the narrow elec-trodes, as shown in Figure 3.8. The incoming positrons are initially confinedalong the full length of the trap. They collide inelastically withN2 molecules,losing energy via electronic excitation. As their energy decreases, they be-come increasingly confined to the low-pressure, low-field region within thelarger-radius electrodes.Finally, a technique known as a rotating wall electrode is applied to com-press the positron plasma. One of the electrodes is divided into six segmentsto accommodate this; the procedure will be discussed in Section 3.5.1. Theresult is a dense, cold plasma which can be transferred to the main ALPHAtrap for use in antihydrogen formation. A typical accumulation cycle of 100seconds yields around 3Ã 106 positrons [1].3.4.3 BeamlineThe overall design of the ALPHA apparatus requires the delivery of an-tiprotons and positrons to both the ALPHA-2 and ALPHA-g atom traps.Since ALPHA-g requires a vertical orientation, while ELENA and all exist-ing ALPHA apparatus is horizontally aligned, transferring both species toALPHA-g while maintaining the possibility of positron transfer to ALPHA-2is not a trivial problem.323.4. The ALPHA apparatusMoving a plasma between Penning-Malmberg traps is already challeng-ing, as it involves guiding particles through regions with strong magneticfield gradients. To understand the impact of these gradients, consider a par-ticle of charge q and mass m in the trap at a Larmor radius r and withvelocity components vâ¥ and vâ¥ with respect to the magnetic field B:vâ¥r=qmB (3.4.2)As B decreases, r will increase and vâ¥ will decrease. Increasing r obvi-ously causes issues for particle transfer; a radial plasma expansion will leadto particles annihilating on the walls of the beamline. Conversely, as B in-creases, r decreases and vâ¥ increases. Since magnetic fields do no work, thetotal kinetic energy is conserved, and so this increase in vâ¥ must correspondto a decrease in vâ¥. If vâ¥ is decreased to zero, then the particle will re-verse direction and begin travelling back towards lower B, in a phenomenonknown as magnetic mirroring. In these ways, any increase or decrease in Bcan cause significant losses during a transfer between two Penning-Malmbergtraps.These effects and many others were extensively studied via simulationin the design of the ALPHA beamline, which is detailed in [101]. Sevensections of water-cooled solenoids provide a weaker magnetic field to guideboth positrons and antiprotons. The polarity of the current in each solenoidcan be reversed, allowing a suitable magnetic field configuration for transfersinto either ALPHA-2 or ALPHA-g. The most complicated section of thebeamline is called the interconnect, which is responsible for the bending ofantiprotons and positrons from opposite sides 90â¦ upwards into ALPHA-gwithout significant beam degradation, while also having a configuration thatallows positrons to be guided through towards ALPHA-2.3.4.4 SticksTo monitor and debug the transfer of particles at various stages during prepa-ration and transfer, ALPHA uses a number of diagnostic stations affection-ately known as sticks: linear actuators which are able to move a number ofdifferent instruments into the beam path. The specific instruments availableon each stick vary depending on its location and usage. I will give a briefoverview of the most common instruments here.Electron guns are used to load a plasma of electrons into any of thePenning-Malmberg traps. This can be useful for trap diagnostics, and is alsoused in electron cooling of antiprotons. A barium oxide filament is heated333.4. The ALPHA apparatusthrough ohmic heating by an applied voltage. This excites electrons in thebarium oxide, which has a low work function of 1 eV to 2 eV, above whichelectrons will escape the material. These electrons are then accelerated by avoltage difference between two plates. The emission current, typically a fewhundred µA, is monitored and a feedback loop adjusts the applied voltageto maintain a stable emission of electrons.Faraday cups are a simple diagnostic tool to destructively measure thetotal charge of a group of charged particles, used for counting the numberof charged particles in a plasma. The particles induce a charge on a metalcup as they strike it, which is read out. Around 106 elementary charges willcreate a measurable current.Microchannel plates (MCPs) are used to image plasmas. An MCPconsists of a resistive plate which has many small (5 µm to 20 µm diameter)cylindrical channels through it. A charged particle striking the MCP willproduce electrons, which are accelerated through the channels by an appliedvoltage of around 1 kV. As the electrons strike the walls of the channels,further electrons are dislodged from an emissive coating. The number ofelectrons is amplified at each successive interaction, increasing the signal byalmost 106. Behind the MCP is a phosphor screen, a panel coated with amaterial which creates scintillation light after it is excited by an incidentcharged particle. These are paired with a mirror at 45â¦ which directs thescintillation light through a vacuum window towards a charge-coupled device(CCD) camera. The highly variable gain of the MCP makes this systemsuitable for imaging plasmas ranging from one to 108 particles.These tools combine to provide essential feedback for beam alignment,plasma manipulation, and real-time monitoring during antiproton and pos-itron transfer operations.3.4.5 Annihilation diagnosticsThe diagnostic sticks work well for understanding plasmas which are con-trolled sufficiently to be propelled out of a Penning-Malmberg trap towardsthem. However, additional diagnostic tools are required for improving thetransfer of antiprotons and positrons between traps, as well as understandinglosses during particle preparation.A number of plastic scintillator panels are used for this purpose. Theseare large (typically 0.4m Ã 0.6m Ã 2.2 cm) sheets of polyvinyltoluene dopedwith a florescent scintillator material. When a charged particle passes throughthe scintillator panel, it will excite a molecule of the scintillator. When itde-excites, the molecule releases a photon of the characteristic wavelength.343.4. The ALPHA apparatusA minimum-ionizing charged particle (such as a charged pion from an anni-hilation) will produce around 2 Ã 104 photons when passing through one ofthese panels. Scintillators will be discussed further in Section 4.3.1.The produced photons will propagate inside the plastic scintillator via to-tal internal reflection before being collected by photosensors mounted on theedge of the panel. The panels surrounding the catching trap and ALPHA-2feature a light guide and PMT, while the newer panels used for ALPHA-grely on SiPMs. The details of these technologies will be discussed in Sec-tion 4.3.2.The scintillator panel + photosensor system is used throughout ALPHAto detect charged particles resulting from antiproton annihilation. They areusually positioned in pairs, so that the coincidence between the two panelscan be used to suppress false triggers due to electronic noise or stray photons,improving the signal-to-noise ratio. The recovery time of the system is onthe order of 50 ns, fast enough to avoid saturation and be able to count manyannihilations in quick succession.In addition to the plastic scintillator panels, ALPHA employs a numberof thallium-doped cesium iodide CsI(Tl) detectors. This is a dense inorganiccrystal scintillator, which is directly coupled to a PMT to detect ionizingparticles in much the same way as the plastic scintillator panels. The CsI(Tl)detectors are particularly efficient at stopping and detecting the 511 keVphotons produced in the annihilation of a positron with an electron, and areused primarily for debugging positron losses during transfers between traps.3.4.6 ALPHA-gAt its core, ALPHA-g is an Ioffe-Pritchard magnetic trap superimposed ona Penning-Malmberg charged particle trap. This is a proven design whichhas been extensively tested by the ALPHA collaboration with the ALPHA-2 atom trap, discussed elsewhere [106]. Whereas ALPHA-2 was designedas a multi-purpose antihydrogen trap, ALPHA-g was purpose built for themeasurement of gravity on antihydrogen.A schematic overview of ALPHA-g is shown in Figure 3.9.a. The designwas intended to be entirely symmetric, to minimize the systematic effects ona measurement of antihydrogen released from the centre of the apparatus byensuring systematic bias in field gradients or trap structure affects upwardand downward-released antihydrogen equally. The initial trap design can beseparated into three distinct parts: the bottom trap (a combined magneticmoment and Penning-Malmberg trap), the top trap (a mirror copy of thebottom trap), and the central precision region (a purely magnetic trap with353.4. The ALPHA apparatusFigure 3.9: (a.) A schematic overview of the full ALPHA-g apparatus,adapted from [1]. The dotted box highlights the bottom Penning trap. (b.)A design schematic for the ALPHA-g Penning-Malmberg and Ioffe-Pritchardtraps, adapted from an upcoming publication. This reflects a recent decisionto include a Penning-Malmberg trap in the precision region (here, analysisregion), due to its utility for magnetic field measurements.363.4. The ALPHA apparatusno Penning-Malmberg electrodes).Recent developments diverge from this initial plan. The complete sym-metry between the top and bottom traps has been forgone, since new trapproduction techniques have made installing a Penning-Malmberg trap in theprecision region possible by extending the top trap, as shown in Figure 3.9.b.The magnetic field characterization techniques used in the initial measure-ment, which will be discussed in Section 9.1.2, rely on electron plasmastrapped within the Penning-Malmberg trap. The additional electrodes allowthe extension of these techniques to the precision region. The implicationsof this modification on the final precision measurement have not been fullyexplored.In the first published ALPHA-g measurement of gravity [1], only thebottom trap was commissioned and used. Antiprotons and positrons werecombined in this region, and antihydrogen was magnetically trapped therebefore being released. In future precision measurements, antihydrogen atomswill be formed in either the top or bottom trap, before being transferred tothe central precision trap and released.The electrodes of the bottom and top traps are further subdivided intotwo sections: the normal trap and the thin trap. The normal trap has aninternal diameter 29.6mm, and is responsible for re-catching the antipro-tons and positrons sent into ALPHA-g. The thin trap has electrodes of only1.5mm thickness, allowing for an increased internal diameter of 44.35mm.Whereas charged particle plasmas can easily be confined to a small radius,this is not the case for antihydrogen atoms in the magnetic minimum trap.Increasing the radius of the trapping area allows for higher energy antihy-drogen atoms to be trapped.The ALPHA-g magnet system involves a large number of superconduct-ing magnet coils, which are shown in Figures 3.9 and 3.10. They are enclosedby a liquid helium cryostat, which cools the magnets and also acts as a cry-opump. This is supplemented by scroll pumps, turbo pumps, and ion pumpsin a scheme similar to the one used in the catching trap.A 1T superconducting solenoid magnet provides the axial magnetic fieldof the Penning-Malmberg trap. This magnet is 3m long with internal di-ameter 50 cm, enclosing the full ALPHA-g apparatus. This magnet uses itsown closed system liquid helium cryostat. In addition to the 1T solenoid,two additional capture solenoids surround the normal section of the top andbottom trap. These increase the axial magnetic field from 1T to 3T, cre-ating a stronger trap for the antiprotons and positrons arriving from theinterconnect. The magnetic minimum trap is formed by a set of octupolesand a number of solenoidal mirror coils. The long octupole spans the length373.4. The ALPHA apparatusFigure 3.10: The layout of the ALPHA-g magnet system, rotated so thatgravity acts in the leftwards direction. The initial measurement was per-formed between mirror coils A and G, in the region labelled âup-down mea-surementâ. Image credit: Dr. Chukman So.of ALPHA-g, and creates a radial magnetic field minimum. This field isincreased by two short octupole magnets covering the top and bottom trap.They provide radial confinement to antihydrogen atoms with kinetic ener-gies corresponding to temperatures of up to 0.5K. Axial confinement in thebottom trap is provided by seven mirror coils, labelled A to G. In the initialmeasurement, only the outermost coils A and G were used to confine theantihydrogen atoms. These were also the coils which were used to test theeffect of gravity.There are two further mirror coils known as the analysis coils, which cre-ate a trapping region in the precision trap, and will be used in the upcomingprecision measurement. The depth of the precision trap is smaller than thetwo end traps due to the smaller octupole field. This necessitates coolingthe antihydrogen from 0.5K to even lower energies, using techniques whichwill be discussed in the next section. Two transfer coils are used to increasethe magnetic field between the top, bottom and precision regions, withoutwhich the field would be too small to facilitate the transfer of antihydrogenatoms without significant losses.The details of how this apparatus is used to measure the effect of gravityare deferred to Chapter 9. This measurement was performed only in thebottom trap, as the top and precision traps are still undergoing installationand commissioning. A simplified version of the procedure was used for the2023 gravity paper: antihydrogen was formed in the bottom trap, in theregion labelled âup-down measurementâ in Figure 3.10. Mirror coils A andG were then ramped down so that the antihydrogen could escape axially,and the antiatoms escaping upwards and downwards were counted. Theeffect of gravity was then extracted from the ratio of the two counts. Future383.5. Particle preparation techniquesmeasurements following the installation and commissioning of the full trapwill be performed in the precision region; this will be discussed in Chapter 9.3.5 Particle preparation techniquesThe techniques used by ALPHA to manipulate the antiprotons, positrons,and antihydrogen atoms within the apparatus have been developed overmany years of experimentation. This section will briefly outline some ofthe techniques used in the antihydrogen gravity experiment.3.5.1 Antiproton preparationElectron coolingOne of the features of a Penning-Malmberg trap is that it has an inherentcooling mechanism called cyclotron cooling. As a trapped particle undergoescircular cyclotron motion as described in Section 3.2.1, it will continuouslyemit photons via a process called cyclotron radiation. Each photon emitteddecreases the kinetic energy E of the trapped particle, at a cooling rate givenby:dEdt= â q4B203ÏÏµ0m3c3E = â 1ÏcE (3.5.1)We define Ïc as the cyclotron cooling time; it is a combination of the trappedparticle charge q, mass m, and the applied magnetic field B0. Here, ϵ0 isthe permittivity of free space, and c is the speed of light. This equation isderived from the Larmor formula [108], which gives the power radiated by anon-relativistic accelerating point charge. We make the approximations thatthe cooling due to the cyclotron motion dominates that due to the magnetronmotion, and that all the energy of the charged particle is kinetic. Note thatthe cooling rate is proportional to the energy, and so the solution is given byE(t) = E0eât/Ïc .In a 3T field such as the catching trap or ALPHA-g bottom trap, theantiproton cooling time is Ïc = 2Ã 109 s, which is unfortunately far too longto be useful. By comparison, the same calculation for an electron yields Ïc =0.3 s; electrons held in Penning-Malmberg trap will naturally cool to theirminimum energy in seconds. This minimum energy is reached when cyclotroncooling is in a balanced equilibrium with heating from thermal radiation ofohmic electrode heating, or from magnetic field inhomogeneities.393.5. Particle preparation techniquesIn ALPHA, we take advantage of electron cyclotron cooling to sympa-thetically cool antiprotons. Before receiving antiprotons from ELENA, asmall electron plasma is loaded from the electron gun on the catching trapstick into a potential well in the catching trap, where it undergoes cyclotroncooling. Antiprotons from ELENA are then caught in an overlapping poten-tial well, and exchange energy with the electrons via Coulomb interactions.Over a few hundred milliseconds, the antiproton temperature is lowered tomatch that of the electron plasma, forming a mixed plasma with a singletemperature confined in a potential well of 50V to 100V. A similar proce-dure is used to catch and cool antiprotons sent from the catching trap intoALPHA-g.Evaporative coolingOne can generally assume that the kinetic energies of charged particles in aplasma follow the thermal Maxwell-Boltzmann distribution. The majority ofparticles have an energy near the mean, but a small fraction form a higher-energy tail. Partially lowering the electrode potentials providing axial con-finement allows the more energetic particles to escape, truncating the highenergy tail of the Maxwell-Boltzmann distribution. The remaining parti-cles undergo Coulomb collisions, redistributing energy and restoring thermalequilibrium. The kinetic energy will re-equilibrate to a Maxwell-Boltzmanndistribution with a lower average temperature such that the high-energy tailis below the escape energy, as shown in Figure 3.11. This process is knownas evaporative cooling (EVC).In reality, the situation is more complicated than this simple picture,and a full understanding of this process must be achieved by modelling thetrajectories of individual charged particles in the trap. This process has beenused on neutral atoms to great success, for example leading to the creation ofthe first Bose-Einstein condensate [109]. However, its previous application tocharged particle plasmas has been limited, and was substantially developedby the ALPHA collaboration [110].Rotating wall electrodesOne commonly-used method to control the size and density of a chargedparticle plasma is the rotating wall technique [111]. In this method, oneelectrode in a Penning-Malmberg trap is segmented azimuthally, into sixsegments in the ALPHA traps. Independent sinusoidal voltages are appliedto each segment, with frequencies of order 100 kHz, and a phase offset of403.5. Particle preparation techniquesFigure 3.11: Left: Sketch of the axial potential before and after EVC. Right:Sketch of the kinetic energy distribution before EVC, after EVC, and afterre-equilibrating to a thermal distribution. The escape threshold energy isdetermined by the depth of the potential well after EVC.2Ï/n between adjacent segments as shown in Figure 3.12.The electric field of the rotating wall applies a torque to the plasma, whichchanges the total angular momentum of the plasma which would otherwiseremain constant as discussed in Section 3.2.2. This also adjusts the radiusof the plasma and the rotation frequency. One particular method of apply-ing the rotating technique is known as the strong drive regime (SDR) [112].Here, the applied rotating wall frequency is close to the initial rotationalfrequency of the plasma, and the torque applied forces the two frequenciesto match. The plasma radius then responds linearly to adjustments in theapplied frequency, allowing for precise control, independent of the magnitudeand duration of the applied rotating wall voltage. Furthermore, by control-ling the plasma radius without changing the plasma length or number ofparticles, this technique also directly controls the plasma density.SDREVCA development made at ALPHA was to combine evaporative cooling andthe strong drive regime rotating wall technique. This is known as strongdrive regime evaporative cooling (SDREVC) [113]. The strong drive regimerotating wall controls the plasma radius and density, while evaporative cool-ing selectively reduces the particle number by removing the higher energyparticles. The combination of the two techniques results in a plasma with asize, density, and number of particles consistent to within 1% across manytrials with different initial parameters.413.5. Particle preparation techniquesFigure 3.12: Left: A diagram showing segmented electrodes used for rotatingwall in the catching trap and ALPHA-g. Right: The voltage applied to eachsegment during a typical rotating wall procedure.SDREVC is featured extensively throughout the ALPHA antihydrogenproduction cycle. It is first used to create reproducible electron plasmas forthe electron cooling of antiprotons, both in the catching trap, and in ALPHA-g. After receiving antiprotons, it is used to further cool and shape the mixedelectron-antiproton plasma. It is also employed to create a reproduciblepositron plasma in ALPHA-g, as well as on Be+ ions, as will be discussedlater in this section.Electron kick-outAfter the capture of antiprotons and subsequent SDREVC of the mixedantiproton-electron plasma, both in the catching trap and in ALPHA-g, it isnecessary to remove the electrons to obtain a pure antiproton plasma. Thisis done by exploiting the large mass difference between the two species.The velocity of a particle with mass m and kinetic energy Ek = 12kBT ,where T is the particle temperature and kB is the Boltzmann constant, isgiven by:v =â2Ekm=âkbTm(3.5.2)Once the antiprotons and electrons are in thermal equilibrium and havethe same temperature, the electrons travelâmp/me = 43 times faster thanthe antiprotons.423.5. Particle preparation techniquesTo make use of this difference, the axial confinement potential is brieflylowered and then rapidly restored. The fast-moving electrons escape duringthis short time window, while the slower antiprotons remain trapped. Thistechnique is known as an electron kick-out, or e-kick.While highly effective at removing electrons, e-kicks can cause heatingof the remaining antiprotons due to abrupt changes in potential. For thisreason, the procedure is staged. After an initial period of SDREVC, a partiale-kick removes most electrons but leaves a small population. These remainingelectrons facilitate further SDREVC and re-cool the plasma. Subsequent e-kicks then remove the remaining electrons.Temperature diagnosticsTo determine the temperature of a given antiproton plasma, a destructivemeasurement is performed. This measurement uses the assumption that thevelocity of the antiprotons is thermal, following a Maxwell-Boltzmann distri-bution with a characteristic plasma temperature. The axial (one-dimensional)kinetic energy E for particles with a Maxwell-Boltzmann velocity distribu-tion follows a Ï2 distribution with one degree of freedom, where T is thetemperature and kB is the Boltzmann constant:f(E) =1âÏE kBTÂ· exp(â EkBT)(3.5.3)To measure the plasma temperature, the confining potential on the elec-trodes is lowered slowly so that all the antiprotons are able to escape. Theyare directed towards a diagnostic stick inserted into the beam path, wherethey annihilate and are detected by the surrounding scintillating panels (seeSection 3.4.5). Because the potential barrier is lowered gradually, the timeat which each antiproton escapes corresponds to a known potential energy.In this way, the energy distribution of the plasma is reconstructed.Instead of fitting the full energy distribution with Equation 3.5.3, onlythe high-energy tail is fit. Here, theâE dependence can be ignored and thedistribution can be approximated as an exponential. In practice, the energydistribution is plotted with the counts on a log scale, so that a linear fit canbe used on the tail of the distribution, as shown in Figure 3.13.3.5.2 Positron preparationPreparation of the positron plasma uses many of the same techniques usedfor antiprotons. Since the number of positrons transferred from the accumu-433.5. Particle preparation techniquesFigure 3.13: Temperature diagnostic of an antiproton plasma. The blue lineis a fit to the data from the range of 0.1 eV to 0.2 eV, and corresponds to atemperature of 259K.lator can vary significantly between cycles, SDREVC is crucial to forminga reproducible positron plasma. A similar temperature diagnostic is used,with the positron signal measured on a Faraday cup instead of measuringannihilations on a scintillator panel.Since the depth of the neutral atom trap is only 0.5T, only the antihy-drogen atoms in the low-energy tail of the energy distribution are trapped,making it imperative to obtain the coldest possible sample of antihydro-gen. The antihydrogen temperature depends strongly on the temperature ofboth the antiproton and the positron. As such, it is desirable to cool thepositrons beyond cyclotron cooling and evaporative cooling; this led to therecent development of beryllium ion (Be+) assisted cooling.This method begins with the creation of a Be+ plasma using a berylliumablation source mounted on a diagnostic stick. A pulsed 355 nm laser ablatesa beryllium target, generating a plasma of Be+ ions in the ALPHA-g trap.A 313 nm laser is then used to Doppler-cool this plasma; the basic principleof laser cooling is described in Section 3.5.4. While laser cooling continues,SDREVC is applied to fix the Be+ plasma size and density.Simultaneously, a positron plasma is received from the accumulator, andstabilized using SDREVC. The positron and Be+ plasmas are then merged,forming a mixed-species plasma, The positrons are cooled sympatheticallyvia Coulomb interactions with the Be+ ions. Laser cooling continues duringthis phase to maintain the low Be+ temperature. The choice to use Be+ ionswas made because they are light enough for effective sympathetic cooling443.5. Particle preparation techniqueswith positrons, easy to produce via ablation, and relatively easy to lasercool. The Be+ assisted positron preparation will be described in detail in anupcoming publication.3.5.3 Antihydrogen formationThe approach used by ALPHA to create antihydrogen was first demonstratedby ATHENA in 2002 [24], whereby cold plasmas of antiprotons and positronsare slowly mixed. The dominant production mechanism is called three-bodyrecombination:p¯+ e+ + e+ ââ H¯ + e+ (3.5.4)Two positrons interact electromagnetically, leaving one positron with lowenough energy to be captured by an antiproton and form a bound state.The excess energy and momentum is carried away by the second positron,essential for conservation of energy. Further photons are then produced asthe antihydrogen atom radiatively cascades into the ground state.Application of this mechanism involves spatially overlapping the antipro-ton and positron plasmas in the Penning-Malmberg trap. This is not trivialsince positrons and antiprotons have opposite charges, and so a single elec-trostatic potential cannot confine both simultaneously; potential wells thatconfine antiprotons will repel positrons and vice versa. A slow merge pro-cess illustrated in Figure 3.14 is used. The antiproton and positron plasmasare initially confined in adjacent potential wells. The electrostatic barrierbetween them is then gradually lowered, allowing the two species to escapefrom their trapping potential well and pass through the plasma of the otherspecies. This process takes around 1 s, determined empirically so that the po-tential manipulations do not excessively heat the antiprotons and positrons.In a typical mixing cycle, almost all antiprotons are converted into anti-hydrogen, yielding typically around 150 000 antihydrogen atoms. However,most of these have kinetic energy above the 0.5K Ioffe-Pritchard trap depth,and immediately escape and annihilate. Only the coldest atoms are retained,typically resulting in around 20 trapped antihydrogen atoms per mixing cy-cle in ALPHA-g. Because neutral antihydrogen atoms are unaffected by theelectrostatic fields of the Penning-Malmberg trap, the mixing process canbe repeated multiple times while the magnetic minimum trap remains ac-tive, accumulating trapped antihydrogen from successive cycles. Followingeach mixing cycle, a large electrostatic potential gradient is applied using thePenning-Malmberg electrodes, in order to clear any remaining antiprotonstrapped by magnetic mirroring.453.5. Particle preparation techniquesFigure 3.14: Schematic diagram showing antiproton and positron plasmasconfined in the ALPHA-2 or ALPHA-g Penning-Malmberg trap in prepara-tion for (a and b), immediately before (c), and during (d) the antihydrogenformation process. From [114].3.5.4 Antihydrogen coolingFor almost any precision measurement involving antihydrogen, it is beneficialfor the sample of atoms to be as cold as possible. This is particularly truefor ALPHAâs laser spectroscopy experiments, where the sample temperaturecontributes directly to the spectral linewidth via Doppler broadening, whichwe will discuss shortly. However, the temperature also plays a role in ameasurement of gravity. The lower the antiatom temperature, the smallerthe thermal velocity of the atom, and so the more precisely its motion dueto gravity can be isolated and measured.To this end, two antihydrogen cooling mechanisms have been developed.Neither was employed in the initial published measurement of gravity [1], butthey will both play a key role in upcoming precision measurements. Bothtechniques have been successfully demonstrated in the ALPHA-2 apparatus,and their implementation in ALPHA-g is ongoing.Laser coolingThe first cooling method is known as laser cooling. This is a well-knowntechnique, for which Chu, Cohen-Tannoudji, and Phillips won the 1997 Nobelprize in physics [115]. In an antihydrogen atom, the positron occupies orbits463.5. Particle preparation techniqueswith discrete energy levels. A transition from a higher energy orbital (e.g.2P) to a lower one (e.g. 1S) releases a photon which carries away the excessenergy. Conversely, the absorption of a photon with energy matching thelevel separation can promote the positron to an excited state. This principlewas first demonstrated on the antihydrogen 1Sâ2P transition by ALPHA in2018 [9].In practice, transitions can be excited by photons with a narrow range ofenergies around the resonance, due to several line-broadening mechanisms.One of the most important is Doppler broadening. If an antihydrogen atommoves with velocity v towards an incident laser photon of frequency f , thenin the frame of reference of the atom, the incident photon will have a Dopplershifted frequency f â² given by:f â² = f(1 +vc)(3.5.5)Thus photons with slightly less energy than the atomic resonance can beabsorbed by antiatoms moving towards the laser source, and photons withslightly more energy can be absorbed by antiatoms moving away from thelaser.Laser cooling takes advantage of this phenomenon by purposefully detun-ing the laser to have a lower frequency than the transition frequency, causingantiatoms moving towards the laser source to be preferentially excited. Sincephotons carry momentum p = hf , each photon absorbed gives a momentumkick away from the laser source. In this way, antiatoms travelling towardsthe laser are preferentially kicked backwards (i.e. opposite to their motion),decreasing the average antiatom momentum.The energy of the absorbed photon is later re-emitted as a new photon, asthe antiatom relaxes to the ground state. However, this emission is isotropic,and so has no effect on the average particle momentum. Over many inter-actions, this photon absorption and subsequent isotropic emission decreasesthe overall temperature of a sample of antihydrogen atoms.This technique was first demonstrated on antihydrogen in ALPHA-2 in2021 [116]. A pulsed 121.6 nm Lyman-α laser is applied to a sample oftrapped antiatoms, detuned by â240MHz from the 1S-2P resonance, typi-cally over a time period of 2 h to 4 h. The transverse kinetic energy of theantihydrogen atoms can be inferred from the time-of-flight distribution ofatoms kicked out of the trap and detected via annihilation; this kickout isperformed by driving a transition to an untrappable high-field-seeking state(see Section 3.2.3). Using this technique, the median transverse energy of theantihydrogen atoms was reduced from 15.1 µeV to 1.3 µeV. It is difficult to473.5. Particle preparation techniquesestimate the change in total kinetic energy as the mixing between transverseand longitudinal energies in the trap is not yet well understood. However,the implementation of laser cooling has already significantly improved recentspectroscopic measurements made in ALPHA-2. Work to implement lasercooling in ALPHA-g is currently underway.Adiabatic coolingThere is a fundamental limit to the temperature attainable through lasercooling, since the average momentum of an atom cannot fall below the mo-mentum imparted by one photon.5 To reach even lower temperatures, analternative method is required.One such method is adiabatic cooling, where the width of the confiningmagnetic potential well is slowly expanded, thereby decreasing the temper-ature of the trapped antihydrogen atom. To understand this effect, considera harmonic approximation of the axial trap potential V (z) = 12mÏ2zz2. Asthe trapping potential is adiabatically (slowly compared to the axial bouncefrequency Ïz) expanded, the axial bounce frequency decreases, since theantiatom has a longer distance to travel per oscillation.This is familiar in a quantum mechanical context, where states |Ïnâ© havequantized energies En = (n + 12)âÏz. By decreasing Ïz adiabatically, eachparticle remains in the nâth state of the perturbed system |ÏËnâ©. Since Ïz hasdecreased, this state now has a lower energy, corresponding to a decrease inthe temperature of the plasma.In classical mechanics, this concept is encapsulated by adiabatic invari-ants. These are quantities which remain constant as the Hamiltonian of thesystem is slowly changed, related to the phase space area of a system. In thecase of a harmonic potential, the adiabatic invariant is the ratio of energyto frequency, E/Ï [118, 119]. This adiabatic invariant makes the principlebehind adiabatic cooling explicit. By slowly expanding the width of the trap-ping potential, and thereby decreasing Ïz, the energy of each antihydrogenatom is decreased to keep the value of E/Ïz constant.In reality, the full trap is three-dimensional and non-harmonic, and themotion of the antiatoms is more complex. We rely on simulations to modelthe cooling effect of adiabatically expanding the magnetic trap, the detailsof which can be found in [120].Prospects for adiabatic expansion were a key consideration in the designof ALPHA-g. In the envisioned precision measurement, antihydrogen will be5There are techniques such as Raman cooling [117] which can cool atoms below thisrecoil limit. However, these require laser systems not currently available at ALPHA.483.5. Particle preparation techniquesinitially formed between two close mirror coils, such as coils B and D (referto Figure 3.9). After many mixing cycles, the trap will be adiabaticallyexpanded to between coils A and G. This technique was not employed inthe initial gravity measurement, but it has since been demonstrated in theALPHA-2 apparatus [121]. Adiabatic cooling will be essential for performingupcoming precision measurements of gravity in ALPHA-g.49Chapter 4The ALPHA-g detectorsMeasuring the effect of gravity on antihydrogen requires determining if eachantiatom exits the magnetic trap in the upwards or downwards direction; inthe absence of other forces, more antiatoms should escape the trap in thedirection of gravity. The simplest method for this is to allow the antihydrogento annihilate on the trap walls, and determine the annihilation positions bydetecting the resulting annihilation products. This is the approach taken bythe ALPHA-g annihilation detectors.Detecting the annihilation of a positron is a well-motivated and well-studied problem, as it forms the basis of a common medical imaging tech-nique known as positron emission tomography (PET). A radioactive nuclideis bonded to a drug or biological compound, and injected into the patient.The compound then accumulates in a target area, such as a cancer tumour.There, the radionuclide undergoes beta decay, producing positrons. Thesepositrons quickly annihilate with electrons, producing primarily two pho-tons emitted back-to-back, as discussed in Section 3.3.1. By detecting bothphotons, the annihilation can be localized along a line between the two detec-tors. With enough such events, regions of concentrated activity will emerge,indicating the position of a cancer tumour.A positron annihilation detector using this principle was employed bythe ATHENA experiment to verify the first production of cold antihydro-gen at CERN [122]. This was used alongside a silicon strip detector whichdetected the charged pions resulting from the antiproton annihilation. Thecoincidence of charged pion tracks in the silicon strip detector, together withback-to-back hits in the positron annihilation detector, confirmed the anni-hilation of an antihydrogen atom.With the routine production and trapping of antihydrogen atoms fullyestablished, the upgrade to the ALPHA-2 apparatus moved away from thedetection of the positron annihilations. Instead, a silicon vertex detector(SVD) was installed, capable of precisely reconstructing the annihilationposition, or vertex. This detector is shown in Figure 4.1 alongside the othercomponents of the ALPHA-2 trap.The SVD is composed of individual rectangular silicon microstrip mod-50Chapter 4. The ALPHA-g detectorsFigure 4.1: The ALPHA-2 apparatus, with the three layers of the siliconvertex detector (SVD) shown in blue. Adapted from [4].ules, each with a sensitive volume of 5.8 cm Ã 11.2 cm Ã 44.8 cm [102]. Thesemodules are arranged in three layers around the trap, with 10, 12, and 14modules per respective layer [123]. When an antiproton annihilates, it typ-ically produces several charged pions, as discussed in Section 3.3.2. Thesetravel through the silicon layers, leaving hits that can be used to reconstructthe pion tracks in three dimensions. The annihilation vertex is then identi-fied by determining the point of closest approach between all reconstructedtracks.The ALPHA-2 SVD has been crucial to the experimentâs precision spec-troscopy program, providing reliable annihilation imaging with high spatialresolution of around 8.5mm [123]. A full discussion of silicon tracking de-tectors and the ALPHA-2 SVD is outside the scope of this dissertation;this summary is intended to provide context for the ALPHA-g detectors.Although the detector technologies differ, the principle of reconstructingcharged pion tracks to determine antihydrogen annihilation positions remainsthe same and forms the foundation for the detection strategy in ALPHA-g.This approach has been used for many years in ALPHA-2, and is acceptedas the most straightforward and reliable method of antihydrogen detection.514.1. Pion scattering on internal materialsFigure 4.2: Diagram of the main components of the ALPHA-g apparatusinside the time projection chamber detector. Components are listed frominnermost to outermost with their respective materials and thicknesses.4.1 Pion scattering on internal materialsThere is a considerable amount of material between the detectors and thetrap wall, including vacuum and cryogenics components, as well as the su-perconducting octupole and mirror coil magnets. A radial cross-section ofthe apparatus is shown in Figure 4.2, with the materials and thicknesseslisted. Before introducing the ALPHA-g detectors, we consider here the ef-fects of this material on an annihilation detection scheme which reconstructsthe annihilation position based on charged pion tracks.While traversing the internal materials, pions lose energy through mul-tiple elastic scatterings on the atomic nuclei. This is a stochastic process,which may lead to an overall large angle deflection of the pion trajectory.This primarily occurs in the octupole magnet and mirror solenoid coils, asthey have are the most dense components and have the largest thickness.In the case of a large angle pion deflection in the material, the ALPHA-gdetectors will then observe an altered trajectory which does not point back tothe annihilation position. The detector must be able to accurately determinethe annihilation position in the presence of highly scattered pions.The dense material around the trap also causes absorption and scattering524.2. The time projection chamberof the 511 keV photons from positron annihilations. Using attenuation coef-ficients from the NIST database [124], we can estimate an attenuation lengthof around 22mm in the NbTi/copper magnet coils. This results in aroundhalf of the photons from positron annihilation being attenuated in the oc-tupole and mirror coils. This is one of the reasons why detection of positronannihilations was not included in the design of the ALPHA apparatus.4.2 The time projection chamberTo maximize the gravitational potential difference in the area accessible tothe antiatoms, the vertical ALPHA-g apparatus (see Figure 3.9) is over 2mlong, significantly larger than the ALPHA-2 apparatus. This increased sizemeant that constructing a detector similar to the ALPHA-2 SVD was nei-ther practical or cost-effective. Instead, a different type of charged particledetector called a time projection chamber (TPC) was developed, capable ofreconstructing the annihilation positions over the larger volume. This sec-tion will begin with a broad discussion of TPC technology and ionizationdrift chambers, before covering specific details of the ALPHA-g TPC. Thereadout and data acquisition will be covered later in Section 4.4.1.4.2.1 Ionization chambersThe ionization chamber is one of the oldest concepts for a charged particledetector [125], and many variants have since been developed to suit differentapplications. The core principle is to use an active medium with a lowionization potential, typically a gas, and then apply an electric field. Whena charged particle traverses the chamber, it ionizes the gas atoms alongits path, creating many pairs of electrons and positive ions. The appliedelectric field prevents recombination by pulling the electrons towards theanode and the ions towards the cathode. In some cases (around 34% inargon [126]), the released electron will ionize another nearby atom, creatingan ionization cluster. More rarely, it will have enough energy to ionize manyatoms, creating an ionization trail known as a delta ray.One common configuration of ionization chamber is the wire chamber,where the anode is a wire with a large positive voltage applied. The electricfield of a cylindrical wire held at a constant voltage is a textbook calculation:E(r) =Î»2ÏÏµ0 r(4.2.1)534.2. The time projection chamberFigure 4.3: A cross-sectional drawing showing the development of an electronavalanche (red) near an anode wire (yellow) in a wire chamber.Here λ is the charge density of the wire, dependent on the applied voltage.