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Charge-breeding studies for high-precision mass measurements on short-lived nuclides at TITAN and a direct… Macdonald, Tegan Danielle 2014

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Charge-breeding studies for high-precision massmeasurements on short-lived nuclides at TITAN and adirect determination of the 51Cr electron-capture Q-valuefor neutrino physicsbyTegan Danielle MacdonaldB. Sc., The University of Waterloo, 2011A THESIS SUBMITTED IN PARTIAL FULFILLMENTOF THE REQUIREMENTS FOR THE DEGREE OFMaster of ScienceinTHE FACULTY OF GRADUATE AND POSTDOCTORALSTUDIES(Physics)The University of British Columbia(Vancouver)April 2014c Tegan Danielle Macdonald, 2014AbstractPenning-trap mass spectrometry (PTMS) is a well-established technique for per-forming high-precision mass measurements on both stable and short-lived nuclides.Achieving high precisions with radioactive isotopes is technically challenging dueto the limited yields and inherent losses from radioactive decay, but it is a worth-while pursuit as the mass is a fundamental property unique to each nuclide. Accu-rate and precise knowledge of the mass plays a critical role in the advancement ofboth theories and applications of nuclear and particle physics. This work providesthe result of a Q-value (mass difference) measurement of the 51Cr(e,ne)51V reac-tion. This first direct Q-value measurement confirmed the neutrino energies thatwere used in calculations for the solar neutrino experiments SAGE and GALLEXand the so-called gallium.Charge breeding to increase the precision of a PTMS measurement on radioac-tive ions is a technique that is unique to the TITAN (TRIUMF鈥檚 Ion Trap forAtomic and Nuclear science) facility; however, this potential increase in precisioncan be diminished by inefficiencies that are introduced by charge breeding. Thisthesis describes the simulations and systematic studies that are used to quantify theprecision gained in a PTMS measurement made with highly charged, radioactiveions. This novel approach has allowed for the identification of key charge-breedingparameters and the determination of the optimal charge-breeding conditions basedsolely on the nuclide of interest and its half-life. Furthermore, experimental in-vestigations were performed to determine the compatibility between the simulatedfindings and experimental observations. These investigations have led to a deeperunderstanding of the charge-breeding process and apparatus and will improve thepredictability and performance of charge breeding at TITAN.iiPrefaceThe TITAN collaboration consists of graduate students, postdocs, technical staff,and professors sharing the goal of performing high-precision mass measurementsto advance the field of nuclear science. As a result the work is highly collaborativewith a number of people at any given time involved with running the experimen-tal apparatus, collecting data, and sharing and interpreting results. The relativecontributions to the work included in this thesis are outlined below.Chapters 1 through 3: The motivation, theory, and experimental setup are en-tirely written by me and discussed in the context of previous work. Appropriatereferences to published work appear throughout.Chapter 4: The charge breeding program CBSIM, as seen in Section 4.1, is apublic domain program maintained by R. Becker [Journal of Physics: ConferenceSeries 58:443 (2007)]. I performed modifications to the program, including theaddition of new elements and exporting of the data from Fortran to C++, with as-sistance from A. T. Gallant and R. Klawitter. I generated all calculations, plots, andinterpretation of the results under the supervision of M. C. Simon and J. Dilling.Portions of the discussion in Section 4.2, including Equation 4.10, have appearedin two publications, both of which I coauthored:鈥 M. C. Simon, T. D. Macdonald, et al., Charge breeding rare isotopes forhigh precision mass measurements: challenges and opportunities, PhysicaScripta, T156:014098 (2013).鈥 S. Ettenauer, M. C. Simon, T. D. Macdonald, and J. Dilling, Advances iniiiprecision, resolution, and separation techniques with radioactive, highlycharged ions for Penning trap mass measurements, International Journal ofMass Spectrometry, 349-350:74-80 (2013).Section 4.3 is based on a proposal for a future experiment at TITAN written by S.Ettenauer and myself:鈥 T. D. Macdonald and S. Ettenauer, S1445: High precision mass measure-ments for the determination of 74Rb鈥檚 Q-value, TRIUMF-EEC proposal, (2013).Chapter 5: The experimental data was collected by M .C. Simon, R. Klawitter,and myself. I designed the experiments, performed the analysis, and prepared theresults. Discussion and interpretation of the results were prepared with assistancefromM. C. Simon and R. Klawitter. The improvements that were made to the appa-ratus as discussed in Section 5.3.3, were a collaborative effort led by R. Klawitter,who was responsible for realigning the electron collector assembly.Chapter 6: The collection of the experimental data was taken during shift work bythe TITAN collaboration. All members of the collaboration assisted with the prepa-ration of the apparatus and collection of the data. B. E. Schultz and I performedthe analysis with assistance from A. T. Gallant and A. A. Kwiatkowski. I wrote thecontents of the chapter, and a version of the work has been accepted for publicationin Physical Review C :鈥 T. D. Macdonald, B. E. Schultz, et al., A precision Penning-trap measure-ment to investigate the role of the 51Cr(e,ne)51V Q-value in the galliumanomaly, Physical Review C,CK10395 (accepted for publication Apr-2014).ivTable of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiPreface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iiiTable of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vList of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viiiList of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ixGlossary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiiAcknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.1 Fundamental Science . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Masses and Motivation . . . . . . . . . . . . . . . . . . . . . . . 21.3 Charge Breeding for PTMS with Highly Charged, Radioactive Ions 31.4 Outline of the Thesis . . . . . . . . . . . . . . . . . . . . . . . . 42 Manipulation and Preparation of Radioactive Ions . . . . . . . . . . 62.1 Paul Traps and the Radio-Frequency Quadrupole Trap . . . . . . 72.2 Penning Traps for PTMS . . . . . . . . . . . . . . . . . . . . . . 92.2.1 Measurement Cycle . . . . . . . . . . . . . . . . . . . . 102.2.2 Accuracy and Precision of a Penning-trapMassMeasurement 112.3 Electron Beam Ion Traps . . . . . . . . . . . . . . . . . . . . . . 13v2.3.1 Processes in an EBIT . . . . . . . . . . . . . . . . . . . . 152.3.2 Properties of the Electron Beam . . . . . . . . . . . . . . 182.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223 Experimental Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . 233.1 Radioactive Beam Production and Delivery at TRIUMF . . . . . . 233.2 The TITAN Experimental Setup . . . . . . . . . . . . . . . . . . 254 The Impact of Charge Breeding on PTMS for Radioactive Ions . . . 304.1 Simulated Evolution of Charge States . . . . . . . . . . . . . . . 314.1.1 Charge Breeding SIMulation (CBSIM) . . . . . . . . . . . 314.1.2 Charge-State Evolution . . . . . . . . . . . . . . . . . . . 324.1.3 Threshold Charge Breeding . . . . . . . . . . . . . . . . 334.2 The Optimal Charge-Breeding Conditions . . . . . . . . . . . . . 354.2.1 Quantifying the Precision Gained (GHCI) in PTMS withHighly Charged, Radioactive Ions . . . . . . . . . . . . . 354.2.2 Evolution of the Precision GainGHCI with Various Charge-Breeding Parameters . . . . . . . . . . . . . . . . . . . . 394.2.3 Optimization of All Charge-Breeding Parameters . . . . . 424.2.4 Trends in the Maximum Precision Gain . . . . . . . . . . 454.2.5 Schematic Outline of the Optimization Procedure . . . . . 484.3 A Case Study on 74Rb . . . . . . . . . . . . . . . . . . . . . . . 494.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 515 Systematic Charge-Breeding Studies . . . . . . . . . . . . . . . . . . 525.1 Theoretical Expectations for Charge Breeding in an Electron Beam 535.2 Experimental Procedure for the Production, Detection, and Analy-sis of Charge-State Distributions . . . . . . . . . . . . . . . . . . 575.2.1 Production and Detection of Charge-Bred Ions . . . . . . 575.2.2 Analysis Method of the Time-of-Flight Spectra . . . . . . 605.3 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . 625.3.1 Effect of Varying the Electron-Beam Current . . . . . . . 625.3.2 Effect of Varying the Magnetic Field Strength . . . . . . 65vi5.3.3 Realignment of the Injection Beam Line and EBIT Compo-nents . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675.3.4 Comparison to CBSIM . . . . . . . . . . . . . . . . . . . 705.4 Recommendation for Future Charge-Breeding Studies . . . . . . . 725.5 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 736 Precision Q-value Measurement of the 51Cr(e,ne)51V Reaction . . 756.1 Motivation for the Direct Q-value Determination . . . . . . . . . 756.2 Experiment Details . . . . . . . . . . . . . . . . . . . . . . . . . 786.3 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . 796.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 827 Conclusions and Outlook . . . . . . . . . . . . . . . . . . . . . . . . 85Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88viiList of TablesTable 2.1 Relevant charge-changing processes in an EBIT. . . . . . . . . 17Table 4.1 Expected values used in determining the true precision gainGHCI for a measurement on highly charged 74Rb ions . . . . . 50Table 5.1 Charge-breeding settings for the production of various charge-state distributions by varying the electron-beam current and thecharge-breeding time . . . . . . . . . . . . . . . . . . . . . . 63Table 5.2 Charge-breeding settings for the production of various charge-state distributions by varying the magnetic field strength in thetrapping region and the charge-breeding time . . . . . . . . . . 66Table 6.1 Results for the Q-value determination of the 51Cr(e,ne)51V re-action . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81Table 6.2 Measured cyclotron-frequency ratios and calculated mass ex-cesses of 51Cr and 51V. . . . . . . . . . . . . . . . . . . . . . . 83viiiList of FiguresFigure 2.1 Typical ion trap electrode configurations: linear, hyperbolic,and cylindrical . . . . . . . . . . . . . . . . . . . . . . . . . 7Figure 2.2 Radial cross-section of a linear Paul trap . . . . . . . . . . . . 8Figure 2.3 Schematic of the axial trapping and extraction potentials forthe TITAN RFQ . . . . . . . . . . . . . . . . . . . . . . . . . 9Figure 2.4 Trajectory of an ion in a Penning trap . . . . . . . . . . . . . 10Figure 2.5 Schematic of the ion extraction electrodes between the MPETand MCP detector . . . . . . . . . . . . . . . . . . . . . . . . 11Figure 2.6 A TOF-ICR resonance for 39K4+ with a TRF = 166 ms excitation 12Figure 2.7 Illustration of an EBIT . . . . . . . . . . . . . . . . . . . . . 14Figure 2.8 Schematic of the TITAN EBIT . . . . . . . . . . . . . . . . . . 14Figure 2.9 Cross-section view of the EBIT gun assembly at TITAN . . . . 18Figure 2.10 Herrmann radius of the electron beam as a function of theresidual magnetic field at the cathode . . . . . . . . . . . . . 20Figure 3.1 The experimental halls at ISAC . . . . . . . . . . . . . . . . . 24Figure 3.2 The TITAN experiment depicting the location of the ion traps . 26Figure 3.3 The trapping region of the TITAN EBIT . . . . . . . . . . . . . 27Figure 3.4 Time-of-flight spectra of highly charged ions after extractionfrom the EBIT with and without BNG operation . . . . . . . . 28Figure 4.1 Charge-state evolution of Rbq+ for E = 1.30 keV . . . . . . . 33Figure 4.2 Charge-state evolution of Rbq+ for E = 1.35 keV . . . . . . . 34ixFigure 4.3 Charge-state evolution of Rbq+ for threshold charge breedingto the Ne-like configuration at E = 3.1 keV . . . . . . . . . . 34Figure 4.4 Evolution of GHCI(q, tCB, 50 A cm2, 3.1 keV) for 74Rbq+ . . 40Figure 4.5 Evolution of GHCI(q, tCB, 500 A cm2, 3.1 keV) for 74Rbq+ . 41Figure 4.6 Evolution of GHCI(q, tCB, 5000 A cm2, 3.1 keV) for 74Rbq+ . 41Figure 4.7 Intensity plot of GHCI(qopt , topt , J, E) for 74Rbqopt+ with con-tours specifying qopt . . . . . . . . . . . . . . . . . . . . . . . 43Figure 4.8 Intensity plot of GHCI(qopt , topt , J, E) for 74Rbqopt+ with con-tours specifying topt . . . . . . . . . . . . . . . . . . . . . . 44Figure 4.9 Plot of GHCI(qopt , topt , J = 50 to 5000 A cm2, E) for 74Rbqopt+ 46Figure 4.10 Plot of GHCI(q= 137+, topt , J =500 A cm2, E) for 74Rb137+ 47Figure 4.11 Schematic outline of the optimization procedure for GHCI . . . 48Figure 5.1 Time-of-flight spectrum of charge-bred Rb for E = 3.1 keV,I = 100 mA, B = 4.28 T, and tCB = 5 ms . . . . . . . . . . . 59Figure 5.2 Time-of-flight spectra of charge-bred 85,87Rb for E = 3.1 keV,I = 100 mA, B = 4.28 T, and tCB = 3.75 ms and 5 ms shownwith envelopes . . . . . . . . . . . . . . . . . . . . . . . . . 59Figure 5.3 Time-of-flight spectra of charge-bred 85,87Rb for E = 3.1 keV,I = 100 mA, B = 4.28 T, and tCB = 3.75 ms and 5 ms shownwith T (dT ) . . . . . . . . . . . . . . . . . . . . . . . . . . . 62Figure 5.4 Results of changing the electron-beam current and charge-breedingtime on the production of charge-state distributions . . . . . . 64Figure 5.5 Results of changing the magnetic field strenght in the trappingregion and charge-breeding time on the production of charge-state distributions . . . . . . . . . . . . . . . . . . . . . . . . 66Figure 5.6 Photograph of the collector misalignment looking down theaxis of the beam line . . . . . . . . . . . . . . . . . . . . . . 68Figure 5.7 Photograph of the realigned collector looking down the axis ofthe beam line . . . . . . . . . . . . . . . . . . . . . . . . . . 69Figure 5.8 Time-of-flight spectrum of charge-bred 85,87Rb for E = 3.1 keV,I = 100 mA, B= 4.28 T, and tCB = 5 ms for comparison to CBSIM 71xFigure 5.9 Charge-state evolution of 85Rbq+ for threshold charge-breedingconditions at E = 3.1 keV for comparison to an experimentalcharge-state distribution . . . . . . . . . . . . . . . . . . . . 71Figure 6.1 Energy spectrum of solar neutrinos and energy thresholds forneutrino detectors. . . . . . . . . . . . . . . . . . . . . . . . 77Figure 6.2 Ratio of observed to predicted event rate for the neutrino sourceexperiments with gallium at SAGE and GALLEX. . . . . . . . 77Figure 6.3 A TOF-ICR resonance for 51Cr5+ with a TRF = 160 ms excita-tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79Figure 6.4 Ratio of cyclotron frequencies between 51Vq+ and 51Crq+ . . 82xiGlossary3D three-dimensionalBNG Bradbury-Nielsen gateCBSIM Charge Breeding SIMulationCX charge exchangeEBIT electron beam ion trapEBIS/T electron beam ion source and trapEEC Experiments Evaluation CommitteeEC electron-captureECRIS electron-cyclotron resonance ion sourceEI electron impact ionizationFEBIAD forced electron beam induced arc dischargeFT-ICR Fourier-transform ion-cyclotron-resonanceGALLEX Gallium ExperimentHCI highly charged ionsIG-LIS ion-guided laser ion sourceISAC Isotope Separator and ACceleratorxiiISOL isotope separation on-lineLEBT low energy beam transportMCP micro-channel plateMPET measurement Penning trapPTMS Penning-trap mass spectrometryRFQ radio-frequency quadrupoleRF radio-frequencyRIB radioactive ion beamRILIS resonant ionization laser ion sourceRR radiative recombinationSAGE Soviet-American Gallium ExperimentSCI singly charged ionsSI International System of UnitsSIS surface ion sourceTITAN TRIUMF鈥檚 Ion Trap for Atomic and Nuclear scienceTOF-ICR time-of-flight ion-cyclotron-resonanceTRIUMF Canada鈥檚 National Laboratory for Particle and Nuclear PhysicsxiiiAcknowledgmentsI would like to extend a special thanks to the TITAN collaboration, in particu-lar Martin Simon, Renee Klawitter, Ania Kwiatkowski, Aaron Gallant, and BradSchultz, for their efforts in assisting with data taking and interpretation, revis-ing of drafts, and providing a supportive work environment. For my supervisor,Jens Dilling, who provided continual insight in to project details, encouragementthroughout the degree, recommendation for local and international conferences,and commitment to helping me succeed, I am extremely grateful.I am grateful for the variety of programs that provide financial support to grad-uate students. The funding that I received from the NSERC CGS-M program, theCanadian Institute of Nuclear Physics, and the University of British Columbia,has allowed me to pursue different ideas and conferences throughout my degree.I would also like to acknowledge the referees that assisted me in obtaining thisfunding: Rob Mann, professor at the University of Waterloo; Jens Dilling, DeputyDivision Head of Science at TRIUMF; and John Behr, Research Scientist at TRI-UMF.This project could not have happened without the continual support from myfriends and family. A special thanks to my parents, Sue and John, for being therethrough the good times and the bad. To my loving husband, Andrew, thank you foryour everlasting patience, editing of manuscripts, and endless enthusiasm. Finally,I would like to thank everyone that I encountered over the course of my degree fortrading stories, keeping things running smoothly, and smiling back.xivChapter 1Introduction1.1 Fundamental ScienceThere are many open questions in the field of nuclear and particle physics thatreveal how little is known about the universe. Consider, for example, that ordinarymatter consists of only about 4% of the entire mass of the universe, and the other96% has not been identified; or that the production of elements heavier than ironis still not understood; or that neutrinos, fundamental