ϵ0 is the permittivity of free space, and r is the distance from the centreof the wire. As the electrons approach the anode wire, they experience anincreasingly strong electric field. The electric field near the wire acceleratesthe electrons to high enough energies to cause additional ionization. Thisbegins an avalanche, where these newly-freed electrons will ionize subsequentatoms, leading to an exponential multiplication of electrons, shown in Figure4.3. The electrons are collected on the anode wire, and the ions driftingtowards the cathode induce a further current on the anode wire. This currentis amplified and read out.In addition to ionization, incident particles also deposit energy via exci-tation of the gas atoms, where an electron is raised to a higher atomic energylevel. These excitations decay to the ground state by emitting a photon. Ifthe active medium is transparent to the photon wavelength, this can allowan additional readout channel via photon detection. However, these photonscan also produce subsequent electrons via the photoelectric effect, and pro-duce after-pulsing or even a continual activation of the wire chamber. Tosuppress this, a quenching gas is often mixed with the ionization gas, whichabsorbs excess photons without re-emitting ionizing radiation.A multiwire proportional chamber (MWPC) is a type of ionization cham-ber which uses multiple anode wires; the wire where a signal is observed givessome spatial knowledge of the ionization position [127]. The signal size isproportional to the energy deposited by the incident charged particle. Thisdesign was iterated upon to create the drift chamber, where further spatialinformation can be obtained from the drift time of the electrons and ions.The ALPHA-g experiment uses a specific variant of a drift chamber544.2. The time projection chamberknown as a time projection chamber (TPC). A traditional TPC design has alarge drift volume with a constant electric field, which drifts electrons towardsmultiple anode wires. The specific wire where an avalanche is detected givesone coordinate of the ionization position. The time of the signal then givesanother coordinate; since the drift velocity is constant in a constant electricfield, the delay is proportional to the distance the electrons travelled. Thethird coordinate of the ionization position must be obtained through othermeans: either by using two planes of anode wires at an angle to each other,or by using a segmented cathode plane with readout of the induced charge.Combining these three coordinates allows full reconstruction of the positionof each gas ionization, making the TPC an effective tracking detector whichhas seen widespread use [128, 129].4.2.2 The ALPHA-g TPCA conventional TPC uses anode wires at the bottom and/or top of the cham-ber, resulting in vertical electron drift. However, this layout was impracticalfor ALPHA-g due to geometrical constraints. To obtain the best annihilationposition resolution, the distance between the annihilation and pion detectionmust be minimized. As such, the TPC must fit in the narrow annular regionbetween the external solenoid and the cryostat, a volume less than 15 cm inradial width. It must also cover the full trap apparatus, over 2m in length.This aspect ratio made the traditional TPC layout unviable, as electronswould diffuse away from their initial x â y positions over the long verticaldrift length, with many being lost on the walls of the TPC.The ALPHA-g TPC uses a less common geometry shown in Figure 4.4,with a ring of 256 anode wires running along the length of the outer edge ofthe TPC. A second ring of 256 field shaping wires is positioned slightly insidethe anode wires. The inner wall of the chamber forms the cathode. Electronsare pulled radially outwards, and ions inwards. In this design, the appliedelectric field is no longer constant at varying radius. Furthermore, there is asignificant deflection from a purely radial drift due to the Lorentz force fromthe external magnetic field; this deflection has no component in the verticaldirection as long as the external magnetic field is purely solenoidal.In typical operation, the cathode surface at radius 10.9 cm receivesâ4 kV,the field shaping wires at radius 17.4 cm receive â0.1 kV, and the anode wiresat radius 18.2 cm receive 3.2 kV. The field shaping wires ensure that the re-gion over which the electrons and ions induce a charge on the anode wires isroughly constant, regardless of the initial ionization position.The outer wall of the TPC, at radius 19.0 cm, is finely segmented into554.2. The time projection chamberFigure 4.4: Left: A top-down schematic diagram of an antihydrogen anni-hilation in the ALPHA-g TPC. Shown are the gas region (blue), the anodewires (yellow), and the cathode pads (dashed line), along with electrons(black arrows) drifting from ionization sites (black circles) along pion tracks(green) from an annihilation (red). Right: A Garfield++ simulation (seeSection 5.3.1) showing electrons drifting towards the anode wires. From[130].cathode pads. It is azimuthally divided into 32 sections each with width of3.7 cm, and these sections are divided into 576 pads with a pitch of 0.4 cm,for a total of 18432 cathode pads. When an electron avalanche occurs nearan anode wire, this also induces a charge on the nearby cathode pads. Boththe anode wires and the cathode pads are read out, and by matching eachanode wire signal to the corresponding cathode pad signals, the location ofthe avalanche can be determined. Once an avalanche has been located, thethree-dimensional position of the corresponding gas ionization is determinedusing the time projection method.The gas used in the ALPHA-g TPC is a mixture of 70% argon and 30%carbon dioxide at atmospheric pressure. The argon is an inert ionizationgas, and the carbon dioxide is a quenching gas; the ratio was decided empir-ically for good signal gain and stable operation. The gas mixture is flowedcontinually through the detector at a rate of 1L/min to ensure a constantpressure.The Lorentz deflection due to the external magnetic field causes electrondisplacement up to 30â¦ from purely radial drift, as shown in Figure 4.4. Tomeasure this effect, a laser calibration mechanism is included in the TPC564.3. The barrel scintillatordesign. Aluminium strips are located on the inner cathode surface at nineaxial positions along the TPC. A pulsed laser is directed towards each ofthese strips in turn, producing free electrons at known positions and timesvia the photoelectric effect. These laser calibration measurements were usedto validate electron drift simulations in the PhD work of Dr. Pooja Woosaree[77], and are periodically repeated to monitor the performance of the TPC.4.3 The barrel scintillatorCosmic rays have been a known source of detector background for the en-tirety of the ALPHA physics program. These rays, primarily high-energyprotons originating from outer space, interact with Earthâs atmosphere toproduce particle showers [131]. These cascades typically include pions de-caying to muons, which are the only charged particle type with a low enoughinteraction cross-section to reach the Earthâs surface. Many of these muonsinteract with the ALPHA detectors as relativistic minimum ionizing parti-cles. Their detector signatures are typically single, straight tracks, with rareshowering interactions or secondary production. These events are identifiedand discarded via a machine learning analysis which will be discussed inChapter 8.The ALPHA-g TPC has a larger volume than the ALPHA-2 SVD, andconsequently presents a bigger target for cosmic rays and thus has a higherbackground rate. To mitigate this, the ALPHA-g detector suite includesa dedicated cosmic ray veto detector, called the barrel scintillator (BSC).The detector is positioned in the region outside the TPC and inside theexternal solenoid. It is designed to measure particle time-of-flight (TOF), todistinguish the direction of charged particles, and identify and reject thoseoriginating outside the detector. This section will first review the scintillatorand photomultiplier technologies used, before describing the details of theALPHA-g BSC detector and the measurement principles.4.3.1 ScintillatorsWhereas atomic excitations are an unwanted energy loss mechanism in gas-eous ionization detectors, they constitute the working principle of scintilla-tion detectors. A scintillator is a material whose electrons are easily excitedby the passage of an ionizing particle; when the electrons return to theirground state they emit photons whose wavelength is fixed by the transitionenergy. The number of photons produced provides a convenient proxy for574.3. The barrel scintillatorthe total energy loss in the scintillator. There are a wide variety of scintil-lating materials used in practical applications, each best-suited to differentexperimental conditions:â¢ Liquid noble elements such as argon and xenon combine large atomicmasses with high scintillation yields. The size of their atoms and thedensity of the liquid gives them large cross sections as a target for rareevent searches, such as in dark matter experiments.â¢ Liquid organic scintillators consist of an organic solvent which absorbsenergy from the ionizing particle, and a fluorophore which producesscintillation light. The high hydrogen content makes this scintillatortype particularly useful for observing neutron-proton scattering, andits scalability makes it a good choice for neutrino detectors.â¢ Inorganic crystals such as NaI(Tl) or CsI(Tl) have a high proton num-ber and are radiation hard, making them suitable for electromagneticcalorimetry in large collider experiments. In ALPHA, CsI crystal scin-tillators are used to detect the 511 keV photons from positron annihi-lation, as discussed in Section 3.4.5.â¢ Plastic scintillators are inexpensive, have fast decay times, and are eas-ily produced in a variety of shapes. This makes them ideal for timingcounters, veto panels, and large area detectors. Plastic scintillator pan-els are used to detect pions from antiproton annihilations in ALPHA,as discussed in Section 3.4.5.The type of plastic used in ALPHA is called polyvinyltoluene (PVT),although a variety of different organic polymers can be used. The key struc-ture is the benzene ring, a hexagonal arrangement of six carbon atoms witha unique set of molecular bonds called pi bonds. Here, electrons are delo-calized over the full benzene ring, supporting low-lying excited states withenergies around 3 eV.Photons are produced as these excited states decay. However, they can-not travel through the scintillator without being reabsorbed by the sametransition in another atom. To address this, the plastic is doped with asmall concentration of an atom called a fluorophore. The level structure ofthese atoms allows them to emit photons with a different wavelength thanthe one absorbed. The wavelength is chosen such that it is minimally atten-uated by the bulk of the scintillator, and can be easily captured by a photondetector.584.3. The barrel scintillatorFigure 4.5: Diagram of a photomultiplier tube (PMT), shown in conjunctionwith a scintillator detecting a high energy photon. Image courtesy: CreativeCommons, used under license 3.0. Author: Qwerty123uiop)4.3.2 PhotosensorsOnce photons are produced in a scintillator, they must be detected. Theclassic technology for this is the photomulitplier tube (PMT), shown in Figure4.5. An incident photon strikes the photocathode and is converted to anelectron via the photoelectric effect. This electron is accelerated towards aseries of dynodes, each held at increasingly high positive voltage. At eachdynode, the electron frees multiple secondary electrons; these are in turnaccelerated towards the next dynode, creating an exponentially increasingnumber of electrons analogous to the avalanche discussed in Section 4.2.After several stages, the electron cascade reaches the anode, where the totalcharge is read out electronically. The combination of a plastic scintillator anda PMT is well-established and has seen widespread general use in ALPHAand elsewhere.However, PMTs have some notable limitations. They have a large phys-ical footprint, require high voltage power supplies, and are sensitive to mag-netic fields as the electrons are deflected away from the dynodes by Lorentzforces. These issues have led to the adoption of a more modern device forphoton detection, called the silicon photomultiplier (SiPM).SiPMs are composed of silicon, which is a semiconductor. Electron energylevels form continuous bands rather than discrete levels. In an insulator, thefilled valence band is separated from the empty conduction band by a bandgap. In a semiconductor, this band gap is small, around 1.1 eV for puresilicon. This allows thermal energy to excite electrons from the valence band594.3. The barrel scintillatorFigure 4.6: Diagram showing the energy levels of intrinsic, p-type, and n-type silicon. Dashed lines indicate additional energy levels of dopant atoms.to the conduction band, producing an electron-hole pair. Both the electronand the hole have some mobility over the silicon lattice.Silicon can be doped with ions to add extra electrons or holes, whoseenergy is slightly above the valence band or below the conduction band.This leads to either n-type silicon, which has extra weakly-bound electrons,or p-type silicon, which has extra vacancies which accept electrons and easilyproduce holes. These are shown in Figure 4.6.A silicon diode is formed by combining p-type and n-type silicon. Freeelectrons produced in the n-type region diffuse across the interface to fill theextra holes in the p-type region. Since both types of silicon begin with a netneutral charge, this creates a buildup of electric charge, causing a potentialgradient which opposes and eventually halts the flow of electrons and holes.When an equilibrium is reached, the area around the interface is called adepletion region, as it has very few free electrons and holes. This is shownin Figure 4.7.In a silicon photodiode, a reverse bias voltage is applied to enhance theintrinsic potential gradient, expanding the depletion region. When a chargedparticle deposits energy in this region, it creates electron-hole pairs andtemporarily allows a current to flow; this is the basis of a silicon detectorsuch as the ALPHA-2 SVD.In a single photon avalanche detector (SPAD), a significantly higher re-verse bias voltage is applied, which accelerates electrons towards the cathodeat the edge of the n-type silicon. Above a certain voltage known as the break-604.3. The barrel scintillatorFigure 4.7: Diagram showing the p-n junction in a silicon diode in an unbi-ased equilibrium, including charge, electric field, and potential. The deple-tion region is indicated by lighter shading.Figure 4.8: Layout of a typical single photon avalanche detector (SPAD). Asilicon photomultiplier is a grid of many neighbouring SPAD cells.614.3. The barrel scintillatordown voltage, the electron drift velocity is sufficient to create additionalelectron hole pairs, causing an avalanche analogous to the gas ionizationavalanche in a wire chamber. In this way, a single photon produces a mea-surable current. The avalanche is eventually halted by a quenching resistor,and the SPAD recovers and returns to its initial state. The sensitivity of theSPAD can also be a downside, as a single thermally-generated electron-holepair will also cause an avalanche. These avalanches are indistinguishablefrom those produced by incident photons, causing a significant dark countrate. Although there are many varieties of SPAD, a typical geometry isshown in Figure 4.8.In a SiPM, many SPADs are grouped together, each functioning indepen-dently. The total output signal is the sum of the pulses from each triggeredcell. This provides some benefits: multiple photons can be detected simul-taneously in different cells, the output signal is proportional to the numberof incident photons, and dead time is minimized as the other cells are stillactive while one cell is recovering.Compared to the PMT, the SiPM is smaller, cheaper, requires lower biasvoltage, and works better in a magnetic field. They are used in the newerexternal plastic scintillator panels in ALPHA, as well as in the BSC.4.3.3 The ALPHA-g barrel scintillatorTo veto cosmic ray background events in the ALPHA-g TPC, it is surroundedby a second detector called the barrel scintillator (BSC). This detector iscomposed of plastic scintillator bars coupled to SiPMs. This design waschosen for a few reasons:â¢ Compactness: The BSC must fit in the small (around 2 cm) radialregion between the TPC and the external solenoid.â¢ Speed: Plastic scintillators and SiPMs are fast enough to measureparticle time-of-flight across a few centimetres, which is required forbackground identification.â¢ Simplicity: They are well-understood technologies which already seeuse in ALPHA external panels.â¢ Cost-effectiveness: They are cheaply commercially available, and ex-pertise is available at TRIUMF for electronics design.The BSC is composed of 64 bars of plastic scintillator. Each bar istrapezoidal in shape, with top width 23.9mm, bottom width 21.9mm, and624.3. The barrel scintillatorFigure 4.9: Left: A photograph of one end of the BSC, fully assembledand awaiting insertion into ALPHA-g. Image credit: CERN, 2018. Right:A diagram showing the coupling of the scintillator bars to the SiPMs, andaccompanying readout electronics. Image credit: Nicolas Massacret.side length 20mm. The length of each bar is 2.604m. They are wrapped inreflective tape to maximize internal reflectivity. The bars are bound togetherby fishing wire and aluminium clamps into a cylindrical shape with an innerradius of 223mm and an outer radius of 243mm, allowing this detector tobe placed around the TPC and inside the external solenoid magnet. Thelayout of the BSC is shown in Figure 4.9.The plastic scintillator chosen for the bars is EJ-200 from Eljen Tech-nologies [132]. A minimum ionizing particle deposits around 2MeVcm2gâ1of energy, or around 4MeV on a 2 cm path through the 1.023 gcmâ3 bar. Thelight yield of EJ-200 is around 10 000 photons/MeV, for a typical productionof around 40 000 photons by an incident charged particle. These photonsare created over a few nanoseconds: the scintillation rise time is quoted at0.9 ns and the decay time at 2.1 ns. The bulk attenuation length of EJ-200 is3.8m; neglecting surface attenuation, at least 10 000 of these photons shouldreach each bar end.As part of this work, a ray tracing simulation was performed to studythe propagation of photons though the scintillator bars. The nominal in-dex of refraction and bulk attenuation lengths were used, while the surfacereflectivity was varied to best match the BSC data. This hinted towards apoor surface reflectivity of around 0.9, resulting in â¼ 80% of photons beinglost due to surface attenuation. If this model is accurate, around 2000 pho-tons should reach each bar end, with this number varying depending on thescintillation position.The scintillator bars are coupled to SensL MicroFJ-60035 SiPMs [133],now produced by ON Semiconductor [134]. These have a size of 6mm by634.3. The barrel scintillator6mm, and so an array of six SiPMs is used to cover each bar end, providing47% surface coverage. They are optically coupled using 1mm to 2mm ofRTV615 silicon rubber to eliminate air gaps, which was found to increaselight transmission by 30%. The maximum efficiency of the SiPM is at 420 nm,a good match with the 425 nm peak emission output of the scintillator.The breakdown voltage of these SiPMs is 24V, and they are operated ata reverse bias of 27V. The variation in breakdown voltage between SiPMsis sufficiently narrow that all SiPMs can be biased using the same voltage.In addition to the standard output, they provide a fast output which has afull width half maximum of 3.0 ns. An air cooling system is used to carryaway heat from the readout electronics, which also serves to slightly lowerthe dark noise rate. A vortex cooler pumps cold air into the volume of theBSC at the top and the bottom, while a fan maintains an air flow in thevolume between the TPC and the BSC to minimize heating of the SiPMsdue to the TPC electronics.4.3.4 Detection principlesIn this discussion, and in the discussion of the BSC data processing andcalibration in Chapters 6 and 7, I will reference some quantities which aremeasured using the BSC. These symbols are listed in Table 4.1 for reference.Each BSC bar is read out at both ends to allow determination of thelongitudinal position of a scintillation. This can be accomplished by twomethods: charge division, and time difference.In the charge division method, the number of photons arriving at eachend of the bar is determined by integrating the SiPM signal. The number ofphotons decreases with light travel distance: N = N0eâx/Î», where λ is theeffective attenuation length, x is the distance travelled, and N0 is the initialnumber of photons travelling towards a photosensor. Thus the hit positionrelative to the bar centre can be determined from the ratio of the top andbottom signal sizes:N topNbot=N0eâdtop/Î»N0eâdbot/Î»= e(dbotâdtop)/Î»=â z = dbot â dtop2=λ2lnN topNbot(4.3.1)Here, we define our coordinate system so that z = 0 is at the centre ofthe bar. Consequently, the distance of the hit from the top and bottomof the bar are given by dtop = L/2 â z and dbot = L/2 + z respectively,644.3. The barrel scintillatorSymbol Descriptionttopi , tboti The start time of the SiPM signal at the top or bottom ofthe iâth bar. This is measured by a TDC (see Section 4.4)and includes all time corrections (see Chapter 7).ttopTDC,i, tbotTDC,i The start time of the SiPM signal at the top or bottom of theiâth bar measured by the TDC, without any time corrections.N topi , Nboti The number of photons detected by SiPMs at the top orbottom of the iâth bar.Atopi , Aboti The amplitude of the SiPM signal at the top or bottom ofthe iâth bar. Measured by an ADC (see Section 4.4).t0,i The bar hit time, the time when a charged particle passesthrough the iâth bar.zi The bar hit z position, the vertical height where a chargedparticle passes though the iâth bar. Defined so that z = 0 isat the centre of the detector.dtopi , dboti The distance from the bar hit z position to the top or bottomof the iâth bar.λi The effective attenuation coefficient of light in the iâth bar.veff,i The effective speed of photon prorogation in the iâth bar.L The length of each bar (L = 2.604m).TOFi,j The time-of-flight between two bar hits on bars i and j.TOFexp,i,j The expected time-of-flight between two bar hits on bars iand j, calculated for a cosmic ray travelling at the speed oflight with a straight trajectory.Table 4.1: A list of symbols used when discussing the data handling of theBSC. The subscript i or superscripts top and bot are often dropped if thebar number or bar end is not relevant to the discussion.654.3. The barrel scintillatorwhere L is the bar length. We also use the assumption that photons areproduced isotropically. Instead of using the total number of photons N , onecan equivalently use the signal amplitude A or even time over threshold.For the time difference method, we use the approximation that photonstravel with a constant effective speed veff along the bar. The differencebetween the scintillation time t0 and the photon detection time ttop or tbotis linear with the distance along the bar between the hit position and theSiPM: ttop = t0 + dtop/veff and tbot = t0 + dbot/veff. As a result, the hitposition along the bar can be determined using the time difference betweenthe top and bottom signals:z =dbot â dtop2=veff2[(tbot â t0)â (ttop â t0)]=veff2(tbot â ttop)(4.3.2)The main purpose of the BSC is to measure the time-of-flight (TOF) ofcharged particles, defined as the time difference between two hits on differentbars. We can find the time t0 that the charged particle hits the bar from thestart time of the top and bottom SiPM signals:t0 =12[(ttop â dtop/veff)+(tbot â dbot/veff)]=ttop + tbot2â L2veff(4.3.3)Taking the length and effective speed of light to be the same across allbars, the second term is a constant of around 10 ns. Thus the time differencebetween two bar hits is given by:TOF = t0,i â t0,j=ttopi + tboti2â ttopj + tbotj2(4.3.4)This TOF can be used to distinguish between cosmic ray muons and an-nihilations, as shown pictorially in Figure 4.10. For relativistic cosmic raymuons, we expect their TOF to be given by TOFexp = D/c, where D isthe distance between where the muon crosses bars A and B, and c is the664.4. Electronics and data acquisitionspeed of light. A horizontal cosmic ray passing through the centre of thedetector has TOFexp â¼ 1.5 ns; typical cosmic rays have TOFexp between1.5 ns and 2 ns. On the other hand, pions produced in an annihilation origi-nate inside the detector, and travel similar distances outwards to the BSC.The TOF, as calculated above, does not represent a true particle path, butrather an effective TOF. Since the distance travelled by each pion is similar,this effective TOF will be close to zero. By comparing the measured TOFto the expected cosmic ray TOFexp, cosmic rays can be distinguished fromantihydrogen annihilations.Using these methods, the longitudinal hit position can be determinedusing either charge division or time difference, and measuring the effectiveTOF, the BSC can be used to distinguish between antihydrogen annihilationsand cosmic ray muons. To fully implement this scheme, many technicaldetails and higher order effects were addressed. These details, and the resultsof this background rejection scheme, are described in Chapters 6, 7, and 8.4.4 Electronics and data acquisitionTo handle data collection, ALPHA-g adopted the MIDAS data acquisition(DAQ) framework [135] developed at TRIUMF and at the Paul Scherrer In-stitute. This software is used in many diverse physics experiments, includingcurrent use in ALPHA-2. It handles many aspects of the experiment:â¢ A web-based user control interface for many experiment subsystems.â¢ Continuous logging of slow control variables.â¢ Hardware frontends for TPC and BSC detector services.â¢ Streaming of digitized data from the TPC and BSC.â¢ An event builder that assembles TPC and BSC data by timestamp.â¢ A configuration database for run control settings.â¢ Data storage on local disks and CERN servers.The remainder of this section describes how the TPC and BSC signalsare processed and digitized by custom ALPHA-g readout electronics beforebeing fed into MIDAS. The full readout chain is shown diagrammatically inFigure 4.11.674.4. Electronics and data acquisitionFigure 4.10: Schematic diagrams of particles traversing the BSC (green),TPC (blue), and trap wall (yellow). Inlaid boxes indicate hit times. (a.)A cosmic ray without interacting. (b.) A cosmic ray with a simple showerinteraction. (c.) An antihydrogen annihilation with two charged pions. (d.)An antihydrogen annihilation with three charged pions.684.4. Electronics and data acquisitionFigure 4.11: Diagram of the readout electronics chain for the TPC and BSCdetectors. Taken from [136].4.4.1 TPC data acquisitionThere are two sources of data from the TPC: signals from the 256 anodewires, and those induced on the 18432 cathode pads. Although there wereoriginally plans to read out the anode wire charge from both ends, only thetop end of the anode wires are instrumented. This is done by custom pre-amplifiers called anode wire boards (AWBs). There are 16 AWBs mounteddirectly to the top of the TPC, each reading out 16 anode wires. The anodewire signal is decoupled from the high voltage and amplified by the AWB.From the AWB, the anode wire signal is carried off the detector to analog-to-digital converter (ADC) digitizers called the Alpha-16, based on the GRIF-16digitizers previously developed at TRIUMF [137]. When triggered, they dig-itize all anode wire signals with a sample rate of 62.5MHz (16 ns samplelength) and a dynamic range of 12 bits. The digitized waveforms are trans-mitted to the DAQ computer via ethernet. There are 8 Alpha-16 digitizers,each receiving signals from 32 wires via 2 AWBs.The readout of the 18432 cathode pads is significantly more challengingdue to the large number of channels. After amplification, these signals aredigitized directly on the detector by application-specific integrated circuits(ASICs), using the AFTER switched capacitor array originally designed forthe T2K experiment [138]. The capacitors are opened and quickly closed,one at a time, so that they are charged by sampling the cathode pad signal.These capacitors are then discharged in turn, and their charge recorded by694.4. Electronics and data acquisitionan ADC mounted on the printed circuit board. This cathode pad datadigitization is the limiting factor for the maximum readout rate of the TPC,nominally 500Hz.Each ASIC reads out 72 cathode pads. Four of these ASICs are groupedtogether on one pad wing board, or PWB, each handling 288 cathode pads.There are a total of 64 PWBs needed for all cathode pads. The digitizeddata from all four ASICs is collected by one central FPGA on each PWB,and then transferred off the detector and to the DAQ computer via a 1gigabit/second optical fibre and ethernet switch.The density of readout and digitization electronics on the detector usessignificant power and creates excess heat. Copper bus bars supply low voltageto the PWBs, which draw close to 1000W across the whole detector. Theheat created is dissipated by water cooling, flowing through copper pipesmounted beside the bus bars, and the temperature is carefully monitored bytemperature probes mounted to the readout electronics.4.4.2 BSC data acquisitionThere are 64 BSC bars, each read out by an array of 6 SiPMs at both ends,for a total of 768 SiPMs. The array of SiPM signals is processed by custom-built analog sum discriminator (ASD) boards. Each ASD handles four barends, requiring a total of 16 ASDs mounted to each end of the detector.After initial pre-amplification, the fast output signals from the 6 SiPMson a bar end are combined by an analog sum circuit. This is followed bysome further amplification and pulse shaping. Here, the signal path is split:â¢ One branch of the signal is passed through an RC low-pass filter pulseshaper, which stretches and lengthens the pulse by an approximatefactor of 5. This signal is carried off the detector to the same ADCswhich digitize the anode wire signals. Each ADC has 16 channelsdedicated to the BSC, which are digitized at 100MHz (10 ns samplelength) and with a dynamic range of 14 bits.