particles in the StandardModel, have only recently been described as having a mass, yet their mass remainsunknown. These are only a few of the greatest unanswered questions in physics[1]. The research dedicated to addressing these and other outstanding questionsin physics will greatly impact the future of research in yet unimaginable ways.TRIUMF, Canada鈥檚 National Laboratory for Particle and Nuclear Physics, has amission 鈥渢o make discoveries that address the most compelling questions in particlephysics, nuclear physics, nuclear medicine, and materials science鈥 and increase ourfundamental understanding of how nature works.Accelerator facilities [2], like TRIUMF, offer a unique opportunity to studyparticle interactions, test and refine new theories, and develop new technologies.Access to radioactive ion beams (RIBS) allows experimenters to perform researchon short-lived isotopes and fundamental particles under extreme conditions that areotherwise inaccessible. This research is typically performed by creating increas-ingly exotic nuclides and by improving the precision of critical measurements [3],1as is done at many of the experiments at TRIUMF. The TITAN (TRIUMF鈥檚 IonTrap for Atomic and Nuclear science) collaboration [4] contributes to the precisionfrontier by measuring the masses [5] and nuclear decay branching ratios [6, 7] ofexotic nuclides with high precision and accuracy. These precision measurementsmake subtle and important contributions to our fundamental knowledge of particleinteractions.1.2 Masses and MotivationHigh-precision mass measurements reveal a fundamental property of each nuclide[8]. Lighter than the sum of all the constituent masses, the mass of a nucliderepresents the net effect of all the interactions within the nuclide, both atomic andnuclear. This value is of critical importance in the study of nuclear and particlephysics as it provides insight into the three primary areas of research: nuclearstructure, nuclear astrophysics, and fundamental symmetries and interactions. Therequired precision of a given mass measurement depends on the science case ofinterest and typically corresponds to a relative mass uncertainty in the range ofdm/m鈬 106109.Penning-trap mass spectrometry (PTMS) currently sets the standard for accurateand precise mass measurements [9]. Reaching precisions of up to 1011 on stablebeam [10], the manipulation of ions for PTMS has been well developed, extensivelystudied, and is fast enough for use with short-lived isotopes. For these reasons,most RIB facilities are coupled to Penning traps across the world, including TITANat TRIUMF [5], ISOLTRAP at ISOLDE (CERN) [11], LEBIT at NSCL/MSU [12,13], JFYLTRAP at the University of Jyva篓skyla篓 [14], SHIPTRAP at GSI [15], andTRIGA-TRAP at the TRIGA Mainz research reactor [16]. These facilities havedifferent RIB production techniques and preparation methods, making a wide rangeof isotopes accessible and providing a unique research niche for each facility.The PTMS technique used to determine the mass of an exotic nuclide resultsin a relative mass precision [17] given by the magnetic field strength B used inconfining the ions, the excitation time TRF of the ions in the Penning trap, thecharge state q of the ions, and a statistical factor depending on the number of ions2N measured: dmm 碌 mq e B TRF pN . (1.1)With the magnetic field strength suffering from technical limitations (currentlyBmax 鈬 9.4 T at LEBIT [13]), and the excitation time limited by the half-life ofthe isotope of interest, there are few strategies left for increasing the relative massprecision in a given measurement. TITAN is the only Penning trap setup at a RIBfacility to take advantage of the potential precision gained by increasing the chargeof the ions prior to a mass measurement. This unique ability becomes more impor-tant as the isotopes of interest lie closer to the limits of existence as they typicallyhave very short half-lives (< 100 ms) and are increasingly difficult to produce. TheTITAN collaboration specializes in the measurement of highly charged, short-livedisotopes with up to part-per-billion precision.1.3 Charge Breeding for PTMS with Highly Charged,Radioactive IonsAny additional stage in beam preparation has to be both fast and efficient in orderto benefit mass measurements on short-lived nuclides with low production rates.During the process of charge breeding many charge states become populated, re-ducing the number of ions available for measurement in any single charge state.However, there are two devices designed for increasing the charge state of ionsthat have been extensively studied and compared for use at accelerator facilities[18]: the electron-cyclotron resonance ion source (ECRIS) and the electron beamion source and trap (EBIS/T). These comparisons have shown that EBIS/Ts producenarrower charge-state distributions, are better at accepting low-intensity beams,and have lower amounts of contamination from charge-bred residual gas. For thesereasons, the TITAN collaboration has built and commissioned an electron beam iontrap (EBIT) [19, 20] for their mass measurement program. Optimization of thisdevice addresses questions like which charge state to use, how long the charge-breeding process will take, and whether or not the losses due to radioactive decayand efficiencies are worth the precision gained by increasing the charge state forthe mass measurement.3Successful measurements on charge-bred RIB have already been made at TITAN.For example, in the study of fundamental interactions, 74Rb was measured in the 8+charge state and a relative mass precision of 81 ppb was obtained in only 22 hours[21]: an improvement over the 53 ppb measured at ISOLTRAP in three combinedmeasurement campaigns [22鈥24]. In nuclear astrophysics, extreme environmentslike neutron star mergers or core-collapsed supernovae result in the production ofexotic nuclides that are difficult, if not impossible, to produce at existing RIB facil-ities. However, the masses of these nuclides are critical for calculations that willhelp explain the production of elements heavier that iron, and researchers oftenhave to rely on extrapolated mass values. Results from an experiment on neutronrich rubidium isotopes [25] provided accurate mass values which differed fromprevious measurements by up to 11s . These results also allowed for additionalextrapolated mass values for more exotic nuclides. Most recently, a mass measure-ment [26] on charge-bred isotopes for neutrino physics studies was able to rule outa potential cause of a calibration discrepancy in the long-standing gallium anomaly[27], and is discussed as a part of this thesis work. Investigations into the efficiencyof charge breeding and developing a systematic way to determine how to balancea reduced excitation time and efficiency with an increased charge state will impactand benefit future mass measurements at TITAN.1.4 Outline of the ThesisThe research described in this thesis investigates how to improve the precision ofPenning-trap mass measurements through charge breeding, in particular for nu-clides with short half-lives that lie at the limits of the nuclear chart. The need forprecision mass measurements and the motivation for charge breeding are presentedin Chapter 1, with an emphasis on the importance of charge breeding as the iso-topes of interest become increasingly exotic. Chapter 2 provides a background onion manipulation, Penning traps, and ion processes in an EBIT. The TITAN experi-mental setup is described in Chapter 3.The detailed studies unique to this thesis begin in Chapter 4 with simulationsof the charge-breeding process. A numerical algorithm that provides a systematicapproach to balancing an increase in charge state with a decrease in efficiency and4excitation time is discussed. Applying the procedure to a proposed part-per-billionmass measurement on 74Rb provides context for the simulations. The assumptionsthat are made in the simulation are discussed in detail and compared to experi-mental results in Chapter 5. A complementary chapter on a mass measurement forneutrino physics studies is motivated and presented in Chapter 6. In this chapter,the gallium anomaly is considered in the context of a possible calibration discrep-ancy at solar neutrino experiments SAGE and GALLEX. The thesis is summarizedin Chapter 7, and possible future developments are suggested. The result of thepresented research will be used in the planning of future mass measurements atTITAN and will enable measurements on isotopes further from stability and to everincreasing precisions.5Chapter 2Manipulation and Preparation ofRadioactive IonsThe 1989 Nobel Prize in Physics [28] was awarded for the development of the ion-trapping technique, which introduced measurement methods that would be used totest fundamental physics principles and theories [29]. Notably, precision measure-ments in ion traps have lead to the development of the frequency standard [30] andoptical clocks [31], allowed for a precise determination of the electron magneticmoment and an improved measurement of the fine structure constant [32], andmost recently, a measurement of the atomic mass of the electron to high precision(dm/m鈬 1011) [33].Most applications of ion trapping rely on three-dimensional (3D) confinementof charged particles. Axial trapping can be achieved by creating a potential wellfor the charged particles, typically done with a series of three or more electrodesof varying bias. Typical electrode configurations are seen in Figure 2.1. Since itis not possible for electrostatic fields to form a 3D potential minimum (Earnshaw鈥檚Theorem) in which the ions can be trapped, radial confinement is achieved usingdifferent techniques. Standard techniques and applications of charged particle trapsare discussed in this chapter in the context of the TITAN facility. These include thebunching and cooling of radioactive ion beams, Penning-trap mass spectrometry(PTMS), and charge breeding, each of which relies on a different technique for ionconfinement.6Figure 2.1: Typical ion trap electrode configurations: a) linear trap consistingof four segmented rods; b) hyperbolic trap consisting of two end capsand a ring electrode; and c) cylindrical trap consisting of a series ofcylindrical electrodes (drift tubes) (modified figures b) and c) from Ref.[29] c2010 Taylor & Francis. Reproduced with permission).2.1 Paul Traps and the Radio-Frequency QuadrupoleTrapA Paul trap [34] uses time-dependent electric fields in the trapping region for 3Dion confinement. In Figure 2.1a), the electrode configuration for a simple linearPaul trap is shown; four rods are segmented into three regions and a potential dif-ference between the end and central electrodes defines the axial trapping region. Inthis region, an electric quadrupole field is created by applying opposite polaritiesto neighbouring rods (Figure 2.2). The resulting field focuses the ions in one di-rection and defocuses in the other. By switching the bias in the trapping region ata radio-frequency, the sign of the quadrupole field alternates and 3D confinementis achieved. The result is the radio-frequency quadrupole (RFQ) linear Paul trap,which has applications in various fields, including at RIB facilities, as discussedbelow.The production mechanism of radioactive ions at RIB facilities is not alwayssuited for precision experiments; the resulting ion beam can have too large ofan emmitance and some experiments, including the mass-measurement setup atTITAN, require small bunches of ions and not a continuous ion beam. An addi-7-V/2 -V/2 +V/2 +V/2 x y z b) a) Figure 2.2: Radial cross-section of a linear Paul trap: a) equipotential lines ofthe quadrupole field, and b) electrode configuration. Neighbouring elec-trodes are of opposite polarity to generate the quadrupole field, which isswitched at a radio-frequency to provide radial ion confinement.tional stage of beam preparation during the production and delivery of the radioac-tive ions can thus be beneficial for many experiments at RIB facilities. An RFQcooler and buncher can be applied for this purpose. In practice, the central trap-ping region of an RFQ can consist of many segmented electrodes that are used tocreate a potential gradient and guide the ions into and out of the trap. The rods ofthe TITAN RFQ consist of 24 segments that are used to create a trapping and extrac-tion potential. These potentials are shown schematically in Figure 2.3. Collisionalcooling takes place by injecting a neutral buffer gas (i.e., H or He) into the trappingregion, and as the ions loose kinetic energy they accumulate in the axial potentialminimum of the trap (Figure 2.3). By switching to the extraction potential, the ionsin the extraction region will exit the trap in a well-defined ion bunch. This coolingprocesses takes place on a sub-millisecond timescale [35], and as a result, manyRIB facilities make use of an RFQ cooler and buncher [36] for beam preparation.Details on the TITAN RFQ cooler and buncher can be found in Ref. [37].8Figure 2.3: Schematic of the axial trapping (black) and extraction (red) po-tentials for the TITAN RFQ. The extraction potential is used to create anion bunch separate from the incoming continuous beam (purple) (figurefrom Ref. [38] cMaxime Brodeur. Reproduced with Permission).2.2 Penning Traps for PTMSAnother way to achieve radial confinement is to apply a strong magnetic field alongthe trap axis, as in a Penning trap [39]. Hyperbolic electrodes, as seen in Figure2.1b), with a potential difference between the end caps and the ring electrode pro-vide axial confinement of the ions while generating an electric quadrupole field.The superposition of electric and magnetic fields results in harmonic ion motion atthree different eigenfrequencies: axial wz, magnetron w+, and reduced cyclotronw, as depicted in Figure 2.4. The two radial motions are coupled to the truecyclotron frequency wc of the ion via:wc = w+ +w , (2.1)which is directly related to the mass m of the ion by:wc = qBm , (2.2)9Figure 2.4: Trajectory of an ion in a Penning trap. The combined motion(black) and independent eigenmotions are shown: harmonic oscillationin the axial direction (blue); reduced cyclotron motion (green) and mag-netron motion (red) (figure from Ref. [29] c2010 Taylor & Francis.Reproduced with permission).Here, q is the charge and B is the magnetic field strength along the trap axis.Both the classical and quantum mechanical physics principles guiding an ion ina Penning trap are well understood [39], which makes manipulation of the ion鈥檚motions and measurement of the cyclotron frequency and mass possible.2.2.1 Measurement CycleDetails on high-accuracy mass spectrometry with stored ions, including differ-ent measurement techniques, can be found in Ref. [9]. At TITAN, the cyclotronfrequency is determined by the time-of-flight ion-cyclotron-resonance (TOF-ICR)technique [40], which requires a prepared bunch of ions for a measurement. Prefer-ably consisting of only one ion, the bunch is set to specific and reproducible initialconditions [41] and injected into the Penning trap on a pure magnetron radius. A10Figure 2.5: Schematic of the ion extraction electrodes between the MPET andmicro-channel plate (MCP) detector. The time of flight of the extractedions to reach the detector is recorded for the TOF-ICR technique (detailsin text) (figure from [38] cMaxime Brodeur 2010. Reproduced withPermission).quadrupole excitation of frequency nRF , amplitude ARF , and duration TRF is thenused to excite the radial motion of the ions [42]. For nRF 鈱 nc a resonance con-dition is satisfied and for a specifically chosen TRF and amplitude ARF , an excita-tion will convert pure magnetron motion into reduced cyclotron motion, changingthe energy of the ion bunch from a minimum to a maximum. The bunch is ex-tracted onto a micro-channel plate detector (Figure 2.5) and the time of flight ofthe bunch to reach the detector is recorded. Repeating the cycle while scanningnRF around the expected cyclotron frequency will produce a resonance spectrum(Figure 2.6) where the true cyclotron frequency corresponds to a minimum in thetime of flight (maximum energy after extraction). For a non-destructive techniquethat does not require extraction of the ions, the Fourier-transform ion-cyclotron-resonance (FT-ICR) [43] technique can be employed; however since the exotic nu-clides studied at RIB facilities typically have short half-lives, injection and extrac-tion of new ions would have to occur on a timescale of a few half-lives regardless.As a result most Penning-trap facilities studying short-lived nuclides employ theTOF-ICR technique, with SHIPTRAP being a notable exception [44].2.2.2 Accuracy and Precision of a Penning-trap Mass MeasurementMass determination by PTMS is currently accepted as the most precise and accu-rate method of determining atomic masses [3]. The technique has been extensivelystudied with stable ions [39], ensuring its accuracy to very high precision; withstable isotopes a relative mass uncertainty of dm/m鈬 1011 [10] has been demon-strated. A considerable advantage of PTMS is that the technique is independent ofwhether it is performed on stable or radioactive ions. All of the systematic inves-11 32 34 36 38 40 42-15 -10 -5  0  5  10  15Time - of - Flight  (碌s)谓RF - 5831553 (Hz)39K4+ Figure 2.6: A TOF-ICR resonance curve for 39K4+ with a TRF = 166 ms ex-citation. The average time-of-flight and one standard deviation uncer-tainties (black) are shown with a theoretical fit [42] to the data (red) asa function of the excitation frequency nRF .tigations and calibrations with stable ions can be directly applied to measurementson radioactive ions. The relative uncertainty for a frequency measurement usingthis technique [17] is approximated by a semi-empirical formula given by:dncnc 碌 1ncTRFpNions , (2.3)where dnc is the uncertainty obtained from the determination of the cyclotron fre-quency nc, TRF is the excitation time of the ions in the Penning trap, andpNions is astatistical factor depending on the number of detected ions Nions. When discussingthe precision of a measurement, the convention taken is that precision is the inverseof the relative uncertainty, and either term may be found in the discussion1.There are a few limitations when dealing with exotic nuclides that reduces1For example, a relative mass uncertainty of 1011 corresponds to a measurement made to 1 partin 1011 or a measurement precision of 1011.12the attainable precision. With either stable or radioactive ions, the excitation timeis limited by the maximum storage time that ions can be trapped; however, withradioactive ions there is a fundamental limit caused by the ion鈥檚 half-life. Thus,as the nuclides become increasingly exotic with shorter half-lives, the maximumstorage time decreases, as does the attainable precision. Another limiting factoris the number of ions that can be measured during an experiment, which relies onthe yield of isotopes and the total allotted measurement time. As the production ofexotic nuclides becomes more difficult, the yield decreases and puts an additionalconstraint on the statistical factor. If this cannot be compensated for by longermeasurement times, the resulting precision will suffer.One way to compensate for these losses in precision is to increase the chargestate of the ion. Since the cyclotron frequency scales linearly with the charge state(Equation 2.2), performing the measurement on a highly charged ion will reducethe relative uncertainty (increase the precision). It is this relationship that moti-vates charge breeding, particularly when the science case demands a certain preci-sion and the aforementioned limitations make the measurement otherwise impossi-ble. Coupling a charge breeder to a Penning-trap facility thus creates opportunitiesto perform high-precision measurements on nuclides further from stability withshorter-half lives and limited yields.2.3 Electron Beam Ion TrapsAn electron beam ion trap (EBIT) [45] consists of a series of cylindrical electrodes(drift tubes, Figure 2.1c)) through which a dense electron beam, compressed bya strong magnetic field, passes. The negative space charge of the electron beamis responsible for the radial confinement, whereas the drift tubes at the end ofthe trapping region create an axial potential barrier. The main components of anEBIT are the electron gun, the drift tubes, the magnet chamber, and the collectorassembly, all shown in Figure 2.7. For external injection and extraction, additionalbeam line elements are required, as seen in the schematic of the TITAN EBIT inFigure 2.8.In the case of external injection, ions are injected into the trapping region andconfined axially by raising the potential on the end drift tubes. The electron beam13Figure 2.7: Illustration of an EBIT. From left to right: the electron gun as-sembly, the magnet coils and drift tube assembly, and the collector as-sembly. Typical trapping potentials are shown. (figure from Ref. [38]cMaxime Brodeur. Reproduced with permission).Figure 2.8: Schematic of the TITAN EBIT. From left to right: the electron gunassembly, the magnet chamber and drift tube assembly, the injectionoptics, and the collector assembly (Credit: Image Courtesy of TITAN).14originates at the cathode, passes through the trapping region reaching a focus at thetrap centre, and diverges onto the collector assembly. In the region of electron-ionoverlap charge-changing interactions occur, where the ions lose electrons to thebeam (ionization), and recombine with electrons from the beam (recombination);these and additional processes are discussed below. After allowing charge breedingto take place, the highly charged ions can either be studied in trap (e.g. [46鈥49]),or extracted by switching to an extraction potential on the drift tubes. Variousapplications for the study of highly charged ions are possible [50], and an EBIToffers advantages in beam preparation, including the rapid production of narrowcharge-state distributions.2.3.1 Processes in an EBITOptimization of the EBIT settings for use with radioactive ions requires a quali-tative understanding of the charge-changing processes that occur in the trappingregion. An overview of the relevant processes and charge-breeding parameters arediscussed below. The notation follows the convention used in Ref. [51], and amore quantitative discussion of the cross-sections and rate equations can be foundin Ref. [52].IonizationThe transition from a singly charged ion A+ to a highly charged ion Aq+ in anelectron beam occurs through successive electron impact ionization. Each electronimpact ionization (EI) depends on the energy of the electron beam E and the ion-ization potential Ip(q+) of the q+ ion. The likelihood of an interaction occuring isdetermined by the cross-section sEI(E, Ip(q+)), which follows the semi-empiricalLotz formula [53]. For the ionization of a given charge state, the cross-sectionhas three main features: it is zero while E < Ip; it peaks for 2Ip < E < 3Ip; andit falls asymptotically back to zero as E ! 鈥. As the ion reaches higher chargestates, the magnitude of the cross-section decreases, although the trends remainthe same. The resulting ionization occurs in a step-wise fashion until the ioniza-tion potential exceeds the electron-beam energy. Given an infinite amount of time,successive electron impact ionization would result in all of the ions accumulating15in the highest possible charge state; however, as electron impact ionization com-petes with recombination processes, an equilibrium charge-state distribution willcomprise many charge states.RecombinationThe relevant recombination processes in an EBIT are radiative recombination (RR)and charge exchange (CX) [51]. In the former, a free electron recombines withan ion resulting in the emission of a photon (reverse photoionization). Qualita-tively, the cross-section for radiative recombination increases with the charge stateand decreases with the electron-beam energy: lower energies and higher chargestates favour recombination. In the latter, an electron bound to one ion or atom istransferred to another. Due to the strong Coulomb repulsion between interactingions, the only relevant charge exchange interaction in an EBIT is between ions andneutral gas atoms or molecules. The recombination formed by charge exchange isindependent of the electron-beam properties, as such it can be reduced to a neg-ligible level by charge breeding in ultra-high vacuum conditions and using shortstorage times. For these reasons, charge exchange is considered to be a negligibleprocess for the remainder of the text.Charge-Changing Rates for Ions in an Electron BeamThe charge-state distribution evolves according to the coupled rate equations of allpossible charge states:dNqdt = REIq1REIq RRRq +RRRq+1 +Rother . (2.4)where dNqdt is the rate of change of the number of ions in charge state q and Rrepresents the rates for electron impact ionization and radiative recombination thatcontribute to the number of ions in charge state q. The rates Rq are summarized inTable 2.1, where J is the current density of the electron beam, Nq is the number ofions in charge state q, and sq represent the respective cross-sections. An additionalfactor fe;q that describes the overlap of the electron beam with the ion bunch hasbeen included to account for the fact that not all ions will be contained within16the electron beam at all times. Lower-order processes, such as charge exchange,resonant processes, and non-charge changing processes, including escape from thetrapping region, are grouped in the term Rother.Table 2.1: Relevant charge-changing processes in an EBIT.Reaction Process RateEI Aq + e ! Aq+1 +2e REIq = J Nq s EIq fe;qRR Aq + e ! Aq1 + g RRRq = J Nq s RRq fe;qSubstituting the information in Table 2.1 into Equation 2.4 and neglecting theterm Rother gives:dNqdt = J fe;q鈬 EIq1 Nq1s EIq Nqs RRq Nq +s RRq+1 Nq+1鈱 . (2.5)This equation brings important features of charge breeding in an EBIT to attention:1. The rate of ions entering and leaving the charge state q scales with theelectron-beam current density and the electron-ion-overlap factor.鈥 Since the electron-beam current density, electron-ion-overlap factor,and interaction time all play the same role in the charge-state evolution,changing the electron-beam current density or electron-ion overlap fac-tor will either speed up or slow down the charge-breeding process.2. The cross-sections couple the evolution of the charge states q 1, q, andq+1:鈥 Since the cross-section depends on the electron-beam energy, changingthe electron-beam energy will change the charge-state abundance atany given time.In terms of optimizing the EBIT for PTMS with radioactive ions, these two featuressuggest that appropriate tuning of the electron-beam properties can reduce radioac-17Figure 2.9: Cross-section view of the EBIT gun assembly at TITAN. The cath-ode (red) emits the electrons, which are pulled by the focus (dark green)and accelerated towards the left through the anode (blue). The buckingcoils (grey) are used to reduce the residual magnetic field at the cathode(Credit: Image Courtesy of TITAN).tive decay losses and maximize the abundance of ions in the desired charge state.A detailed discussion of the electron-beam properties follows.2.3.2 Properties of the Electron BeamThe properties of the electron beam in the trapping region are determined by a num-ber of factors, including elements in the electron gun assembly, the trap electrodes,and the magnetic field. The gun assembly, which consists of a cathode, anode andfocus electrodes, and bucking coils, is shown in Figure 2.9 for the TITAN EBIT.The cathode is biased and heated resulting in thermionic emission of the electrons[54] which are pulled off of the cathode by the focus and accelerated towards the18anode. The electron-beam current can thus be controlled by adjusting the bias onthe focus electrode. The electron-beam energy at the trap centre is defined by thepotential difference between the bias on the cathode and the bias on the central trapdrift tube (Figure 2.7). Since the drift tube potential should be fixed to within a fewtens of volts of the ion beam transport energy for optimal trapping, the cathode biascan be adjusted to obtain the desired electron-beam energy. Finally, the electron-beam current density will depend on the electron-beam current and the size of theelectron beam, which is in part shaped by the bucking coils. The bucking coils areused to reduce the magnetic field at the position of the cathode (discussed below).The equations and discussion relevant to calculating the electron-beam radiuscan be found in Ref. [51] and are summarized herein. The smallest possibleelectron-beam radius would occur if the electrons were pulled off the cathode atzero-temperature and in a magnetic field free region. Under these conditions, theelectrons, compressed by the magnetic field B in the trapping region, would forma beam with the Brillouin radius [55]:rb[m] = 1.5鈬104B[T] s Ie[A]pE[keV] (2.6)However, this is an overestimate of the compression achieved since the cathode isheated and not located in a magnetic field free region.Herrmann theory [56] defines the electron-beam radius through which 80% ofthe beam passes as:rH = rbvuut12 + 12s1+4鉁8kTcr2cmee2r4bB2 + B2cr4cB2r4b鈼 , (2.7)rminH = limBc!0(rH) 鈬 2.50 路104 T 1/4c rrcB . (2.8)Here, Tc, is the temperature of the cathode; Bc is the residual magnetic field at thecathode; rc is the cross-sectional radius of the cathode鈥檚 emitting surface; k is theBoltzmann constant; me is the mass of the electron; e is the charge of the electron;all units are in SI. Making use of the bucking coils in the gun assembly to zero19 0 100 200 300 400 500 600 0.1  1  10  100  1000Herrmann Radius (碌m)Magnetic Field at the Cathode (G)(0.1 G,  30.7 碌m) (10 G,  33.9 碌m)(350 G, 150.1 碌m)(2000 G, 358.4 碌m)(4000 G, 506.9 碌m)Herrmann Radius (碌m)Figure 2.10: Herrmann radius of the electron beam as a function of the resid-ual magnetic field at the cathode for typical values in the TITAN EBIT:Tc = 1470 K, rc = 0.00170 mm, B= 4.5 T, E = 2.5 keV, Ie = 0.100mA.the magnetic field at the cathode results in the minimum attainable beam radius,shown in Equation 2.8.At TITAN, the cathode is typically heated to Tc = 1470 K and has an emis-sion surface with rc = 1.70 mm [19]. For an electron-beam energy of 2.5 keVand current of 100 mA, the resulting smallest possible electron-beam radius whenoperating in a 4.5 T magnetic field is 30 碌m. However, simulations of the EBITmagnetic field show that the residual magnetic field at the cathode can exceed 0.2 T(2000 G) [57]. The growth of the electron-beam radius as a function of the mag-netic field at the cathode for these conditions is shown in Figure 2.10; a factor of5 increase in the Herrmann radius is possible with a magnetic field of only a fewhundred Gauss at the cathode.The electron-beam radius will affect both the current density and the electron-20ion-overlap factor. A beam radius of rH=30-150 碌m corresponds to a current den-sity ranging from 110-2700 A cm2 according to:J = 0.8 Ie[A]p rH [cm]2 . (2.9)This range of electron-beam current densities has the potential to change the rate ofcharge evolution by more than an order of magnitude. Thus, correcting for residualmagnetic field at the cathode to reduce the electron-beam radius is a critical stepin preparing for charge breeding. Despite this, the smallest possible electron-beamradius is not necessarily optimal if it is smaller than the initial radius of the injectedions. In this case, the electron-ion-overlap factor, defined as the ratio of the numberof ions inside the electron beam Ninq to the total number of trapped ions Nq:fe;i 鈱 NinqNq , (2.10)will increase with the electron-beam radius. The so-called effective current densityJe f f = J fe:q , (2.11)takes both the true electron-beam current density and electron-ion overlap factorinto account, and a balance needs to be achieved between having a radius that islarge enough to overlap with the ions while still maximizing the current density.Procedurally it is best to optimize the ion injection to achieve a small initial radius,minimize the residual magnetic field at the cathode, and provide smaller electronbeam compression as needed by reducing the magnetic field at the trap centre untilan optimal balance has been obtained.These theoretical foundations provide the necessary framework for modellingcharge breeding in an electron beam (Chapter 4). Furthermore, assuming that thesefoundations are a good description of the experimental conditions (Chapter 5), theywill also provide a guideline for optimizing the electron-beam properties in anEBIT for PTMS with highly charged, radioactive ions. From the cross-sections, itfollows that the charge-state distribution depends on the electron-beam energy Eand the resulting balance between ionization and recombination processes. Since21the rates for both electron impact ionization and radiative recombination scale withthe effective current density, the evolution of charge states depends on the productJe f f 路 t, where t is the amount of time the ions interact with the electron beam. Bycombining Equations 2.8 and 2.9 the charge-state evolution can be written in termsof parameters that can be independently controlled: the electron-beam current, themagnetic field in the trapping region, and the charge-breeding time. Applicationof the information from this section benefits the goal of optimal charge breedingfor PTMS on radioactive ions, creating an efficient stage of beam preparation andallowing for the maximum increase in precision.2.4 SummaryStandard applications of ion traps have been discussed in context of the TITANexperiment. The three different types of ion traps that were discussed, the Paul trap,Penning trap, and electron beam ion trap, have niche applications that complementeach other for precision mass measurements on radioactive ions. For example,the cooling and bunching of ions in an RFQ linear Paul trap occurs on a sub-millisecond time scale, making it a preferred stage in beam preparation at RIBfacilities. On the other hand, the extensive work that has been put into developingPenning traps for precision mass measurements have made it the most precise andaccurate tool for determining the masses of both stable and exotic nuclides.Finally, the use of an EBIT for charge breeding is discussed in some detail,specifically in the context of improving the precision of a mass measurement withradioactive ions. The most relevant charge-changing processes in an EBIT havebeen identified and the rate equation for the evolution of charge states is dis-cussed in detail along with the properties of the electron beam. These foundationshave provided the necessary framework for both modelling and optimizing chargebreeding for PTMS with radioactive ions.22Chapter 3Experimental SetupThe Penning-trap mass measurements made at TITAN are the result of a complexand integrated mixture of experimental apparatuses and techniques that have beendesigned for the production, preparation, and precision manipulation of radioactiveions. An overview of the experimental setup, including the production of exoticnuclides at TRIUMF, is provided in this chapter. Typical operating conditions forthe preparation traps at TITAN are given along with a description of a typical massmeasurement cycle. The discussion provides context for Chapters 4, 5, and 6.3.1 Radioactive Beam Production and Delivery atTRIUMFExotic nuclides are produced at the Isotope Separator and ACcelerator (ISAC) fa-cility [58] at TRIUMF for study in one of the two experimental halls (Figure 3.1).ISAC is an isotope separation on-line (ISOL) [59] facility, where a proton beam isreceived from the TRIUMF main cyclotron. With beam energies reaching up to 500MeV and beam currents