â¢ A second signal branch is passed through a fast comparator on theASD. A programmable threshold voltage is generated by a digital-to-analog converter (DAC) on the ASD; the comparator outputs a digitalpulse when the combined SiPM signal exceeds the threshold. Thisdigital signal is carried off the detector to a time-to-digital converter(TDC).704.4. Electronics and data acquisitionALPHA-g uses a single 256-channel TRB3 TDC manufactured at the GSIHelmholtz Centre for Heavy Ion Research, which has a precision better than20 ps [139]. The TDC digitizes the signal arrival time using an FPGA delayline. It uses an externally-supplied 200MHz clock; when a signal arrives fromthe BSC, it propagates through the delay line until it is frozen at the start ofthe next clock cycle. The number of delay elements traversed by the signalindicates the signal time relative to the clock cycle. The leading and fallingedge of the signals are digitized separately, although only the leading edgeis used in the BSC analysis. When triggered, all TDC events in a roughly10 µs window are sent from the TDC to the MIDAS event builder.Further details on the implementation of the BSC readout electronicsand data acquisition are provided in Appendix A.4.4.3 Clock, trigger, and test pulseSynchronization of the ADCs, TDC, and other readout electronics in ALPHA-g is maintained using a dedicated clock distribution system. A custom clockmodule based on the clock developed by the GRIFFIN collaboration at TRI-UMF [137] provides a stable timing reference. This module receives an input10MHz clock from the AD, and distributes derived clocks at 100MHz and62.5MHz to the ADCs, and at 200MHz to the TDC.The triggering of the detectors is handled by a custom ALPHA-T triggermodule developed at TRIUMF, based on the GRIFFIN GRIF-C module[137]. Fast discriminated detector hit information is transmitted from theADCs to the trigger module. The trigger module processes this data andmakes a trigger decision, then distributes a global trigger signal via theclock module to synchronize data acquisition across all subsystems. Thetriggers are sent directly from the trigger module to MIDAS, allowing forfast counting of annihilations which is not limited by the 500Hz readoutrate of the detectors.Many trigger configurations are available via the MIDAS run control sys-tem. The original design intention was to trigger on a multiplicity of BSCbar hits, and this scheme has been tested successfully. However, the operat-ing configuration for the initial gravity measurement instead uses anode wiresignals from the TPC as the trigger source. A trigger is sent when signalsare received on two or more AWBs, with a gap of at least one AWB betweenthem with no signal. This trigger condition was chosen to suppress cosmicray events which create signals on only a single contiguous group of AWBs.An additional feature implemented is a built-in test pulser system, whichcan inject known signals into the TPC and BSC electronics to verify system714.4. Electronics and data acquisitionfunctionality. Each ADC module includes a programmable digital-to-analogconverter (DAC) capable of generating a test pulse with adjustable shapes.To test the readout of the TPC anode wires and cathode pads, this signal canbe fed into the field wires, which induces a pulse on the anode wires. For theBSC, the test pulse is injected immediately after the first pre-amplificationstage of the SiPM signal path, enabling testing of the full analog and digitalreadout chain.72Chapter 5TPC event reconstructionThis is the first of four chapters describing my original contributions toALPHA-g. I have spent a significant fraction of my time improving the re-construction of the TPC data, resulting in considerable developments whichdirectly lead to the detector performance meeting the resolution and back-ground rate targets. An attempt is made to quantify the effects of theseimprovements on the gravity measurement in Section 9.4.1.This chapter is organized as follows. Section 5.1 outlines the data process-ing strategy for TPC data. Section 5.2 describes my work on the ALPHA-gevent display, which was used to inform improvements to the TPC recon-struction. Section 5.3 describes in detail the annihilation position reconstruc-tion algorithm, clearly distinguishing my own improvements and originalcontributions, primarily in Sections 5.3.4, 5.3.5, 5.3.6, and 5.3.7. Section 5.4will quantify the results of these improvements. I have also been involved inan effort to develop an alternative vertex finding algorithm based on machinelearning and neural networks, which is briefly discussed in Section 5.5.5.1 TPC data processingThe MIDAS data acquisition system described in the previous chapter readsout the raw data signals from the TPC and BSC into events based on theirtimestamp. The acquired data is stored in a memory buffer before beingwritten permanently to disk. The data structure follows a MIDAS-specificopen-source format. Due to the large number of cathode pads, a substantialquantity of data is produced: around 60GB per hour for cosmic ray datawith the typical trigger configuration, and up to 100GB per hour duringtypical antihydrogen production. This data is automatically copied fromlocal ALPHA storage drives to CERNâs EOS servers [140] for redundancyand long-term storage.ALPHA has developed a dedicated alphasoft software suite [141] to ana-lyze this data, primarily written in ROOT/C++ and based on the MIDASanalyzer [135, 142]. This framework has been used for some time to an-alyze data from the ALPHA-2 SVD. It is modular in structure, allowing735.2. Event displaydifferent executable programs to be constructed from a list of independentlyprogrammed modules. This functionality is used to maintain distinct offlineand online analysis programs which share many elements. The offline anal-ysis reads the MIDAS data files stored locally or on the EOS servers andhandles the reconstruction steps leading to the determination of the annihi-lation position. The alphasoft output is a distilled data file in ROOT formatwhich contains higher-level information such as the reconstructed annihila-tion position and the number of tracks.The online analysis mode performs the same reconstruction of the anni-hilation vertex position, but instead reads directly from a MIDAS memorybuffer filled in real time by the dedicated MIDAS event builder. It is runon a dedicated computer with 32 cores and 252GB of RAM so that it cankeep pace with the TPCâs 500Hz maximum event rate. The alphasoft suiteincludes tools for quickly visualizing the time and position of annihilationevents, including a real-time online display of annihilation positions, to whichI have directly contributed.A number of summary plots are automatically generated at the end ofeach run, allowing detector data to be used in real time for the developmentand debugging of antihydrogen production. Quality-of-data monitoring his-tograms are also produced both online and offline to assess detector andreconstruction performance.5.2 Event displayBefore discussing the vertex reconstruction algorithm and my contributionsto it, it is prudent to cover the ALPHA-g event display. This was a crucialtool for finding issues with the reconstruction and testing solutions, withoutwhich many improvements would not have been possible. To this end, Imade considerable contributions to the event display in parallel to my workon the reconstruction algorithms. This section will give an overview of theALPHA-g event display and highlight my contributions. My implementationof the BSC into the event display will be discussed later in Section 6.9.The event display for ALPHA-g is based on the XSNOED event displayused for the SNO experiment [143]. Integrated into the alphasoft recon-struction software as an analysis module, it generates an interactive three-dimensional rendering of each event. Figures 5.1 and 5.2 show the eventdisplay across a range of events.To inform the modifications to the reconstruction algorithms, I spentconsiderable time debugging and improving the event display, which was not745.2. Event displayFigure 5.1: The ALPHA-g event display, side-on and top-down views. Space-points are shown as small dots, helix fits as curved lines, and the vertexposition as a red square. Larger dots represent barrel scintillator hits (Sec-tion 6.9). Simple wireframe mesh cylinders mark the outer TPC radius andthe trap radius. (a.) An annihilation where a vertex (red square) was foundfrom two helices (purple lines). An attempt was made to add one helix(green line) to the vertex, but this worsened the fit. Many helices failed theselection cuts (grey lines). (b.) A simpler annihilation event. A third helix(cyan line) was successfully added to improve the vertex fit.755.2. Event displayFigure 5.2: The ALPHA-g event display, side-on and top-down views. (a.)An annihilation event where some pair production tracks have been includedin the vertex fit. (b.) A cosmic ray which was fit with one double-sided helix.(c.) A cosmic ray which was initially two tracks, but was joined into one bythe track joiner.765.2. Event displayFigure 5.3: The TPC waveform display window in the event display. Boththe anode wire waveform (top) and matched cathode pad waveform (bottom)are shown. The x-axis is time in 16 ns bins, and the y-axis is voltage in ADCbits.previously in a functional state. This work included fixing a number of bugsin the geometry which caused helices and vertices to be drawn in the wrongplace. I also added a number of features, such as:1. An option to colour spacepoints based on their track grouping.2. Inclusion of the truth vertex in simulated events, representing the sim-ulated annihilation position.3. Options to display only a subset of events matching given criteria, sothat the event display could be used to diagnose specific problems.Alongside the visualization, quantitative information are available in pan-els for the event, for each spacepoint, and for each helix fit. The visualizationis fully interactive: individual spacepoints and helices can be selected to dis-play their corresponding information panel. I added the helix fit informationpanel and greatly extended the data available in these panels, making thempowerful diagnostic tools. A waveform viewer is also built into the event dis-play. Selecting a spacepoint displays the associated anode wire and cathodepad signals, as shown in Figure 5.3.775.3. Annihilation position reconstruction5.3 Annihilation position reconstructionThe goal of the TPC reconstruction is to determine the three-dimensionalposition of each antihydrogen atom as it annihilates, called the annihilationvertex. In most cases when antihydrogen is released, the vertex lies along theinside wall of the trap, as this is the first matter the atom will encounter.However, antihydrogen can also annihilate on background gas inside thevacuum chamber, and so the reconstruction algorithm must be able to handleannihilations occurring at any position inside the trap.The reconstruction proceeds in nine stages, which are illustrated picto-rially in Figure 5.4 and as a block diagram in Figure 5.5. To aid the reader,each stage is first introduced in the text with the number corresponding tothese diagrams. These stages roughly correspond to individual modules inthe alphasoft analysis chain.This section will describe each stage of the TPC event reconstruction inconsiderable technical detail. It will also distinguish between three historicalversions of the software: the original pre-2022 version, the version used inthe gravity paper, and the current improved version.The reader who is not interested in understanding the minutia of howTPC data is processed to recover annihilation vertices should feel free toskip ahead to Section 5.4 for a summary of the impact of the changes madethroughout this work.5.3.1 Signal deconvolutionA charged particle ionizes the TPC gas along its path, as discussed in Sec-tion 4.2.1. A minimum ionizing cosmic ray muon produces around 0.6 ion-ization clusters per millimetre, as does a charged pion from an annihilation;each cluster consists of one or more electron-ion pairs. Many of these ion-ization electrons drift towards the same anode wire, or induce signals on thesame cathode pads. As a result, the recorded waveforms can be complex,requiring deconvolution to resolve the individual electron arrival times. Intypical TPC geometries, this can be mitigated by designing the drift direc-tion to be orthogonal to the expected track directions, so that ionizationclusters along a track are more likely to to drift to different wires. Given thegeometry of the ALPHA-g TPC, this was not practical, and so the need foraccurate signal deconvolution is increased.The deconvolution procedure is similar for both the anode wire signalsand the cathode pad signals. The goal of the anode wire deconvolutionmodule (1) and cathode pad deconvolution module (2) is to extract785.3. Annihilation position reconstructionFigure 5.4: A diagram showing the nine stages of the annihilation vertexreconstruction in relation to the TPC geometry. The geometry is not to scale,and the number of wires and pads is significantly reduced for readability.Inlays show simplified anode wire and cathode pad waveforms.1. Anode wire signals are deconvolved. 2. Cathode pad signals are decon-volved. 3. Nearby pad signals are grouped. 4. Corresponding wire andpad signals are matched. 5. Ionization positions are determined via timeprojection. 6. Tracks are identified. 7. Tracks are fit. 8. Segmented tracksare joined. 9. The vertex position is determined.795.3. Annihilation position reconstructionFigure 5.5: A block diagram indicating the reconstruction stages, roughlycorresponding to modules in the alphasoft analysis chain. The stages arenumbered corresponding to Figure 5.4, and also indicate the section of thisdissertation where they are discussed.signal start times and amplitudes from individual waveforms which maycontain many overlapping signals.The deconvolution is based on template waveforms which correspond tothe response of the anode wire and cathode pad to a single electron avalanche.These response functions were produced using Garfield++ simulations of theavalanche process [5] and verified experimentally.The deconvolution process for the two types of TPC signal is shown inFigure 5.6. It begins by iterating through each bin of the digitized waveforms.For each waveform, if the value in that bin exceeds a given threshold, theresponse function is subtracted from the waveform, scaled to account forthe number of electron-ion pairs in the ionization cluster. This process isrepeated for each waveform above the threshold, before proceeding to thenext bin.In the case of anode wires, additional care is taken to account for in-duction between adjacent wires. An avalanche will induce an opposite-signsignal on neighbouring wires [127]. To account for this, a copy of the responsefunction is also subtracted from the four closest wires on either side. Thiscopy is inverted and scaled by factors of 12%, 4%, 1%, and 0.4% respectively,calculated using Garfield++ simulations.805.3. Annihilation position reconstructionFigure 5.6: Deconvolution of cathode pad (left) and anode wire (right) sig-nals. Yellow indicates the digitized signal, red indicates the number and timeof single electron avalanches determined by the deconvolution algorithm, andblack shows the residual waveform after subtracting the response functions.The x axis is time in 16 ns time bins, and the y axis is signal amplitude inADC units. Credit: Lars Martin.5.3.2 Signal groupingWhen an avalanche occurs on an anode wire, a signal is induced on multiplenearby cathode pads. The goal of the pad signal grouping module (3) isto group these nearby cathode pad hits together. These combined cathodepad hits are then associated with their corresponding anode wire hit by thesignal matching module (4).To speed up computation given the large number of cathode pad chan-nels, neighbouring pads are not deconvolved simultaneously, as was done forthe anode wires. Instead, each pad signal is deconvolved independently, al-lowing for parallelization of this computationally expensive task. The signof the induced signal is the same for all pads, enabling the pad hits to beidentified individually and grouped later.As a result of this choice, many pad hits are produced by a single electronavalanche. The pad signal grouping module merges these neighbouring padsignals together. First, deconvolved pad signals are grouped by time: thosein the same or adjacent 16 ns time bins are eligible for matching. They arethen grouped by pad column, so that only hits in a single vertical columncan be grouped together. A blob-finding algorithm then identifies groups ofpad signals on contiguous pads. The central z position (i.e. along the TPCaxis) of the group of pad signals is then determined, using either a weightedaverage or by fitting the pad signal heights with a Gaussian function.815.3. Annihilation position reconstructionFigure 5.7: Garfield++ simulation of a charged pion (green) in the TPC.The orange lines represent the path of electrons from ionization sites alongthe pion path to the anode wires. These simulations were used to createspace-time relation lookup table. Published in [130].Following cathode pad grouping, next in the analysis chain is the signalmatching module, responsible for combining the pad hit groups with theanode wire hits. The time difference ât and the difference in the azimuthalcoordinate âÏ between each wire hit and each pad hit group are calculated.Each anode wire hit is matched to the pad hit group which minimizes thetwo-dimensional distance D =â(ât)2 + (α Â·âÏ)2, where α = 3 is a scalingfactor empirically chosen to correctly prioritize ât (in ns) or âÏ (in radians).This matching strategy was implemented using a k-d (k-dimensional)tree data structure, which is commonly used for nearest neighbour searchesin multidimensional spaces. The technique is similar to a binary tree search,and avoids computing the distance between all pairs of wires and pads, whichgreatly improves computational performance [144].5.3.3 Spacepoint reconstructionAfter matching the anode wire avalanche signals to the cathode pad signalsthey induce, the exact position of the avalanche can be determined: theradial r position is fixed at the anode wire radius, the azimuthal Ï positionis given by the wire number, and the axial z position is given by the centreof the group of cathode pad hits. The goal of the spacepoint formationmodule (5) is then to determine the original position of the ionization whichcreated the free electron responsible for the avalanche.825.3. Annihilation position reconstructionThis requires a detailed knowledge of the electronâs path through the driftgas as it is guided by both the electric field between the anode wires andinner cathode, as well as the magnetic field created by the external solenoidmagnet. To this end, detailed electron drift simulations were performedusing Garfield++ [5], illustrated in Figure 5.7. These simulations were usedto create a lookup table for the space-time relation (STR), the relationshipbetween ionization position and drift time.To define the drift time, a global zero time for the event is needed. This istaken as the time of the first signal observed on any anode wire, utilizing theassumption that a charged particle traversing the TPC will almost certainlypass close to at least one wire, creating an avalanche with near-zero drifttime. The drift time for each avalanche is then defined as the differencebetween this zero time and the start time of the anode wire signal. Usingthe STR lookup table, this drift time is converted into a drift length, whichgives the r coordinate of the original ionization. The electron drift is notcompletely radial; there is an azimuthal deflection due to the magnetic field,called the Lorentz angle. This angle is also included in the STR lookuptable, and is used to correct the reconstructed Ï coordinate. The ionizationz coordinate remains unchanged from the central z position of the pad hitgroup.The final output of this process is a three-dimensional estimate of eachionization position in the TPC gas volume, referred to hereafter as space-points. They are assigned a three-dimensional position uncertainty. TheSTR lookup table is used to determine this uncertainty from the hit timeuncertainty (from the ADC bin width and the deconvolution), avalanche zposition uncertainty (from the pad signal weighted average or fit), and wireposition pitch.5.3.4 Track findingThe track finding module (6) attempts to group these reconstructed ion-ization spacepoints into tracks, which correspond to the paths of individualcharged particles through the TPC.The original track finding algorithm, termed the adaptive finder, wasable to identify pion tracks sufficiently for vertex position reconstruction.However, using the ALPHA-g event display discussed in Section 5.2, I iden-tified some flaws with this method. I addressed these by implementing twofurther track finding algorithms. The first improved track finder, coinedthe iterative finder, was developed to directly address the issues identifiedwith the adaptive finder, and was used in the data analysis for the 2023835.3. Annihilation position reconstructionFigure 5.8: Cartoon diagram of the adaptive finder. (1.) Spacepoints inthe TPC. (2.) A seed point is chosen close to the anode wires. (3.) Thenext point within a cutoff distance (dashed circle) is added to the track. (4.)This is repeated until the track is completed, adapting the cutoff distance asrequired. (5.) A seed point for a new track is chosen. (6.) This is repeatedfor all possible seed points at large r.gravity paper. However, some issues still persisted. The second improvedtrack finder, called the exhaustive finder, introduced a more fundamentalchange to the track finding technique.Original method: adaptive finderThe original method of track finding, the adaptive finder, was developedbased primarily on simulation and data from a prototype TPC at TRIUMF[145]. An illustration of this track finding procedure is shown in Figure 5.8.It begins by sorting spacepoints by radial position r, and then proceedsas follows:1. The largest r spacepoint is chosen as a seed point for a new track.2. If the next spacepoint is within a fixed cutoff distance from the currentpoint, it is added to the track and becomes the new current point.3. This is repeated for every remaining point at smaller r.4. Once there are no further points within the cutoff distance, the cutoffdistance is incrementally increased.5. The track is completed after the cutoff distance is increased to a max-imum value.845.3. Annihilation position reconstructionFigure 5.9: Cartoon diagram of the iterative finder. (1.) Spacepoints in theTPC. (2.) A seed point is chosen close to the anode wires. (3.) Spacepointswithin a fixed cutoff distance from the previous point are added to the track.(4.) The first point in the track is checked for missed points within the cutoffdistance. (5.) The tracking process is restarted from each missed point. (6.)Each point in the track is checked twice before a new track is seeded.6. The process repeats from the remaining spacepoints with a new seedpoint, until all unused spacepoints up to a cutoff radius have been triedas a seed point.In this way, the track is built from large to small r, i.e. from near theanode wires towards the TPC centre. This algorithm was effective at findingtracks which could be used to reconstruct the vertex position. However,some issues became evident once the event display was used to examine thetrack finding process:â¢ Spacepoints would often be missed from a track.â¢ In many cases, these missed spacepoints would form a second, overlap-ping track (i.e. the blue points in Figure 5.8).â¢ Tracks would be missed entirely if no spacepoint had large enough rto be chosen as a seed point.First improvement: iterative finderTo address these issues, I developed a new iterative finder, which is shownschematically in Figure 5.9. It includes three key changes. The first differenceis that there is no adaptation of the cutoff distance; the maximum cutoff855.3. Annihilation position reconstructiondistance is always used. The second key difference is an additional iterativestep once the initial track has been built. Specifically:1. After the initial track is formed, each of its spacepoints is recheckedfor nearby, unused neighbours.2. If a new point is found within the cutoff distance, it is added, and thetrack finding process is restarted from that point.3. The full track is re-scanned twice (i.e. two further iterations).This iterative augmentation significantly reduced the number of missedspacepoints and prevented the formation of spurious overlapping tracks. Thethird key change was a retuning of the parameters of the track finding algo-rithm, which led to fewer missed tracks overall.Second improvement: exhaustive finderWhile the iterative finder was a clear improvement over the adaptive method,it still suffered from two failure modes:â¢ It would miss tracks that did not extend to large r, since only outerspacepoints were used as seeds.â¢ It would fail to correctly handle more complicated events, particularlythose involving pair production from Ï0 â γ â e+eâ, which featurehighly curved tracks that meet at a displaced vertex.Ideally, the tracking algorithm would identify these lepton pair produc-tion tracks, and either exclude them or treat them separately. However, theadaptive and iterative finders would fail in this situation. Since the trackfinders start at high r and move inwards, they tend to find subsets of pointswhich form straight and centrally-pointing false tracks. These false tracksdo not represent real particle trajectories, but are still used in the vertexposition calculation, often leading to an incorrect vertex.These flaws became clear during manual inspection using the event dis-play. To address them, I developed a third method: the exhaustive finder,which is illustrated in Figure 5.10. The exhaustive finder proceeds as follows:1. Precompute the distance between each pair of spacepoints and compareit to a cutoff distance.865.3. Annihilation position reconstructionFigure 5.10: Cartoon diagram of the exhaustive finder. (1.) Spacepoints inthe TPC. (2.) A seed point is chosen at random. (3.) Points within thecutoff distance are added recursively. (4.) A new seed point is chosen fromthe remaining points. (5.) This process is repeated until all tracks are found.2. Randomly choose a seed spacepoint, and recursively add each space-point within the cutoff distance to a track.3. Repeat this with a new seed chosen from the remaining spacepoints,until each spacepoint has been tried as a seed.This method is less computationally efficient, but the analysis is still farfaster than the pad signal deconvolution and matching steps. In exchangefor the additional computation, this approach is far more robust. It does notmiss tracks which do not approach the anode wires, and does not find false,artificially straight tracks in events with complex topologies.Summary of track finding improvementsFrom the initial adaptive finder, two improved track finding algorithmswere implemented: the iterative finder was used for the gravity paper, andthe exhaustive finder is used in the most recent reconstruction versions.A summary of the three track finding methods is given in Table 5.1.Both improved track finders were informed by problems observed usingthe ALPHA-g event display. The iterative finder fixed the issue where manypoints were missed from a track, frequently resulting in a second (or eventhird) overlapping track being formed from those points. It also led to fewermissed tracks overall. The exhaustive finder was able to find all possibletracks in the dataset, regardless of their orientation.875.3. Annihilation position reconstructionTable 5.1: Comparison of track finding algorithms used in ALPHA-g TPCreconstruction. Statistics are approximate and were collected by visual in-spection of 50 annihilation events using the event display. Charged piontracks and other tracks were manually categorized, and the following werecounted by hand: missed points in each track, missed tracks, overlappingtracks formed from the spacepoints of a single charged particle, and falseradial tracks formed from complicated non-radial trajectories.Feature AdaptiveFinderIterativeFinderExhaustiveFinderCutoff distance 8mm â 45mm 30mm 30mmSeed point r > 168mm r > 168mm AnyMethod Single pass Two refinementiterationsRecursivesearchMissed points pertrackâ¼ 2.4 â¼ 0.02 NoneOverlappingtracksâ¼ 48% None NoneMissed tracks(pion)â¼ 38% â¼ 12% NoneMissed tracks(other)â¼ 42% â¼ 28% NoneFalse tracks â¼ 40% â¼ 21% NoneRadial bias Strong Strong NoneComputationtime per event96 µs 139 µs 236 µsThe iterative finder was primarily motivated by a desire to improve theannihilation vertex position resolution; we shall see in Section 5.4 that itwas successful in this goal. By contrast, the exhaustive finder was motivatedby the desire to successfully find all tracks, to extract the most informationpossible from the detector.5.3.5 Track fittingAfter grouping spacepoints into the tracks, the track fitting module (7)fits each track with a helical functional form using independent transverseand axial fits. In the original and gravity paper versions of the reconstruction,these helices were parametrized in terms of the radial variable r. However,885.3. Annihilation position reconstructionthis was not compatible with highly curved tracks, which were much morereliably identified by the exhaustive track finder. To address this, the heliceswere reparameterized, and considerable changes were made to the track fit-ting logic and initial conditions. This section will first describe the elementscommon to both the original and current reconstruction versions, then de-scribe the original fitting routine, and finally describe the changes made inthe current version.Helix fit functionThe trajectories of charged particles in the ALPHA-g TPC are reconstructedby fitting a helical model to the spacepoints of each track. The mathematicalform of the helix is adapted from [146], and represents the expected three-dimensional path of a charged particle in a uniform magnetic field. In thetransverse (râÏ) plane, the path of the particle traces the arc of a circle dueto the Lorentz force from the axial solenoidal magnetic field. In the axial (z)direction, where no forces act on the particle, the motion is linear.This functional form assumes that the charged particleâs energy is con-stant over its trajectory. The density of the 70:30 ArCO2 gas mixture atatmospheric pressure is 1.7 kg/m3, and so a minimum-ionizing particle willdeposit around 3.4 keV/cm in the TPC gas. Over a 20 cm path length, whichis longer than a typical charged pion path in the TPC, this results in a totalenergy loss of around 68 keV. Thus the constant energy approximation isvalid for the charged pions, which are typically produced in the annihilationwith around 100MeV of kinetic energy.Mathematically, the helix is described by five free parameters, which areillustrated in Figure 5.11:â¢ Rc â the radius of curvature in the râÏ plane.â¢ Ï0 â the azimuthal angle at the point of closest approach to the origin.â¢ D â the distance of closest approach to the origin in the râÏ plane.â¢ z0 â the z coordinate at the point of closest approach.â¢ λ â the pitch of the helix (slope in z as a function of arc length).This parametrization takes advantage of the fact that the trajectory isperpendicular to the radius vector at the point of closest approach, meaningthe track is uniquely described by (Rc, Ï0, D) in the transverse plane. Thefinal two parameters (z0, λ) describe the z component of the helix.895.3. Annihilation position reconstructionFigure 5.11: The free parameters of the helix functions used in track fitting.(1.) shows the projection of the helix function (red) in the r â Ï plane,illustrating the three radial fit parameters. (2.) shows the projection of thehelix function in the r â z plane, illustrating the two axial fit parameters.The track can be parameterized with respect to a track variable t, whichrepresents arc length from the point of closest approach:x(t) = Rc sin (t+ Ï0)â (Rc +D) sinÏ0y(t) = âRc cos (t+ Ï0) + (Rc +D) cosÏ0z(t) = z0 + λt(5.3.1)This model was successfully used to fit tracks prior to my contributions.However, the original implementation made a number of further simplifyingassumptions, which I will now discuss. I will then outline the changes Imade to the track fitting algorithms: first relaxing some of these simplifyingassumptions, and then improving the initial fit parameters for more stabletrack fitting.Original method: single-valued helix fittingGiven that we are primarily fitting charged pion tracks originating fromnear the centre of the TPC and propagating outwards, we can impose someconstraints on the helix. Firstly, we restrict the track parameter t to bestrictly positive or strictly negative, such that the helix extends in onlyone direction from the point of closest approach. Secondly, we require thatthe helix does not curve backwards towards the origin. Together, theseconstraints ensure that the helix is single-valued in the radial coordinater. This allows us to re-parameterize the helix function in terms of r, asx(r), y(r), z(r).The helix function is fit to the track in two stages:905.3. Annihilation position reconstructionâ¢ Transverse (râÏ) fit: The parameters Rc, Ï0, and D are determinedby minimizing the transverse residuals:RT =âi[(x(ri)â xi)2+(y(ri)â yi)2] (5.3.2)where (xi, yi) is the i-th spacepoint in the track, and x(ri), y(ri) is thehelix function evaluated at the radius ri =âx2i + y2i of that space-point.â¢ Axial (z) fit: The parameters z0 and λ are then determined by min-imizing the axial residuals:RZ =âi[(z(ri)â zi)2] (5.3.3)where zi is the i-th spacepoint, and z(ri) is the helix function evaluatedat that spacepoint.This track fit is repeated twice, once with t > 0 and once with t < 0,and the fit with the lower transverse residual is selected. These correspondto the track extending either clockwise or anticlockwise from the point ofclosest approach.Current method: changes to helix fitting routineThe main modification I made to the helix fitting routine was to lift theconstraint that the track be single-valued in r. This enables the fitting ofhelices that curve back on themselves or extend in both directions from thepoint of closest approach. These are cases that arise frequently in ALPHA-gdata for particles other than the charged pions around which the helix fittingprocedure was previously designed:â¢ e+eâ pairs from neutral pion decay tend to have small momentum, andso are strongly curved in the magnetic field. They frequently producetracks which curve back on themselves and are not single-valued in r.â¢ Cosmic ray muons either produce straight line tracks which span bothsides of the point of closest approach, or produce two back-to-backtracks on opposite sides of the detector.To accommodate these cases, I retained the helix parametrization ofEquation 5.3.1, but introduced two types of helix:915.3. Annihilation position reconstructionâ¢ A single-sided helix which retains the restriction t > 0 or t < 0, ex-tending in one direction only from the point of closest approach.â¢ A new double-sided helix which has no restriction on t and extends inboth directions from the point of closest approach.This adjustment required a considerable rewriting of the helix fittingframework and routine; since we no longer assume the helix is single-valuedin r, we can no longer re-parameterize the helix equations in terms of r.For the transverse fit, we can no longer evaluate the helix function at thespacepoint radius. Instead, the smallest distance from the spacepoint to thecircle defined by (Rc, Ï0, D) is found analytically. The transverse residualsare defined as the sum of this distance squared, and the radial parametersare determined by minimizing these residuals:RT =âi[(x(tclosest)â xi)2+(y(tclosest)â yi)2] (5.3.4)For the axial fit, the residual to be minimized is defined as the differencein z between the spacepoint and the point on the helix that is closest in(x, y):RZ =âi[(z(tclosest)â zi)2] (5.3.5)These changes allow the fitting routine to handle a broader class of tracksmore accurately. They also represent a fundamental shift in the tracking phi-losophy with regards to unwanted tracks from cosmic ray muons and pairproduction. Previously, these tracks were implicitly excluded by reconstruc-tion algorithms which would fail to find or properly fit them. However, thiswould often result in mis-reconstructed false tracks which could interfere withthe vertex fit. The new philosophy is to successfully find and fit these tracks,and then explicitly exclude them from the vertex fit. This track selectionstep will be described in Section 5.3.7.Current method: improved initial fit conditionsAnother area where I significantly improved the helix fitting routine is theinitialization of the fit parameters. Using the event display to visualize thehelices with their initial parameters, I identified and corrected several er-rors. There were a number of simple mistakes such as a missing factor of Ï,which caused the initial transverse fit to be placed on the opposite side of925.3. Annihilation position reconstructionthe detector, or an omitted minus sign that inverted the initial value of λ.Improving the initial conditions yielded more stable fitting for the gravitypaper with fewer failed fits.In the original reconstruction, the initial conditions for the radial fit wereset using the spacepoints with the smallest and largest r. A straight line wasdrawn between these two points: its angle determined the initial Ï0, andits distance of closest approach set the initial D. A very large radius ofcurvature was used for the initial Rc.In the current reconstruction, the transverse fit is repeated four times,each with different initial conditions:1. r-ordered curved initialization: The points are ordered by r, andthe inner, outer and middle points are found. A circle is drawn throughthese points and used to define the initial Rc, Ï0, and D.2. z-ordered curved initialization: The points are ordered by z, andthe top, bottom, and middle points are found. A circle is drawnthrough these points and used to define the initial Rc, Ï0, and D.3. Straight positive initialization: The points are ordered by z, anda straight line is drawn through the top and bottom points. A slightpositive curvature is applied.4. Straight negative initialization: The points are ordered by z, anda straight line is drawn through the top and bottom points. A slightnegative curvature is applied.The fit is repeated with each set of initial conditions, and the fit with thelowest Ï2 is used. Each initialization strategy is better suited to a certaintype of track; while repeating these calculations is computationally slower,this stage is not a bottleneck, and so the higher number of successfully fittedtracks is worth the marginal increase in analysis time.For the axial fit, the original reconstruction sorted the points by r, anddrew a straight line between the closest point and the middle point to findthe initial z0 and λ. The new method is similar, but takes care to only usespacepoints on one side of the point of closest approach (i.e. either t < 0 ort > 0). It uses the points with the smallest and largest t value to draw theline z(t) = λt+ z0, and uses these λ and t parameters to initialize the axialfit.935.3. Annihilation position reconstructionFigure 5.12: Cartoon diagram of cosmic ray tracks in the TPC. (1.) A cosmicray skims the edge, and is identified as one double-sided track. (2.) A cosmicray passes through the centre, and is identified as two back-to-back tracks.(3.) The track joining module recombines these into one double-sided track.5.3.6 Track joiningAlthough these changes led to improved track finding and fitting behaviourfor many types of tracks, there were two further cases which were not ad-dressed properly:â¢ Cosmic rays passing through the centre of the TPC would produce twoback-to-back tracks.