of up to 100 碌A, this high-power proton beam is incidenton a target chosen to optimize production of the desired isotope. The radioac-tive isotopes are produced inside the target and diffuse out directed towards an ionsource. The ion source is either a surface ion source (SIS), resonant ionization laserion source (RILIS) [60], forced electron beam induced arc discharge (FEBIAD) ionsource [61], or the newly developed ion-guided laser ion source (IG-LIS) [62], de-23Figure 3.1: The experimental halls at ISAC. The beam line for the ISOL production of radioactive ions at TRIUMFis shown, and includes the proton beam line, target / ion source combination, mass separator, and ion transportsystem. Various experimental setups, including TITAN, are shown. (Credit: Image Courtesy of TRIUMF).24pending on the isotope of interest and the required suppression of contaminationcoming out of the target.The resulting RIB passes through a dipole mass separator with a mass resolvingpower of R= mDm 鈬 3000. All nuclides that have a mass within this resolving powerare separated out, leaving only the isotope of interest, excited nuclear states, andisobars that are too close together in mass. A low energy beam transport (LEBT)line is used to transport the ions as a continuous beam into the ISAC experimentalhall, where yields can be determined based on measurements of characteristic ra-diation (i.e., a , b , g). Subsequently, the beam is delivered as a low-energy beamor reaccelerated for high-energy delivery to the ISAC experimental halls. As seenin Figure 3.1, the ISAC experimental halls hosts a variety of Canadian and interna-tional experiments, including TITAN, that are grouped into experimental areas forlow-energy experiments (60 keV), medium energy experiments (1.8 MeV/nucleon)and high energy experiments (up to 鈬12 MeV/nucleon).3.2 The TITAN Experimental SetupThe TITAN facility is located in the low-energy experimental hall at ISAC and con-sists of three ion traps that are dedicated to the preparation and manipulation ofshort-lived ions for high-precision mass measurements [5] and in-trap decay spec-troscopy [6, 7]. These ion traps are an RFQ [37] linear Paul trap (the TITAN RFQ,Section 2.1), a precision measurement Penning trap (MPET) [63] (Section 2.2), andan EBIT [20, 64] (Section 2.3); their respective locations in the TITAN setup areshown in Figure 3.2. The RIB delivered from ISAC is received at the TITAN RFQ,accumulated, and the energy spread of the beam is reduced through thermalizationwith a helium buffer gas. The ions are extracted as a bunch with a transport energythat is typically in the range of 1 to 3 keV. The ion bunch has two possible paths,as seen in Figure 3.2, depending on whether the experiment is to be performed onsingly or highly charged ions.In the case of highly charged ions, the ions are transported from the TITANRFQ to the EBIT where they undergo charge-changing processes in an electronbeam (Section 2.3.1). The EBIT was built in collaboration with the Max PlanckInstitute for Nuclear Physics in Heidelberg, Germany [65]. The trapping region,25Figure 3.2: The TITAN experiment depicting the location of the TITAN RFQ,the EBIT, the Bradbury-Nielsen gate (BNG), and the MPET. The respec-tive ion paths are shown for SCI A+ (solid purple) and for HCI Aq+(dashed orange) (Credit: Image Courtesy of TITAN).shown in Figure 3.3, consists of eight cylindrical drift tubes placed symmetricallyabout the trapping centre, and a central drift tube separated into eight segmentsto allow radial spectroscopic access to the trapping region for decay-spectroscopy.The central drift tube (Figure 3.3 S1-8), is biased to a voltage near the ion beamtransport energy and the small drift tubes on either side (Figure 3.3 C1 and G1) areused to create the axial potential barriers.The electron gun and collector assembly are designed to allow electron beamcurrents of up to I = 5 A and electron beam energies of up to E = 70 keV. Cur-rently, typical operating values are I = 100 mA and E = 1 to 6 keV. The cryogen-26Figure 3.3: The trapping region of the TITAN EBIT. The trap drift tubes arelabeled out from the central drift tube (S) towards either the gun (G) orcollector (C) assembly, with C1 corresponding to the first drift tube onthe collector side and so on. S1 through S8 denotes the eight segmentsof the central drift tube (Credit: Image Courtesy of TITAN).free magnet chamber holds two superconducting magnetic coils in a Helmholtzconfiguration designed to provide magnetic fields of up to B = 6 T (typically op-erated at B = 4.5 T). On each side of the collector assembly, additional electrodes(Figure 2.8) allow control of the injection into and extraction from the trapping re-gion. Technical details of the design of the TITAN EBIT and first tests with RIB canbe found in Ref. [19, 20]. Many successful measurements for PTMS with highlycharged, radioactive ions have already been demonstrated [21, 25, 66, 67].The ions extracted from the EBIT have velocities that depend on their mass-to-charge ratio, which creates a separation in the time of flight T of different chargestates and species according to:T =s鉁搈q鈼 d22U , (3.1)27Figure 3.4: Time-of-flight spectra of highly charged ions after being ex-tracted from the EBIT with and without Bradbury-Nielsen gate (BNG)operation. 85Rb charge states 4-11+ are marked, as are peaks of nitro-gen, oxygen, and other gas ions (Oq+, Nq+). The red spectrum identifiesthe 85Rb9+ that has been selected by the BNG for injection into the MPET(details in text).where d is the distance to the detector andU is the potential on the segmented drifttube in the EBIT. A micro-channel plate detector can be inserted into the beam lineto produce a time-of-flight spectrum of the extracted ions; an example is shownin Figure 3.4 for charge-bred 85Rb and residual gas ions. The separation in timeof flight allows for charge-state identification, and charge states 4+ through 11+of 85Rb are marked along with peaks corresponding to various residual gas atoms(e.g., nitrogen and oxygen). Since ions in higher charge states move faster throughthe beam line, they have a shorter time of flight and appear closer to the y-axis. Aspecific mass-to-charge ratio is selected for measurement by a BNG [68] before theions are injected into the MPET. The time-of-flight spectrum of ions after selectionby the BNG is also shown in Figure 3.4. For experiments without charge breeding,the ions will bypass the EBIT and be transported directly into the MPET.Once the ions are inside the MPET, they are manipulated with RF-excitationsand extracted to apply the TOF-ICR technique for mass determination (Section282.2.1). A sample resonance curve taken using the TOF-ICR technique with sta-ble 39K4+ beam is seen in Figure 2.6. During a mass measurement each exper-imental resonance is compared to the theoretical resonance curve [42] to deter-mine the best fit for the true cyclotron frequency; in the example resonance curve,nc = 5.831 553 105(77) MHz. Using precise knowledge of the charge state andmagnetic field strength, the mass of the isotope can thus be extracted from:nc = qB2pm . (3.2)The magnetic field strength at the time of measurement is determined by perform-ing reference measurements on an isotope with a well-known mass before and aftereach measurements on the isotope of interest, and interpolating the result. This in-terpolation accounts for linear variations of the magnetic field strength with time[63]. Here, the 39K4+ cyclotron frequency was used as a reference measurementfor a Q-value determination of the 51Cr(e,ne)51V reaction (Chapter 6).During an experiment, data are collected for an amount of time that is chosento minimize the statistical uncertainty while also keeping time-dependent system-atic effects [63] at a minimum. More details regarding the analysis proceduresand systematic effects for a mass measurement can be found in Ref. [63] and arediscussed and applied in more detail in Chapter 6. Future additions to the TITANbeam line will include a multi-reflection time-of-flight spectrometer [69] for beampurification and a cooler Penning trap [70, 71] for reducing the energy spread ofhighly charged ions prior to injection into the MPET. A detailed overview of theTITAN facility can be found in Ref. [5].The TITAN collaboration has demonstrated high-precision mass measurementsand directQ-value measurements with both singly and highly charged ions, rangingfrom studies on the nuclear structure of light halo nuclides 6,8He+ [72], 11Li+ [73],11Be+ [74], to Standard-Model tests with 74Rb8+ [21], and neutrino physics studieswith 71Ga22+, 71Ge22+ [67]. These measurements have covered the shortest half-life and most exotic nuclide measured in a Penning trap as well as new charge-breeding techniques, making TITAN and ISAC a well-established pairing for high-precision mass spectrometry on exotic nuclides.29Chapter 4The Impact of Charge Breedingon PTMS for Radioactive IonsThe techniques for Penning-trap mass measurements on singly charged radioactiveions [17] and on highly charged stable ions [75] were independently developed andcombined for the first time at the TITAN facility. The potential for more than anorder of magnitude in precision gain by increasing the charge state of an ion priorto a measurement makes charge breeding an attractive option; however, employingthis technique with radioactive ions has additional complications due to the limitedyields and inherent losses from radioactive decay. If these losses affect the numberof ions that can be measured, the statistical precision will decrease, possibly negat-ing the precision gained by increasing the charge state. As the only collaborationthat performs PTMS on highly charged, radioactive ions, TITAN has a unique needto address this concern. For the first time, a quantitative and systematic approachthat is based on theory has been established to determine the benefits of chargebreeding on PTMS with radioactive ions.Simulations are a valuable tool in theoretical science as they provide insightinto general trends even before experiments can be performed. Charge breedingin an electron beam is well suited to numerical simulations, where numerical in-tegration of the rate equations from Section 2.3.1 provides the evolution of chargestates as a function of the different charge-breeding conditions. In this chapter, theoutput of a charge-breeding simulation is combined with radioactive decay losses30and experimental efficiencies to allow for a comparison of the precision that wouldbe obtained by performing a measurement on highly charged, radioactive ions toone with singly charged ions. This gain factor, which is sensitive to the charge-breeding conditions and specific to PTMS, forms the basis for an optimization pro-cedure that has been designed to provide the optimal charge-breeding conditionsfor PTMS with highly charged, radioactive ions. The discussion is framed in thecontext of the charge-state evolution of the exotic nuclide 74Rb, which has a half-life of t1/2 = 65 ms. This nuclide has been chosen for two reasons: stable Rb,which has the same electronic properties as exotic Rb nuclides, is easily obtainedfrom a surface ionization source for off-line experiments (Chapter 5); and 74Rblies at the proton drip-line of the nuclear chart and has the shortest half-life of allneutron-deficient Rb isotopes. Hence, 74Rb makes an excellent case study of theeffect of charge breeding for PTMS with short-lived exotic nuclides.4.1 Simulated Evolution of Charge States4.1.1 Charge Breeding SIMulation (CBSIM)Understanding the evolution of charge states of ions in an electron beam and the ef-fect of the charge-breeding parameters is central to preparing for a PTMS measure-ment that will be more precise than one made with singly charged ions. The well-established CBSIM (Charge Breeding SIMulation) [76] is a program that providesthe fraction of ions hpop(q) in a given charge state q for a specified electron-beamcurrent density J, electron-beam energy E, and charge-breeding time tCB. Featuringelectron impact ionization with Lotz cross-sections [53], radiative recombinationand charge exchange (Section 2.3.1), loss of ions by Coulomb heating, and inte-gration on a logarithmic time scale, CBSIM performs numerical integration over thecoupled rate equations from Section 2.3.1 and provides a graphical representationof the result.Since the evolution of charge states under electron impact ionization and ra-diative recombination evolves with the product of J and tCB (Section 2.3.1), thedependent variable in CBSIM is their product, or J-time, in units of A cm2 s. Inputparameters include the electron-beam energy E, the electron ionization potentials31Ip(q+) and binding energies Be(q+) for the nuclide of interest, and the atomic num-ber Z and mass number A of the nuclide. The program also includes the ability toturn processes off and the option to run the simulation with a single ion bunch in-jected at a fixed time or by adding ions to the electron beam at constant rate. For thepurpose of studying the charge evolution at TITAN, the simulation was used withsingle ion bunch injection. Since charge exchange is not an interaction between theions and the electron beam and since the vacuum conditions in the TITAN EBIT arebetter than 109 Pascals, processes involving charge exchange were omitted fromthe simulation. The output of the program is the fraction of ions hpop(q,Jt,E)in each charge state q+, for a range of J-time values, and a given electron-beamenergy E.4.1.2 Charge-State EvolutionAn example of the charge-state evolution of Rb ions calculated with CBSIM for anelectron-beam energy of E = 1.30 keV is shown in Figure 4.1. The initial condi-tions are chosen such that the ion bunch begins with all of the ions in the 1+ chargestate and the electron beam and ion bunch perfectly overlap throughout the evolu-tion. The early transitions out of the low charge states occur relatively quickly, thenas the magnitude of the electron impact ionization cross-section decreases with thecharge state, the evolution slows down. The result, when plotted on a logarithmicJ-time scale, is the nearly equidistant appearance of successive charge states. Avertical line drawn at any given J-time intersects with the charge-state abundancesof the corresponding charge-state distribution. For example, at a J-time of 0.1 Acm2 s, the charge-state distribution runs from charge state 5+ to 11+ with the8+ charge state having the maximum abundance of about 30%. For most valuesof J-time, the maximum abundance in a single charge state is around 30%, witha notable exception for a J-time greater than 500 A cm2 s. For greater values,the relative composition of the ion bunch is no longer changing. This equilibriumcharge-state distribution consists of about 70% of the ions in the 26+ charge state,20% in the 25+ charge state, and only 10% populating the maximum charge stateof 27+.32 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1e-05  0.0001  0.001  0.01  0.1  1  10  100  1000  10000Charge state abundance 畏popJ-time (A cm-2 s)Rb1-27+1.30 keVFigure 4.1: Charge-state evolution of Rbq+ for E = 1.30 keV. A vertical sliceat fixed time shows the charge-state distribution of an ion bunch aftera given J-time. Every fifth charge state (bold red) and the maximumcharge state (dashed black) are emphasized to guide the eye.4.1.3 Threshold Charge BreedingA Rb27+ ion is in a Ne-like electronic configuration, which forms a closed elec-tronic shell. At closed shells there is a gap in ionization potentials to reach the nextcharge state: here Ip(26+) = 1294 keV and Ip(27+) = 3129 keV. This gap allowsfor a wide range of electron-beam energies to produce Ne-like Rb without ionizingRb27+. From the discussion in Section 2.3.1, the maximum value of an electronimpact ionization cross-section is for an electron-beam energy that is 2-3 times theionization potential, and the radiative recombination cross-section decreases withenergy. Thus, by changing the electron-beam energy within this gap in ionizationpotentials, the relative abundances of the equilibrium charge states can be changed.Figure 4.2 shows that a change in the electron-beam energy of only 50 eV, fromE = 1.30 keV to E = 1.35 keV, significantly changes the equilibrium charge-statedistribution: the fraction of ions in the 27+ charge state has increased to over 50%33 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1e-05  0.0001  0.001  0.01  0.1  1  10  100  1000  10000Charge state abundance 畏 popJ-time (A cm-2 s)Rb1-27+1.35 keVFigure 4.2: Charge-state evolution of Rbq+ for E = 1.35 keV. As the en-ergy increases from 1.3 keV, the equilibrium begins to favour 27+ over26+. Every fifth charge state (bold red) and the maximum charge state(dashed black) are emphasized to guide the eye. 