â¢ Delta electrons would create long spiralling tracks which were falselyidentified as multiple tracks.These cases both contribute significantly to the cosmic ray background rate,as they produce enough tracks to form a false annihilation vertex. To addressthem, I implemented a new reconstruction module called the track joiningmodule (8), with the goal of recombining initially distinct tracks createdby the same charged particle. This module proceeds in two steps, eachaddressing one of the cases above.Step 1: cosmic ray track joiningCosmic ray tracks are frequently misidentified as an annihilation with twoback-to-back pions. Indeed, these events are the main background in an-nihilation detection. If these back-to-back tracks could be easily identifiedas belonging to the same charged particle, then the background rate wouldimmediately be substantially reduced.945.3. Annihilation position reconstructionWhen a cosmic ray skims the edge of the TPC, as shown in Figure 5.12(1.), then the track is fully identified by the exhaustive track finder and canbe fit with a single double-sided helix. However, if the cosmic ray passesthrough the antihydrogen magnetic trap, the spacepoints appear separatedinto two back-to-back tracks, as shown in Figure 5.12 (2.). Track identifi-cation ambiguity can be resolved by combining these into one double-sidedtrack, as shown in Figure 5.12 (3.).The cosmic ray track joining step attempts to combine each pair of twotracks into a single track. The spacepoint groups of both tracks are merged,and the procedure described in the previous section is used to fit the com-bined track. The combined helix is used in place of the old ones if thecombined goodness of fit is not significantly worse than either of the indi-vidual track fit goodness of fits: RT,comb. < 2 Â·RT,indiv. for the transverse fitresiduals, and RZ,comb. < 1.5 Â·RZ,indiv. for the axial fit residuals.Since a set of N tracks has 12N(N â 1) combinatorial pairs, this step isonly applied to events with 6 or fewer tracks, which is the case for almost allcosmic ray events. This step was highly successful at combining back-to-backcosmic ray tracks, approximately halving the rate of false annihilation ver-tices found in cosmic ray events from 13.65Hz in the original reconstructionto 6.35Hz in the current reconstruction.Step 2: cyclotron trapped electron track joiningWhen a charged particle ionizes the TPC gas, the freed electron will occa-sionally be released with a large amount of kinetic energy. This delta electronis itself an ionizing particle, and travels through the TPC, creating a trail ofadditional ionizations. Since these electrons have relatively low momentumcompared to the initial cosmic ray, they bend more in the external magneticfield, experiencing the type of cyclotron motion discussed in Section 3.2.1.This creates a tight spiral track in the TPC, often with ten or more full ro-tations over the length of the detector. As they are less massive than pions,these delta electrons transfer less energy per interaction with the gas, andso are more inclined to create atomic excitation rather than ionization. Thisleads to fewer ionization clusters per unit distance, with larger gaps betweenionizations, making these tracks very difficult to identify and reconstructcorrectly. They are often fit with a stack of multiple short false tracks ontop of each other (see Figure 5.13), which can cause problems for the vertexfinding.These events with delta electrons are rare with an estimated rate of0.05Hz, less than 1% of the 6.35Hz rate of false vertices due to cosmic955.3. Annihilation position reconstructionFigure 5.13: The ALPHA-g event display (see Section 5.2) showing an eventwhere a cosmic ray interaction produces two cyclotron-trapped delta elec-trons which travel the full length of the detector (from left to right here).The colouring of the small dots indicates the grouping of the spacepointsinto many distinct tracks. The purple lines are helix fits used in the vertexfit, the grey lines are helix fits excluded from the vertex fit, and the largeblue dots are BSC hits (see Section 6.9).rays. However, they are much more problematic than simple cosmic rayevents. A machine learning classification algorithm is used to reject thecosmic ray background, which will be discussed further in Chapter 8. Sincethese delta electron events are not well represented in the training sample,they are almost always incorrectly classified as annihilation events due totheir apparent high number of tracks. These events constituted roughly40% of the background surviving the machine learning background rejectionalgorithm.The second stage of track joining was designed empirically to addressthese events. It searches for helices fit with a radius of curvature smallerthan 25mm, which was determined using the event display to be larger thana typical delta electron cyclotron radius. If found, it looks for further trackswhich have 90% of their spacepoints contained in a vertical column aroundthe centre of the small track. If at least five further tracks are found, threeof which have a radius of curvature smaller than 25mm, then the tracksare joined. The spacepoints are combined into a single track, which is refitwith a helix function according to the previous section. This procedure wasdeveloped such that it is almost never triggered by annihilation events, whilereasonably identifying and fitting cyclotron trapped electrons.965.3. Annihilation position reconstructionFigure 5.14: Cartoon diagram of the original vertex fit method. The leftpanel shows the vertex seeding from the closest two helices. A point on eachvertex initialized at the trap radius (dark blue), and then allowed to movealong the helix to minimize the distance between them (light blue). The seedvertex (pink) is the point halfway between them. The right panel shows thestep where additional helices are added in turn. The new vertex (green) ischosen to minimize its distance from all helices.5.3.7 Vertex fittingThe final reconstruction stage is to determine the annihilation vertex posi-tion from the set of fitted helices, performed by the vertex fitting module(9). To accommodate the reparameterization of the fit helices, this stage wasalso heavily modified between the original and current versions of the recon-struction. This section will compare both reconstruction versions, which areillustrated in Figures 5.14 and 5.15.For both versions, the vertex calculation proceeds in four steps:1. A set of selection criteria are applied to the helices, so that only asubset of the helices are used to find the vertex.2. A seed vertex position is determined analytically from two helices.3. The seed vertex is refined by a fit using only those two helices.4. Additional helices are added in turn, and the vertex is refit.Helix selectionThe vertex fitting procedure is designed to recover the common origin of anumber of near-straight pion tracks. However, a number of particles suchas delta electrons (Section 5.3.6) or pair produced electrons and positrons975.3. Annihilation position reconstructionFigure 5.15: Cartoon diagram of the current vertex fit method. The leftpanel shows the vertex seeding from the closest two helices. The circlestraced by the helix projection into the râÏ plane are used. The seed vertex(pink) is the point closest to both circles, found analytically. The right panelshows the step where further helices are added. The distance squared fromeach circle to the new vertex (green) is minimized.(Section 5.3.4) often lead to tracks that originate at a secondary vertex.Furthermore, the track finding and fitting process often yields poorly fitor false helices that do not match a real particle trajectory. To properlydetermine the vertex position, these tracks must be excluded from the vertexfit.To do this, only helices passing certain selection criteria are included inthe vertex fit:â¢ Helix fits which did not converge are discarded.â¢ Cuts are applied on the goodness of fit of both the transverse and axialfits. These are the residuals RT and RZ defined in the previous section,divided by the number of degrees of freedom Ndof.â¢ A cut on the minimum number of spacepoints in a track discards poorlyconstrained helices.â¢ A cut on the distance of closest approach of the helix discards thosewhich do not pass near the trap, the site of all annihilations.â¢ A cut on the radius of curvature excludes charged particles with lowmomentum, such as delta electrons or eâe+ pairs, which originate froma displaced vertex.My changes improved the reconstructionâs ability to identify and fit trackswith smaller radius of curvature, and so accurately discarding them became985.3. Annihilation position reconstructionfar more important. With these changes, I undertook a campaign to optimizethe helix selection criteria for the best vertex position resolution, and for themaximum number of successfully fit vertices. The updated selection criteriaare given in Table 5.2.Table 5.2: Helix selection criteria before and after reconstruction updates.Selection Criterion Original CurrentTransverse goodness of fit RT /Ndof None < 60Axial goodness of fit RZ/Ndof None < 110Number of spacepoints > 7 > 5Distance of closest approach < 110 mm < 80 mmRadius of curvature None > 50 mmFit convergence required Yes YesVertex seedingAfter discarding the helices not meeting the selection criteria, a seed vertex isinitialized using the two helices which pass closest to each other. Originally,each pair of helices was used in the following manner:1. A point along each helix (i.e. a t value) is initialized at the trap radiussuch that |râi(ti)| = rtrap.2. The t values are varied to minimize the three-dimensional distanced = |râ1(t1)â râ2(t2)| between the two points.3. This is repeated for each pair of helices, and the pair with the smallestsuch distance d is chosen.4. The seed vertex is set to the point sâ = 12 [râ1(t1)+râ2(t2)] halfway betweenthe two helices.While this method is possible with my modifications to the helix fits, Itook the opportunity to remove this minimization step. Instead, the pointof closest approach of each helix to the z axis (the axis of the TPC) is found.The two helices whose points of closest approach are closest to each other areused to seed the vertex. Since each helix traces a circle in the r â Ï plane,the closest point between the two circles can be found analytically and isused to seed the vertex.995.4. Performance improvement resultsInitial vertex fitThe vertex fitting proceeds with an initial fit, using only the two heliceswhich were identified in the vertex seeding step. In the original analysis, afive-parameter minimization is performed: as well as the t value along eachhelix, the vertex position is also varied. The minimization finds a new vertexposition with a minimum distance to the two helices.In the revised analysis, only the three dimensions of the vertex positionare varied. The closest point to the vertex on the circle traced by each helixin the râÏ plane is found analytically, and the sum of their distances squaredto the candidate vertex is minimized. If this distance squared exceeds a fixedthreshold, then the vertex fit is aborted and no vertex is found for the event;otherwise the seed vertex position is updated.Adding further helicesFinally, an attempt is made to incorporate each other helix into the vertexfit. The helices are tried one at a time, and the fit is seeded from the currentvertex position. The fitting procedure is identical to the one described inthe previous section. In the original analysis, the dimension of the fit isincreased by one with each added helix, due to the additional t value for thenew helix. In the new analysis, the dimension of the fit is unchanged, sinceonly the vertex position is varied.After each helix is added, if the total squared distance exceeds the fixedthreshold (the same as above), the helix is removed again. Otherwise, thehelix is kept and the vertex is updated. In this way, only helices which arecompatible with the existing seed vertex are included in the fit.5.4 Performance improvement resultsTo benchmark the vertex position resolution of various algorithms, antipro-tons are held in a narrow and deep potential well in the ALPHA-g Penning-Malmberg trap. They are held for 2000 s, during which they annihilate onbackground gas atoms due to the imperfect vacuum.6 This provides a closeapproximation of an annihilation point source.6The primary use of this procedure is to measure the quality of the vacuum. Remainingantiprotons are counted by scintillator panels after the 2000 s wait; the number of anni-hilations is compared with and without the wait to determine the number of antiprotonslost to background gas collisions. This measurement is repeated regularly.1005.4. Performance improvement resultsFeature Original Gravity ImprovedpaperTrack finder Adaptive Iterative ExhaustiveHelix initialization Bugged Fixed ImprovedHelix selection optimized · â âHelices reparameterized · · âDouble-sided helices · · âTrack joiner module · · âVertex fit modified · · âTable 5.3: Summary of the improvements made between the three recon-struction version: the original pre-2022 reconstruction, the version used forthe gravity paper, and the current improved version. For more informationon each item, see Section 5.3.The potential well is produced by an electrode held at +150V betweentwo electrodes held at â150V, where the length of the electrodes is approx-imately 21mm. This creates an on-axis potential well V (z) = âkz2, wherethe well constant is k â¼ 0.35V/mm2. An antiproton with a temperature of1000K, higher than typical antiproton temperatures used for this measure-ment, has a kinetic energy of 0.08 eV. This sets a bound on the axial lengthof the antiproton plasma of around 1mm in the quadratic well.This point source is used to quantify the resolution of the many versionsof the reconstruction. We will examine three: the original pre-2022 versionof the reconstruction, the one used for the gravity paper, and the currentimproved reconstruction. The improvements made between the versions aresummarized in Table 5.3 and described fully in Section 5.3.The annihilation z position distributions for each of these reconstructionversions are shown in Figure 5.16. A double Gaussian function is fit to eachdistribution. The integrals of the fit functions are used to determine theamount of data in each population. The detector vertex resolution is definedby the combination of the two Ï values of the inner and outer Gaussian fits;it is most insightful to define an inner resolution and outer resolution.The use of a double Gaussian reflects two populations of events. Around60% are simple events with vertices which can be reconstructed easily andprecisely from two or more unscattered charged pion tracks which can betraced back to the annihilation vertex. The remaining 40% are those eventswithout two charged pion tracks which can be traced back to the annihila-tion vertex. This can be either because fewer than two charged pions were1015.4. Performance improvement resultsFigure 5.16: Vertex position resolution across three reconstruction versions:the original pre-2022 reconstruction (top), the reconstruction used for thegravity paper (centre), and the current improved reconstruction (bottom).Shown with a linear (left) and logarithmic (right) y-axis. Data shown is fromantiprotons annihilating on background gas. The most recent online back-ground rejection cut (see Section 6.7) is used; the same events are includedin all three plots.1025.4. Performance improvement resultsproduced (around 18% of pn annihilations and 4% of pp annihilations, seeTable 3.1), because one or more pions were scattered or absorbed on theinternal material of the magnet system, or because reconstruction of one ormore charged pion tracks failed. In these events, other tracks from eâe+pairs or scattered pions must be used, which do not originate exactly at theannihilation vertex. As a result, the vertex determination is less precise forthese events.There is a clear improvement in resolution from the original reconstruc-tion to the gravity paper version. This was in large part due to the intro-duction of the iterative track finder, which improved the overall resolutionby roughly a factor of two. Further refinements were made to the helix fitinitialization and helix selection, as well as contributions from other collab-orators on other aspects of the reconstruction. This ultimately improvedthe inner resolution from 2.80 cm to 1.18 cm, and the outer resolution from14.58 cm to 3.90 cm.The gravity paper requires the localization of annihilations into one oftwo regions separated by 25.6 cm. The improvements presented here ensuredthat annihilation mis-classification to the wrong region was not a majorexperimental systematic; this will be explored further in Section 9.4.1. Theimprovements to the outer resolution are the most relevant, as the outerresolution describes the events most likely to be misclassified.The resolution improvement between the gravity paper reconstructionto the current reconstruction is significant but less pronounced: the innerresolution was improved from 1.18 cm to 1.06 cm, and the outer resolutionfrom 3.90 cm to 3.02 cm. This reflects a shift in the main purpose behind thereconstruction changes: while the gravity paper reconstruction was the resultof a focused effort to lower the detector vertex resolution, the changes leadingto the current version were aimed to create a more physically-motivatedreconstruction procedure.To illustrate this, a number of intermediate metrics are compared acrossthe three reconstruction versions in Table 5.4. Some limitations of the grav-ity paper reconstruction are visible here: the track selection criteria do notreject any tracks, and each vertex is fit using only two helices. The improvedreconstruction fixes these issues, returning to the original intention of in-corporating as many useful tracks as possible into the vertex fit, explicitlyexcluding those which are not useful.It must be noted that with these improvements, the percentage of anni-hilation vertices successfully fit decreases from 86% to 67%. Most of thosevertices lost were those which were more difficult to constrain; as a resultof not reconstructing these vertices, the position resolution of the detector1035.5. Future work: machine learning vertex findingis improved. This was an active choice in the redesign of the reconstructionalgorithms. However, should statistics become more important than positionresolution in a future experiment, the parameters of the reconstruction canbe easily tweaked to recover some of these vertices.My efforts have led to significant improvements in the detector vertexposition resolution, ensuring that the detector resolution did not constitutea major systematic uncertainty to the experiment. In addition, this work hasmade a tangible improvement to the rate with which cosmic ray backgroundevents are mis-identified as annihilation vertices. Furthermore, it has led thereconstructed tracks to match physical particle trajectories more accurately,improving the foundation for studies of ALPHA-g data extending beyondthe annihilation z position.5.5 Future work: machine learning vertex findingAlongside the algorithmic approach to vertex finding described here, I havealso contributed to the development of a second vertex reconstruction methodusing machine learning. This method follows the analysis chain up until thespacepoint reconstruction stage. However, instead of using helix fitting todetermine the annihilation vertex, a neural network is trained to predict thevertex position directly from the spacepoints. My primary contribution tothis effort has been the design and implementation of a data pipeline to con-vert raw detector data and simulation output into a dense data structuresuitable for machine learning training.The initial results of this effort are published in a recent preprint [147].An architecture called point net ensemble is used for the regression. This isbased on the point net model which is commonly used for object classifica-tion from a three-dimensional point cloud; our novel architecture is trainedfor regression instead of classification, and combines an ensemble of similarmodels for enhanced accuracy.The project, called the point net ensemble for annihilation reconstruction(PEAR), has successfully learned the z position of the vertex for simulatedannihilations. This method already demonstrates more precise annihilationvertex positions with a lower fail rate compared to the helix fit method de-scribed in this chapter. The z position resolution on simulation7 is compared7It should be emphasized that this method was trained and benchmarked using simu-lated TPC data; a discussion of the TPC simulation is outside the scope of this disserta-tion. The helix fit method yields an improved vertex resolution when applied to simulationcompared to real data, the reason for which is still under investigation.1045.5. Future work: machine learning vertex findingFigure 5.17: Performance of machine learning PEAR vertex finder, comparedto the helix fit method of this chapter. Left: Simulated vs PEAR annihilationz position. Right: Residuals for PEAR and helix fit method, fit with a doubleGaussian. Taken from [147].to that of the helix fit method in Figure 5.17, showing a full-with at half-maximum (FWHM) of 6.6mm compared to the 14mm FWHM of the helixfit method. If the reconstruction of the vertex (x, y) position is equally suc-cessful, and if PEAR performs equally well on real data as on simulation,then the machine-learning based vertex finder should be implemented along-side the algorithmic approach in the upcoming years.1055.5. Future work: machine learning vertex findingTable 5.4: Comparison of analysis performance across historical snapshots atthree times: the original pre-2022 analysis, the analysis used for the gravitypaper, and the current improved analysis. Values are averaged over 2 hoursof cosmic ray (µÂ±) data and 50 1 s antihydrogen (H) formation periods (seeSection 3.5.3). Spacepoints indicates the average number of spacepoints inan event, and (in tracks) indicates how many of these were use by the trackfinding algorithm. Tracks indicates the average number of tracks found, (fitsuccessfully) indicates how many of these had helix fits which converged,and (pass selection) indicates how many of these helices passed the selectioncriteria for use in vertex fitting. RT /Ndof and RZ/Ndof indicate the averagetransverse and axial goodness of fit for each track. % vertices fit indicatesthe percent of events for which a vertex position was successfully found.Candidate helices indicates the average number of helices available for use insuccessfully fit vertices, and used helices indicates how many of those wereactually included in the vertex fit.AnnihilationsMetric Original Gravity paper ImprovedSpacepoints 327.1 297.7 298.4(in tracks) 99.1 115.5 211.4Tracks 5.05 3.40 5.55(fit successfully) 4.30 3.06 5.39(pass selection) 4.30 3.06 2.35RT /Ndof 9.41 9.09 4.75RZ/Ndof 57.18 11.63 7.64% vertices fit 85.77 85.81 66.96Candidate helices 4.87 3.43 2.96Used helices 4.87 2.00 2.62Cosmic raysMetric Original Gravity paper ImprovedSpacepoints 196.5 180.8 182.3(in tracks) 54.7 41.9 137.2Tracks 2.65 1.48 1.86(fit successfully) 1.87 0.83 1.49(pass selection) 1.87 0.83 0.60RT /Ndof 3.98 3.80 3.34RZ/Ndof 55.51 8.51 6.43% vertices fit 55.09 31.98 14.9Candidate helices 3.23 2.06 2.01Used helices 3.23 2.00 2.01106Chapter 6Barrel scintillatorcommissioning and dataprocessingThe primary project of this dissertation is the commissioning of the barrelscintillator (BSC) detector which is described in Section 4.3. The BSC andassociated detector electronics were developed at TRIUMF by other collab-orators prior to the start of this work. However, minimal testing had beenperformed beyond a precursory inspection of the waveforms recorded by theDAQ.Over the course of this dissertation work, I was responsible for the com-missioning of the BSC hardware, as well as the implementation of the low-level data processing routine analogous to the TPC reconstruction algorithmdescribed in the previous chapter. These two tasks were strongly intertwined,and were performed simultaneously; as the data processing was implemented,this often revealed underlying hardware problems, and vice versa. This workultimately resulted in the successful implementation of time-of-flight mea-surement using the BSC, which was used to significantly enhance the rejec-tion of the cosmic ray background (discussed in Chapter 8).The hardware commissioning included a variety of tasks such as:1. Diagnosing and solving problems leading to dead or poorly-performingchannels for the ADC and TDC digitizers.2. Replacing malfunctioning detector electronics components.3. Determining optimal values for the SiPM bias voltage, ADC and TDCdigitizer threshold voltages, and TDC timing window.4. Evaluating the in-situ temperature dependence of the SiPMs.5. Evaluating the z position resolution along each bar using cosmic raycoincidence with two external scintillator panels.107Chapter 6. Barrel scintillator commissioning and data processingFigure 6.1: The stages of analysis for the BSC and TPC data.The BSC data processing and event reconstruction is performed in thesame alphasoft framework as the TPC analysis. BSC reconstruction modulesare interleaved with the TPC modules, as the two analyses are interdepen-dent. However, while the TPC analysis was in place and functional before myrevisions, the BSC analysis was entirely my own design and implementation.There are two data sources corresponding to each scintillation event in abar of the BSC: the waveforms recorded by the ADC, and hit time data fromthe TDC. The data acquisition system and MIDAS event builder describedin Section 4.4 groups these data into events based on their timestamp.The data processing and event reconstruction procedure is illustratedin Figure 6.1. Each step is handled by an individual module in the alpha-soft analysis. The data processing begins by extracting ADC hits from theADC waveforms (Section 6.1), and TDC hits from the TDC data packets(Section 6.2). These hits are then matched together to form end hits, cor-responding to a single SiPM-array signal with both waveform and timinginformation (Section 6.3). Pairs of end hits from opposite ends of the samebar are combined into bar hits, which contain all the information from asingle scintillation event (Section 6.4), including a calculated scintillation zposition along the bar (Section 6.5). These bar hits are then matched tocorresponding charged particle tracks in the TPC (Section 6.6). Finally, barhits are grouped into clusters (Section 6.7), and the time-of-flight (TOF)between pairs of bar hits is calculated (Section 6.8). These data structuresare saved in the output ROOT file alongside the vertex information from theTPC, for use in higher level physics analyses.This section will further discuss the integration of the BSC into the event1086.1. ADC waveform signal processingdisplay (Section 6.9). A description of the online quality of data checks forthe BSC will be reserved for Appendix B, and an investigation into pileupevents using the BSC is given in Appendix C.This section will present the data processing for the BSC detector inconsiderable detail. If the reader is not excited to learn about the signalprocessing and hit matching algorithms employed to extract hit bar clustersand time-of-flight measurements from the the BSC data, they should feelfree to skip this chapter entirely without loss of continuity.6.1 ADC waveform signal processingThe first task in BSC event reconstruction is to examine each ADC waveformto determine whether a hit occurred and, if so, to extract the amplitude ofthe SiPM signal. A hit finding algorithm is used which does not rely onany pre-programmed threshold value, instead analyzing the electronic noiseand continually updating hit thresholds for each channel. To address ADCsaturation which occasionally produces truncated waveforms, a waveformfitting procedure is implemented. Examples of fitted ADC waveforms areshown in Figures 6.2 and 6.3.6.1.1 Hit findingUnlike the TPC anode wire or cathode pad signals, it is rare for multiplehits to occur within a single ADC waveform. Since the width of one binin the ADC waveform is 10 ns, much larger than the charged particle traveltime across the BSC, it is not possible to resolve two pions from the sameannihilation striking the same bar. As a result, a waveform with two distinctsignals only occurs via the coincidence of multiple cosmic rays or antihydro-gen annihilations within the 7µs ADC window. Since this will still occur,albeit rarely, our waveform analysis should be designed to handle this case.The analysis begins with baseline subtraction. The first 100 samples(1 µs) of the waveform are before the trigger, and so are assumed to containno signal. The baseline is estimated as the mean of the first 100 samples,and subtracted from all samples.8The simplest technique to find a signal in the ADC waveform, which wasinitially tested, uses a predefined threshold level. A hit is declared when the8After the end of the SiPM signal, once it returns below a programmable data sup-pression threshold, the ADC firmware does not send any further samples to MIDAS in aneffort to lower the data rate. The MIDAS event builder populates the remainder of thewaveform with a constant value based on a similar baseline calculation.1096.1. ADC waveform signal processingFigure 6.2: An unsaturated ADC waveform. The x-axis is time in 10 nsbins, and the y-axis is voltage in ADC units. The red indicates a fit withthe skewed Gaussian of Equation 6.1.1. Data suppression at the DAQ levelhas zeroed all samples after 280.Figure 6.3: A saturated ADC waveform, fit with the skewed Gaussian fromEquation 6.1.1. The waveform saturation is visible as the data (blue) flat-tening at y = 32768.1106.1. ADC waveform signal processingwaveform crosses the threshold, and ended when it falls back below. Thethresholds were set on a per-channel basis, and regularly recalculated withthreshold scans. However, this approach invariably led to missed hits: eventswhere the SiPM signal would trigger the TDC comparator, but would notexceed the predefined ADC threshold.To find as many ADC hits as possible, a dynamic hit finding algo-rithm was adapted from the ALPHA-2 SVD calibration approach, whereper-channel hit thresholds are recomputed for each run in an ADC calibra-tion routine:1. The electronic noise level of each waveform is estimated by the standarddeviation Ï of the first 100 samples (the samples also used to computethe baseline).2. A level-one threshold is set at +5Ï. Hits are saved whenever the wave-form crosses this threshold. This threshold is recomputed for everywaveform.3. The amplitude of the hit is defined as the maximum baseline-subtractedvalue within the hit window, i.e. while the waveform stays above thelevel-one threshold.4. A level-two threshold for each channel is read from a precalculatedADC calibration file. If the amplitude of the hit is above this threshold,the hit is marked as good for analysis.The computation of the level-two thresholds is handled by a separateADC calibration routine, which is combined with the TDC calibration rou-tine which will be described in Chapter 7. This calibration routine is per-formed automatically at the end of each run. In online analysis, the calibra-tion file from the last run is used; otherwise, the calibration file from the runof interest can be used.The ADC calibration routine takes advantage of electronic noise crossingthe level-one threshold:1. A histogram of hit amplitude is built for each channel, as shown inFigure 6.4.2. The hits due to electronic noise, those with low amplitude, are fit witha Gaussian.3. The level-two threshold is set to µ+ 5Ï using the Gaussian fit param-eters.1116.1. ADC waveform signal processingFigure 6.4: The baseline-subtracted amplitude of all ADC hits. The elec-tronic noise portion is fit with a Gaussian, and only hits with amplitudegreater than µ + 5Ï (the level-two threshold indicated by the dashed greenline) are used in the analysis.In this way, the hit thresholds are dynamically adjusted after each run.Accurately setting these thresholds is important to avoid missing the smallestSiPM signals, typically those from scintillations far from the bar end, wheremost of the scintillation photons have been attenuated.6.1.2 Waveform fittingThe primary motivation for full digitization of the SiPM waveforms is to ex-tract their amplitude. This is useful for estimating the number of scintillationphotons produced, as well as for correcting the time walk effect on TDC timemeasurements, which will be covered in Chapter 7. For most ADC hits, itis adequate to use the simple amplitude defined as the maximum minus thebaseline.However, a complication is presented by waveform saturation. The ADChas a fixed dynamic range, with a maximum voltage of 1V corresponding toa maximum ADC value of 32768. This maximum was chosen to exceed mostSiPM signals sizes; the 16-bit values represent a trade-off between digitizercost, data size, and precision. When the true signal exceeds this threshold,such as when a scintillation occurs close to the SiPM, the waveform is trun-1126.2. TDC event extractioncated at the maximum value, producing a flat top. In this case, the size ofthe SiPM signal is no longer measurable as the maximum minus the baseline.There are many approaches to recover an approximate signal amplitude.A common method is to find the length of the flat top; assuming all sig-nals share the same general shape, this can be used to calculate the signalheight. Instead, the approach chosen for the BSC was to fit the waveform.A skewed Gaussian function was chosen empirically as it gives a good fit tothe waveforms. The fit function is similar to a Gaussian, with an additionalparameter k which introduces an asymmetry:f(x) =ï£±ï£²ï£³A · eâ 12(xâµÏ )2x > µA · eâ12(xâµÏâk(µâx))2x < µ(6.1.1)The fit is applied to the waveform within the hit, i.e. where it is abovethe level-one threshold. Bins are weighted uniformly, except for saturatedbins, which are assigned zero weight to exclude them from the fit. Theamplitude of the waveform is then defined as the fit parameter A (afterbaseline subtraction).This procedure was validated on both saturated and unsaturated wave-forms. Figure 6.2 shows an unsaturated waveform fit, while Figure 6.3 illus-trates the recovery of an amplitude from a saturated waveform. In typicaloperation, only the saturated waveforms are fit.In future work, alternative methods for recovering the amplitude fromsaturated waveforms could be explored. If the waveforms are shown to havea sufficiently uniform shape, a template function could be found. This couldeither be used to fit the waveforms directly, or used to calculate the relation-ship between the amplitude and the length of the flat top. However, this isnot a priority; the primary use for the hit amplitude is in correcting for thetime walk effect, which is strongest for small signals which do not requirefitting.6.2 TDC event extractionThe TRB3 TDC records time information using three counters with integervalues, described in the TRB3 manual [139]:â¢ The coarse time counter tracks the number of 200MHz clock cycles.It is stored in 11 bits, corresponding to a range of 10.24 µs.1136.2. TDC event extractionâ¢ The 28-bit epoch counter increments each time the coarse counteroverflows, extending the time range to approximately 45 minutes.â¢ The fine time counter resolves time within a single 5 ns clock cycle.It indicates the number of elements traversed in the FPGA delay line.There are two methods to calculate precise hit times from these counters.The first uses a fine time linearity approximation, while the second requiresprecision calibration.6.2.1 Fine time using linearity approximationRecall from the discussion in Section 4.4.2 that TDC signals propagatethrough a series of FGPA delay elements; the number of delay elementstraversed by a signal at the start of the next clock cycle is recorded in thefine time counter. The first method to extract the fine time uses the ap-proximation that each FPGA delay element in the TDC has the same signalpropagation time. This results in a fine counter which increases linearly withtime. The overall hit time can be calculated as:tTDC = toverflow + tepoch + tcoarse + tfine=[(228 · 211 Â·Noverflow)+(211 · cepoch)+(ccoarse)+(cfine âmM âm)] · 5ns(6.2.1)Here, Noverflow is the number of epoch counter resets, which must betracked by the data processing module for runs longer than 45 minutes.cepoch, ccoarse, and cfine are the respective counter values, and m and M arethe minimum and maximum fine time counter values. These limits must bedetermined via calibration for each channel.This method is simple to implement, and correct to within 100 ps, withtypical systematic errors of around 20 ps on most channels. This is an ac-ceptable precision for TOF measurements in the BSC; as we shall see inSection 6.8, the final TOF resolution is around 325 ps, and so using thelinear approximation does not limit the TOF resolution. This method isavailable as an alternative in cases where the more precise calibration is notavailable.6.2.2 Fine time using delay element calibrationFor the highest precision TDC timing, we instead approximate the true prop-agation time of the individual delay elements. This is done statistically, using1146.2. TDC event extraction0 50 100 150 200 250 300 350 400 4500200400600800Fine CounterCountsFigure 6.5: Histogram of fine time counter values for one TDC channel,used to determine propagation times for each delay element. Credit: DanielDuque.a large sample of randomly distributed data such as SiPM signals from cos-mic rays. When the clock signal arrives and the delay line is checked, theprobability of the signal currently propagating through a given delay elementis proportional to the propagation time of that delay element. A histogramof the fine time counter values can then be used to determine the time ofeach delay element, shown in Figure 6.5. The propagation time âti of eachelement is computed from the counts ci in the corresponding bin as:âti =ciâj cj· 5ns (6.2.2)The propagation times for each delay element for each channel are savedin a lookup table. During event reconstruction, the final tfine term in Equa-tion 6.2.1 is replaced by a fine time calculated from the lookup table âtivalues of all preceding delay elements:tfine(cfine) =âi<cfineâti (6.2.3)This calibration is repeated approximately yearly to account for drift in delayelement behaviour or degradation of the TDC. A standalone calibration algo-rithm which populates the fine counter histogram and generates the lookuptable was written by PhD student Daniel Duque.1156.2. TDC event extraction6.2.3 TDC time correctionsAfter calculating the TDC hit time, two additional corrections are applied todetermine the accurate arrival time of the first photon at the SiPM. Thesecorrections rely on careful calibration; Chapter 7 will describe the TDCcalibration algorithms used to determine their values.The first correction is a constant, channel-dependent offset. These timedelays could be caused by variations in signal path length, although in oursystem they are dominated by internal delays within the TRB3 TDC hard-ware itself.The second is an amplitude-dependent correction known as the time walkcorrection. Recall that the digital signal fed to the TDC is generated whenthe SiPM voltage crosses a fixed reference voltage. For two pulses of identicalshape but different amplitudes, the larger amplitude pulse will cross thethreshold first, introducing a timing bias known as time walk.Consider a pulse with a quadratic rising edge, which is a good approxi-mation for our SiPM signals: f(t) = A · (t â t0)2. We can analytically findthe time t1 where this rising edge crosses a constant threshold value B, inorder to recover the true pulse start time t0:f(t1) = A · (t1 â t0)2 = B=â t0 = t1 ââBA(6.2.4)This is the primary reason for full ADC waveform digitization: we applya correction for this effect based on the amplitude of the signal measuredby the ADC. This correction has the form ât =âB/A, where A is thesignal amplitude, and B is the threshold value. The threshold values foreach channel are determined using a calibration procedure which will bedescribed in Chapter 7.Including both the channel dependent time offset δ and the time walkcorrectionâB/A, the final hit time used for reconstruction is derived fromthe hit time reported by the TDC as:t = tTDC + δ ââBA(6.2.5)Both of these corrections are on the order of ns, comparable to or largerthan the measured TOF values themselves. As a result, they are crucialto the successful operation of the BSC as a timing detector. These timecorrections will be explored further in Chapter 7.1166.3. ADC-TDC matching6.2.4 Cable reflectionsThe transmission boards which receive the TDC signals (see Appendix A)include a design flaw where the differential signal lines are improperly ter-minated. This causes a reflection of the signal, which generates repeatedTDC hits approximately 165 ns after the initial signal. Although there wasdiscussion on modifying the transmission boards with proper termination,ultimately it was decided to address these cable reflections in software.A final stage of TDC data processing identifies and removes these re-flected hits. Any TDC hit occurring between 160 ns and 170 ns after a pre-vious TDC hit on the same channel is marked as a reflection, and excludedfrom further analysis.6.3 ADC-TDC matchingThe next stage of the event reconstruction aims to match ADC hits withTDC hits. A pair consisting of one ADC hit and one TDC hit is combinedinto a bar end hit, which contains complete information from a single SiPMsignal on one end of a bar. This ADC-TDC matching is performed beforeapplying the time walk correction described in the previous section.Since the data acquisition system compiles events based on timestamp,ADC and TDC hits can usually be matched based on channel number alone,using a known channel mapping. However, to handle cases where multiplehits occur on the same channel within a single readout window, a timing-based matching is also performed.The ADC hit time is defined as the first sample in the waveform thatcrosses the level-one threshold (see Section 6.1), and is relative to the eventtrigger. In contrast, the TDC time is absolute: it is measured relative to thestart of the run. Therefore, the key task in this time-based matching schemeis to estimate the time of the event trigger ttrig relative to the start of therun, so that ADC and TDC times can be compared.For each pair of ADC and TDC hits on matching channels, we define acandidate trigger time ttrigi as the difference between the ADC and TDC hittimes:ttrigi = tTDCi â tADCi (6.3.1)If both hits are from same SiPM signal, ttrigi should approximate the trueevent trigger time. A time residual ϵ for each other pair of ADC and TDChits can be calculated using this candidate trigger time:1176.4. Bar end matchingϵ = (tTDC â ttrigi )â tADC (6.3.2)The candidate trigger time ttrigi which minimizes these residuals over allpairs of hits is selected as the final trigger time ttrig.If there are multiple ADC or TDC hits on the same channel, the timeresidual ϵ for each pair of ADC and TDC hits is calculated as above, usingthe final ttrig. Each ADC hit is matched to the TDC hit which yields thesmallest time residual ϵ. Hits are not reused; a TDC hit matched to one ADChit cannot later be matched to a different ADC hit. If there are multipleADC hits in the same channel, they are matched in order of ADC amplitude,so that the larger signals are prioritized. Furthermore, ADC and TDC hitsare only paired if ϵ < 1µs.6.4 Bar end matchingOnce ADC and TDC hits have been combined into end hits, the next stepis to combine two hits on opposite ends of the same bar into bar hits. Eachbar hit represents the detection of scintillation light in a BSC bar resultingfrom a single charged particle interaction.Ideally, each bar hit contains ADC and TDC data from both ends ofthe bar. However, in practice, some data may be missing. This can becaused by hardware issues such as a dead ADC or TDC channel9, by photonattenuation if the scintillation light is fully absorbed before reaching one endof the bar, or by differing thresholds between the ADC and TDC.To account for this, we define different categories of bar hits. A completebar hit has ADC and TDC data from both ends. We also define eight typesof incomplete bar hits, depending on which data is missing from the bar hit.Hits where one end of the bar has both ADC and TDC data are consideredhalf-complete; these are used later in clustering.The definition of these hit types, as well as their relative frequencies, aresummarized in Table 6.1. The frequencies are calculated for cosmic ray data.The probability and type of observed incomplete bar hits is correlated to thehit position along the bar. Since the distribution of cosmic ray hits is roughlyuniform along the length of the bar, the listed frequencies approximate anaverage over the length of the bar.In most cases, each bar end has no more than one end hit. Matchingthe top and bottom end hits to create bar hits can then be done trivially9For the 2023 gravity paper, there were four fully dead (ADC and TDC) bar ends dueto a lack of bias voltage, and one further dead TDC channel.1186.4. Bar end matchingType ADC 1 TDC 1 ADC 2 TDC 2 Frequency (%)1 â â â â 61.8± 0.62 â â · â 2.63± 0.093 â â â · 8.5± 0.24 â â · · 10.9± 0.25 · â · â 1.24± 0.066 · â â · 0.21± 0.027 â · â · 0.41± 0.038 · â · · 3.3± 0.19 â · · · 11.0± 0.2Table 6.1: The definition of the nine bar hit types, depending on the presenceof ADC and TDC data, and their relative frequencies in cosmic ray data.The columns ADC 1 and TDC 1 refer to one end hit on either the top orbottom of a bar, while ADC 2 and TDC 2 refer to the end hit on the oppositeend. Type 1 (green) represents a complete bar hit, while types 2â4 (yellow)are half-complete. The remaining types (red) are denoted incomplete.using the channel mapping. However, as in the ADC-TDC matching step,this process should be robust to multiple hits on the same bar during asingle readout window. For this reason, a timing-based matching procedureis implemented. The bar hits are created through the following procedure,applied to each bar in turn:1. Identify the top and bottom end hits which have the smallest TDCtime difference. If the difference is less than 1µs, combine these into atype 1 (complete) bar hit.2. Repeat this process with remaining unpaired end hits to form addi-tional type 1 bar hits.3. After all type 1 bar hits have been formed, attempt to create type 2bar hits by matching remaining end hits with an unpaired TDC hit onthe opposite end.4. Once all type 2 bar hits are formed, repeat this for bar hits of type 3,and so on for the other bar hit types, in order of decreasing complete-ness.Only complete or half-complete bar hits are used for clustering, and onlycomplete bar hits are used for TOF calculation. All types of bar hits are1196.5. Bar hit z calculationsaved for use in event visualization and machine learning event classification.Further work is required to recover the timing of incomplete bar hits for usein TOF analysis.6.5 Bar hit z calculationAt this stage, the z position of each bar hit, i.e. the point where scintillationlight was produced, can be calculated. As discussed in Section 4.3.4, there aretwo available methods: charge division and time difference. Both methodsare implemented and recorded, but only zTDC calculated using the TDC timedifference is used in the subsequent analysis. The zADC from ADC chargedivision is recorded in each event for future studies.The zTDC position is calculated as:zTDC =veff2(tbot â ttop) (6.5.1)Here, ttop and tbot are the TDC times described in Section 6.2, includingchannel offset and time walk corrections. The parameter veff â¼ 0.53c isthe effective speed of light propagation through the scintillator, which isdetermined in the TDC calibration routine discussed in Chapter 7.The zADC coordinate is calculated using the charge division method as:zADC =λ2lnAtopAbot+ z0 (6.5.2)Here, Atop and Atop are the ADC pulse amplitudes for the top and bottomSiPM signals, described in Section 6.1. The parameter λ is the photon atten-uation length in the scintillator, including both bulk and surface absorption,and z0 is the position where a scintillation creates equal top and bottomsignal amplitudes.The values of these parameters are determined in the ADC calibrationroutine, which is performed alongside the TDC calibration routine of Chap-ter 7. As shown in Figure 6.6, the zTDC is plotted against 12 lnAtopAbotfor eachbar, and the slope and y-intercept of a linear fit yield λ and z0 respectively.This is performed individually for each bar, with typical values of z0 â¼ 0.2mand λ â¼ 0.9m. These parameters vary between bars by up to 20%.One notable feature of this plot is the apparent kink at x â â0.2, sug-gesting a change in slope of around 30% in some bars. This indicates aninconsistency between the two z reconstruction methods. The origin of thisdiscrepancy remains unresolved. However, a comparison between zTDC andthe zTPC of matched TPC tracks showed good agreement, while zADC was1206.6. BSC-TPC matchingFigure 6.6: zTDC plotted against 12 lnAtopAbotfor one bar in cosmic ray data.The red line indicates a linear fit, the parameters of which are used to set λand z0 in Equation 6.5.2. The colour scale denotes counts per bin.systematically inconsistent with both. For this reason, only zTDC is used insubsequent analysis.6.6 BSC-TPC matchingThe next stage of the event reconstruction matches bar hits in the barrelscintillator (BSC) to helices reconstructed in the time projection chamber(TPC). The BSC has full azimuthal coverage of the TPC, with gaps onlyat the top and the bottom of the detector. As such, nearly every chargedparticle that produces an ionization track in the TPC is also expected todeposit energy in the BSC and generate scintillation light.Until this point, the BSC and TPC event reconstruction routines havebeen entirely independent. The BSC-TPC matching is the first stage wheredata from the two detectors is combined. This analysis module is placedafter the helix fitting and track joining modules, so that the final helicesare available. However, it precedes the vertex fitting module. This orderingenables exclusion of unmatched helices from the vertex fit, to reduce con-tamination from poorly reconstructed tracks. Although this approach hasbeen tested, it did not yield immediate improvements, and so the technique1216.7. Bar cluster formationis not adopted in the current analysis.Each bar hit is matched to the closest helix, with multiple bar hits al-lowed to be associated with the same helix. This design is compatible withobservations made using the event display, where a single charged particleoften produces bar hits on multiple neighbouring bars. Furthermore, onlycomplete bar hits are used in matching, although this constraint could berelaxed in the future.The matching for a given bar hit proceeds as follows:1. The closest point on each helix to the bar hit is found, using the barhit zTDC from the TDC time difference method.2. The transverse (xây) distance between the bar and this point on eachhelix is calculated.3. The bar hit is matched to the helix with the smallest transverse dis-tance, provided the separation in Ï between the bar centre and thehelix point is smaller than 17.2â¦, approximately the angular width ofthree bars.This is a robust procedure which results in 84.7± 0.7 % of complete barhits being successfully matched to a TPC helix. The matching performanceis illustrated in Figure 6.7. The residual Ï between the bar and the matchedhelix has a full width at half maximum (FWHM) of roughly 5.5â¦, comparableto the angular width of one bar (5.625â¦). The residual in z has a FWHM ofroughly 12 cm. This can be taken as an indication of the z position resolutionof the BSC using the time difference method. While far worse than that ofspacepoints in the TPC, this resolution matches design expectations, and ismore than sufficient for validating hit matching between the two detectors.6.7 Bar cluster formationSince a charged particle can produce bar hits on multiple neighbouring bars,the next event reconstruction stage groups bar hits into clusters. These extrabar hits are most commonly produced by charged particles with a sharpangle of incidence to the BSC, which directly pass through multiple bars.However, secondary particles are occasionally produced inside the bars or insurrounding material, leading to additional neighbouring bar hits. Clusteringaims to group together all bar hits from a single initial particle, helping tosimplify events and create a higher level of abstraction.1226.7. Bar cluster formationFigure 6.7: Left: Ï residuals between bar hits and matched TPC helices, fitwith a double Gaussian function. Angular units are converted to bars (1 bar= 5.625â¦). Right: z residuals between bar hits and matched TPC helices, fitwith a double Gaussian function.The main motivation for implementing bar hit clustering was to optimizethe identification of cosmic ray background events. There are typically morecharged particle tracks in an annihilation, and so the number of bar hits canbe used to distinguish these events. However, the number of bar hit clustersis a far more powerful discriminator. Since cosmic rays often strike the BSCat an angle, they are more likely to create bar hits on multiple neighbouringbars. On the other hand, pions produced by annihilations have a mostlyradial trajectory, and so mostly strike only a single bar.Clusters are formed by grouping together all bar hits on contiguous neigh-bouring bars. A key design decision was the choice of which bar hit types toinclude in clustering. Including all nine bar hit types increases the numberof clusters but introduces significant noise. Using only complete bar hits iscleaner but omits useful information. The final choice was to include onlycomplete or half-complete bar hits, balancing data quality with granularity inthe number and size of clusters. A comparison of these clustering strategiesis shown in Figure 6.8.In the real-time online event reconstruction described in Section 5.1, acut on the number of clusters is used to classify events and reject verticescaused by the cosmic ray background. A comparison of the performance ofthis discriminator with different cluster definitions is given in Table 6.2.1236.7. Bar cluster formationFigure 6.8: Number of clusters per annihilation (a.) or cosmic ray (b.) event.Shaded (grey) is current definition of a cluster, using only complete or half-complete bar hits. Red and blue lines indicate other possible definitions,using all bar hits (red) or only complete bar hits (blue).All Bar Hits Half-Complete CompleteNumber of clusters to pass cut >= 4 >= 4 >= 3Annihilations passing cut 87.3% 72.7% 76.1%Cosmic rays failing cut 89.3% 97.1% 93.5%Cosmic ray pass cut rate 0.73 Hz 0.20 Hz 0.44 HzTable 6.2: Comparison of the performance of the online BSC cluster-basedclassifier with different cluster definitions. The half-complete bar hit clustercut is currently used in online analysis.1246.8. Time-of-flight calculation6.8 Time-of-flight calculationThe final stage of the BSC event reconstruction is the calculation of time-of-flight (TOF) between pairs of bar hits. As described in Section 4.3.4, thetime of a single bar hit is calculated from the TDC times at both ends ofthe bar:t0 =ttop + tbot2â L2veff(6.8.1)Here, ttop and tbot are the TDC times including the channel offset andtime walk corrections described in Section 6.2. L refers to the bar length of2.604m. Although each bar has its own calibrated effective speed of lightveff,i for z reconstruction, a single average value is used for all bars in thistiming calculation. This approximation was verified to have a minimal effecton the resulting TOF resolution.The TOF between two bar hits is calculated by taking the differencebetween their reconstructed hit times:TOF2,1 = t2 â t1 = ttop2 + tbot22â ttop1 + tbot12(6.8.2)Note that the second term in Equation 6.8.1 cancels out in this subtraction,due to our approximation of equal veff across all bars.For cosmic rays travelling between two bars, the TOF is set by the dis-tance D between the two bar hits and the speed of the cosmic ray. The meanenergy of a cosmic ray muon at the surface is 4GeV [148], corresponding toa relativistic speed of β = 0.9997. With the approximation that all cosmicrays travel at the speed of light c, we define an expected TOF as:TOFexp =Dc(6.8.3)The expected TOF of cosmic rays is used to benchmark the timing perfor-mance of the BSC. Figure 6.9 compares the expected TOF to the measuredTOF in cosmic ray events. Two populations are visible: a large-TOF groupcorresponding to muons passing entirely through the BSC, and a small-TOFgroup due to hits on neighbouring bars. The population separation is dueto the trigger condition, which selects only cosmic rays passing through theTPC as well as the BSC.The residual TOF, defined as the difference between the measured andexpected TOF, is plotted in Figure 6.10. The width of the residual TOF dis-tribution is used to characterize the detector resolution. A double-Gaussian1256.8. Time-of-flight calculationFigure 6.9: Measured vs expected TOF in cosmic ray data. In events withmore than two bar hits, the TOF of all pairs of bar hits is included. The signof the measured TOF is given by the assertion that the higher z position hitis the first one, which will be substantiated in Section 7.2.2.fit to the residual distribution shows that the inner Gaussian (82% of events)has a width of Ï = 325 ps, which is taken as an upper bound on the TOFresolution of the BSC. The outer Gaussian corresponds to more complicatedcosmic ray event topologies.In annihilation events, charged pions originate at the trap wall and travelradially outward. The time difference between two bar hits does not corre-spond to the time-of-flight of a physical particle. Instead, it represents aneffective TOF. This is typically small, since all pions travel similar distancesfrom the annihilation point to the bars, at similar velocities of around β = 0.8(for a pion with kinetic energy 100MeV). Thus the effective TOF will besmall; when compared to a cosmic rayâs expected TOF, these annihilationevents show large negative residuals. This difference is the key principle forTOF-based background rejection, which will be covered in Chapter 8.The two-dimensional distribution of measured (effective) TOF comparedto expected TOF is shown in Figure 6.11 for antiproton annihilations. Thekey feature of this plot is that events are far from the line TOF=TOFexp,indicating that TOF can be effectively used to distinguish between the an-nihilations and cosmic rays.Similarly to cosmic rays, this distribution contains two populations. Thefirst with TOFexp â¼ 0.1 ns corresponds to hits on neighbouring or nearby bars1266.9. Event display implementationFigure 6.10: The residual TOF, i.e. the diagonal projection of Figure 6.9.The histogram (black) shows the data, which is fit with a double Gaussian(red). The inner Gaussian (blue) contains 82% of the data by total integraland has Ï = 325 ps. The outer Gaussian (green) has Ï = 1.149 ns.caused by the same charged particle. The second population at TOFexp â¼1.5 ns corresponds to hits on opposite sides of the detector. Since annihilationevents are much less vertical than cosmic rays, with hits at nearby z positions,the spread in TOFexp is much smaller.Currently, TOF is calculated only for pairs of complete bar hits, i.e., thosewith both TDC times and ADC waveforms available. In future work, theanalysis could be extended to include the significant fraction of incompletebar hits. For example, if a signal is only recorded on one bar end, the hit timecould be inferred using the z position of a matched TPC track to estimatethe scintillation light travel time.6.9 Event display implementationThe development of the ALPHA-g event display was previously discussedin the context of the TPC reconstruction in Section 5.2. The BSC wasintegrated into the ALPHA-g event display to verify and demonstrate theeffectiveness of the BSC analysis. Bar hits are visualized as larger circlespositioned in the x-y plane at the centre of the corresponding bar, with their1276.9. Event display implementationFigure 6.11: Measured vs expected TOF in antiproton annihilation data.Note the change in x axis from Figure 6.9, as the hit ordering based on zposition can no longer be used to determine the sign of the TOF. The redline indicates the expectation TOF=TOFexp for cosmic rays.z position derived using the TDC time difference method. Only completebar hits are shown by default, with an option to show incomplete hits withan artificial z position. The event display is shown here in Figure 6.12, aswell as Figures 5.1 and 5.2.Several colouring options are available for bar hits. The default assignseach bar hit the same colour as the spacepoints of its matched TPC track,to visually verify track matching. Additional options include colouring byADC amplitude, TDC time, or by cluster, to demonstrate the cluster findingalgorithm. These colouring modes are useful for quickly verifying correctanalysis of a given event, and for quickly visualizing the event structure andtiming.Bar hits can be interactively selected by clicking, with an info panel dis-playing detailed information about the selected hit. Another panel10 showsthe ADC waveforms and TDC hit times for the selected hit, as shown in Fig-ure 6.13. A further panel displays the TDC timing for the selected bar hit,visually indicating the channel offset correction and time walk correction.10The event display uses a âdark modeâ by default, which is somewhat easier to interpret,but sadly unsuitable for print.1286.9. Event display implementationFigure 6.12: Event display of an antiproton annihilation. Large circles cor-respond to bar hits, while small dots correspond to TPC spacepoints. Thecolour of the spacepoints indicates the track finding, with blue indicatingthose not included in a track. The colour of the BSC hits is the same asthe colour of the matched TPC track. Two tracks with one matched bar hiteach are visible on the right of the image, and a single track is matched tothree bar hits in the centre.1296.9. Event display implementationFigure 6.13: BSC waveform panel showing ADC waveforms (green) and TDChit times (solid pink) from top and bottom of a selected bar hit. Also shownare the region above threshold (grey), the waveform fit in case of saturation(black), other TDC hits on the channel (dashed orange), and 165 ns cablereflections (dashed red) from Section 6.2.4. The x-axis is time in 10 ns bins,and the y-axis is voltage in ADC units.130Chapter 7Precision time calibrationsAs discussed in Section 6.2, there are two corrections which are appliedto SiPM signal start time measured by the TDC: individual channel timeoffsets, and the time walk correction. The form of these corrections is givenby Equation 6.2.5, repeated here:t = tTDC + δ ââBA(7.0.1)The meaning of these symbols, and the symbols which will be usedthroughout this chapter, are given in Table 7.1 for reference.These time corrections use correction constants δtopi , δboti and Btopi , Bbotifor each bar end which must be calibrated prior to running the alphasoftanalysis. Accurate calibration is essential to achieve the time resolutionnecessary for cosmic ray identification and rejection using the time-of-flight(TOF) method. Initial simulations [149] indicated that a time resolutionbetter than 500 ps is required for effective background suppression. Thechannel offset correction and time walk correction are each on the order ofmultiple ns, and so any attempt to measure TOF without first implementingthese corrections was futile.Traditional calibration methods, which are described in Section 7.1, werefound to be inapplicable due to the constraints of the ALPHA-g detector sys-tem. Instead, a novel calibration procedure was developed to meet the re-quirements. This procedure updates the values of these calibration constantsfor each run, based on the cosmic ray data recorded between antiproton in-jections to ALPHA-g. The calibration algorithm was designed to yield thebest possible time resolution, as well as to be robust and require minimummanual intervention.A schematic diagram of the calibration procedure is shown in Figure 7.1;the calibration steps will be discussed in the remainder of this chapter. Sec-tion 7.2 describes the determination of the time walk correction parametersBtopi and Bboti . Section 7.3 outlines the calibration of the bar hit z posi-tion. Section 7.4 details the calculation of the channel offsets δtopi and δboti .The specifics of the implementation of this algorithm into the ALPHA data131Chapter 7. Precision time calibrationsSymbol Description TypettopTDC,i,tbotTDC,iThe raw hit time measured by the TDC for a hiton the top or bottom for the iâth bar.MeasuredAtopi , AbotiThe ADC waveform amplitude of a hit the topor bottom of the iâth bar.Measuredttopi , tbotiThe hit time measured by the TDC for a hiton the top or bottom for the iâth bar, with thechannel offset and time walk corrections applied.Calculatedδtopi , δbotiThe channel offset time correction for the top orbottom of the iâth bar.CalibrationconstantBtopi , BbotiThe time walk correction parameter for the topor bottom of the iâth bar.Calibrationconstantveff,i The effective speed of photon propagation in theiâth bar.Calibrationconstantâbot-topiâbot-topi = δboti â δtopi â The difference betweenbottom and top channel offsets of the iâth bar.Intermediateδiδi = (δboti +δboti )/2âThe average of the bottomand top channel offsets of the iâth bar.Intermediateâi,jâi,j = δi â δj â The difference between theaverage offsets of the iâth and jâth bars.IntermediateTable 7.1: A description of the symbols used throughout this chapter. Sub-scripts and superscripts are dropped when the specific bar end or bar numberi is not relevant to the discussion. A distinction is drawn between quantitieswhich are directly measured or calculated in each event, constants whichmust be calibrated beforehand, and intermediate values used in the calcula-tion of these calibration constants.1327.1. Issues with traditional methodsFigure 7.1: Schematic diagram of the BSC calibration algorithm. The stepsleading to the calibration of channel time offsets and time walk correction arediscussed in this chapter, while the ADC calibration procedure is discussedin Sections 6.1 and 6.5.processing framework is reserved for Appendix D. This chapter will describethe calibration algorithm and methods in considerable detail, and can beskipped without loss of continuity.7.1 Issues with traditional methodsIn many particle physics experiments, channel offsets are determined using apulsed calibration source which generates simultaneous signals across manychannels. This source can take various forms, such as a laser calibrationsystem [150], low rate bunch crossings in collider experiments [151], or a testpulse injected directly into the readout electronics.For the BSC, the initial design aimed to use the test pulse generatordescribed in Section 4.4.3 to inject signals after the first stage of SiPM signalamplification. However, this approach encountered several issues.Firstly, the observed pulses in the ADC were too small for use in timingcalibration. In many channels the signal was below the readout threshold.Furthermore, smaller pulses are more susceptible to the time walk effect,and so amplitude variation between channels caused calibration pulse timevariation between channels which was difficult to quantify. The test pulse is1337.1. Issues with traditional methodsdifferentially coupled to the readout electronics, and so increasing the sizeof the response required a faster rise time in the injected signal. This wasachieved to a degree by introducing a fast external pulser.Secondly, the test pulse is distributed to each ASD board by interfacemodules called rear transmission modules (RTMs), described in Appendix A.Due to a design fault, these modules introduce significant noise into the ADCwaveforms when the test pulse distribution is enabled. Furthermore, thebehaviour of these modules was inconsistent: with a common input pulse,the output pulse distributed to the ASD boards differs significantly betweenmodules.A third issue is presented by the TRB3 TDC itself. The magnitude ofthe channel offsets observed in TDC data cannot be explained by differencesin signal path length alone. Instead, the channel offsets are dominated by in-ternal behaviour of the TDC. These channel offsets change significantly afterpower cycling of the TDC. Compounding this issue, the TDC was found tobe unstable during continuous operation, crashing frequently. These crashesare believed to be due to an unstable clock signal provided to the TDC fromthe CDM (see Section 4.4.3), which would require a significant hardwareupgrade to address. With each crash scrambling the internal TDC chan-nel offsets, any one-time or periodic calibration would be quickly renderedobsolete.Traditional time walk calibration methods also proved unfeasible. Thesetypically rely on events with a known initial time t0, such as calibrationtest pulses, or bunch crossing times in collider experiments. The signal timedelay δt = t â t0 is typically plotted against the pulse amplitude, and therelationship is parameterized, often using the ât =âB/A parametrizationfrom Section 6.2 [152â156].In ALPHA-g, with the calibration pulser deemed unreliable, there is nomechanism to generate events with a well-defined t0. Instead, events arespontaneous and self-timed, and so the traditional time walk calibrationmethod is not applicable. A laser-based calibration source could have beenconsidered in the initial BSC designs for in-situ calibration; however, signif-icant problems with the timing calibration were not foreseen, and so such asystem was not included.A further limitation is presented by the nature of the ALPHA-g exper-iment. Given the fast pace of work at ALPHA, any calibration procedurewhich takes operator time or requires specific data collection would not beideal. Such a procedure would be increasingly problematic if it is slow orrequires frequent repetition.With this in mind, cosmic rays were chosen as the source of calibration1347.2. Time walk correction calibrationdata. Cosmic ray data is already routinely collected, both in pure back-ground runs used to verify detector functionality, as well as between cyclesof antihydrogen formation. Cosmic ray detector signatures are simple andwell understood, as they travel at roughly the speed of light and strike typ-ically only two or three bars. The rate of cosmic ray events is sufficientlyhigh for timely collection of a good calibration dataset, and their uniformdistribution prevents any bias.7.2 Time walk correction calibrationThe first stage of the calibration algorithm determines the correction fortime walk, the effect where smaller SiPM signals will cross the fixed TDCthreshold later than larger signals of the same shape. As discussed in Sec-tion 7.1, this effect cannot be measured by directly comparing signal timeand amplitude, since the true hit time is unknown. However, we can stilluse the parametrization of the time walk effectât =âB/A (7.2.1)where ât is the time correction to be subtracted from a TDC hit time, A isthe pulse amplitude, and B is an effective threshold constant which must becalibrated using data.We use cosmic ray data to determine unique values of Btopi and Bboti forthe two ends of each of the 64 bars. These time walk correction parameterswill vary between bar ends based on a number of factors, such as SiPMbreakdown voltage and gain, coupling between the scintillator and SiPM,and readout electronics amplification and signal shape.7.2.1 Determining the time walk correction parametersThe time walk correction parameters are inferred from the cosmic ray data.A brute-force search of different values of Btopi and Bboti is used. For agiven set of B values, the TOF distribution of cosmic rays between twobars is calculated. The time walk correction parameters which lead to thenarrowest TOF distribution are chosen; this method ensures that the TOFresolution is minimized.The computation of Btopi and Bboti for a given bar i is performed usingcosmic rays interacting with bar i and one other specific bar. Usually, the bardirectly opposite (bar i±32) is chosen. This maximizes the available numberof cosmic rays passing through both bars, and provides good time separation1357.2. Time walk correction calibrationbetween the two hits. In the case where the readout of the opposite baris malfunctioning, the closest fully functioning bar is chosen instead. Thesample is further limited to events with three or fewer bar hit clusters, whichminimizes the interference of annihilation events11 or other events with morecomplicated topologies, such as scattering inside the detector.The TOF calculation on this sample of cosmic rays involves four param-eters: Btopi , Bboti , Btopi±32, and Bboti±32. To properly minimize the width of theTOF distribution, all four B values must be varied simultaneously. This isdone by a grid search, where 10 different values are tried for each B, fora total of 104 combinations. The combination yielding the smallest TOFdistribution width is chosen. The grid search is then repeated once, tryinga further 104 combinations, centred on the current best combination of Bvalues and with a smaller step size.The approach follows these steps:1. Apply a time walk correction ât =âBi/A to each bar end.2. For each cosmic ray, calculate the expected TOFexp = D/c based onthe distance between the bar hits, with z from the TDC time difference.3. Plot the residual TOF, i.e. after subtracting the expected TOF:TOFres = TOFâ TOFexp =ttopi±32 + tboti±322â ttopi + tboti2â Dc(7.2.2)4. Fit this distribution with a Gaussian and extract the width Ï.5. Repeat this for many different values ofBi, performing a four-dimensionalgrid search to vary the values of Bi individually for each bar end.6. Repeat this grid search once with a finer step size.7. Select the Bi values which minimize the width Ï of the residual TOFdistribution.Figure 7.2 shows an example of a residual TOF distribution before andafter applying the time walk correction, with the associated Gaussian fits.11The calibration procedure is designed to use pure cosmic ray data. However, themajority of cosmic rays collected during ALPHA-g data taking are not in dedicated cosmicray background runs, but between antihydrogen formation periods, while waiting to receiveantiprotons from ELENA. Low rates of antihydrogen annihilations on background gas arepossible during this time period, and so methods to exclude them are still helpful. Moreinformation on which time periods are used in long runs is given in Appendix D.1367.2. Time walk correction calibrationFigure 7.2: Residual TOF distribution from a bar to the opposite bar, withno time walk correction (left) and with the time walk correction parameterswhich minimize the distribution width (right). Both are fit with a Gaussian(red), with Ï improving from 582 ps to 283 ps.The Ï of these fits are plotted for each bar in Figure 7.3. Note that theresidual TOF distributions are not centred around zero; there is a large offset,due to the channel time offset between the two bars in question. However,this offset is constant for all events, and does not affect the width of theTOF distribution.7.2.2 Determining the direction of cosmic raysThe sample of cosmic ray events contains two distinct classes: cosmic raystravelling from bar i to bar i± 32, and cosmic rays travelling in the oppositedirection from bar i± 32 to bar i. These classes must be separated in orderto properly subtract the expected TOF. Due to the potentially large channeltime offsets shifting the TOF distribution away from zero, this cannot bedone using the sign of the TOF.Instead, we can identify the direction of the cosmic rays based on the zposition of each bar hit. Since cosmic ray muons are unable to penetrate