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1e-05  0.0001  0.001  0.01  0.1  1  10  100  1000  10000Charge state abundance 畏 popJ-time (A cm-2 s)Rb1-27+3.10 keVFigure 4.3: Charge-state evolution of Rbq+ for threshold charge breeding tothe Ne-like configuration at E = 3.1 keV. Depletion of the 1+ chargestate takes slightly longer than at E =1.3 keV due to the smaller EIcross-section at low charge states, but the equilibrium charge-state dis-tribution greatly favours 27+ by taking advantage of the threshold effect(see text). Every fifth charge state (bold red) and the maximum chargestate (dashed black) are emphasized to guide the eye.34from 10% due to the increased ionization cross-section and reduced recombinationcross-section. By choosing an electron-beam energy that is just below the thresh-old for ionizing 27+, as in Figure 4.3, the fraction of ions in a single charge state ismaximized, with nearly all the ions in the 27+ charge state and only a small amountin the 26+ charge state.It is worth mentioning that this so-called threshold charge breeding has anotherpractical application: it can be used to separate isobars (i.e., isotopes with the samemass number A and different proton number Z). For an electron-beam energy thatis at the threshold of opening a closed electronic shell, the maximum charge statewill be element specific, changing the mass-to-charge ratio of the highly chargedisobars. Once the charge breeding is complete, the ions can be extracted and sub-jected to any number of separation techniques that selects only the desired isotopethrough its mass-to-charge ratio. At TITAN this is done by taking advantage ofthe time-of-flight separation and selecting the desired mass-to-charge ratio with aBradbury-Nielsen gate (Section 3.2). This was successfully demonstrated during ameasurement where 71Ge and 71Ga were charge bred to their Ne-like charge statesand separated [67].Threshold charge breeding to a closed electronic shell other than Ne-like (e.g.,He-like, Ar-like) is also possible; however, since the number of ions in a singlecharge state q+ is maximized for 2Ip(q 1) < E < 3Ip(q 1), only closed shellswith a gap in ionization potentials satisfying 2Ip(q 1) < Ip(q) offer this advan-tage. For typical beam energies in the 1 to 6 keV range the Ne-like gap is favourablefor all nuclides with Z = 32 to 52 [77], and for this reason it is the only case con-sidered herein. The advantages of threshold charge breeding are well-known andhave been discussed in Refs. [76, 78, 79].4.2 The Optimal Charge-Breeding Conditions4.2.1 Quantifying the Precision Gained (GHCI) in PTMS with HighlyCharged, Radioactive IonsThe benefits of threshold charge breeding became apparent in the previous sec-tion by studying various equilibrium charge-state distributions produced by CBSIM.35Since threshold charge breeding offers the greatest number of ions in a singlecharge state, it is likely that it offers the optimal charge breeding when prepar-ing for a Penning-trap mass measurement. In order to verify this and to derivemore general and quantitative statements, a variable that is sensitive to the charge-breeding conditions and specific to PTMS is required.For this purposed, a factor that relates the attainable precision of a mass mea-surement made on highly charged ions (HCI) to one made without charge breedingon singly charged ions (SCI) is defined:GHCI = (dm/m)SCI(dm/m)HCI , (4.1)where the relative mass uncertainty from Equation 2.3:dmm 碌 mq B TRFpNdet (4.2)is used. Here q is the charge state, B is the magnetic field strength, TRF is theexcitation time, and Ndet is the number of detected ions. Substituting Equation 4.2into Equation 4.1 for both HCI and SCI gives:GHCI = qsNHCIdetNSCIdet . (4.3)This relative precision gain provides the expected linear increase with charge statewhile including the important contribution from changes in the statistical factorpN. A comprehensive comparison of NHCIdet and NSCIdet follows.The number of ions detected in a measurement will depend on the productionrate of the isotope of interest and the experimental efficiencies; however, specialconsideration needs to be made for when the yield at the MPET, denoted by c ,exceeds one ion per cycle. The TOF-ICR technique is best carried out with only asingle ion in the trap, therefore losses due to transportation, trapping, and chargebreeding will not affect the measurement precision, so long as a single ion is de-livered to the MPET each cycle (c  1). The number of detected ions during ameasurement is then the product of the number of measurement cycles Ncycle with36the number of ions measured per cycle (i.e., either 1 or c):Ndet = ( Ncycle if c  1 (4.4a)Ncycle c if c < 1 . (4.4b)For a measurement with HCI, the number of ions arriving at the MPET is thesame as for a measurement made without charge breeding, but scaled by a survivalfraction: x (q)鈱 2tCB/t1/2 hpop(q) eqHCI/eSCI , (4.5)which accounts for additional radioactive decay losses during the time taken tocharge breed the ions 2tCB/t1/2 , the fraction of ions hpop(q) in the q+ charge stateafter charge breeding, and the losses due to HCI related efficiencies eqHCI (Equation4.7) as compared to the SCI related efficiencies eSCI (Equation 4.6). The efficien-cies: eSCI = eRFQ etrans ePTMS edet , (4.6)eqHCI = eRFQ eqtrans eqPTMS eqdet ein j eext , (4.7)describe how well the system is optimized for a charge state q. This includesthe efficiency for bunching and cooling in the RFQ eRFQ , transportation through therespective beam lines (Figure 3.2) etrans, all efficiencies related to the PTMS processePTMS , detection edet , and the additional HCI efficiencies for injection ein j into andextraction eext from the EBIT. Charge-state dependent efficiencies are marked witha superscript eq.The number of ions arriving at MPET each cycle c can now be defined in termsof the production yield of ions from ISAC, denoted Yp in ions per second, the cy-cle length tcycle, the SCI efficiency eSCI , and the HCI survival fraction x (q) fromEquation 4.5: cSCI = Yp tcycle eSCI (4.8a)cHCI (q) = cSCIx (q) . (4.8b)It is worth noting that since x (q) 铮 1, cHCI (q) will always be less than or equal to37cSCI .When comparing a measurement made with HCI to a measurement made withSCI, three possible scenarios arise:鈥 more than one ion per cycle arrives at the MPET: cSCI ,cHCI  1鈥 more than one ion per cycle arrives at the MPET for SCI only: cHCI < 1铮 cSCI鈥 less than one ion per cycle arrives at the MPET: cSCI ,cHCI < 1Making the appropriate substitution for the number of detected ions per cycle fromEquations 4.4 and 4.8 into Equation 4.3 the complete description of the precisiongained is:GHCI = qsNHCIdetNSCIdet = 8>>><>>>: q if cSCI ,cHCI  1 (4.9a)qqYp tcycle eSCIx (q) if cHCI < 1铮 cSCI (4.9b)qpx (q) if cSCI ,cHCI < 1 (4.9c)In the first case, all losses in the system with either HCI and SCI are compensatedfor by a high production yield, allowing the full factor of q to be exploited. This isusually the case with isotopes in a stable beam. In the second case, the productionyield is enough for an SCI measurement to have more than one ion at the MPETevery cycle, but charge breeding introduces losses after the surplus number of ionsfrom an SCI measurement Yp tcycle eSCI is depleted. Finally, in the third case, theproduction yield is too low for one ion per cycle to arrive at the MPET with eitherSCI or HCI: all additional losses introduced by charge breeding impact the precisiongained.Equation 4.9 fully encompasses all of the independent parameters that affectthe benefit of charge breeding for PTMS with radioactive ions. Careful evaluationof GHCI provides a realistic estimate of the precision gained under the given con-ditions. Many of the relevant terms, like the yield cSCI and the efficiencies eSCI andeHCI , are independent of the actual charge-breeding process and give an indicationof how well tuned the experimental apparatus must be in order to perform a pre-cision measurement. The only term that is affected by the charge breeding is thesurvival fraction x (q).38The rest of the chapter discusses how x (q) can be maximized with an appro-priate choice of charge-breeding conditions. Since Equation 4.9a is trivial, andEquation 4.9b can be obtained by scaling Equation 4.9c bypYp tcycle eSCI , onlyEquation 4.9c is discussed. Furthermore, since the efficiencies serve only as ascaling (which can be factored in as needed) and are independent of the charge-breeding conditions, the following discussion assumes negligible losses, and as-sumes eHCI = eSCI = 1. The resulting expression to be evaluated is:GHCI = qq2tCB/t1/2 hpop(q) . (4.10)The optimization of GHCI in this form balances the seeking of higher charge stateswith the losses introduced by additional radioactive decays and distributing theions over many charge states. Once optimized, both the yields and efficiencies canbe folded in according to Equations 4.5 and 4.9 to determine the actual precisiongain (for an example see Section 4.3).4.2.2 Evolution of the Precision Gain GHCI with VariousCharge-Breeding ParametersThe precision gain, as defined in Equation 4.10, can be calculated for any situa-tion in which the half-life t1/2, the charge state q, the charge-breeding time tCB,and the fraction of ions in the given charge state hpop(q) are known. Experimen-tally, tCB and q are choices that result in a particular fraction of ions, which can bedetermined by performing time-of-flight identification on the extracted ion bunch(Section 3.2). Although it is possible to perform this exercise and calculate GHCIfor various charge states and charge-breeding conditions, it is much simpler andequally informative to use the fraction of ions as determined by CBSIM in the cal-culation of GHCI .Figure 4.4 displays the evolution of GHCI taken from the data in Figure 4.3 withan electron-beam current density of J = 50 A cm2 for 74Rb with a half-life t1/2 =65 ms. At these settings, threshold charge breeding has populated the 27+ almostexclusively once equilibrium is reached, yet a mass measurement on charge state27+ would not offer the optimal precision gain. Rather, the maximum precisiongain is GMAXHCI 鈬 7 6= q for a measurement made on the 17+ charge state. This is a39 0 1 2 3 4 5 6 7 1e-06  1e-05  0.0001  0.001  0.01  0.1  1Effective Precision Gain GHCICharge-Breeding Time (s)Rb1-27+t1/2 = 65 msE = 3.10 keVJ = 50 A cm-2Figure 4.4: Evolution of GHCI(q,tCB, 50 A cm2, 3.1 keV) for 74Rbq+ (t1/2 =65 ms). The maximum precision gain occurs in the 17+ charge state fortCB 鈬 t1/2. When the charge-breeding time exceeds the half-life, GHCIfalls off due to losses from radioactive decay. Every fifth charge state(bold red) and the maximum charge state (dashed black) are emphasizedto guide the eye.consequence of the amount of time it takes to reach the equilibrium distribution:approximately two seconds or more than 30 half-lives. As a result, a measurementmade with the 27+ charge state is comparable to or worse than a measurementmade without charge breeding. This maximum precision gain in the 17+ chargestate occurs after a charge-breeding time that is just less than one half-life.Increasing the current density speeds up the charge-state evolution, as seen inFigures 4.5 and 4.6 for J = 500 and 5000 A cm2, so that higher charge states canbe reached within a few half-lives. In the first plot, Figure 4.5, the optimal chargestate is 27+ after a charge-breeding time of about 100 ms. The maximum precisiongain of 15 is a result of the threshold charge breeding and higher current density40 0 2 4 6 8 10 12 14 16 1e-06  1e-05  0.0001  0.001  0.01  0.1  1Effective Precision Gain GHCICharge-Breeding Time (s)Rb1-27+t1/2 = 65 msE = 3.10 keVJ = 500 A cm-2Figure 4.5: Evolution of GHCI(q, tCB, 500 A cm2, 3.1 keV) for 74Rbq+(t1/2 = 65 ms). The maximum precision gain occurs in the 27+ chargestate since the increased current density makes threshold effects ad-vantageous before radioactive decay-losses diminish GHCI . Every fifthcharge state (bold red) and the maximum charge state (dashed black)are emphasized to guide the eye. 0 5 10 15 20 25 1e-06  1e-05  0.0001  0.001  0.01  0.1  1Effective Precision Gain GHCICharge-Breeding Time (s)Rb1-27+t1/2 = 65 msE = 3.10 keVJ = 5000 A cm-2Figure 4.6: Evolution of GHCI(q, tCB, 5000 A cm2, 3.1 keV) for 74Rbq+(t1/2 = 65 ms). The maximum precision gain occurs in the 27+ chargestate and the full advantage of the threshold effect is available result-ing in GHCI 鈬 q. Every fifth charge state (bold red) and the maximumcharge state (dashed black) are emphasized to guide the eye.41allowing the Ne-like configuration to be reached without substantial decay losses.In Figure 4.6, the optimal charge state is still 27+, but after a charge breeding timeof about 15 ms. This substantial difference in charge-breeding time results in farless radioactive decays during the charge breeding. The full advantage of thresholdcharge breeding is made possible, resulting in a GHCI = 24鈬 q.4.2.3 Optimization of All Charge-Breeding ParametersThe goal of simulating the precision gained by producing HCI under differentcharge-breeding conditions is to provide insight into the optimal way to operatethe EBIT for PTMS. The effect of charge breeding with different electron-beam en-ergies and current densities can be studied by carrying out simulations for a full setof GHCI versus tCB; however, this task would be tedious due to the number of vari-ables and amount of data to consider. Instead of tracking the trends for all chargestates at all charge-breeding times, the problem can be reduced by only consideringthe maximum GMAXHCI (J,E), the optimum charge state qopt(J,E) and the optimiumcharge-breeding time topt(J,E) that result in this gain:GMAXHCI (J,E) = GHCI(qopt , topt ,J,E) . (4.11)As a function of only two variables, this information is easily summarized inan intensity plot with the electron-beam energy on the x-axis, the electron-beamcurrent density on the y-axis, and the maximized precision gain represented by acolour gradient. The optimal charge state and charge-breeding time can be super-imposed on the intensity plot as contours, fully specifying the ideal charge breedingsettings as a function of electron-beam energy and current density. This is shownin Figures 4.7 and 4.8 for contours with qopt and topt respectively. A practical rangeof electron-beam energies (1 to 6 keV) and electron-beam current densities (50 to5000 A cm2), from the discussion of the TITAN EBIT in Section 3.2, were usedto create the intensity plots. A choice of a particular electron-beam energy andcurrent density means that GMAXHCI , qopt , and topt can be identified. For example, ata current density of 50 A cm2 and energy of 3.1 keV, the optimal charge stateis q =17+ after a charge-breeding time between 40 and 60 ms, in agreement withFigure 4.4. At a current density of 500 A cm2 and energy of 3.1 keV, the optimal42 1000  2000  3000  4000  5000  6000Energy (eV) 100 1000Current Density (A cm-2 ) 6 8 10 12 14 16 18 20 22 24 26Effective Precision Gain GHCIRb (t1/2 = 65 ms)Current Density (A cm-2 )27+23-24+21-22+19-20+17-18+Figure 4.7: Intensity plot of GHCI(qopt , topt , J, E) for 74Rbqopt+ with contours specifying qopt . In this range of typicalelectron-beam energies and current densities, charge states q = 17+ or greater provide the maximum precisiongain. As the electron-beam current density increases, so does GMAXHCI , and after a certain critical current density(here about 2000 A cm2) it becomes possible to take advantage of the threshold effect (Ne-like closed electronicshell and an electron-beam energy of 3.1 keV) to maximize the precision gain reaching GHCI 鈬 q = 27+.43 1000  2000  3000  4000  5000  6000Energy (eV) 100 1000Current Density (A  cm-2 ) 6 8 10 12 14 16 18 20 22 24 26Effective Precision Gain GHCIRb (t1/2 = 65 ms)Current Density (A  cm-2 )  0-20 ms 20-40 ms 40-60 ms 60-80 ms 80-100 ms 40-60 ms 20-40 ms 40-60 ms Figure 4.8: Intensity plot of GHCI(qopt , topt , J, E) for 74Rbqopt+ with contours specifying topt . In this range of typicalelectron-beam energies and current densities, the optimal charge-breeding time never exceeds two half-lives, withmost lying in the range topt = 12 t1/2 to t1/2. As the electron-beam current density increases, threshold chargebreeding to Ne-like 74Rb27+ becomes advantageous and the charge-breeding time decreases.44charge state is q =27+ after a charge-breeding time between 80 and 100 ms, whichis in agreement with Figure 4.5.From these intensity plots some general trends for optimizing the charge breed-ing of 74Rb (t1/2 = 65 ms) for PTMS are apparent:1. For any given electron-beam energy in the range shown, GmaxHCI increases withthe current density.2. At high electron-beam current densities, threshold charge breeding to theNe-like configuration creates a clear global maximum in GHCI .3. At lower electron-beam current densities, lower electron-beam energies arefavoured.4. The optimal charge-breeding time does not exceed 2 half-lives.5. The optimal charge state is always q 17+, which corresponds to an empty3d electronic shell, or Ca-like electronic configuration.The most important of these trends is that the electron-beam current density is thelimiting factor in maximizing the precision gained for PTMS with highly charged,radioactive ions. With the potential to increase the precision gained by more thana factor of four, experimentally this means that the current density should be op-timized to be as large as possible. Once this has been accomplished, and the cur-rent density is known, the optimal electron-beam energy, charge state, and charge-breeding time can all be determined; fully specifying the optimal conditions forcharge breeding and the resulting maximum precision gain.4.2.4 Trends in the Maximum Precision GainExperiments often come with undesired constraints, which may make the optimalconditions, as discussed in the previous section, unattainable. For this reason, it isworth exploring what GMAXHCI are possible subject to certain constraints. For exam-ple, once the electron-beam current density has been maximized and determined tobe Jmax, it is no longer necessary to consider the gain that would result from valuesof J. Instead, a two-dimensional slice can be taken at a constant current densityallowing GMAXHCI (Jmax,E) to be graphed as a function of the electron-beam energy.45 10 15 20 25 1000  2000  3000  4000  5000  6000Effective Precision Gain GHCIElectron Beam Energy (eV)505005000Rb (t1/2 = 65 ms)J = [50;89;160;280;500;890;1600;2800;5000] A cm-2                                                             Figure 4.9: Plot of GHCI(qopt , topt , J =50 to 5000 A cm2, E) for 74Rbqopt+(t1/2 = 65 ms). Each curve represents a slice from Figure 4.7 at constantelectron-beam current density. As J increases so does GHCI and thethreshold effect at E = 3.1 keV provides a significant advantage overother electron-beam energies. The curves for J = 50, 500, and 5000A cm2 are highlighted (red) to guide the eye.Figure 4.9 shows a two-dimensional plot of these slices for a set of