theEarth, the flux of cosmic rays at the surface is highly directional. The angulardistribution of cosmic rays at the surface is approximately I(θ) â cos2 θ [148],where θ is the zenith angle, with no cosmic rays coming from below. Thus1377.3. Bar hit z position calibrationFigure 7.3: Ï parameters of TOFres fits, such as in Figure 7.2, for eachbar. White diamond indicates with no time walk correction applied, and redsquare indicates with the final choice of time walk correction parameters.we can use the vertical position of the hits to determine the direction of thecosmic ray: the hit with the higher z position must have occurred first. Thisphenomenon is shown in ALPHA-g data in Figure 7.4.The direction of the cosmic ray, and hence the sign of TOFexp, is deter-mined by the sign of âz. With the order of hits determined in this way,the residual TOF can be calculated properly and used to determine the timewalk correction parameters.Note that the alignment between the two directions of cosmic rays stillhas a small unexplained systematic shift, visible as a slight mis-alignment(around 0.5 ns) of the two populations in the right of Figure 7.4. For thisreason, the positive âz component was excluded. When determining thetime walk correction parameter for bar i, only cosmic rays hitting first bari and then bar i ± 32 were used. The cause of this shift requires furtherinvestigation.7.3 Bar hit z position calibrationSince no reference time is available, such as a precise annihilation time,we cannot measure absolute hit times. Instead, only the time differencebetween two SiPM signals can be measured; this limits our ability to directly1387.3. Bar hit z position calibrationFigure 7.4: Left: The TOF of cosmic rays between a given bar and itsopposite, plotted against the difference in hit z position. Note the linearcorrelation, where cosmic rays appearing to go upwards (positive âz) havenegative TOF, corresponding to an inverted hit ordering. Right: The resid-ual TOF after subtracting the expected TOF, plotted against the differencein hit z position. The sign of the TOFexp is determined by the sign of z.determine the individual channel offsets.There is one important time difference for which we have a good calibra-tion reference: the difference between the top and bottom of a bar, whichis proportional to the z position of the bar hit. The z position of matchedTPC tracks is used as an independent reference to calibrate this bar hit zposition.7.3.1 Determining âbot-top and veffRecall the calculation of z position from Equation 6.5.1, written here withthe channel offset corrections δ explicitly included:zTDC =veff2[(tbot â Î´bot)â (ttop â δtop)]=veff2(tbot â ttop ââbot-top) (7.3.1)Here, δtop and δbot represent the channel offset corrections for a givenbar, and âbot-top = δbot â δtop represents the offset difference between thetop and bottom of the bar.1397.3. Bar hit z position calibrationFigure 7.5: The TDC time difference between two ends of an individualbar, plotted against the z position of the matched TPC track. The red lineindicates a linear fit, whose parameters are used to define âbot-top and veff.The next stage of the calibration routine is to determine the offset differ-ence âbot-top for each bar. This is done using cosmic ray bar hits which weresuccessfully matched to TPC tracks. The relationship between tbotâttop andzTPC is plotted and fit with a line, shown in Figure 7.5. Setting zTDC = zTPCin Equation 7.3.1 allows us to extract the offset and effective speed of lightfor each bar from the fit parameters:veff =2slopeâbot-top = y-intercept(7.3.2)Typical values of âbot-top and veff are shown in Figures 7.6 and 7.7 respec-tively. The veff values are slightly lower than those expected based on thenominal index of refraction of 1.58 [132]. There is a range of path lengthstaken by photons to reach the SiPMs, depending on the number of reflections.This discrepancy in veff corresponds to a non-zero number of reflections forthe average photon reaching the SiPMs.This method takes advantage of the good matching between TPC tracksand BSC hits. It ensures that, to first order, there is no systematic biasin the z position of hits measured in the BSC compared to the TPC. It is1407.3. Bar hit z position calibrationFigure 7.6: Time offsets between the top and bottom of each bar, determinedvia linear fit (shown in Figure 7.5). Data is from October 26, 2024.Figure 7.7: Effective speed of photon propagation in each bar, determinedvia linear fit (shown in Figure 7.5).1417.3. Bar hit z position calibrationimportant to note that this step defines only the difference in channel offsetsâbot-top = δbot â δtop, which is used in the calculation of zTDC. It does notfix the sum of channel offsets δbot + δtop, which is the relevant quantity forcalculations of TOF. These channel offsets will be determined individuallyin a later step.7.3.2 Interplay between time walk correction and hit zpositionAs we have seen in Section 7.2, the bar hit z position is used in calibratingthe time walk correction. Thus the calibration of the bar hit z position mustcome before the calibration of the time walk correction. However, the hitz position calibration described in this section is highly impacted by anycorrection for the time walk effect.To understand this, consider the case where a large time walk correctionât is applied to only the bottom end of a bar. The calculation of zTDCfollowing Equation 7.3.1 is then shifted:zTDC =veff2[(tbot âât)â ttop ââbot-top]=veff2[tbot â ttop ââbot-top]âveff2ât(7.3.3)With this in mind, it should be clear that the calibration of âbot-topand veff should be done with the time walk effect properly corrected for.Ideally, the time walk correction would be calibrated first, and only thenwould âbot,top and veff be determined. However, since the z position is usedin the time walk calibration procedure, this is not possible. Instead, thecalibration of âbot-top and veff is repeated for each given set of time walkcorrection parameters Bi, before building the residual TOF distribution.Figure 7.6 shows typical values ofâbot-top with and without the time walkcorrection. There is an interesting systematic increase when the values arecalculated after the time walk correction is applied, corresponding to earliertop hit times. The SiPMs on the top of the detector have systematicallysmaller signals (see discussion in Appendix A), and hence later hit times dueto the time walk effect. Correcting for time walk thus makes the top hitsdisproportionately earlier, increasing the âbot-top values.Figure 7.7 shows typical values of veff with and without the time walkcorrection. These also exhibit a significant systematic increase when calcu-lated after the time walk correction is applied. To understand this, considera scintillation event near the top end of a bar. Many photons will quickly1427.4. Bar to bar offsetsreach the top SiPMs, resulting in quick signal with very little time walk ef-fect. Due to attenuation, fewer photons will reach the bottom SiPMs, andthose that do will arrive later due to the longer propagation distance. Thusthe bottom signal, which is already later, will be made even later by thetime walk effect. In this way, time walk has the effect of slowing down theapparent speed of photon propagation in the bar. It is expected, then, thatcorrecting for the time walk effect will increase veff.7.3.3 Summary of time walk and hit z position calibrationsFor a given bar i, 10 values of each time walk correction parameter Btopi ,Bboti , Btopi±32, and Bboti±32 were tried, in a grid search over 104 possible config-urations. For each configuration of B values, the calibration of âbot-topi andveff,i was performed first. Then, a residual TOF distribution was built up,using only cosmic rays hitting first bar i and then bar i ± 32, determinedusing their z position. This distribution was fit, and the width Ï of the dis-tribution was saved. The configuration with the smallest width was chosenas the best. A finer grid search of 104 more configurations is then performed,centred on those values. After this finer search, the best time walk correctionparameters Btopi and Bboti for bar i are saved, alongside the correspondingvalues of âbot-topi and veff,i.7.4 Bar to bar offsetsIn Section 7.3, we determined the difference between the offsets of the endsof the same bar, âbot-topi = δboti âÎ´topi . In this section, we will determine thevalue of each δboti and δtopi individually. This is done by decomposing eachoffset as follows:δboti =δboti + δtopi2+δboti â δtopi2= δi +âbot-topi2Î´topi =δboti + Î´topi2â δboti â δtopi2= δi â âbot-topi2(7.4.1)With no fixed reference time, we cannot measure the value of each δidirectly. We can, however, measure the difference between two channels toobtain âi,j = δi â δj . The approach taken is to extract these âi,j valuesfrom cosmic ray data, and then use them to determine the δi values, whichare finally used to determine the δtopi and δboti values.1437.4. Bar to bar offsetsFigure 7.8: Residual TOF distributions from bar 0 to bar 38 (left), and frombar 5 to bar 29 (right). Gaussian fits are used to extract the time offsetbetween the two bars.7.4.1 Determining time offsets between pairs of barsThe determination of the offset between a given pair of bars i and j isperformed using a similar method to the previous section. The residual TOFdistribution is built from cosmic rays hitting first bar i and then bar j, withthe order of hits determined using the hit z position. Since there are 64 bars,64Ã 63 = 4032 residual TOF distributions are populated simultaneously. Inevents with three or more bar hits, each combination of two hits is used.The same selection criteria as the previous section is applied: events mustcontain no more than three clusters of bar hits.The determination of the time offset âi,j between bars i and j proceedsas follows:1. Populate the residual TOF distribution using cosmic rays hitting firstbar i and then bar j (determined using hit z positions).2. Fit the residual TOF distribution with a Gaussian function.3. Set the offset to the mean of the Gaussian âi,j = µgaus.Examples of the residual TOF distributions between pairs of bars are shownin Figure 7.8, populated using 12.75 hours of cosmic ray data.1447.4. Bar to bar offsets7.4.2 Determining time offsets of individual barsAt this point, the time offset difference âi,j = δi â δj between most pairsof bars is known. The remaining step is to use these 4032 measured valuesof âi,j to determine the 64 individual channel offsets δi. These can then beused in Equation 7.4.1 to determine each δtopi and δboti .From our measurements of the differences âi,j , we can determine theindividual offsets δi as follows:âall jâi,j =âall j(δi â δj)= 64 · δi ââall jÎ´j=â δi =âall j âi,j64+âall j δj64(7.4.2)Note that here, the second term is a constant. Since only time differencescan be measured in the BSC, adding a constant time to every hit has noeffect. Thus the second term can be safely dropped, and the individualchannel offset δi can be found by averaging all the âi,j âs.While mathematically valid, this approach has some practical flaws. Itrequires successful measurement of all âi,j values, and quickly breaks downonce we introduce fit failures, malfunctioning bars, or low statistics. A morerobust approach is to relax the sum to include only a subset of bars. Whencalculating the offset δi for bar i, we define Gi to be the subset of bars j â Gifor which the difference âi,j was successfully measured. The calculation ofδi then becomes:âjâGiâi,j =âjâGi(Î´i â δj)= |Gi| · δi ââjâGiÎ´j=â δi =âjâGi âi,j|Gi| +âjâGi δj|Gi|(7.4.3)Here, |Gi| represents the size of Gi.Note that the second term is no longer constant, and so can no longerbe dropped from the calculation. As a result, the offset δi can no longer1457.4. Bar to bar offsetsFigure 7.9: Time offsets for each bar, measured on October 26, 2024. Errorbars are covered by the symbol.be calculated analytically. Instead, we have a system of 64 equations in 64unknowns (the δi values), which must be solved simultaneously numerically.An iterative approach is taken. The δi values from Equation 7.4.2 aretaken as starting values δ0i . These are then substituted into Equation 7.4.3alongside the âi,j values to find updated values δ1i . These updated valuesare then plugged into Equation 7.4.3 to find δ2i , and so on, following:δn+1i =âjâGi âi,j|Gi| +âjâGi δnj|Gi| (7.4.4)This is repeated for 50 iterations; in practice, fewer than 10 iterationsare required for convergence. The set of offsets δ50i are then taken as thefinal values of δi for each bar. These final offsets are plotted for each barin Figure 7.9. Note that there is not one unique solution to this systemof equations: since we can measure only time differences, a constant canbe added to every δi without affecting the measurements. This procedureconverges on a set of offsets with a mean of µ = 0.146Chapter 8Cosmic ray backgroundrejectionCosmic rays are a substantial background for the TPC detector, triggeringthe detector at a rate of 58Hz. Of these events, the reconstruction algorithmof Chapter 5 creates false annihilation vertices at a rate of 6.35Hz; this isimproved from 13.65Hz as a result of my work on the TPC track reconstruc-tion. This is problematic for physics measurements in ALPHA-g, as only asmall number (â¼ 20) of antihydrogen are created per experiment cycle. Thegeneral strategy to address this background is to record all events, and dis-tinguish between annihilations and cosmic ray background events afterwardsat the analysis stage.There are two methods used to reject the cosmic ray background inALPHA-g. The first is with the BSC cluster-based cut described in Sec-tion 6.7. This method is used primarily in the live online alphasoft recon-struction described in Section 5.1, so that annihilation vertices can be usedas a real-time diagnostic for antihydrogen production, with some straight-forward background rejection.The second method is using a machine-learning-based classifier called aboosted decision tree (BDT). This method combines many variables, whicheach provide a small degree of separation between signal and background,into a single strong classifier. A decision tree is a classification method whichuses a branching structure, with the decision path split into two branchesat each node. At each node, one of the input variables is compared toa cut value, and the result of the comparison specifies which of the twobranches should be traversed. After reaching the end of the tree, each eventis assigned a classifier value. The boosted decision tree is a method of trainingsuccessive decision trees in an ensemble. Events which were misclassified bythe previous decision tree are boosted, i.e. given higher weight in training;this focus on the harder-to-classify events results in a more accurate classifier.This is an established method which has been successfully used to rejectcosmic ray background events from the ALPHA-2 silicon vertex detector(SVD) [157]. A version using similar input variables was implemented in1478.1. BDT background rejection in ALPHA-2the ALPHA-g analysis for the 2023 gravity paper [1]. Following the timecalibration work described in Chapter 7, TOF variables from the BSC wereadded to the ALPHA-g BDT, leading to a new classifier with significantlyimproved background rejection capability.For context, Section 8.1 will briefly detail the BDT used in ALPHA-2. Section 8.2 will then describe the adaptation of this BDT to ALPHA-gfor the gravity paper, and Section 8.3 outlines how the BSC TOF mea-surements were later included to further enhance the ALPHA-g BDT. Thevariables used as inputs to these two versions are listed in Section 8.4, andthe final performance of each background rejection method is summarized inSection 8.5. Conlusions are drawn in Section 8.6.8.1 BDT background rejection in ALPHA-2Decision trees are regularly used to identify and reject cosmic ray eventsin the ALPHA-2 SVD [157]. This classifier is periodically retrained usingantihydrogen production data as signal and pure cosmic ray backgrounddata, in order to keep the model updated as the performance of variousdetector components changes over time. The variables included are listed inTable 8.1. These variables were selected for their separation between signaland background events, and to be minimally correlated to each other [75].Variable DescriptionNhit Number of SVD hits.Nhelices Number of reconstructed tracks.NËhelices Number of reconstructed tracks used in vertexing.Ïvertex Ï component of the reconstructed vertex position.rvertex r component of the reconstructed vertex position.δ Squared residual (measures track straightness).Î£Ï Ï component of the sphericity tensor eigenvector.Σz z component of the sphericity tensor eigenvector.âÎ»21 + λ22 Combination of the two largest sphericity tensor eigenvalues.Table 8.1: Discriminating variables used to distinguish signal (annihilation)and background (cosmic ray) events in the ALPHA-2 SVD.The last three variables make reference to the sphericity tensor of an1488.2. BDT background rejection in ALPHA-gevent, given by:Sab =1NhelicesNhelicesâi=1pia pib|pâi|2 , (8.1.1)Here, pi is the momentum of the ith track, and a, b refer to x, y, z. Bydiagonalizing this matrix, the eigenvalues and eigenvectors are found. Theeigenvector Σ corresponds to the largest eigenvalue, and can be thought ofas the principle direction of momentum in the event. The sphericity tensoreigenvalues, as well as the first eigenvector, are frequently used for describingevent shapes in collider experiments [158].The classifier yields a score c from â1 (background-like) to 1 (signal-like)for each event. A cut value C is then chosen to enable a binary classification:events with c < C are rejected as background, while events with c > C areaccepted as signal. The cut value C is chosen based on the requirements ofeach individual physics analysis, depending on the required level of signalpurity.8.2 BDT background rejection in ALPHA-gBased on the success of the BDT classifier in rejecting cosmic rays in theALPHA-2 SVD, a similar classifier was trained for offline background rejec-tion in ALPHA-g. This effort was lead primarily by Dr. Lukas Golino aspart of his PhD project [75]. An initial version of this BDT classifier, usingvariables inspired by the ones used in the ALPHA-2 classifier, was used inthe data analysis for [1]. The variables used in this classifier are primar-ily based on the TPC; only numbers of hits and hit clusters are used fromthe BSC. A full description of the variables used in this analysis is given inSection 8.4.The training of a BDT classifier requires labelled data: events which areknown to be either antihydrogen annihilation signal, or cosmic ray back-ground. A sample of 255 000 cosmic ray background events was recordedbetween experiments when there are no antiprotons in ALPHA-g. A sam-ple of 179 000 annihilation signal events was recorded during antihydrogenproduction, when a fraction of the newly formed antiatoms annihilate onthe walls of the trap because their kinetic energy exceeds the magnetic trapdepth. This is an intense 1 s time window with a TPC trigger rate of around40 000Hz. To ensure signal purity, this time window is subdivided into 2mssub-windows, and only those sub-windows where the detector readout rateis saturated at 500Hz are used in training.1498.3. Inclusion of TOF in background rejection8.3 Inclusion of TOF in background rejectionAfter finishing the calibration described in Chapter 7, I worked to implementTOF measurements from the BSC into the BDT classifier. The measuredTOF and the residual TOF (after subtracting expected TOF for cosmic rays)were both expected to be powerful discriminatory variables, supplementingthe existing variables along a new axis. However, it was not initially clearhow to combine the timing information of complicated events with manydifferent hits.A pragmatic approach was taken. Many quantities with possible discrim-inating power were calculated for each event utilizing the TOF informationfrom the BSC. A total of 107 new variables were implemented and tested,in addition to the 20 variables used in the gravity paper version. A finalset of 20 variables was selected by dropping those with high correlations toeach other, as well as those with low separation between signal and back-ground. These final variables are described in Section 8.4. The BDT trainedwith these 20 final variables had equivalent performance to the BDT trainedwith the full set of 127 variables. The classifier output is shown in Figure 8.1,which indicates very good separation between annihilation signal and cosmicray background. The performance of this classifier is discussed in Section 8.5.The introduction of variables based on TOF adds considerable complex-ity to the training procedure, as it requires the generation of BSC calibra-tion files for the entire training dataset. A version of the offline calibrationpipeline described in Appendix D is used to generate the training data in areproducible fashion, and perform the BDT training. This allows the classi-fier to be easily retrained periodically, so that the model can be updated toreflect hardware performance changes.8.4 Input variablesAs described previously, an initial BDT was trained for use in the gravitypaper analysis. This initial classifier used 20 input variables, primarily basedon TPC data, but including some basic information from the BSC. Manyof these variables were inspired by those used successfully in the ALPHA-2classifier. After completing the TOF calibration for the BSC, I added manyadditional variables based on BSC data, and retrained a new BDT. Thelist of variables was then slimmed to the current 20 input variables with nosignificant decrease in classifier performance.The variables used as input to the initial and final classifiers are summa-1508.4. Input variablesFigure 8.1: Classifier output c of the best-performing BDT trained withTOF and other variables. Classifier values range from â1 (background-like)to 1 (signal-like). The y-axis indicates counts, with data from a portionof the training dataset which was set aside for validation. Signal refers toantihydrogen annihilation data, and background to cosmic ray data.rized in Table 8.2. Only 8 variables are shared between the new classifier andthe initial version used for the gravity paper. While the initial version usedonly 4 variables based on BSC data, the new classifier uses 15 BSC variables.Of these, 9 rely directly on the calibrated timing information, either for thedetermination of the bar hit z positions, or for measurements of the TOFbetween bars. The remaining 6 are simple counting variables, or use onlythe ADC waveform.It is notable that three quarters of the 20 variables selected are based onthe BSC. This indicates that the BSC is fulfilling its role as an importantdetector for cosmic ray background rejection. It successfully measures eventfeatures which are not captured by the TPC, such as hit time and TOFinformation, and these features are powerful contributors to the backgroundrejection algorithm.The distributions of some of these input variables in signal and back-ground are shown in Figure 8.2. These variables were selected to illustratethat the BSC calibration campaign has ultimately lead to a number of TOF-based variables with good separation between annihilation signal and cosmicray background.Given that the measurement of the z position of annihilations is central1518.4. Input variablesto the gravity measurement strategy, special care was taken to ensure thatthe classifier output is completely independent of the vertex z position. Theannihilations used for training take place in a very small region of ALPHA-g, and so any variable with correlation to z could be used to efficientlyrecognize annihilation signal based on z position, leading to a highly biasedclassifier. For this reason, each input variable was checked to ensure it hasno correlation with vertex z position in both signal and background.Table 8.2: Comparison of variables used in the BDT trained for the gravitypaper (initial), and the BDT trained incorporating my BSC work (final).Variables using calibrated hit times are highlighted in blue, and other BSCvariables are highlighted in green.Variable Description Initial FinalNhit Number of TPC spacepoints. â âNhelices Number of reconstructed tracks. â âNpads Number of TPC cathode pad hits. â âÎ£TPCz z component of the sphericity tensoreigenvector using TPC tracks.â âÎ£TPCÏ Ï component of the sphericity tensoreigenvector using TPC tracks.â âNclusters Number of bar hit clusters. â âNbars Number of bar hits. â âNADC Number of BSC ADC hits. â âmax(A) Largest bar hit ADC amplitude. âNunmatchedhelices Number of reconstructed tracks notmatched to a bar hit.âNmatchedhelices Number of reconstructed tracksmatched to a bar hit.â(âÎ»21 + λ22)BSC Combination of the two largestsphericity tensor eigenvalues, calcu-lated using bar hit positions.âTÎ¸ Polar angle of the vector from first tolast bar hit, determined using TDCtime.âmax(TOF) Largest TOF between two bar hits. âmin(TOF4) Smallest TOF between bar hits sep-arated by at least 4 bars.âmax(âz) Largest âz between two bar hits. â1528.4. Input variablesVariable Description Initial FinalNTOF Number of pairs of bar hits withvalid TOF measurements.âmax(âTOF) Largest difference in TOF betweentwo pairs of bar hits.âmax(âTOFbar-to-bar) Largest difference in TOF betweentwo pairs of bar hits, calculated us-ing the 4032 directly measured bar-to-bar offsets (see Section 7.4).âstddev(TOF) Standard deviation of TOF mea-surements between all pairs of bars.âNends Number of bar end hits. âNËhelices Number of tracks used in vertexing. âNAW Number of TPC anode wire hits. âRmin Minimum helix radius of curvature. âRmean Mean helix radius of curvature. âÎ»min Minimum helix slope. âÎ»mean Mean helix slope. ââc± Integer sum of helix curvature (+1for right curved tracks, -1 for leftcurved tracks).âµpoints Mean spacepoints per track. âµÏ2r Mean Ï2 of track radial fit. â(âÎ»21 + λ22)TPC Combination of the two largestsphericity tensor eigenvalues, calcu-lated using TPC tracks.âvstatus Vertex status, indicates if tracks be-yond the first two were added.â1538.4. Input variablesFigure 8.2: Six of the 20 variables used in the final BDT classifier, chosento illustrate the separation between annihilation signal and cosmic ray back-ground in TOF-based and other BSC variables. Values of -20 are assignedto events with no good TOF pairs.1548.5. Background rejection performance improvement8.5 Background rejection performanceimprovementAs this work was carried out concurrently with the development of antihydro-gen production in ALPHA-g, the first measurement of gravity was performedbefore the background rejection work was completed. As such, there havebeen numerous historical background rejection methods. The annihilationsignal acceptance and cosmic ray background rates are shown in Figure 8.3.The following methods are compared:â¢ Initial online cut: During the commissioning of the ALPHA-g trapsleading up to the first measurement, a simple cut on the number of barhit clusters Nclusters was used in online analysis (see Section 6.7).â¢ Initial BDT: A BDT classifier was trained for use in the first grav-ity measurement, using primarily TPC variables modelled after thesuccessful classifier used in ALPHA-2 (see Section 8.2).â¢ Improved online cut: Following many of the TPC track fittingchanges described in Section 5.4, the cosmic ray background vertexrate in ALPHA-g was significantly reduced. The same simple cut onNclusters now yields improved performance.â¢ Improved BDT: After the implementation of the BSC calibrationroutine, a new BDT classifier was retrained using TOF variables (seeSection 8.3).It should be noted that the TPC tracking changes and inclusion of TOFinformation both had the effect of lowering the background rate of the im-proved BDT. No intermediate BDT was trained with the improved trackingbut without TOF variables, and so the contributions of the two improve-ments are difficult to disentangle.8.6 Background rejection conclusionsOverall, the results shown here indicate that an order of magnitude improve-ment in the background rate of the ALPHA-g detectors has been achieved.This is the result of my work developing the BSC event reconstruction, whichincludes a substantial TOF calibration algorithm, and my work includingTOF measurements into the BDT classifier. My work on the TPC track re-construction algorithms also benefited the background rate. The impact of1558.6. Background rejection conclusionsFigure 8.3: Comparison of signal efficiency and background rejection perfor-mance between the initial (2023) analysis used for the gravity paper [1], andthe improved (2025) analysis at the completion of this work. The dashedline indicates the background detector trigger rate, and the circles indicateevents for which a vertex is successfully found. The Nclusters cut used foronline analysis is indicated by triangles, while the BDT classifier is indicatedby the stars. The choice of cut C = 0.146 on the classifier output is shownfor the 2023 BDT, which was used in the gravity paper, chosen to optimizethe significance for an expected 1 count of signal in a period of 8 seconds.For the 2025 BDT, the choice C = 0.134 is shown. This choice is arbitrary,and should be re-examined prior to interpreting experimental results.1568.6. Background rejection conclusionsthis improvement on the measurement of antihydrogen gravity in ALPHA-gwill be the focus of the next chapter.This improvement comes at the cost of a lower signal yield: the an-nihilation vertex is found successfully in around 15% fewer antihydrogenannihilations, translating to around 9% fewer annihilations being acceptedby the BDT classifier. This reflects an intentional choice where events withcomplex topologies, for which the annihilation vertex can not be accuratelyfound, no longer yield a vertex position. If a future analysis requires a highnumber of vertices, parameters of the vertex reconstruction could easily bere-tuned in order to recover some of these lost vertices.157Chapter 9Measuring antihydrogengravity with ALPHA-gThe first results from ALPHA-g, constituting the first direct measurementof gravity acting on an antihydrogen atom, were published in 2023 [1] basedon data collected in 2022. The main result of this publication, referredto throughout this dissertation as the gravity paper, was that the Earthâsgravitational acceleration g on antihydrogen has the same sign as the Earthâsgravitational acceleration g on regular matter. The ratio of the two constantswas determined to be:g/g = (0.75± 0.13 (statistical+systematic) ± 0.16 (simulation)) (9.0.1)The probability that this measurement is consistent with no gravitationalaction on antihydrogen is 3Ã10â4, and the probability of it being consistentwith repulsive gravity (g = âg) is less than 10â15.The first three sections of this chapter will summarize the key elements ofthe gravity paper. Section 9.1 describes the experimental procedure, includ-ing the magnetic field control and characterization, details of the recordeddata set, and the unprocessed results. Section 9.2 presents the statisticalanalysis used to extract the results quoted above. Section 9.3 addressesstatistical and systematic uncertainties on the results, which inform futuremeasurements.Section 9.4 highlights the authorâs contributions in the broader contextof ongoing and upcoming ALPHA-g measurements. It discusses how theimproved track reconstruction and background rejection impacted the grav-ity paper, and how they will benefit subsequent measurements using thesame apparatus. It concludes with a discussion of long-term plans involvingthe precision trapping region of ALPHA-g, and outlines possible alternativemeasurement schemes enabled by this work.1589.1. Gravity measurement procedure9.1 Gravity measurement procedureThe design of the ALPHA-g trap apparatus was presented in Section 3.4.6.The reader should refer back to Figures 3.9 and 3.10 in particular. The mea-surement procedure of the gravity paper used only a subset of the ALPHA-gtrap magnets, as commissioning of the full magnet system is still ongoing. Amore precise measurement using the full apparatus will be performed in thefuture. This section will describe the procedure used in the gravity paper,with upcoming measurements discussed in Section 9.4.9.1.1 Measurement techniqueThe measurement strategy begins with the accumulation of antihydrogenatoms in ALPHA-g, as described in Chapter 3. The accumulation cycle isrepeated 50 times in each run, trapping around â¼ 50 antihydrogen atomsover 3-4 hours. During this time, the antihydrogen atoms are held by themagnetic field of mirror coils A and G (see Figure 3.10), collectively referredto here as the mirror coils or simply mirrors. They are radially constrainedby the combined field of the long octupole magnet and the short octupolemagnet.The key step in the gravity measurement is to slowly release the trappedantihydrogen atoms from their axially confining magnetic potential (shownin Figure 9.1), while keeping them radially constrained. This is done byramping down the current in the mirror coils simultaneously over 20 seconds,hereafter called the mirror rampdown. The antiatoms can then escape thetrap axially, either upwards or downwards. They remain radially constrainedby the octupole field until they exit the short octuple magnet, at which pointthey annihilate on the trap walls. The ALPHA-g detector system is usedto count the annihilations in the up and down regions, and the asymmetrybetween the counts in these regions indicates the net vertical force acting onthe antihydrogen atoms.The success of the experiment depends on precise magnetic field control.Mirror coils A and G are separated by 25.6 cm; the gravitational potentialdifference (for matter) between the two mirrors is mgâz = 2.6 Ã 10â8 eV.This corresponds to a Zeeman energy µâ · Bâ for a magnetic field of 4.53 Ã10â4T. This sets the necessary precision for the control of the magneticfield.Simulations indicate that under the effect of gravity with g = g, around80% of the trapped antiatoms should annihilate in the down region. How-ever, this ratio can be adjusted by holding one of the mirror coils at a slightly1599.1. Gravity measurement procedureFigure 9.1: A sketch of the on-axis potential (magnetic + gravitational) inthe ALPHA-g trap, with different applied magnetic biases compensating forgravity. The dotted purple line indicates the maximum magnetic potentialunder mirror A, which sets the kinetic energy required for antihydrogenatoms to escape into the down region.higher current than the other throughout the magnet ramp. This applies amagnetic bias which can either counteract or enhance the effect of gravity.For example, by decreasing the field of mirror G by 1g = 4.53 Ã 10â4T asshown in Figure 9.1, gravity can be compensated for and the balance of anni-hilations restored to 50% up, 50% down. Here, we introduced the conventionof using units of g for magnetic field difference. It should be emphasized thatthis magnetic bias must be applied before, after, and throughout the mirrorrampdown.To accomplish precise magnetic control, the mirror coils are energized inseries by a 70A power supply, ensuring the two magnets receive equal cur-rent regardless of power supply noise or drift. A differential current is thensupplied to mirror G alone to generate the magnetic bias. Direct-currentcurrent-transformers (DCCTs) are used in combination with a 50 kHz ADCto precisely measure the current flowing through the mirror coils. The mea-sured current is then used to control the output of the magnet power supplyusing a proportional-integral-derivative (PID)-based loop, as well as to con-firm consistent magnet power supply behaviour throughout the experiment.The reader should note that the one-dimensional picture presented hereis highly simplified. In reality, almost all antihydrogen atoms escape thetrap off-axis, and so the entire three-dimensional magnetic field profile ofthe trap should be considered. The gravity compensation is only approx-1609.1. Gravity measurement procedureimate: for example, mirror coil currents which balance the up and downpotentials on-axis (the gravity compensation curve in Figure 9.1) will notnecessarily balance the potentials at all radii. As such, an accurate inter-pretation of the experiment relies on the antihydrogen trajectory simulationsdescribed in Section 9.2.3, which must be informed and validated by accuratemeasurements of the magnetic fields throughout the measurement.9.1.2 Magnetic field measurementsTo ensure precise and repeatable control of the magnetic fields, and to char-acterize the applied bias in each configuration, a magnetic field measurementtechnique called electron cyclotron resonance (ECR) was developed at AL-PHA. A small plasma, or reservoir, of electrons is created by an electron gunmounted on the ALPHA-g bottom diagnostic stick (Section 3.4.4), and pre-pared using the SDREVC technique (Section 3.5.1). For each measurement,a small bunch of electrons is extracted from the reservoir, and moved to thetarget region of the trap.As discussed in Section 3.2.1, the electrons undergo cyclotron motion inthe Penning-Malmberg trap, with cyclotron frequency Ïc = qB/m dependingon the magnetic field strength. By determining the cyclotron frequency,the local magnetic field strength can be inferred. This is accomplished byinjecting microwaves into the ALPHA-g bottom trap. When the microwavefrequency matches the cyclotron frequency, the electron plasma undergoesresonant heating.The temperature of the electron bunch is measured via slow extraction tothe MCP mounted on the bottom diagnostic stick, in a procedure similar tothe one described for antiprotons in Section 3.5.1. As the confining potentialis slowly lowered, the electrons escape, and the kinetic energy of each electronis determined from its arrival time at the MCP. The energy distribution isfit to determine the plasma