electron-beamcurrent densities ranging from J =50 to 5000 A cm2.Another possible experimental constraint is on the charge state. For example,if threshold charge breeding is required to separate the desired isotopes from con-tamination (Section 4.1.3) the charge state must be fixed. Since Figure 4.9 onlyconsiders the optimal charge state, the procedure can be extended to identifyingGMAXHCI (q, t,CB J,E) for all charge states. Then, GMAXHCI (q, topt ,Jmax,E) can be plottedagainst the electron-beam energy for each charge state. For a known electron-beamcurrent density, this type of graph provides the most information as it containsGMAXHCI for all charge states and all energies.In Figure 4.10, this has been done for Jmax = 500 A cm2, where the maximumprecision gain from this plot represents GHCI(qopt , topt , Jmax, E). Starting with46 0 2 4 6 8 10 12 14 16 1  2  3  4  5  6Precision Gain GHCIElectron Beam Energy E (keV)Rb1-37+t1/2 = 65 msJe = 500 A cm-21+27+35+Figure 4.10: Plot of GHCI(q = 1  37+, topt , J =500 A cm2, E) for74Rb137+ (t1/2 = 65 ms). For a known electron-beam current den-sity, this plot provides the maximum GHCI for every charge state. Atall energies, GHCI = 1 for q = 1+ and as the charge state increases upto q = 27+, GHCI also increases. After an electron-beam energy of 3.1keV is reached higher charge states become accessible, however GHCIbegins to decrease with the charge state all the way to zero for q = 36+and 37+ (see text). The curve for every 5th charge state (bold red) ishighlighted to guide the eye.q = 1+ and a flat GMAXHCI 鈬 1, the gain increases with increasing charge state up to27+. At electron-beam energies greater than 3.1 keV, the Ne-like shell is openedallowing charge states higher than 27+ to be populated; however, the fraction ofions in these charge states is too small to improve GMAXHCI , which starts to decreasewith increasing charge states. Finally, GMAXHCI is zero for q =36+ and 37+ since theelectron-beam energy does not exceed the ionization potential of Ip(q = 35+) andno ions occupy these charge states. This plot readily provides information on theattainable GMAXHCI if a certain charge state is required for an experiment.47CBSIM&飪&max(GHCI)&Isotope&Z,A(Half4life&t1/2((Breeding&Time&tCB&Charge&State&q&Electron&Beam&E(Electron&Beam&J&Figure 4.11: Schematic outline of the optimization procedure for GHCI . Byspecifying the isotope of interest and its half-life, the optimization pro-vides the optimal q, tCB, E, and J, fully specifying the optimal charge-breeding conditions for PTMS with highly charged, radioactive ions.4.2.5 Schematic Outline of the Optimization ProcedureThe numerical optimization procedure (Figure 4.11) using CBSIM to arrive at theintensity plots and all of the intermediary steps is:1. Populate the precision gain using hpop(q,Jt,E) from CBSIM:=) GHCI(q, tCB,J,E) =q2tCB/t1/2hpop(q,Jt,E)2. For each charge state, electron-beam energy, and electron-beam current den-sity, maximize GHCI(q, tCB,J,E) with respect to time and store the optimaltime:=) GMAXHCI (q,J,E) = GHCI(q, topt ,J,E)=) topt(q,J,E)3. For each electron-beam energy and current density, maximize GMAXHCI (q,J,E)with respect to the charge state, determine the optimal time that correspondsto the charge state, and store the optimal charge state:=) GMAXHCI (J,E) = GHCI(qopt , topt ,J,E)=) topt(J,E) = topt(qopt ,J,E)48=) qopt(J,E)Thus, by specifying the isotope of interest and its half-life, performing a trans-formation to a variable sensitive to the charge-breeding conditions and specific toPTMS, and simulating the precision gained, all of the charge-breeding parameterscan be optimized for PTMS with highly charged, radioactive ions. This stage inpreparation for an experiment with RIB allows for a theoretical start to the opti-mization of charge breeding for PTMS and reduces the amount of time requiredduring an experiment. An example of how this procedure can be used for planningan experiment is provided in the following case study.4.3 A Case Study on 74RbThe 74Rb nuclide is an extremely neutron-deficient nuclide that lies near the protondrip line of the nuclear chart. With a half-life of only 65 ms, it undergoes super-allowed nuclear b -decay to 74Kr. The mass difference, or Q-value, between themother and daughter nuclides in this reaction plays an important role in discrimi-nating between theoretical models of the isospin symmetry breaking correction dc[80]. As a result, the mass of 74Rb has been the subject of a number of investiga-tions [21鈥24] that have aimed for higher and higher precision. The experimentalchallenges in making a high precision measurement on 74Rb lie in its short-halflife and relatively modest yields. This makes it an excellent candidate for a mea-surement in high charge states. Despite the number of measurements that havebeen made thus far, improvements to the precision carry enough importance thatthe Experiments Evaluation Committee (EEC) at TRIUMF has approved a proposalto measure the masses of both 74Rb and 74Kr to even higher precision by usinghigh charge states at TITAN [81].When determining which charge state should be used for the measurement,Figures 4.7 and 4.8 provide full details on the optimal precision gain at the cor-responding EBIT settings. The current densities of 110 and 2700 A cm2, whichrepresent extreme values calculated in Section 2.3.2, offer different optimal charge-breeding conditions and precision gains. At an electron-beam current density of110 A cm2, the optimal charge breeding for PTMS for low electron-beam ener-gies and charge-breeding times on the order of 0.5 t1/2. The optimal charge state49Table 4.1: Expected values used in determining the true precision gain GHCIfor a measurement on highly charged 74Rb ions74Rb Experiment Variables Symbol Value SourceCycle length tcycle 3t1/2 typicalSCI efficiency eSCI 0.1 estimatedHCI efficiency eHCI 0.0009 [81]Production yield (ions/s) Yp 103 [81]SCI yield at MPET (ions/cycle) cSCI = Yp tcycle eSCI 19.5 calculatedHCI yield at MPET (ions/cycle) cHCI = cSCIx (q) < 1 calculatedScaling factorpcSCIeHCI/eSCI 0.42 calculatedis 19+ resulting in GMAXHCI 鈬 9. In this case, threshold charge breeding does notoffer any advantages. At 2700 A cm2, however, threshold charge breeding tothe Ne-like configuration becomes advantageous for an electron-beam energy of3.1 keV, resulting in GMAXHCI 鈬 21. In order to take full advantage of the thresh-old charge breeding and obtain GMAXHCI 鈬 q, an even greater electron-beam currentdensity would be needed.The actual precision gained from performing this measurement depends onthe production yield and expected efficiencies. Expected values at the time of theproposal are found in Table 4.1. Since the expected SCI yield at the MPET cSCI > 1,and the expected HCI yield at the MPET cHCI < 1, the trueGHCI is given by Equation4.9b. The calculated values must be scaled bypcSCIeHCI/eSCI = 0.42. Taking thisinto account for the respective current densities, the expected precisions gained areapproximately a factor of 4 and 10.This information reiterates the importance of maximizing the electron-beamcurrent density for experiment. Based on estimates of the effective electron-beamcurrent density at TITAN (see Section 5.3.4 for details), J 鈬 100 A cm2. Forthe proposed measurement, this implies that TITAN is ready to perform the mea-surements on charge state 19+; however, in order to pursue the full advantages ofthreshold charge breeding to the 27+ Ne-like shell closure, including maximizingthe precision gained while allowing for isobaric separation of possible contaminant50ions, further improvements to the current density are required. Further discussionof the experimental electron-beam current density and possible improvements arediscussed in Chapters 5 and 7.4.4 SummaryTwo open concerns in the field of PTMS with highly charged, radioactive ions havebeen addressed in this chapter for the first time: the first was the lack of a quan-titative description of the benefit of charge breeding for PTMS with radioactiveions; and the second was the need of a systematic way to optimize the charge-breeding conditions before receiving radioactive ions for measurement. For theformer, the precision gain GHCI was defined to reflect the relative precision gain byusing highly charged ions in a measurement instead of singly charged ions. Thisfactor reflected the linear increase with the charge state as well as accounted forall parameters that would affect the statistical precision of a measurement. Afterseparating this precision gain into three different cases that reflected whether theproduction yield was able to fully, partially, or unable to compensate for efficiencyand radioactive decay losses, only the terms that depended on the charge-breedingconditions were extracted to assist in the optimization of GHCI .Based on the intensity plots of GHCI(J,E) there are two steps in optimizingthe charge breeding for any given measurement. Since the maximum precisiongain increases with the electron-beam current density at all electron-beam energies,optimal charge breeding will take place for the maximum possible current density.Since practical limitations will impose an upper limit, it is important to maximizeand determine the operational current density. Once this has been accomplished theoptimal charge-breeding conditions are fully determined from the intensity plotsand contours that provide the optimal electron-beam energy, charge-breeding timeand charge state.51Chapter 5Systematic Charge-BreedingStudiesIn order to gain a deeper understanding of the charge-breeding process, theoreticaldescriptions (Section 2.3) and simulations (Chapter 4) have to be complementedwith experimental studies. In this chapter the theory that was used in the develop-ment of CBSIM is compared to experimental findings. The results will help identifyunder what conditions the findings from Chapter 4 are applicable and will allow forrefinements that improve the compatibility between theory and experiment. Oncethe theory and simulations accurately represent the experimental conditions, thequalitative and systematic approach that was developed to optimize the charge-breeding conditions for PTMS with highly charged, radioactive ions can be appliedexperimentally.The chapter begins with an overview of the theoretical description of chargebreeding in an electron beam (Section 2.3.1), the properties of the electron beam(Section 2.3.2), and some testable predictions for producing experimental charge-state distributions. The variables that theoretically have the greatest impact on thecharge-breeding conditions are discussed throughout the overview. Based on thisdiscussion, the experimental procedure is defined and described. This is followedby a quantitative way to summarize an experimental charge-state distribution byanalyzing time-of-flight distributions, which provides a simple way to comparedifferent charge-breeding conditions. Experimental data were taken with the EBIT52at TITAN under various charge-breeding conditions and compared to expectations.The findings, including deviations from the expected results, are discussed alongwith possible causes. A comparison of an experimental charge-state distributionwith those produced in CBSIM is provided. Finally, additional investigations andimprovements are suggested.5.1 Theoretical Expectations for Charge Breeding in anElectron BeamIn order to define an experimental procedure that can be used to compare exper-iment and theory, it is necessary to review the theoretical descriptions of chargebreeding in an electron beam (Section 2.3) and propose some trends that can betested experimentally. All of the relevant charge-changing processes and charge-breeding parameters were combined in the set of coupled differential equations(Equation 2.5) that describes the rate of change of the number of ions Nq in thecharge state q+:dNqdt = J fe;q鈬 EIq1 Nq1s EIq Nqs RRq Nq +s RRq+1 Nq+1鈱 . (5.1)From this equation, the important charge-breeding parameters were identified: theseare the electron-ion overlap factor fe;q, the electron-beam current density J, thecross sections sq(E) which depend on the electron-beam energy E, and the inter-action time t (i.e., charge-breeding time tCB).Each of these parameters is discussed below in the context of their expectedeffect on an experimentally produced charge-state distribution. Two assumptionsthat were used in the design of the experimental investigations are discussed. Theseassumptions are a direct result of comparing CBSIM to experimental conditionsand they direct the studies towards specific charge-breeding parameters. The the-oretical properties of the charge-breeding parameters of interest are also provided.These are the properties that will be tested experimentally in order to determinethe compatibility between theory and experiment. The provided assumptions andproperties are combined to give one concise testable prediction which forms thefoundation for the experimental studies.53Assumption I: There is perfect overlap between the electron beam and the ionsThe electron-ion-overlap factor fe;q depends on the fraction of ions inside the elec-tron beam, which not only depends on the electron-beam properties, but also onthe initial conditions of the trapped ions. In an ideal scenario there would be per-fect overlap between the electron beam and the ions ( fe;q = 1). One way to obtainthis, regardless of the electron-beam properties, is to deliver a cooled ion bunchto the trapping region on axis with the electron beam with no angular momentum[82]. As CBSIM considers the evolution of charge states for ions in an electronbeam and does not account for any time ions might spend outside of the electronbeam, fe,q = 1 will be assumed for the experimental investigations and the possibleconsequences of this assumption will be discussed.Assumption II: The gain factor GHCI is more sensitive to changes in the electron-beam current density than the electron-beam energyThe electron-beam energy E and resulting cross sections sq(E) couple the rateequations in Equation 5.1. Since the electron-beam energy determines the magni-tude of the cross sections, it is responsible for the fraction of ions in a given chargestate throughout the evolution. In contrast, the electron-beam current density J isa scaling factor in Equation 5.1, and only changes the rate of evolution. Chapter4 discussed the effects of changing both J and E on the factor GHCI (Figure 4.9);while changes in the electron-beam current could increase the expected precisiongain GHCI by more than a factor of three, the electron-beam energy only providedimprovements of up to 50% for threshold charge breeding, and marginal improve-ments otherwise. As a result, the electron-beam current density is expected to playa more crucial role than the electron-beam energy for improving PTMS with highlycharged, radioactive ions. For experimental studies, the energy can be fixed tosome reasonable value (e.g., a threshold energy from Section 4.1.3).Property I: The charge-state evolution scales with the product of the electron-beam current density and the charge-breeding time54Another way to write the rate equations, seen above in Equation 5.1, is by rearrang-ing the scaling factors J and fe;q and grouping them with time in the derivative:dNqd(J fe;q t) = s EIq1 Nq1s EIq Nqs RRq Nq +s RRq+1 Nq+1 .This rearrangement emphasizes the property that J, fe;q, and t play the same role inthe evolution of charge states. Operating under the assumption fe;q = 1 (Assump-tion I), the resulting evolution of charge states scales with the product of J and tCB,or J-time.Property II: The electron-beam current density is proportional to both the electron-beam current and the magnetic field strength in the trapping regionIn order to determine how to produce various charge-breeding conditions, the rel-evant properties of the electron beam from Section 2.3.2 are reintroduced. Theelectron-beam current density, defined in Equation 2.9:J = 0.8 I[A]p rH [cm]2 ,depends on the electron-beam current I and the Herrmann radius of the electronbeam rH in a simple proportionality: J 碌 I r2H . The Herrmann radius was providedin Equation 2.7: rH = rbvuut12 + 12s1+4鉁8kTcr2cmee2r4bB2 + B2cr4cB2r4b鈼 ,where Tc is the temperature of the cathode; Bc is the residual magnetic field at thecathode; rc is the cross-sectional radius of the cathode鈥檚 emitting surface; k is theBoltzmann constant; me is the mass of the electron; e is the charge of the electron;and rB is the Brillouin radius (Equation 2.6):rb[m] = 1.5鈬104B[T] s Ie[A]pE[keV] .Since the cathode temperature and radius are fixed, the best way to control the55electron-beam radius is with the magnetic field at the cathode or in the trappingregion. For typical operation, it is best to minimize the residual magnetic field at thecathode, so the magnetic field strength in the trapping region is a more appropriatevariable to change.The terms in brackets in the Herrmann radius are much larger than unity for thetypical values considered (see Section 2.3.2), consequently, the Herrmann radiusdepends on B according to rH 碌 1pB . Substituting this into the definition of theelectron-beam current density gives:J 碌 I B .It is worth noting that a change in the electron-beam current also changes the Bril-louin radius, however, this has a negligible effect on the Hermann radius for the typ-ical values discussed in Section 2.3.2. For example, for Tc = 1470 K, rc = 0.00170mm, B = 4.5 T, E = 2.5 keV, changing the electron-beam current by more than anorder of magnitude from I = 10 mA to I = 100 mA changes the Herrmann radiusby less than 2% for all values of Bc.Result) a unique charge-state distribution is produced for a uniquecombination of electron-beam current, magnetic field, and charge-breedingtimeThe above assumptions from CBSIM and expected properties derived from a the-oretical description of charge breeding in an electron beam combine to give thefollowing concise statement about charge-state evolution: a unique charge-statedistribution is produced for a unique combination of electron-beam current, mag-netic field, and charge-breeding time. To determine whether or not this condition issatisfied experimentally, different tests can be performed by producing charge-statedistributions under various charge-breeding conditions and comparing the results.Two questions that will be addressed experimentally are the following:鈥 can a change in the electron-beam current or the magnetic field strengthchange the resulting charge-state distribution in a predictable way?鈥 are charge-state distributions that were produced under a constant J-time, ormore specifically a constant product I 路B 路 tCB, unique?56The experimental procedure for these investigations is described in the followingsection.5.2 Experimental Procedure for the Production,Detection, and Analysis of Charge-StateDistributions5.2.1 Production and Detection of Charge-Bred IonsStable Rb isotopes were obtained from a surface ion source below the RFQ in theTITAN experimental set-up (Figure 3.2). The ions were accumulated in the RFQ for100 ms, and were extracted at a beam transport energy of 2.0 keV along the samepath as ions delivered from ISAC (Section 3.2). The potentials that were appliedto the trap drift tubes were optimized to maximize the capture of ions into theEBIT (i.e., biased to approximately 2 kV). For the capture process, the potential onthe first trapping drift tube (Figure 3.3 C1) was raised to create an axial potentialbarrier once the ions were inside the segmented drift tube (Figure 3.3 S1-8). Thetrapped ion bunch was radially confined by the electron beam, which had an energyof E = 3.1 keV. The electron-beam energy was kept constant for the duration ofthe experiments. After allowing the charge-state evolution to occur for a certaincharge-breeding time tCB, the ions were extracted from the EBIT, directed throughthe beam line, and analyzed.The charge-breeding conditions were varied by changing the electron-beamcurrent I, the magnetic field strength in the trapping region B, and the charge-breeding time tCB. The components responsible for changing these parameterswere discussed in Section 2.3.1 and are briefly described here. To change theelectron-beam current, the bias of the focus electrode was varied to change thenumber of electrons being extracted from the cathode. To change the magneticfield in the trapping region, the current in the superconducting coils was variedusing a power supply. This allowed the adjustment of the magnetic field strength.Finally, the charge-breeding time was changed by adjusting the time interval be-tween injecting and extracting the ion bunch into / out of the EBIT.After charge breeding, the extracted ions were transported along the beam line57towards the MPET and a micro-channel plate detector was inserted into the bend inthe beam line (Figure 3.2). The ions had velocities that depended on their mass-to-charge ratio m/q and this created a separation in the time of flight T of differentcharge states to reach the detector according to Equation 3.1:T =s鉁搈q鈼 d22U ,where d is the distance from the EBIT to the detector andU is the potential that wasapplied to the segmented drift tube in the EBIT. The time of flight was recorded,and time-of-flight spectra, like the ones shown in Section 3.2, were created forvarious charge-breeding conditions. This allowed for a qualitative description ofthe charge-state distributions.A time-of-flight spectrum of charge-bred 85,87Rb ions is shown in Figure 5.1for an electron-beam current of I = 100 mA, a magnetic field of B = 4.28 T, and acharge-breeding time of tCB = 5 ms. In this spectrum, charge states q = 4+ through14+ are marked from right to left. Since ions with higher charge states move fasterthrough the beam line, they have a shorter time of flight and appear closer to they-axis. The charge-state distribution peaks for q = 10+, and charge states aboveq = 14+ are hidden in peaks resulting from residual gas (i.e., H, C, N, O) ions.These ions have a shorter time of flight due to their lower mass-to-charge ratio.A double-peak structure is present in the data, where each dominant peak has asecondary peak at slightly larger times. This double-peak structure of the 85,87Rbspectrum could have been caused be a number of effects, including time-of-flightseparation of the two isotopes, a detector effect caused by too many ions saturatingthe micro-channel plate, or a signal effect caused by reflections in the cables. Thesehypotheses were investigated, but none were confirmed experimentally, and nofurther attempts were made as the double-peak structure is inconsequential for theexperimental investigations herein.Decreasing the charge-breeding time shifts the charge-state distribution to lowercharge states and thus appears as a longer time of flight, as seen in Figure 5.2 fortCB = 3.75 ms and tCB = 5 ms. An envelope, drawn through the peak numberof counts in each charge state, assists in comparing the charge-state distributions.58 0 0.5 1 1.5 2 2.5 12  14  16  18  20  22  24  26  28Average Number of Counts per CycleTime of Flight (碌s)85,87Rb tCB=5.00 msI = 100 mAE = 3.1 keVB = 4.28 T4+5+6+7+8+9+10+11+12+13+14+Figure 5.1: Time-of-flight spectrum of charge-bred Rb for E = 3.1 keV, I =100 mA, B = 4.28 T, and tCB = 5 ms. Higher charge states appear at alonger time of flight. The charge states of Rb 4+ to 14+ are labeled. 0 0.5 1 1.5 2 12  14  16  18  20  22  24  26  28Average Number of Counts per CycleTime of Flight (碌s)85,87Rb tCB=5.00 ms85,87Rb tCB=3.75 msI = 100 mAE = 3.1 keVB = 4.28 T4+ 17.57(1)+3.93-2.35 碌s 16.451(8)+2.846-1.871 碌s 0 0.5 1 1.5 2 12  14  16  18  20  22  24  26  28Average Number of Counts per CycleTime of Flight (碌s)85,87Rb tCB=5.00 ms85,87Rb tCB=3.75 msI = 100 mAE = 3.1 keVB = 4.28 T4+ 17.57(1)+3.93-2.35 碌s 16.451(8)+2.846-1.871 碌sFigure 5.2: Time-of-flight spectra of charge-bred 85,87Rb for E = 3.1 keV,I = 100 mA, B = 4.28 T, and tCB = 3.75 ms (shaded blue) and 5 ms(solid black). An envelope passes through the peak number of counts ineach charge state to show qualitative differences between the two distri-butions (details in text). No corrections have been made for backgroundor residual gas ions.59After 3.75 ms of charge breeding, lower charge states have become more popu-lated, higher charge states have become less populated, and the general trend inthe time-of-flight spectrum is to populate longer times. Superimposing the time-of-flight spectra, as in Figure 5.2, is a useful way to compare qualitative featuresbetween charge-state distributions; however, for subtle changes or for comparingmany charge-state distributions, a quantitative indicator that summarizes the keyfeatures of a charge-state distribution is beneficial to the analysis.5.2.2 Analysis Method of the Time-of-Flight SpectraEach experimental charge-state distribution will be analyzed by examining its timeof flight T spectrum and by identifying the time of flight T of the average chargestate Q. Additional information will be obtained by calculating the range of chargestates in the distribution sQ, which leads to asymmetric widths in time of flights卤T . This asymmetry is caused by a decreasing separation in time of flight betweenconsecutive charge states as the charge state increases. The time of flight of theaverage charge state T and the width of the charge-state distribution in time of flights卤T was found to provide a complete description of a distribution for comparingvarious experimental settings in this thesis.The time of flight of the average charge state is found by first mapping thetime-of-flight axis to a continuous spectrum of charges Q = k/T 2, where k is anarbitrary constant. In order for Q to correspond to the charge states marked inFigure 5.1, the constant must be defined as k = pmd2/2U as per Equation 3.1.However, since the procedure is to determine Q and then transform back to timeof flight, the transformation does not depend on the value of k and it can be set tok = 1 for simplicity. Then Qbin = 1T 2bin , (5.2)where Tbin is the time of flight for a single bin in a time of flight spectrum and Qbinis its corresponding charge. The average charge state Q and spread sQ is then:Q = 脗NbinQbin脗Nbin (5.3)60and, sQ =vuut脗QbinQ2Nbin脗Nbin . (5.4)Here, Nbin is the number of counts in a single bin of the time-of-flight histogram,and Qbin is the charge corresponding to the respective bin. The uncertainty in Q isgiven by: dQ = sQ脗Nbin (5.5)Finally, converting back to T gives the time of flight of the average charge state T ,its uncertainty dT , and the asymmetric widths s+T and sT :T = 1pQ , and dT = dQ2pQ3 , (5.6)s+T = 1qQsQ , and sT = 1qQ+sQ . (5.7)Graphically, when T is plotted on the time-of-flight spectrum, it overlaps withthe average charge state of the distribution. Since dT scales with 1/pN, the sizeof the uncertainty in T represents the number of counts in the distribution. Thewidth of the distribution is shown by s卤T . This value represents how spread out thedistribution is in time of flight and how many charge states are in the distribution.Thus all charge-state distributions can be summarized by the quantity:time-of-flight spectrum =) T (dT )s+TsQ . (5.8)The charge-state distributions taken for tCB = 3.75 ms and 5 ms are shown in Fig-ure 5.3, with T (dT )s+TsQ at the top of the graph. As expected, for tCB = 5 ms thedistribution is narrower and T is smaller than for the distribution resulting fromtCB = 3.75 ms. Furthermore, the total number of counts in each distribution hasreduced the uncertainty on T so that the two different charge-state distributions areclearly distinguished by comparing the time of flight of the average charge state forthe two spectra. In order to compare the effect of different charge-breeding condi-tions on the resulting charge-state distributions the quantity T (dT ) is used rather61 0 0.5 1 1.5 2 12  14  16  18  20  22  24  26  28Average Number of Counts per CycleTime of Flight (碌s)85,87Rb tCB=5.00 ms85,87Rb tCB=3.75 msI = 100 mAE = 3.1 keVB = 4.28 T4+ 17.57(1)+3.93-2.35 碌s 16.451(8)+2.846-1.871 碌sFigure 5.3: Time-of-flight spectra of charge-bred 85,87Rb for E = 3.1 keV, I =100 mA, B = 4.28 T, and tCB = 3.75 ms (shaded blue) and 5 ms (solidblack). The time of flight of the average charge state and the asymmetricwidths are shown at the top of the graph in the format T (dT ) s+s .than providing the entire time-of-flight spectrum.5.3 Results and Discussion5.3.1 Effect of Varying the Electron-Beam CurrentData were collected for various combinations of electron-beam current and charge-breeding time at a fixed magnetic field strength of B = 4.28 T. The different com-binations of I and tCB are provided in Table 5.1. For each setting, the resultingcharge-state distribution was analyzed using the time-of-flight method described inthe previous section. A comparison of all the combinations was made by plottingT (dT ) against the product of I and tCB, as seen in Figure 5.4. Lines connect pointstaken at the same electron-beam current and labels indicate the charge-breeding62times. This is done to assist in identifying trends and interpreting the results.Table 5.1: Charge-breeding settings for the production of various charge-state distributions by varying the electron-beam current and the charge-breeding time. Three different values of I 路 tCB were considered. Allexperiments were performed with B = 4.28 T.Electron Charge-breeding time for I 路 tCBbeam current 375 mA ms 500 mA ms 750 mA ms100 mA 3.75 ms 5 ms 7.5 ms75 mA 5 ms 6.67 ms 10 ms50 mA 7.5 ms 10 ms 15 msThere are three trends in the time of flight of the average charge state T that canbe identified from Figure 5.4: changes for constant I; changes for constant tCB; andchanges for constant I 路 tCB. For each electron-beam current, T gradually decreaseswith an increase in the charge-breeding time; this is the same result that was seen inthe comparison of the charge-state distributions in Figure 5.3: higher charge statesare produced after a longer charge-breeding time. A similar trend is noticed fordata taken at constant tCB: increasing the electron-beam current density results in alower T . This trend supports the statement that increasing the electron-beam cur-rent increases the rate of charge-changing interactions and produces higher chargestates in otherwise identical conditions.Increasing either the charge-breeding time or the electron-beam current densityresults in the production of higher charge states; however if the rate of chargeevolution scales with the product I 路 tCB, then T should respond in the same wayto changes in I as changes in tCB. Three different values of I 路 tCB are shown inFigure 5.4 and for any one, T varies greatly for different combinations of I andtCB despite their constant product. Thus, increasing the electron-beam current willresult in higher charge states, as expected; however, charge-state distributions thatwere produced with a constant product of I and tCB are not unique.To explore the effect of changing the electron-beam current further, considerthe point taken for I = 50 mA and tCB = 7.5 ms. Doubling the charge-breeding timeto tCB = 15 ms leads to a shift in T of 2.5 碌s, confirming that higher charge states63 15 16 17 18 19 20 21 22375 500 750Time of Flight of the Average Charge State  (碌s)Electron Beam Current (mA) x Charge Breeding Time (ms)100 mA75 mA50 mA7.5 ms5 ms3.75 ms10 ms6.67 ms5 ms 15 ms10 ms7.5 msFigure 5.4: Results of changing the electron-beam current and charge-breeding time on the production of charge-state distributions. TheT (dT ) from each charge-state distribution is plotted agains the prod-uct of I and tCB for the different charge-breeding settings. Lines repre-sent constant electron-beam current (100 mA in solid black, 75 mA indashed red, 50 mA in dotted blue) and labels indicate the tCB.are reached. However, if instead the electron-beam current is doubled, the shift inT is 5.9 碌 . This implies that doubling the electron-beam current results in a shiftto higher charge states than when the charge-breeding time was doubled. Similartrends can be identified for other combinations of I and tCB, showing experimen-tally that increasing the electron-beam current is more favourable than increasingthe charge-breeding time for producing higher charge states. Returning to Proper-ties I and II, it was originally suspected that the charge-state evolution would scalewith J-time 碌 fe;q I B tCB. Since the magnetic field was not changed, the deviationfrom this expectation can be interpreted in the context of the electron-ion-overlapfactor, which was assumed to be fe;q = 1 (Assumption I). If instead, fe;q was lessthan one and increased with the electron-beam current, then a change in I could64have changed J-time by more than the equivalent change in tCB.The electron-beam current could change the overlap between the electrons andtrapped ions in two ways: the increased number of negative charges in the trap-ping regions could have attracted the positive ions outside of the electron beamcausing them to spend more time in the electron beam; and the electron-beam ra-dius could have increased with the electron-beam current. A better model of thecharge-breeding conditions tested here can be made by comparing charge-state dis-tributions that have the same value of T . For example, assuming instead that J-time碌 Ix 路 tCB, the points sharing the same T can be used to determine the exponent x onthe electron-beam current. Here, I = 75 mA, tCB = 5 ms and I = 50 mA, tCB = 15ms produce the most similar charge-state distributions, resulting inx = ln(t2/t1)ln(I2/I1) 鈬 2.7at the time of these studies. Hence, for a more general model, the assumptionfe;q = 1 is not valid and moreover, fe;q appears to change with the electron-beamcurrent.5.3.2 Effect of Varying the Magnetic Field StrengthData were collected for various combinations of magnetic field strength and charge-breeding time at an electron-beam current of I = 50 mA. The different combina-tions of B and tCB are provided in Table 5.1. For each setting a charge-state distri-bution was analyzed using the time-of-flight method described in Section 5.2.2. Acomparison of all of the combinations was made by plotting T (dT ) against B, asseen in Figure 5.5. Lines connect points taken at the same charge-breeding timeand labels indicate the values of B tCB in tesla-milliseconds. This is done to assistin identifying trends and interpreting the results.There are three trends in the time of flight of the average charge state T thatcan be identified from Figure 5.5: changes for constant B; changes for constant tCB;and changes for constant B 路 tCB. For the former, the same trend that was observedin Section 5.3.1 was confirmed: a longer charge-breeding time results in a lowerT due to a shift to higher charge states over the course of the charge breeding. Asfor constant values of B 路 tCB, only 64.2 T ms is duplicated, and the two settings65Table 5.2: Charge-breeding settings for the production of various charge-statedistributions by varying the magnetic field strength in the trapping regionand the charge-breeding time. All data were taken for I = 50 mA.Magnetic field Charge-breeding time Respective B 路 tCB4.28 T 15 ms 30 ms 64.2 T ms 128.4 T ms3.03 T 15 ms 30 ms 45.5 T ms 90.9 T ms2.14 T 15 ms 30 ms 32.1 T ms 64.2 T ms 15 15.5 16 16.5 17 17.5 182.14 3.03 4.28Time of Flight  of  the Average Charge State  (碌s)Magnetic Field (T)15 ms30 ms64.2 T ms 45.5 T ms 32.1 T ms 128.4 T ms90.9 T ms64.2 T msFigure 5.5: Results of changing the magnetic field strength in the trappingregion and charge-breeding time on the production of charge-state dis-tributions. The T (dT ) from each charge-state distribution is plottedagainst the value of B for different charge-breeding settings. Linesconnect constant charge-breeding time (15 ms in solid black, 30 ms