temperature.Many small bunches of electrons are extracted from the reservoir andmoved to the target location in rapid succession. Each is exposed to mi-crowaves of a different frequency. The temperature at each frequency ismeasured, and the spectrum is fit to determine the resonance peak frequency,which corresponds to the cyclotron frequency. The magnetic field strengthat the target location is determined from this measured frequency. Two ex-ample frequency measurements are shown in Figure 9.2. For further detailson the ECR technique, see [78] and [1] (Methods).This technique was used to measure the magnetic field under the mir-ror coils three times during the measurement procedure: before the mirror1619.1. Gravity measurement procedureFigure 9.2: Frequency spectra measured in ALPHA-g using ECR. Orangeand blue lines represent measurements at the same location in the samemagnetic field, but with different Penning-Malmberg confining potentials.For further information, see image source [78].rampdown, after the mirror rampdown, and after zeroing all mirror coil andoctupole magnet currents. This procedure helped ensure that the magneticfield behaved as expected across all trials. In addition, the ECR techniquewas used to map the magnetic field produced by each of the magnets, andthese field maps were used as inputs to the antihydrogen simulations dis-cussed in Section 9.2.3. ECR was also used to study persistent magneticfields after the end of the rampdown caused by persistent currents in thesuperconducting mirror coils.A complementary technique for measuring the magnetic field, calledmagnetron-metry, was also developed based on the electron magnetron fre-quency. A small plasma of electrons is displaced from the trap axis, andprecesses around the trap centre due to its magnetron motion described inSection 3.2.1. By imaging the plasma using the ALPHA-g MCP after ashort time, the number of precessions around the trap centre can be countedto extract the magnetron frequency, and thus determine the local magneticfield. This technique was used to further constrain the magnetic field modelsused in simulation, and is described further in [27] and [1] (Methods).1629.1. Gravity measurement procedureFigure 9.3: A block diagram of the measurement procedure for each run.Antihydrogen accumulation is shown in green, the main mirror rampdownin pink, other magnet ramps in grey, and ECR measurements in blue.9.1.3 Data collectionThe data collection process for the gravity paper was divided into experi-mental runs. Each run consisted of 3-4 hours of antihydrogen accumulation,followed by a measurement with a specific magnetic bias. A total of 11 dis-tinct bias values were used, each repeated 6 or 7 times depending on thenumber of collected events. To minimize systematic effects, the bias valueswere interleaved in a pseudo-random sequence.Figure 9.3 illustrates the measurement process for a single run. Theantihydrogen accumulation period was chosen to achieve a good signal-to-background ratio in the mirror rampdown. Following accumulation, the longoctupole magnet was ramped down, leaving the antihydrogen atoms confinedonly by the mirror coils and short octupole. This step avoids potential sys-tematic bias due to the asymmetry of the long octupole around the bottomtrap. However, it lowers the depth of the radial confining potential, whichcauses slightly more than half of the trapped antihydrogen to escape. Thefraction of antihydrogen lost is independent of the magnetic bias, which al-lows for a calibration of the total number of antihydrogen atoms accumulatedin each run.After an ECR measurement of the initial field, the mirror coil currentsare ramped down while maintaining the magnetic bias. Counting the annihi-lations in the up and down region during this mirror rampdown constitutes1639.2. Analysis procedurethe main measurement. A second ECR scan measures the final field wherethe trap depth is near zero, but the magnetic bias is still maintained. Theshort octupole magnet is then ramped down, and finally the mirror coil cur-rents and octupole currents are fully zeroed. A final ECR measurement istaken to monitor the background field of the external solenoid magnet.In addition to the main dataset of 75 runs across 11 magnetic biases,two supplementary datasets were taken. An additional ±10g calibrationdataset of 12 runs was taken where the applied bias was large enough thatalmost all antiatoms annihilate in the same (either up or down) region. Thisdataset was used to determine the relative detector efficiency in the tworegions, and to evaluate cross-contamination due to annihilation positionmis-identification. A second auxiliary dataset of 18 runs was taken wherethe mirror rampdown was carried out over 130 s instead of 20 s. This was usedto crosscheck the robustness of the result, and the outcome was consistentwith the main dataset (see [1]).The results of these runs are given in Table 9.1, including the numberof annihilations in the up and down regions during the mirror rampdown,and the annihilations in the long octupole rampdown. The expected cosmicray background (using the BDT background rejection of Chapter 8) was de-termined using dedicated cosmic ray runs with no antimatter in the system,and has been subtracted from the given counts. The z distributions of theannihilation events for each bias are shown in Figure 9.4.9.2 Analysis procedureThe analysis strategy used in the gravity paper was to construct an escapecurve â a plot of the probability that an antihydrogen atom escapes the trapdownwards (or upwards) as a function of applied magnetic bias. We definePdn as the probability that an antihydrogen atom annihilates in the downregion, and the asymmetry as A = 2Pdn â 1; the escape curve plots thesequantities as a function of the applied magnetic bias. The final measuredescape curve is shown in Figure 9.5. A naive estimate of g can be made fromthis curve by identifying the bias value for which Pdn = 0.5, correspondingto the point where the magnetic bias precisely compensates for gravity, andup/down annihilations are balanced.A more precise determination of g was obtained using simulation. Foreach assumed value of g and for each magnetic bias, the trajectories ofmany antihydrogen atoms were simulated using a magnetic field model ofthe ALPHA-g trap. This process generated a family of simulated escape1649.2. Analysis procedureFigure 9.4: Annihilation position z distributions for different applied biases.Lines at ± 12.8 cm and ± 32.8 cm indicate the z cuts used to define the upand down regions. Figure from [1].Figure 9.5: The measured escape curve, the probability that an antihydrogenatom annihilates in the down region plotted for different magnetic biases.The data is compared to simulations described in Section 9.2.3. Figure from[1].1659.2. Analysis procedureTable 9.1: Measured antihydrogen annihilation counts for each magneticbias. Bias of ±10 indicates calibration dataset, and 130s indicates cross-check with slower mirror rampdown. Event counts have expected cosmic raybackground subtracted, and are subject to data selection cuts described inSection 9.2.1. LOc indicates annihilations during the long octupole rampdown. Adapted from [1].Nominalbias (g)Numberof trialsNup (events) Ndn (events) LOc (events)â3.0 7 151.7 16.5 199.2â2.0 7 128.7 33.5 168.2â1.5 6 128.9 57.7 192.0â1.0 7 69.7 62.5 183.2â0.5 7 55.7 67.5 201.20 7 36.7 94.5 144.20.5 7 36.7 124.5 177.21.0 7 17.7 119.5 185.21.5 6 13.9 180.7 234.02.0 7 6.7 163.5 228.23.0 7 7.7 147.5 199.2â10.0 6 142.9 0.7 169.010.0 6 â0.1 185.7 213.0â2.0 (130 s) 6 22.6 145.2 219.0â1.0 (130 s) 6 70.4 85.2 249.00 (130 s) 6 125.4 26.5 239.01669.2. Analysis procedurecurves, each corresponding to a different gravitational acceleration. Thesecurves were then compared to the experimental data to quantify compatibil-ity with various g hypotheses. Three simulated escape curves are includedin Figure 9.5.To extract Pdn for each bias setting from the experimental data, a Bayesianlikelihood analysis was employed. This analysis was then extended to esti-mate the value of g by directly incorporating the simulated escape curves.This section is organized as follows. Section 9.2.1 describes the data se-lection criteria used to obtain the annihilation counts presented in Table 9.1.Section 9.2.2 outlines the Bayesian methodology used to derive the values ofPdn and the final value of g. Section 9.2.3 describes the antihydrogen trajec-tory simulations and magnetic field models used to generate the simulatedescape curves.9.2.1 Data selectionTo maximize sensitivity to the few antihydrogen annihilation events whileminimizing contamination from the cosmic ray background, selection cutswere applied to both the z position of the annihilation vertex and the eventtime.The accepted z range for the down region is â32.8 cm < z < â12.8 cm,and for the up region is 12.8 cm < z < 32.8 cm. In this coordinate system,the centre of mirror coils A and G are located at â12.8 cm and 12.8 cmrespectively, which define the inner boundaries of the selection regions. Theouter boundaries were chosen based on the annihilation distribution of the±10g calibration runs. These spatial cuts are indicated in Figure 9.4.A time cut was also applied to exclude events outside the main measure-ment window. Only annihilations occurring during the second half of the20 s mirror coil rampdown were accepted, since the first half of the ramp-down did not contain any annihilations significantly above the backgroundrate. Although there was a significant number of antihydrogen annihilationsafter the end of the mirror coil rampdown, these were excluded. This timeselection is illustrated for the 0g bias trials in Figure 9.6.9.2.2 Bayesian analysisA Bayesian approach is taken to determine the most likely values of Pdn foreach bias given the observed annihilation counts. This method is outlinedhere and described more fully in [159]. Other methods were also explored[76] and yielded similar results.1679.2. Analysis procedureFigure 9.6: Time distribution of annihilations during the mirror coil ramp-down. Only events in the window 10 s< t <20 s are accepted. Figure from[1].For a given bias index i, the counts in the up and down regions nup,iand ndown,i during the mirror coil rampdown, as well as during the long oc-tupole rampdown nLOc,i, are assumed to be independent Poisson-distributedrandom variables. The means of these distributions are calculated from themodel parameters given in Table 9.2. These parameters include the under-lying downwards annihilation probabilities pi for each bias.Given values for the model parameters, the probability P (O|Ï,Î·,Î», β,p)of making a set of observations O (comprising up, down, and long octupolecounts from each bias) can be calculated.The prior distributions for the probabilities pi are set to uniform proba-bilities between 0 and 1. The priors for the detection efficiencies and cross-contamination η were based on the ±10g calibration dataset. Broad uniformpriors were assigned to λi and β. The priors for the detector backgroundrates Ïup, Ïdown and ÏLOc were based on cosmic ray measurements. A globalprior probability P (Ï,Î·,Î», β,p) is then assigned to each set of parametersbased on the independent prior distributions.Using Bayes theorem, the posterior parameter probability distributiongiven a set of observations is:1689.2. Analysis procedureTable 9.2: Model parameters used in the Bayesian analysis of the gravitypaper dataset.Parameters DescriptionÏup, Ïdown Cosmic ray background rate in the up and down regions.ÏLOc Cosmic ray background rate during long octupole ramp.ηu,u, ηd,d Detection efficiency in the up and down regions.ηu,d, ηd,u Cross-contamination between the up and down regions.β Proportionality constant between long octupole and mirrorrampdown annihilations.λi Annihilations during long octupole ramp at bias i.pi Down region annihilation probability for bias i.P (Ï,Î·,Î», β,p|O) â P (O|Ï,Î·,Î», β,p) P (Ï,Î·,Î», β,p) (9.2.1)The marginalized posterior distribution for each pi is then obtained byintegrating over the other variables (nuisance parameters):P (pi|O) ââ«dÏâ«dÎ·â«dÎ»â«dÎ²â«j Ì¸=idpj P (O|Ï,Î·,Î», β,p) P (Ï,Î·,Î», β,p)(9.2.2)These distributions of P (pi|O) are determined via the Markov ChainMonte Carlo (MCMC) method, using the STAN package [159]. The maxi-mum of the posterior probability distribution P (pi|O) is taken as the bestestimate of Pdn in Figure 9.5.To determine the most probable value of g, this analysis was extended byincorporating the simulation results described in Section 9.2.3. The escapecurves generated via simulation (which will be shown in Figure 9.7) aregiven by the same functional form differing by a horizontal shift. Thesesimulated escape curves were aligned and interpolated in order to determinethe simulated down annihilation probability psim(Ï) as a function of themagnetic bias Ï, in the absence of gravity.In this extended analysis, the independent parameters pi were replacedwith the simulated probability psim(Ïi+ag) evaluated at each bias value, withan additional offset ag due to the effect of gravity. The posterior distributionof ag was then determined using the MCMC method by integrating over allother parameters:1699.2. Analysis procedureP (ag|O) ââ«dÏâ«dÎ·â«dÎ»â«dÎ² P (O|Ï,Î·,Î», β, ag) P (Ï,Î·,Î», β, ag)(9.2.3)The value of ag with the maximum posterior probability P (ag|O) isquoted as the final measurement of g.9.2.3 Escape curve simulationTo quantify the compatibility of the ALPHA-g measurements with differentgravitational scenarios, the observed annihilation distributions were com-pared to trajectory simulations of antihydrogen atoms escaping from ALPHA-g under different magnetic biases. As outlined in the previous section, theextraction of a value of g relies directly on simulation, and so the accuracyof these simulations is central to the experiment.One crucial input to the simulations is a precise model of the magneticfield in the ALPHA-g trap region. The field model was constructed to matchmeasurements as closely as possible. It is divided into independent modelsof the magnetic field produced by each magnet: the main external solenoid,and each individual octupole and mirror coil.The external solenoid field model was initially computed based on thedesign geometry, and updated to reflect measurements taken with an NMRprobe. This field was then perturbed by the insertion of the inner cryostatand internal magnets. The resulting modified field was measured on-axisusing ECR (Section 9.1.2), and the field model updated to reflect these in-situ measurements.The magnetic fields of the octupole and mirror coils were calculated basedon the winding geometry measured during construction. These field modelswere also fine-tuned to match both ECR and magnetron-metry. To reproducethe time evolution of the magnetic fields during magnet ramps, the currenthistories measured using DCCTs were applied in the simulation. The com-bined field model matched all ECR and magnetron-metry measurements,both offline and those taken during the measurement procedure, to within2Ã 10â5T, and to within 1Ã 10â6T in the region under the mirror coils.The total magnetic field was precomputed and stored in a grid with0.5mm spacing, which was then interpolated during the simulation. Tomodel the antihydrogen accumulation cycles, atoms were initialized in acylinder near the bottom of the trap and allowed to evolve for a random du-ration between 0 and 4 h. The time evolution followed a stepping algorithmwith step sizes of 1 µs or 3mm, whichever was smaller. The atoms were1709.3. Measurement uncertainties and systematicsFigure 9.7: Escape curves generated using antiatom trajectory simulations.Each line corresponds to a different assumed value for the antihydrogengravitational acceleration g, and each data point represents a simulationwith a different magnetic bias applied during the mirror coil ramp down.Figure from [1].initialized with a 50K thermal energy distribution and a principal quantumnumber of 30, then allowed to radiatively cascade to the ground state. Afterthis process, 6726 antihydrogen atoms remained trapped.These surviving atoms were then used as initial conditions for every mir-ror coil rampdown simulation. Their trajectories were evolved using thestepping algorithm and time-dependent field models described above, andtheir annihilation positions and times were recorded. This process was re-peated for each of the 11 applied magnetic biases and for a range of assumedvalues of g. The resulting escape curves are shown in Figure 9.7.9.3 Measurement uncertainties and systematicsTo contextualize my contributions within the broader ALPHA-g measure-ment program, it is important to discuss the sources of uncertainty andsystematic effects in the gravity paper. There are three types of uncertaintyquoted:â¢ Magnetic bias uncertainty: the uncertainty in the magnetic fieldapplied to the antihydrogen atoms during the mirror coil rampdown,which affects the x-axis values of the escape curve.1719.3. Measurement uncertainties and systematicsâ¢ Statistical uncertainty: the uncertainty in the measured probabilityof downward annihilation at each magnetic bias, reflected in the y-axiserror bars of the escape curve.â¢ Simulation uncertainty: the uncertainty arising from the modellingof antihydrogen trajectories and magnetic fields used to generate thesimulated escape curves.These three components contribute respectively to the horizontal, verti-cal, and model-based uncertainties shown in Figure 9.5. Each is propagatedinto the final quoted uncertainty on the gravitational acceleration g.9.3.1 Magnetic bias uncertaintiesFor each trial, the currents in mirror coil A and G were ramped down ina way intended to maintain a constant magnetic bias between the two, asdescribed in Section 9.1.1. However, the actual magnetic bias experiencedby the antihydrogen atoms may have deviated from the nominal value. Un-certainties reflecting how well the true magnetic bias is known define thehorizontal error bars in Figure 9.5.The dominant contribution arises from the precision with which the mag-netic field difference between the two mirror coils can be measured using theECR technique. As shown in Figure 9.2, the cyclotron frequency resonancehas a finite width. The standard deviation of a Gaussian fit to each spectrumdefines the ECR spectrum width uncertainty, which was found to be0.07g across all measurements.A second contribution arises from trial-to-trial variability in the ECRmeasurements of the magnetic bias. The standard deviation of the measuredbias values defines the repeatability uncertainty, with a value of 0.014g.Due to the influence of background field gradients, the maxima of themagnetic field do not lie directly under the geometric centres of the mir-ror coils. The peak positions were determined in each configuration via aquadratic fit to ECR measurements at different axial positions. The uncer-tainty in this fit contributes a peak field fit uncertainty of 0.009g.Another contribution stems from persistent currents in the superconduct-ing mirror coils, which create residual magnetic fields that decay slowly afterthe rampdown ends. Because there is a delay of approximately 96 s betweenthe end of the mirror rampdown and the second ECR measurement, themeasured magnetic field does not exactly match the field during the ram-pdown. Offline ECR measurements showed a decay of 6 Ã 10â5T over the1729.3. Measurement uncertainties and systematics96 s following the rampdown, with a decay rate difference between the twomirror coils leading to a field decay asymmetry uncertainty of 0.02g.The magnetic bias is not constant during the mirror rampdown. Usingthe field model described in Section 9.2.3, the magnetic bias felt by eachantihydrogen atom is calculated based on its annihilation time. The meanof these values defines the x-axis position of each data point in Figure 9.5,and the standard deviation defines a bias variation uncertainty of 0.02gacross all measurements.This bias determination for each antiatom depends on the accuracy ofthe magnetic field model, particularly for determining the bias off-axis. Thelevel of agreement between ECR/magnetron-metry measurements and thefield model defines a field modelling uncertainty, estimated at 0.05g.9.3.2 Annihilation counting uncertaintiesThe second major type of uncertainty arises when determining the probabil-ity that antihydrogen atoms annihilate in the up or down detector region ateach magnetic bias. This defines the vertical error bars in Figure 9.5.There are two main contributions to this uncertainty. The first uncer-tainty is statistical uncertainty in the main measurement dataset, with onlyaround 200 annihilation events for each magnetic bias value. This statisticalfinite data size uncertainty is estimated at 0.06g across all measurements.The second contribution is from uncertainty on the detector efficiencyasymmetry, the difference in annihilation detection efficiency between theup and down regions. This is calculated using the ±10g calibration dataset,where the applied biases are large enough to force all antihydrogen atomsto one of the two regions. However, less than 200 rampdown annihilationswere detected for each calibration bias, leading to a statistical detectorefficiency calibration uncertainty estimated at 0.12g.9.3.3 Simulation uncertaintiesWhile the mirror rampdown measurements agreed well with simulation, therewere discrepancies between measurement and simulation in other time peri-ods. In the measurement, fewer atoms survived the mirror coil rampdown,more atoms escaped during the post-rampdown waiting/ECR period, andfewer atoms were released in the final short octupole rampdown.The trajectory simulations were repeated with a series of systematic per-turbations. Some of these perturbations were able to explain the differences1739.4. Future measurements and the impact of this workbetween measurement and simulation. The largest changes in the resultingPdn values were used to define the simulation error band in Figure 9.5.The change to the fraction of antiatoms surviving the mirror coil ramp-down was found to be consistent with different initial antihydrogen energydistributions between simulation and experiment. Modifying the initial an-tihydrogen energy distribution in simulation was found to produce an anti-hydrogen initial energy distribution uncertainty of 0.03g.Field model perturbations compatible with ECR and magnetron-metrymeasurements were explored. These include dipole, quadrupole, sextupole,and octupole perturbations with zero on-axis component applied to the bot-tom half of the trap field model, as well as misalignment of the axes of themirror coils, octupole magnets, and external solenoids. These produced thedominant uncertainty of the measurement, a magnetic field modellinguncertainty of 0.16g.Other simulation perturbations included adding an artificial mechanismfor mixing the parallel and transverse energy of the antihydrogen atoms,which was consistent with the increased annihilation count in the post-rampdown waiting period. A final change investigated was the additionof physical vibrations of the magnets. These did not produce a significanteffect on the escape curve.9.3.4 Summary of experimental uncertaintiesA summary of the experimental uncertainties considered in the gravity paperis presented in Table 9.3. It should be noted that most of these uncertainties,including the dominant uncertainty, reflect our limited understanding of themagnetic field during the mirror coil rampdown. These will be significantlyreduced in future measurements using the precision region of the ALPHA-gtrap, which was designed to reduce the magnitude and possible asymmetriesof the magnetic fields involved. The other main uncertainties stem fromlimited annihilation statistics, especially in the calibration dataset. Theseare already being mitigated by improvements in the antihydrogen trappingrate in ALPHA-g.9.4 Future measurements and the impact of thisworkAlthough only partially completed at the time of its publication, the workdescribed in Chapters 5-8 has had a substantial impact on the gravity paper.1749.4. Future measurements and the impact of this workTable 9.3: Summary of uncertainties affecting the measurement of g in thegravity paper. Adapted from [1].Uncertainty Value (units of g)Uncertainties in bias determinationECR spectrum width uncertainty 0.07Field modelling uncertainty 0.05Field decay asymmetry uncertainty 0.02Bias variation uncertainty 0.02Repeatability uncertainty 0.014Peak field fit uncertainty 0.009Annihilation counting uncertaintiesDetector efficiency calibration uncertainty 0.12Finite data size uncertainty 0.06Simulation uncertaintiesMagnetic field modelling uncertainty 0.16Initial energy distribution uncertainty 0.03This is evidenced by the list of dominant uncertainties in the previous section,which notably excludes any contributions due to misidentification of theannihilation region or contamination from the cosmic ray background, issueswhich were mitigated through these improvements. The full implementationof the improved tracking algorithms and TOF-based background rejectionwas completed for the 2024 data taking run, leading to improvements inmultiple metrics.A significant impact of this work will be on upcoming future precisionmeasurements using the complete ALPHA-g apparatus. This section willdiscuss future directions for ALPHA-g as the experiment progresses towardsa more precise determination of g, and highlight the role played by the im-proved tracking and background rejection. Following the medium-term planto use the precision trap region of ALPHA-g, there are some more speculativealternative approaches which are directly enabled by these improvements tothe background rate and position resolution.Section 9.4.1 will discuss and attempt to quantify the impact of this workon the published gravity paper. Section 9.4.2 will outline ongoing and short-term improvements using only the ALPHA-g bottom trap. Section 9.4.3will discuss medium-term measurements which will be taken using the fullALPHA-g trap. Finally, Section 9.4.4 will outline potential alternative ap-proaches, and the future of antihydrogen gravity measurements.1759.4. Future measurements and the impact of this work9.4.1 Impact on the gravity paperMy work contributed to the gravity paper in two key ways: improvement ofthe annihilation vertex finding algorithm, and development of backgroundrejection techniques using the BSC.As discussed in Section 5.4, the annihilation z position resolution forthe more poorly-constrained vertices (the larger of two values) was orig-inally 14.6 cm. Given the 25.6 cm distance between the mirror coil cen-tres, this resolution was insufficient to reliably distinguish between up anddown annihilations, and would have necessitated a careful treatment of ver-tex misidentification as a systematic uncertainty. After the introduction ofmy iterative track finding routine and subsequent refinements, the resolu-tion was improved to around 3 cm for the more poorly-constrained vertices.This greatly reduced the number of misidentified vertices, such that vertexmisidentification was no longer a significant source of uncertainty.In addition, my work on the BSC was crucial for background rejectionin the gravity paper. While the BDT background rejection algorithm wasbeing developed, an online cut based on the number of bar hit clusters servedas the primary tool for background suppression. Given the trapping rateof less than 2 antihydrogen per 4-minute accumulation cycle, this onlinecut was instrumental for antihydrogen trapping optimization, which requiresaccurately measuring the number of trapped antiatoms as the accumulationsequences are incrementally adjusted.Furthermore, BSC variables were crucial in the machine learning back-ground rejection algorithm used in the gravity paper. Without the BSC, thebackground rejection performance would have been significantly worse. Al-though a background rejection BDT was never trained using only the TPC(i.e. without the BSC), we can attempt to estimate the performance of sucha classifier. As the online BSC cluster cut reduced the background rate by afactor of 10 (shown in Section 8.5), it is reasonable to estimate that a clas-sifier trained without the BSC would have a similarly worse performance,yielding a background rate of around 2Hz instead of the 0.19Hz achieved inthe final analysis.Impact estimate via simulationTo evaluate the quantitative impact of the improvements introduced in thiswork, a toy model simulation was developed to reproduce the annihilationdetection process. Annihilation positions were sampled from Gaussian dis-tributions based on the ±10g data. These positions were convoluted with1769.4. Future measurements and the impact of this workFigure 9.8: 200 simulated up annihilations and 200 simulated down annihila-tions, under different detector performance assumptions. Top: Gravity paperperformance of Ïinner = 1.06 cm, Ïouter = 3.02 cm, λbkg = 0.19Hz. Bot-tom: Hypothetical worse performance of Ïinner = 2.80 cm, Ïouter = 14.58 cm,λbkg = 2Hz.a double-Gaussian detector resolution function using the Ïinner and Ïouterparameters from Figure 5.16. Cosmic ray background events, uniformly dis-tributed in z, were added based on a Poisson distribution with the measuredaverage background rate. The annihilation z distributions of a typical sim-ulation are shown in Figure 9.8, comparing the analysis used in the gravitypaper with a hypothetical analysis lacking the vertex resolution and back-ground rate improvements developed in this work.Two key effects arise from the degraded detector performance. Firstly,the fraction of events reconstructed in the correct annihilation region de-creases from â¼ 99% to â¼ 71%, reducing measurement statistics. Secondly,the fraction of events reconstructed in the wrong annihilation region increasesfrom â¼ 0% to â¼ 9.5%, leading to cross-contamination.A true Pdown value was assumed as an input for each simulation. Roughly200 events were simulated per trial: the number of events simulated in thedown and up regions were drawn from Poisson distributions with λ = 200 Â·Pdown and λ = 200·(1âPdown) respectively. The z position of each event wassampled from the corresponding Gaussian, and convoluted with the detectorperformance. After each trial, the events in the up and down regions were1779.4. Future measurements and the impact of this workFigure 9.9: The Pdown measured from simulated data, as a function of thesimulation input Pdown values. (Left:) With perfect detector resolution andzero background. (Centre:) With the detector resolution of 1.06 cm innerGaussian and 3.02 cm outer Gaussian, and background rate 0.19Hz, used inthe gravity paper. (Right:) With the detector resolution of 2.80 cm innerGaussian and 14.58 cm outer Gaussian, and background rate 2Hz, in theabsence of this work.counted, and a measured Pdown = ndown/(nup + ndown) was computed.To quantify the purely statistical uncertainty, for each input Pdown =[0, 0.1, ..., 0.9, 1], 5000 trials were performed with no cosmic ray backgroundbackground and perfect detector resolution. The mean and standard de-viation of the measured Pdown values are shown in the left panel of Fig-ure 9.9. The largest standard deviation is taken as the purely statisticaluncertainty u[Pdown] (stat.) = 0.035, corresponding to the statistical uncer-tainty u[g] = 0.06g quoted in Section 9.3.2.To include the impact of the finite detector resolution and the cosmic raybackground rate into this uncertainty, these simulations were repeated withthe resolution and background rate values from the gravity paper (Figure 9.9centre), and with the hypothetical worse detector performance without my1789.4. Future measurements and the impact of this workInput parameters Simulation resultsÏinner Ïinner Bkg. u[Pdown] u[Pdown] u[Pdown] u[g][cm] [cm] [Hz] (stat.) (stat. & mis.) (mis.) (mis.)0 0 0 0.035 0.035 0 01.06 3.02 0.19 0.035 0.036 0.006 0.01g1.06 3.02 2.0 0.035 0.038 0.019 0.03g2.80 14.58 0.19 0.035 0.039 0.016 0.03g2.80 14.58 2.0 0.035 0.042 0.024 0.04gTable 9.4: Uncertainty values derived from toy model simulation, for the ver-tex resolution and background rate values from before and after this work.(stat.) indicates Poisson statistical uncertainty, while (mis.) indicates un-certainty from misidentifying the annihilation region. u[g] is calculated fromu[Pdown] by a scaling factor.improvements (Figure 9.9 right). The largest standard deviations are givenas the u[Pdown] (stat. & mis.) values in Table 9.4, which summarizes theresults of these simulations.To examine the uncertainty due purely to annihilation region misclassi-fication, i.e. not including the statistical uncertainty, these simulations wererepeated where the number of events in the bottom and top regions werefixed exactly to Nbot = 200 · Pdown and Ntop = 200 · (1 â Pdown) instead ofbeing drawn from a Poisson distribution. The results from these simulationsare reported as the u[Pdown] (mis.) values in Table 9.4.We can conclude that the uncertainty on Pdown was marginally improvedby this work, which prevented an uncertainty on the measured gravitationalacceleration of around u[g] = 0.04g. It is worth noting that this toy simula-tion did not include any correction for the detector efficiency asymmetry inthe two regions. As we have seen in Section 9.3.2, the uncertainty based onthe measurement of the detector efficiency asymmetry using the the ±10gcalibration samples is dominant over the purely statistical uncertainty. De-graded detector performance would also have a large impact on our abilityto measure the detector efficiency asymmetry, leading to a further increasein uncertainty not quantified here.9.4.2 Repeated measurements in the same apparatusThere are at least four short-term avenues of improvement available using thetrap apparatus which was used in the gravity paper, the ALPHA-g bottomtrap. Proof of principle demonstrations for three of these were performed1799.4. Future measurements and the impact of this workFigure 9.10: Preliminary results from the 2024 data-taking run, showing im-proved trapping rate only (orange), slower rampdown (green), and adiabaticcooling (red), compared to gravity paper data (blue).during the 2024 data-taking run: improved antihydrogen production usingBe+, slower mirror coil rampdown speed, and adiabatic expansion. Prelimi-nary results from these methods are shown in Figure 9.10. All new results arecompatible with the gravity paper results. The adiabatic expansion yieldsa slightly steeper escape curve, which corresponds to improved precision inthe determination of g. The fourth avenue of improvement, laser coolingof the antihydrogen atoms, will be attempted in the current or upcomingexperimental campaigns.Improved production rateAs described briefly in Section 3.5.2, a positron plasma cooling method us-ing laser-cooled beryllium ions was developed and implemented after the2022 measurement. The reduced positron temperatures leads directly to acolder initial temperature distribution for the produced antihydrogen. Con-sequently, a higher fraction of the antihydrogen atoms have kinetic energiesbelow the trap depth, significantly improving trapping rates from < 2 percycle to â¼ 20 per cycle in the 2024 data taking run.This has multiple advantages. Firstly, experiments can be conductedmore rapidly, reducing susceptibility to long-timescale systematic drifts. Sec-ondly, this enhances the signal-to-background ratio by allowing the exper-1809.4. Future measurements and the impact of this workiment to be performed only once per bias. Thirdly, increased annihilationcounts per trial reduces statistical uncertainties, which is especially relevantfor the detector calibration dataset. Finally, a shorter experiment time al-lows for a higher number of systematic checks to be performed, such as tovalidate various aspects of the antihydrogen trajectory simulation.Mirror rampdown speedDuring the mirror coil rampdown, when the confining potential of a mirrorcoil is lowered below the kinetic energy of an antihydrogen atom, it does notinstantaneously escape the trap. It continues on its trajectory, and escapesonly if it encounters the magnetic field minimum under the mirror coil. Thisis highly likely given enough time to explore the phase space. However, if thepotential of the second mirror coil drops below the antiatomâs kinetic energybefore it has a chance to escape through the first, the atom may escape ineither direction. This weakens the correlation between escape direction andgravitational bias.To mitigate this effect and improve directional sensitivity, a slower mirrorcoil rampdown can be employed. Increasing the ramdpown duration fromthe 20 s used in the gravity paper improves the likelihood that the antiatomescapes in the preferential direction, leading to a steeper escape curve.This technique is only feasible as a result of the lower background ratesprovided by the BSC TOF analysis. Taking advantage of this, a 600 s ramp-down was attempted in 2024. However, this technique did not immediatelyyield a noticeably steeper escape curve. Further trajectory simulations andsystematic investigations will be important to understand the level of im-provement expected from this change.Adiabatic expansion coolingThe temperature of the trapped antihydrogen plays a large role in the gravityexperiment. Colder antiatoms have reduced thermal motion, allowing theirtrajectories to be more strongly influenced by gravity and applied magneticbias, steepening the escape curve.There is no intrinsic cooling mechanism for trapped antihydrogen. Theimplementation of adiabatic cooling (described in Section 3.5.4) provides amechanism to reduce the temperature of the antihydrogen atoms. Prac-tically, however, there are losses in the adiabatic expansion process, andso decreasing the antihydrogen temperature comes at the cost of reducedstatistics. Adiabatic cooling has been demonstrated in ALPHA-2 [121], and1819.4. Future measurements and the impact of this workin 2024, it was first demonstrated in ALPHA-g, producing a marginallysteeper escape curve.Laser coolingLaser cooling (see Section 3.5.4) is another promising approach to reduce thekinetic energy of trapped antihydrogen, and has been successfully utilizedin the ALPHA-2 apparatus. There, laser cooling was typically applied overseveral hours. The time-of-flight (between a laser pulse and annihilation)during spectroscopy experiments provides a method to estimate the anti-hydrogen temperature, indicating a temperature of less than 35mK [160].When combined with adiabatic expansion, significantly lower temperaturescan be achieved. Preliminary attempts to combine these strategies have beenmade in ALPHA-2.Efforts are currently underway to implement laser cooling in the ALPHA-g apparatus. The combination of laser cooling and adiabatic cooling promisesto provide much cooler antihydrogen for the gravity experiment, improvingthe steepness of the escape curve and the precision of future determinationsof g.Laser cooling offers a further benefit to the gravity experiment, beyonda steeper escape curve. The cooling laser in ALPHA-g decreases the averageaxial velocity of the antihydrogen atoms; however, the axial and transversekinetic energy mix over time, and so this also leads to a decrease in thetransverse temperatures. As a result, the antiatoms will be more radiallyconfined and stay closer to the central trap axis, which is the deepest part ofthe trapping potential. This is beneficial since the magnetic fields are betterunderstood closer to the trap axis: fringe effects due to the magnet wind-ings are minimized, and the field can be better measured using ECR. Withantihydrogen trajectories more constrained to the centre of the trap, the tra-jectory simulations will be more accurate and present smaller uncertainties.The magnetic bias felt by each antiatom as it exits the trap will also bebetter known, since only the on-axis magnetic bias is measured throughoutthe rampdown.9.4.3 Measurements using the precision trap regionWhile the gravity paper measurements were performed using only the bot-tom trap, the most precise measurements will be performed using the fullALPHA-g apparatus. As discussed in Section 3.4.6, the ALPHA-g trappingsystem is divided into three sections: the top, bottom, and precision mag-1829.4. Future measurements and the impact of this worknetic traps. The bottom and top traps are reflected copies of each other,with stronger radial confinement provided by short octupole magnets. Thecentral precision trap has a lower octupole field from only the long octupolemagnet, leading to smaller magnetic field uncertainties. Furthermore, themagnet layout is symmetrical around the centre of the precision trap, mini-mizing systematic uncertainties of the magnetic field.To enable measurements in the precision trap, a method of transferringantihydrogen atoms between traps must be developed. This will involveslow manipulations of multiple mirror coil currents in order to adiabaticallytranslate the magnetic trapping potential, using a procedure which must bedeveloped.The improved background rejection and vertex resolution resulting fromthis work could play a crucial role in the development of this transporttechnique. Given the antihydrogen trapping rate of around 20 antiatoms per4-minute cycle, identifying antihydrogen losses requires sensitivity to singleannihilations. Furthermore, the improved vertex reconstruction will be veryhelpful to localize any antihydrogen losses, helping to optimize the transportprocedure.A laser- and adiabatically-cooled antihydrogen atom with 1mK of kineticenergy travels at approximately 4m/s, corresponding to an axial bounce timeof 100ms in a 25 cm trap. To avoid unintentional heating or antiatom loss,the mirror coil current adjustments must be slow relative to this timescale.Consequently, this transport process will take several seconds. The improvedbackground rejection developed in this dissertation will be essential for diag-nosing losses during antihydrogen transfer, by allowing the transport processto be improved using only the trapped atoms from a single accumulation cy-cle.9.4.4 Alternative measurement schemesAll of the improvements discussed thus far retain the same core measurementprinciple: antihydrogen is confined in a magnetic trap, and the trappingpotentials are slowly lowered, allowing the antiatoms to escape under theinfluence of gravitational and magnetic biases. This rampdown method hasproven effective, and will remain the core ALPHA-g measurement principlein the medium-term. However, alternate techniques do exist, each withdistinct advantages and systematic uncertainties.After the rampdown technique has been implemented in the precisiontrap region, the ALPHA collaboration will explore these alternative measure-ments schemes. Independent confirmation of the gravitational acceleration1839.4. Future measurements and the impact of this workg using a different technique will be critical for validating and establishingthe robustness of the ALPHA-g results. This will be particularly importantto the broader community in the event that the other antimatter gravityexperiments at CERN (i.e. GBAR and AEGIS) have not published results.Even if many underlying components in ALPHA-g are the same, using anew technique will inevitably lead to a different set of systematic measure-ment uncertainties. A successful cross-check using an alternative methodwould lend strong credibility to the ALPHA-g results. For this reason, itis important to consider other measurement schemes which could be imple-mented using the ALPHA-g apparatus.This section will discuss some alternative and speculative possible mea-surement schemes. These are preliminary ideas, and their realization willrequire further considerations and developments, but they are presented hereto stimulate the discussion of these approaches. Many of these techniquesare directly enabled by my work on the vertex reconstruction and back-ground rejection, and this section will highlight the importance of my workto each potential measurement. It concludes with a discussion of the futureof antihydrogen gravity research.Smaller trapping regionsThe improved vertex resolution may allow a class of measurements wherethe separation between the up and down regions is smaller. Recall fromSection 3.4.6 that both the ALPHA-g bottom and top traps are constructedwith many independent mirror coils. An escape-curve-type measurementcould be performed using antihydrogen trapped between any two mirrorcoils, for example between mirrors A and B; the distance between thesemirror coils is much smaller than the distance between mirrors A and G. Assuch, the vertex position resolution improvements presented here would becrucial for such a measurement.These measurements could be used to test some of the systematics of themain measurement. The results from escape curves generated from manysmall regions within the ALPHA-g trap could be compared to antihydrogentrajectory simulations. This could serve as a cross-check to validate themagnetic field models used in the simulation, independently studying thefields in each small region.1849.4. Future measurements and the impact of this workMagnetic heatingAn alternative method for constructing an escape curve involves inducingantihydrogen loss not by lowering the confining potentials, but by heatingthe antihydrogen atoms until they have sufficient energy to escape. Thismethod offers one significant advantage: the axially confining mirror coilfields remain static throughout the experiment. As a result, the magneticbias between the top and bottom mirror coils remains fixed, and is much eas-ier to characterize using ECR and other techniques. The would significantlyreduce the uncertainty arising from knowledge of the magnetic bias.A possible method to heat the antihydrogen atoms out of the trap isstochastic heating. By applying an oscillatory time-varying magnetic fieldusing the internal mirror coils, the antihydrogen atoms experience randommagnetic kicks, each imparting a small amount of momentum. The combinedeffect of many such kicks is to raise the antihydrogen kinetic energy; aftersufficient heating time, the antiatoms will escape the confining well. Thekinetic energy imparted by a single interaction must be significantly lowerthan the trap depth, and so such a measurement would take hundreds ofseconds, if not hours. Without the improvements in background rejectiondescribed in this work, such a measurement would not be feasible.Laser heatingAnother possible method of inducing antihydrogen escape is laser heating.By tuning the cooling laser frequency slightly above the 1S â 2P resonance,atoms moving away from the laser source are preferentially excited, trans-ferring momentum and increasing the kinetic energy by around 1.3mK perphoton [160]. If laser excitations occur too rapidly, the resulting momentumkick can introduce a directional bias and potentially interfere with the grav-ity measurement. To mitigate this, excitation rate must be slow compared tothe axial bounce frequency; there are also practical laser power constraintswhich limit this excitation rate.Consequently, the laser heating must proceed gradually over multiplehours, similar to the laser cooling process demonstrated in ALPHA-2. Thismeans that the BSC TOF-based background rejection would be crucial toany laser heating measurement. For example, the 0.01Hz background rateillustrated in Section 8.5 would yield around 100 background counts over a 3hour measurement. This would be acceptable given the current antihydrogenaccumulation rate of â¼ 1500 antiatoms over a 4 hour accumulation period.1859.4. Future measurements and the impact of this workTOF-based techniquesThe TPC has inherently poor time resolution, as it relies on electron drifttimes on the order of microseconds. By contrast, building upon the calibra-tion work presented here, it is possible to use the BSC to obtain annihilationtimes accurate to within a nanosecond.This precise event time could be used directly in a determination of g. ATOF-based method is proposed by the GBAR experiment [161], where H¯+ions are created and held in a Penning-Malmberg trap, and then ionized usinga pulsed laser. The time between the ionization and annihilation detection isused in combination with the annihilation position to determine the degreeto which the antihydrogen atom was accelerated or decelerated by gravity.A similar TOF-based measurement method is possible in ALPHA-g us-ing existing apparatus and techniques. In ALPHA-2, the 1S-2P resonanceis driven to laser cool trapped antihydrogen atoms, as described in Sec-tion 3.5.4. Antiatoms can be driven to the 2Pc hyperfine state, the relaxationof which yields antiatoms in both high-field-seeking and low-field-seekingstates [116]. Those antiatoms in the high-field-seeking state are immediatelyejected as the direction of the confining magnetic force is reversed. The1S-2P laser is pulsed, with a pulse length of 10 ns.A possible TOF-based gravity measurement in ALPHA-g could beginwith antihydrogen collection in a small trapping region. The pulsed 1S-2Plaser is used to drive transitions to untrappable states, ejecting the antiatoms.The time between the laser pulse and the annihilation is then measured usingthe BSC.In an axially symmetric trapping potential, the TOF of the antiatomswould be equal in the up and down directions. However, under the ac-celeration of gravity, the TOF of antiatoms escaping downwards would beshortened, and the TOF of antiatoms escaping upwards would be increased.For example, a laser-cooled antiatom with 50mK of axial energy wouldhave an axial speed of roughly 30m/s, taking 0.33ms to travel 1 cm. Gravityalters this velocity by around 0.01% over 1 cm, leading to an annihilation timedifference of around 100 ns between antihydrogen annihilating 1 cm aboveand 1 cm below the trapping region. This measurement is feasible using theBSC detector for time measurement, and with the improved vertex positionresolution presented in this dissertation.1869.4. Future measurements and the impact of this workAtomic fountainsFundamentally, ALPHA-g is limited by the inhomogeneous magnetic fieldrequired to trap antihydrogen. The ultimate precision which is expected tobe attainable using ALPHA-g is predicted to be around the 1% level. Tosurpass this, future antihydrogen gravity experiments will require measure-ments performed in a region free of large magnetic fields and field gradients.The HAICU project is taking the first steps towards this next generationof experiments, by constructing an atomic fountain compatible with bothhydrogen and antihydrogen. The apparatus uses a hydrogen source anda Zeeman decelerator which supplies a normal-conducting Ioffe-Pritchardquadrupole trap. In this trap, laser cooling will be applied in three dimen-sions [162].To measure gravity, antihydrogen atoms will be ejected vertically fromthe trap, forming an atomic fountain. They will be interacted with while infree fall using lasers to perform Raman interferometry [163]. In this tech-nique, each atom is split into a quantum superposition of two momentumstates which follow spatially separated trajectories. These states are thenmade to reconverge to the same position. Since each path is accelerateddifferently by gravity, there will be a relative phase shift between the twostates, causing interference. The interference pattern can be used to ex-tract the gravitational acceleration. This technique has already been usedto measure gravity in matter to a precision of 3Ã10â9g [164]. If successfullyapplied to antihydrogen, it would improve upon the gravitational sensitivityof ALPHA-g by several orders of magnitude.187Chapter 10ConclusionsThis dissertation presents the first results from the ALPHA-g experiment,which constrain the acceleration of antihydrogen atoms due to the Earthâsgravity. Published in [1], this is the result of work by the entire ALPHAcollaboration. My personal contributions outlined here are centred on thecommissioning of the antihydrogen detectors, and development of the de-tector data reconstruction algorithms. I was able to dramatically improvethe annihilation position resolution, as well as implement time-of-flight mea-surements using a newly commissioned scintillator detector, improving thebackground rate by over an order of magnitude. These improvements mit-igated uncertainties in the published result, and will directly enable newtechniques in the future.The measurement presented in this dissertation represents the culmina-tion of a decades-long effort to investigate the effect of gravity on antimatter,a project first undertaken by Witteborn and Fairbank in the 1960s [26, 28].It is the first direct confirmation of Einsteinâs weak equivalence principle forantimatter, supporting the long-predicted gravitational equivalence betweenmatter and antimatter. This result constrains many speculative theoreticaland cosmological models, and has already impacted the antimatter gravitycommunity [165, 166].In the ALPHA-g experiment, antiprotons are supplied by CERNâs ELENAdecelerator to a Penning-Malmberg catching trap, where they are preparedand subsequently transferred to the ALPHA-g apparatus. Simultaneously,positrons from a 22Na source are accumulated, trapped, and also transferredto ALPHA-g. The two particle species are combined to form antihydrogen,some of which is trapped in an Ioffe-Pritchard magnetic trap.To measure gravity, the vertical confining magnetic potentials are grad-ually lowered, allowing antiatoms to escape out of either the top or bottomof the trap. The subsequent annihilations are detected, and the ratio ofcounts in the two regions is plotted as a function of an applied magneticbias. By comparing the results to antihydrogen trajectory simulations, thegravitational acceleration of antihydrogen was found [1] to be:188Chapter 10. Conclusionsg/g = (0.75± 0.13 (statistical+systematic) ± 0.16 (simulation)) (10.0.1)where g â 9.81m/s2 is the gravitational acceleration of matter at the Earthâssurface.This measurement depends upon detection of the annihilations, with pre-cise determination of the annihilation positions. This was achieved using atime projection chamber (TPC) detector. The first of my individual contri-butions was a significant improvement to the track reconstruction and vertexfinding algorithms, described in Chapter 5. The track finding algorithm wasrewritten to be much more exhaustive, accurately finding different types oftracks which previously avoided reconstruction. The track fitting and ver-tex fitting functions were then rewritten to properly accommodate the morecomplete set of tracks. This lead to a vertex reconstruction algorithm whichreflects the underlying charged particles much more accurately. This ulti-mately improved the vertex position outer resolution from approximately15 cm to 3 cm, effectively eliminating annihilation position misidentificationuncertainty as a significant uncertainty in the overall measurement.Cosmic rays represent a substantial background in the TPC, and TPCdata alone was insufficient for accurate background rejection. To addressthis, a barrel scintillator (BSC) detector was incorporated in ALPHA-g, ca-pable of identifying cosmic rays based on their time-of-flight. The secondof my individual contributions was the commissioning of the BSC detector,and the development of the low-level BSC event reconstruction described inChapter 6. For the published gravity measurement, I used BSC hit informa-tion to reduce the cosmic ray background rate to an acceptable level.This work also included an extensive time-of-flight calibration effort, de-scribed in Chapter 7, and the integration of BSC information into a machine-learning-based background rejection algorithm described in Chapter 8. Thesuccessful measurement of particle time-of-flight using the BSC has furtherimproved the background rate, reducing the 58Hz cosmic ray trigger rateto a false vertex rate of 10mHz. The combination of the improvements tothe vertex position resolution and to the cosmic ray background rate wasestimated to have prevented an uncertainty on the measured gravitationalacceleration of around u[g] = 0.04g. Beyond these main contributions, Imade a number of smaller contributions also described here, such as de-veloping the ALPHA-g event display used to visualize detector data andunderstand events.Looking forward, there are several short- and medium-term improve-ments to the ALPHA-g method which could enable a measurement of g with189Chapter 10. Conclusionsprecision at the 1% level. With the improved detector performance presentedhere, such a measurement would feature a slow release of a large number oflaser- and adiabatically-cooled antihydrogen atoms from the ALPHA-g pre-cision trap. These experimental efforts will be complemented by trajectorysimulations using a precise field model consistent with an extensive magneticfield measurement campaign.Beyond the 1% measurement, this work paves the way for alternativemeasurement strategies in ALPHA-g. The improved detector backgroundrate unlocks a new category of experiments with a duration of hours, suchas slowly heating antihydrogen atoms out of a fixed magnetic trap. Whilethese techniques may not significantly outperform the current method inprecision, they offer valuable complementary measurements with a differentset of systematic uncertainties.Alongside the detector-focused contributions presented here, I was heav-ily involved in other aspects of the experiment while on shift at CERN, suchas the optimization of antihydrogen production, cryogen management, designof auxiliary systems, and many other tasks essential to the functioning of theALPHA-g experiment. 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Itis intended as a reference for future work on the BSC, or for those who arehighly interested in the readout electronics. A diagram of the BSC electronicsand DAQ system is shown in Figure A.1.Power distribution boardThe ASD boards require low voltage power, requiring inputs of 5V, 3V, andâ5V. These are supplied by a low voltage power supply via a customizedpower distribution board. This board is also nominally responsible for thedistribution of the 27V SiPM bias voltage from an external high voltagepower supply.Due to a design or fabrication error, the power distribution boards arenot able to distribute this high voltage; instead, one wire is removed fromeach connector and routed into two common connectors which are connectedto the high voltage power supply via a custom implementation. The seatingof these wires in the common connectors is not secure, and commonly leadsto ASD boards without bias voltage. This power distribution board will soonbe redesigned.Rear transmission moduleThe signals from the 128 ASD boards are carried off the detector by ribboncables. To distribute these signals to the ADC and TDC, a custom reartransmission module (RTM) was designed. Eight of these modules are used,with each module receiving signals from four ASD boards, corresponding to205Appendix A. BSC electronics and DAQ implementationFigure A.1: A diagram of the detector electronics and DAQ system for theBSC. Customized modules and circuit boards developed at TRIUMF areshown in yellow, commercially available units in purple, and power suppliesin red.206Appendix A. BSC electronics and DAQ implementationthe top and bottom of eight bars. Each RTM passes the analog SiPM signalsto the ADC sitting opposite it in a Versa Module Eurocard (VME) crate. Italso passes the digital discriminated signals to the TDC via a twisted pairribbon cable.One further feature of the RTM is to pass an electronic test pulse to eachASD board, which is injected directly after the first preamplification stageof the SiPM signal. The test pulse is supplied to each RTM via lemo cablefrom a digital-to-analog converter (DAC) on an ADC module. The RTMalso includes a set of switches to enable or disable this test pulse for eachASD board.There were numerous problems observed with this test pulse circuit. De-spite each RTM being given identical input pulses, there was significantvariation in the test pulses observed in the ASD boards. Furthermore, leav-ing the switches open during data-taking couples a large electronic noise intothe system. For these reasons, a test-pulse-based TOF calibration cannot beused with the current RTMs12.SiPM gainOne issue is that the gains of the SiPM arrays show variation between eachbar end, with some bar ends yielding consistently larger SiPM signals. Inparticular, the signals are significantly larger on the bottom end of each bar.This SiPM signal amplitude discrepancy is higher than can be explainedthrough factors such as temperature variation.One working theory was that the physical seating of the BSC bars wasnot robust. The force of gravity could have pushed the bar into the SiPMsat the bottom, increasing the coupling of photons into the bottom SiPMs.To address this, I performed a compression test using two prototype bars atTRIUMF, with a replica of the DAQ system. The bars were clamped intoplace and a metal plate pushed into one end of the bars by tightening a pairof screws. Increasing the compression pushing the bars and SiPMs togetherhad no affect on the signal sizes observed by the ADC.With this theory ruled out, the most likely cause now seems to be asystematic drop in the bias voltage applied to the bottom SiPMs. Theredesign of the power distribution board could lead to individual bias voltagesbeing supplied to each SiPM array, which could help to ameliorate this issue.12There are other reasons to want a redesign of the RTMs: poorly soldered ground pinson the ribbon cable connectors often fall out, and the cable retention of the ribbon cablesis poor, frequently leading to ADC or TDC channels with no signal.207Appendix A. BSC electronics and DAQ implementationBias voltage selectionWith the current external bias voltage supply, one common bias voltage mustbe chosen for all SiPMs in the BSC. The maximum bias voltage recommendedby [133] is 30.7V, corresponding to 6V over the breakdown voltage. Initially,a bias voltage of 30V was used: the larger the bias voltage, the larger theSiPM signals, and so the more accurately the signal start time can be found.When a bias voltage of 27V was tested, the performance of the bar hitcluster background rejection was found to be similar, and so the lower 27Vbias voltage was used instead for the initial gravity measurement.Once the TOF calibration was completed, the bias voltage was revisited.Cosmic ray data was taken with 27V, 29V, and 30V bias voltage. The TOFcalibration algorithm was run using each dataset, and the data analyzed.The results indicated minimal change to the TOF resolution between 27Vand 29V, but that increasing the bias voltage to 30V led to larger ADCwaveforms, more bar hits, but worse TOF resolution. For this reason, thebias voltage was not changed from 27V.This bias voltage selection could be revisited in future work. After adjust-ing the bias voltage, many further parameters may have to be reoptimized,such as the TDC thresholds. It is also possible that the TOF calibrationalgorithm should be modified for better performance using data taken withhigher bias voltages.TDC threshold selectionThe digital signals sent to the TDC are produced by a comparator whichcompares the SiPM signal to a reference threshold voltage. This thresh-old voltage is produced by a digital-to-analog converter (DAC) on the ASDboard. The voltage is determined by a Raspberry Pi mounted on the powerdistribution board, which can specify a unique threshold voltage for each barend.To choose the value of the TDC threshold, a threshold scan is regularlyperformed. The thresholds are decreased from 30mV to 0mV in steps, and 5minutes of cosmic ray data is taken at each step. The TDC hit rate is plottedagainst the threshold voltage for each channel. The hit rate increases steadilyas the threshold is lowered, before a dramatic increase once the thresholdreaches the electronic noise level. The threshold for each channel is then setto the voltage immediately before this sharp increase in hit rate.208Appendix A. BSC electronics and DAQ implementationMalfunctioning TDC channelsThe digital signal output from the comparator is carried into one of 8 RTMs,and then into the TDC by twisted pair ribbon cable. The TDC uses fourFPGAs to perform the time digitization, with 64 channels per FPGA. EachFPGA has its own circuit board with four connector ports. The ribboncables from the eight RTMs are fed into eight of these connectors.After the TOF calibrations were completed, it quickly became obviousthat some of the TDC channels had problems. Despite a successful finetime calibration, 11 of the 128 TDC channels used had a curious 6-peakedtime structure when probed with the test pulser, and similar timing issuesin cosmic ray data. The timing variation on these channels was around 4 ns,which made them unusable for TOF measurements.To circumvent this issue, the signals from these 11 bar ends were reroutedinto different TDC channels. This was done by splitting the correspondingwires from the twisted pair ribbon cable carrying the signal into the TDC,and recombining them into a 9th connector, which was plugged into anempty port on the TDC. This successfully recovered the time measurementson these 11 bar ends, allowing them to be used for TOF measurements.209Appendix BBSC quality of dataTo check the BSC detector quality of data during normal operation, a numberof plots are automatically generated during each run. These plots can bemonitored by detector experts, to ensure proper functioning of the BSC.These plots have already proven useful for diagnosing both hardware andsoftware issues.The set of plots is shown here in Figure B.1; the meaning and use of eachplot is described in Table B.1. This information is provided primarily as areference to those who will be working with the BSC in the future.Table B.1: Descriptions of the quality of data plots shown in Figure B.1.Row Col Description1 1 Occupancy plots for the 128 bar ends. Shows ADC hits,TDC hits, and matched ADC+TDC end hits. Used tofind bars with no signal, or too many signals, or failedADC+TDC matching.1 2 Occupancy plots for the 64 bar ends. Shows all bar hit types,complete bar hits, and bar hits matched to the TPC. Usedto validate bar end matching.1 3 Number of end hits per event, including ADC hits, TDChits, and ADC+TDC matched.1 4 Number of bar hits and bar hit clusters per event. Used tovalidate hit clustering.2 1 ADC hit amplitude, including raw amplitude and amplitudefrom waveform fits. Used to validate waveform fitting.2 2 ADC hit amplitude per channel. Used to monitor variationin gain for each channel.2 3 Fine time per channel. Used to ensure fine time is calculatedcorrectly for each channel: if some channels do not have auniform distribution from 0 ns to 5 ns, the fine time calibra-tion of Section 6.2.2 should be repeated.2 4 Time difference between matched ADC and TDC hits.210Appendix B. BSC quality of dataRow Col Description3 1 Bar hit z position from TDC time difference between barends.3 2 Difference between bar hit z position and matched TPCtrack z position. Used to validate TPC matching and timecalibrations.3 3 TOF between bars plotted against expected cosmic ray TOF.3 4 Residual TOF (TOF â expected TOF) for each bar. Usedto validate TOF calibrations per bar.211Appendix B. BSC quality of dataFigure B.1: The quality of data plots automatically generated during regularoperation of the BSC. Data is from cosmic rays, with BSC calibration.212Appendix CPileup rejectionThe maximum drift time of ionization electrons in the TPC is around 4 µs; ifa second charged particle crosses the TPC during this time, the two eventscannot be separated. This can be problematic for vertex reconstruction;since the time projection step uses the first anode wire signal as the zerotime, electron drift times will be miscalculated for the second track.The 325 ps time resolution of the BSC provides a convenient methodto address this. If the effective TOF between a pair of bar hits exceeds200 ns, the later bar hit is flagged as being caused by pileup. Any TPC trackmatched to this hit can be excluded from the vertex reconstruction. Thismodification to the vertex reconstruction was tested, but is current disabledas it did not yield significant improvements to any metric.Currently, the main use of this pileup tagging is to exclude events con-taining pileup from the machine learning training set (see Chapter 8). Thisis crucial as pileup is prevalent in the high rate antihydrogen mixing datawhich is used for training, but rare in the low rate annihilations typical ofgravity experiments.The theoretical pileup rate can be estimated by modelling detector trig-gers as a Poisson process. This makes the approximation that there is onlyone underlying process; if both cosmic rays and annihilations are present inthe data, the cosmic rays are neglected. For a Poisson process, the timebetween successive hits follows an exponential distribution. The theoreticalpileup rate can then be obtained integrating this probability density functionP (t) = Î»eâÎ»t over the maximum drift time:P (t < 4µs) =â« 4µs0Î»eâÎ»tdt (C.0.1)This relies upon knowledge of the average trigger rate λ. This value isbased on the measured detector trigger rate (using the trigger-level data sentfrom the ADC to the trigger module, as described in Section 4.4.3). Thisreported trigger rate is not limited by the readout rate of the TPC.These theoretical pileup rates are compared to the pileup rates measuredusing the BSC for different ALPHA-g data-taking modes in Table C.1. The213Appendix C. Pileup rejectionEvent Type Trigger Rate Theoretical Pileup Measured PileupCosmic ray µ 78Hz 0.03% 0.338± 0.008%H release 200Hz 0.08% 4.3± 0.1%H mixing 44.3 kHz 16.2% 20.9± 0.5%Table C.1: Comparison of theoretical and measured pileup probabilities fordifferent ALPHA-g data-taking modes.measured and theoretical rates are roughly comparable, but inconsistent.To investigate this, the event display was used to examine pileup events.Many of these events included tracks of secondary particles in the TPC,hinting towards other processes which could mimic pileup. For example, thedecay of a captured muon creates a secondary electron approximately 2.2µsafter the initial muon track. The time between successive bar hits in thesame readout window exhibited a distribution with a similar time constant,consistent with the hypothesis that some of these secondary particles arecaused by muon capture.Events including delayed-secondary-producing processes such as muoncapture are also tagged as pileup by the BSC. Since these processes affectonly a small fraction of events, and the magnitude of their effect is small,further investigation and proper treatment of them is left for future work.214Appendix DBSC calibration algorithmimplementationThe calibration procedure described in Chapter 7 is implemented into astandalone ROOT macro, which takes as input one or more ROOT filesproduced by the alphasoft analysis of MIDAS data. This macro typicallytakes 20 minutes to process 3 hours of cosmic ray data. The output of themacro is a new calibration ROOT file, which contains:â¢ Individual time offsets δtopi and δboti per bar end.â¢ Time walk correction parameters Btopi and Bboti per bar end.â¢ Effective speed of photon propagation veff per bar.â¢ ADC thresholds per bar end (see Section 6.1).â¢ z0 and λ per bar end (see Section 6.5).â¢ Diagnostic plots to verify the success and quality of each stage of cali-bration.â¢ The overall cosmic ray residual TOF distribution with these correctionsapplied, with a double Gaussian fit (see Figure 6.10). This indicatesthe TOF resolution achieved via the calibration.The alphasoft event reconstruction will search for the most recent calibra-tion ROOT file, with a run number at most 100 runs before the run numberbeing analyzed, to extract the calibration constants. It is also possible torun the alphasoft reconstruction with a manually specified calibration file.The online mode of alphasoft (described in Section 5.1) is used to providereal-time diagnostics, and so it is essential that an up-to-date calibration fileis available. After each run, the BSC calibration macro is run automaticallyusing data from that run. If it does not meet the predefined threshold of3 hours of cosmic ray data, it will include data from additional previous215Appendix D. BSC calibration algorithm implementationruns to reach this threshold. This automatic calibration procedure was usedsuccessfully over the 2024 ALPHA-g data-taking period.Two countermeasures are taken to prevent contamination of the calibra-tion cosmic ray dataset by annihilations; these allow the calibration to beperformed even using runs where antiprotons or antihydrogen were presentin ALPHA-g. Firstly, only events with three or fewer clusters of bar hits areused. This removes around 70% of annihilation events, while removing lessthan 1% of cosmic ray events. The second method is to use our knowledgeof the antihydrogen production cycle to automatically exclude time windowswhere antiprotons are present in ALPHA-g.As well as being executed automatically after every run for live onlinecalibrations, the calibration macro described in this section is used for of-fline, publication-quality data. An offline calibration pipeline was developedwhich is compatible with CERNâs condor batch computing grid. It was de-signed to be entirely decoupled from any ROOT files produced by the onlinealphasoft reconstruction, allowing full reproducibility from the MIDAS datafiles alone. This pipeline performs the BSC calibration and runs the alpha-soft reconstruction with the resulting calibration file, following these stepsfor each run:1. Perform a lightweight analysis of the previous 20 runs to determine thetotal time without antiprotons in ALPHA-g.2. Starting with the given run, add runs in reverse chronological orderuntil a pre-defined total time without antiprotons is reached.3. Analyze these runs with alphasoft to produce the ROOT output files.4. Execute the BSC calibration macro on the produced ROOT output,creating a calibration ROOT file.5. Check the calibration file to ensure successful calibration, with a TOFresolution better than 500 ps.6. Run the alphasoft analysis again, using the new calibration file.The most likely cause of calibration failure is if the calibration datasetcontains runs from before and after a TDC power cycle (see Section 7.1), i.e.where the channel offsets shift partway through the calibration dataset. Inthis case, the pipeline looks for a run shortly after which was also analyzed,and for which the calibration was successful. This calibration file is used ifone is available; otherwise, the analysis is aborted.216Appendix D. BSC calibration algorithm implementationFigure D.1: Time-of-flight resolution dependence on the length of the datasetused for BSC calibration. Based on 2023 data which does not reflect TOFresolution improvements.One major question is how much cosmic ray data is required for accuratecalibration. This is addressed in Figure D.1, using data from 2023 whenthere were still some hardware issues limiting the TOF resolution. Theresolution appears to flatten out with around 3 hours of calibration data,and so the threshold was set to use at least three hours of data for the 2024run. Figure D.1 should be regenerated using 2024 data to update the datarequirements.A further area of investigation is the stability of the calibration constantsover time. While they are known to change after a TDC power cycle, if theyare otherwise stable, a single calibration file per inter-power-cycle periodcould be used for offline analysis.217
Thesis/Dissertation
eng
Physics
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Fujiwara, Makoto C.
Momose, Takamasa
Detecting antihydrogen annihilations in ALPHA-g for measurement of gravitational free fall
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