indashed red) and labels indicate the product of B and tCB.66produce charge-state distributions that have values of T that are different by morethan 2 碌s. Finally, for a constant charge-breeding time, increasing the magneticfield can cause either a decrease or an increase in T , which occurs for the transitionfrom 2.14 T to 3.03 T and from 3.03 T to 4.28 T respectively. Since a lower Trepresents higher charge states and more effective charge breeding, this suggeststhat charge breeding was most effective at 3.03 T. This is despite the fact that theelectron beam should be more compressed and thus have a higher current densitywith the stronger magnetic field at 4.28 T. Thus, increasing the magnetic field inthe trapping region does not have a consistent effect on the resulting charge-statedistribution. Furthermore, charge-state distributions that were produced under aconstant product of B and tCB are not unique.Since the expected trends are not clearly present in the experimental data, amore complete description of the experimental conditions is needed. A possibleexplanation for the observed trends could again stem from the idealistic assump-tion that fe;q = 1. The magnetic field in the trapping region is responsible for thecompression of the electron beam, as discussed in Section 2.3.2; however, in thissection it was also mentioned that the smallest possible electron beam is not nec-essarily optimal if it lowers the electron-ion-overlap factor. Since the observedcharge-state distributions combine the effects of charge breeding with ion injectioninto and extraction out of the EBIT, the interpretation of these results is more com-plicated. In the context of Figure 5.5, a possible interpretation is that the charge-breeding conditions were optimal for 3.03 T and that decreasing the magnetic fieldfrom 3.03 T results in a loss of electron-beam current density that outweighs a gainin fe;q. When increasing the magnetic field from 3.03 T the loss in fe;q possibly out-weighs the gain in electron-beam current density. Thus, in order to determine theeffect of electron beam compression on the rate of charge evolution, experimentalconditions where fe;q 鈬 1 are needed.5.3.3 Realignment of the Injection Beam Line and EBIT ComponentsOne of the outcomes of the experimental investigations was the need to determinethe potential cause of poor overlap between the electron beam and the trapped ions.Alignment studies were performed as misalignment between the beam line and the67Figure 5.6: Photograph of the collector misalignment looking down the axisof the beam line. The front and back ends of the ion injection optics(green) and the front of the collector assembly (red) are visible. Thecollector assembly is 7 mm off of the beam line axis.magnetic field axis could cause asymmetric ion injection conditions, leading to apoor electron-ion-overlap factor. The alignment procedure at TITAN has all com-ponents of the beam line aligned to within a millimetre or less. Despite this, it wasdiscovered that there was a misalignment between the electron collector and thebeam axis by 7 mm, as shown in Figure 5.6. The electron gun assembly, whichwas aligned with respect to the cathode assembly, was also misaligned with re-spect to the magnetic field axis by the same amount as a result. This misalignmentcould have had two effects on the charge-breeding investigations: one in regardsto the ion injection and one in regards to the electron-beam properties. These arediscussed below.In an ideal set-up, the magnetic field axis shares the same axis as the beam line.Careful alignment of the TITAN EBIT magnet chamber was performed to achievethis during its initial commissioning. In this case, ion injection can occur on-axisso that the incoming ion bunch only sees an axial magnetic field gradient. This68Figure 5.7: Photograph of the realigned collector looking down the axis ofthe beam line. The cathode is warm and glowing in the centre of thephotograph. The collector assembly, illuminated by the cathode, and ison-axis with both the electron gun and the beam line.on-axis injection minimizes the initial radius of the trapped ions, improving theelectron-ion overlap factor, and maximizing the injection efficiency [82]. A collec-tor assembly misalignment of 7 mm has two effects on incoming ions: since thecollector is no longer aligned with the beam line, part of the opening is blocked(Figure 5.6), and the injection efficiency decreases; and additional steering is re-quired to bring the ions off-axis and through the collector opening, giving thempoor initial conditions and decreasing the electron-ion overlap factor.As for the electron-beam properties, the theory that describes the electron-beamradius from Section 2.3.2 only applies to an electron beam moving along the mag-netic field axis. An electron beam originating off axis suffers from less compres-sion [82], decreasing the current density of the electron beam, and responds lesspredictably to changes in the magnetic field. As a consequence, the assumptionJ 碌 B is not valid with the misalignment present in the system. In order to restorethe system to the desired operating conditions, the electron collector and gun as-semblies were realigned with the beam line, as seen in Figure 5.7. With the electron69gun, magnetic field, collector assembly, and beam line all sharing the same axis, theelectron-ion-overlap factor should be significantly improved and the experimentalconditions should be better described by the outlined theory. Experimental inves-tigations are underway to determine the full impact of this realignment on chargebreeding; these are, however, outside the scope of this thesis.5.3.4 Comparison to CBSIMThe systematic studies of charge breeding under controlled conditions have beenprovided in Sections 5.3.1 through 5.3.3. The experimental findings have demon-strated the importance of the electron-ion-overlap in realizing experimental condi-tions that agree with theoretical expectations. Since the theory used in develop-ing CBSIM is not compatible with the experimental findings from this work, it isnot possible to determine the electron-beam current density based on theoreticalcalculations for use in the optimization of GHCI . Despite this, however, a directcomparison between an experimental charge-state distribution and the charge-stateevolution in CBSIM can be made to determine the electron-beam current densityJCBSIM that is in agreement with CBSIM for the specific charge-breeding settings.To illustrate an example of how this can be done, Figure 4.3 (zoomed in onthe x-axis) and Figure 5.1 have been provided here for comparison in Figures 5.8and 5.9. From the experimental charge-state distribution, after 5 ms of chargebreeding, the maximum charge state is 10+ with small amounts in 5+ and 15+ oneither end of the time-of-flight distribution. In the spectrum from CBSIM, the 10+charge state peaks for a J-time of approximately 0.35 A cm2 s, suggesting that theeffective electron-beam current density in the trapping regions is approximatelyJCBSIM = J-timetCB 鈬 70 A cm2. Since the fraction of ions in 5+ and 15+ in CBSIMis almost zero when the fraction in 10+ reaches a maximum, a more conservativeestimate would be to consider when small but non-negligible amounts of 5+ and15+ are present in the charge-state distribution from CBSIM. Qualitatively, thismight correspond to a J-time of 0.2 to 0.6 A cm2 s, an electron-beam currentdensity of JCBSIM = 40 to 120 A cm2, and an electron-beam radius of rH = 146to 252 碌m (Equation 2.9).70 0 0.5 1 1.5 2 2.5 12  14  16  18  20  22  24  26  28Average Number of Counts per CycleTime of Flight (碌s)85,87Rb tCB=5.00 msI = 100 mAE = 3.1 keVB = 4.28 T4+5+6+7+8+9+10+11+12+13+14+Figure 5.8: Time-of-flight spectrum of charge-bred 85,87Rb for E = 3.1 keV,I = 100 mA, B = 4.28 T, and tCB = 5 ms for comparison to CBSIM.The charge-state distribution peaks at q = 10+ with a small but non-negligible amounts in the 5+ and 15+ charge states. 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.1  1Charge state abundance 畏 popJ-time (A cm-2 s)Rb1-27+3.10 keV10+5+15+Figure 5.9: Charge-state evolution of 85Rbq+ for threshold charge-breedingconditions at E = 3.1 keV for comparison to an experimental charge-state distribution. The 10+ charge state peaks for a J-time 鈬 0.35 Acm2 s and there is a near-negligible fraction of ions in the 5+ and 15+charge states (red) at this value of J-time.715.4 Recommendation for Future Charge-BreedingStudiesBased on the results of these first systematic experimental studies, a series of futureinvestigations and improvements can be recommended. With the discovery of theelectron collector misalignment, it was found that the theoretical descriptions didnot accurately represent the experimental conditions. The subsequent reposition-ing of the electron collector and gun assemblies (Section 5.3.3), will change theion injection conditions as well as the properties of the electron beam. As such,the extent of the improvement to the charge breeding and compatibility with theorywith the realigned system should be investigated. Additional studies could be per-formed for an enhanced understanding of the charge-breeding conditions. Theseinclude:1. Investigating the role of the bucking coils: in Section 2.3.2 the effect ofthe residual magnetic field at the cathode on the electron-beam radius wasdiscussed. With possible changes to the electron beam of more than a factorof five (Figure 2.10), significant changes to the electron-beam current densitycould be made by changing the residual magnetic field at the cathode.The effect of changing the residual magnetic field at the cathode on thecharge-state evolution could be studied by changing current in the buck-ing coils. Experimentally this would be similar to changing the magneticfield in the trapping region; however, the opposite effect is expected sincean increase in the residual field at the cathode expands the electron beam,effectively slowing down the charge-breeding process. This effect could bestudied and quantified.2. Investigating the role of the electron-beam energy: in Section 2.3.2 the ef-fect of the electron-beam energy on the charge-state abundances was dis-cussed. Since the electron-beam energy determines the magnitude of thecross sections for both electron impact ionization and radiative recombina-tion, changes to the electron-beam energy should change the abundance ofions in a given charge state. This was demonstrated with CBSIM for a closedelectronic shell (Section 4.1.3).72Experimentally this can be studied by varying the electron-beam energywithin the gap of ionization potentials and observing the width of the charge-state distribution (s卤T ). If the width of the distribution begins to shrink with-out significantly affecting the centre T , this would indicate that the ions havebegun to occupy fewer charge states and are fully populating the thresholdcharge state.The results of these improvements and investigations will provide additional in-formation on the operation of the EBIT and provide enhanced performance andpredictability of the system.5.5 SummaryA series of experimental studies were designed to test the applicability of the the-ory discussed in Section 2.3.2 as well as the assumptions made when simulat-ing the charge breeding of an ion bunch in an electron beam. The properties ofthe electron-beam current density were the primary focus of the studies due toits potential to improve the precision gained in a PTMS measurement with highlycharged, radioactive ions (Section 4.4). It was found that a charge-state distribu-tion theoretically evolves with the product of the electron-beam current density andthe charge breeding time, and that current density theoretically follows J 碌 B 路 I.Therefore, the primary relationship that was investigated was whether or not I, B,and tCB provided equal contribution to the evolution of charge states.The studies were carried out independently for the electron-beam current andthe magnetic field strength in the trapping region. For the first study, a set ofcharge-state distributions was produced under various combinations of I and tCB.By analyzing the time of flight of the average charge state, it was found that chang-ing the electron-beam current changed the charge-state distribution in a predictableway. Despite this, the charge-breeding time and electron-beam current were notfound to contribute equally to the charge-state evolution as charge-state distribu-tions produced for a constant product of I and tCB were not unique. In the study ofthe magnetic field in the trapping region, changes in B did not have a predictableeffect on the charge-state distributions since an increase in B could either cause ashift to lower or higher charge states for the same charge-breeding time. These73results indicated that the idealistic assumption fe;q = 1 is not valid in our stud-ies. It also demonstrated that fe;q also changes with the electron-beam current andmagnetic field strength in the trapping region.A possible explanation for the observed trends was provided: a misalignedelectron gun and collector assembly. The electron collector and gun assemblieswere found to be 7 mm off from the axis shared by the beam line and the magneticfield. This misalignment could have been responsible for experimental results thatdid not agree with the the theoretical expectations. Additional studies with the elec-tron gun assembly, magnetic field axis, collector assembly, and beam line all on-axis with one another are recommended to determine the effect of these enhancedcharge-breeding conditions. Furthermore, additional tests including varying theresidual magnetic field at the cathode and testing the effect of the electron-beamenergy on the production of charge-state distributions were recommended.74Chapter 6Precision Q-value Measurementof the 51Cr(e,ne)51V ReactionThe technical work outlined in this thesis was complemented by a precision mea-surement [26] of the 51Cr electron-capture Q-value. Both 51Cr and its daughternucleus 51V were produced at ISAC in August 2012. The simultaneous produc-tion of the two isotopes allowed a direct Q-value measurement to be made. TheMPET had been prepared for measurements on ions with a mass-to-charge ratiom/q 鈬 10 as this regime of m/q has been extensively studied at TITAN [63]. Toaccommodate this setup, the EBIT was optimized to maximize the abundance inthe 5+ and 6+ charge states rather than striving for high charge states. The resultsof this experiment are provided in this chapter.6.1 Motivation for the Direct Q-value DeterminationPrecision experiments at radioactive beam facilities [3] have made a significant im-pact on the field of neutrino physics. With the goal of identifying yet undeterminedproperties of the neutrino, high-precision measurements of branching ratios, half-lives, and Q-values have guided the construction of next generation experimentsand refined theoretical models, advancing the field. Penning-trap mass spectrome-try is at the precision frontier for performing direct Q-value measurements [3, 9],providing accurate results that have included shifts from reaction-based measure-75ments of more than five standard deviations (5s ) [83鈥86]. These measurementshave contributed to the search for neutrinoless double-beta decay [87], resonant-enhanced double-electron capture [88], and the determination of the absolute massscale of the electron neutrino [86, 89]. Such experiments, described in detail in Ref.[90], have affirmed the value of Penning-trap measurements in the broad contextof neutrino physics research.A persistent discrepancy in the field of neutrino physics is the so-called galliumanomaly, which resulted from the calibration measurements that were performedat the solar neutrino experiments SAGE and GALLEX. Both SAGE and GALLEXused the 71Ga(ne,e)71Ge neutrino-capture reaction to detect solar neutrinos. Thisreaction offered the advantage of being sensitive to the more abundant, lower en-ergy, solar neutrinos produced from the p-p chain [91]. The range of sensitivityfor different solar neutrino detectors is shown with the calculated energy spectrumof solar neutrinos in Figure 6.1. The results from the experiments with Ga con-firmed the solar-neutrino deficiency [92] that was observed with earlier chlorinedetectors [93]. Calibration measurements were performed using terrestrial neutri-nos from 51Cr electron-capture at GALLEX and both 51Cr and 37Ar electron-captureat SAGE, which 鈥渄emonstrated the absence of any significant unexpected system-atic errors鈥 [94] in the solar neutrino measurements. Despite this, the observedevent rate [95] with these terrestrial sources revealed a 13(5)% deficit when com-pared to the rate predicted by theory [92]. The results of the four calibration mea-surements performed at SAGE and GALLEX are summarized in Figure 6.2. Thisdiscrepancy between observed and predicted event rate has become known as thegallium anomaly [27].Missing knowledge of the underlying nuclear structure involved in the calibra-tion reactions is thought to be a possible cause of the discrepancy. Other possibleexplanations include a statistical fluctuation with 5% probability, miscalculated ef-ficiencies, or physics of unknown origin [95]. A recent white paper [27] exploresthe gallium anomaly in the context of sterile neutrinos and notes that it could be ac-counted for by a massive sterile neutrino. Precision measurements have been madeon the nuclear structure of the detector materials, confirming the 71Ga(ne,e)71GeQ-value of 233.5(1.2) keV [67] and re-evaluating the contribution of the 71Ge ex-cited states to the neutrino capture cross-section for a total of 7.2卤 2.0% [96].76Figure 6.1: Energy spectrum of solar neutrinos and energy thresholds forneutrino detectors. The energy spectrum of the neutrinos from the p-p chain as predicted by the Standard Model is shown. The arrows at thetop indicate the energy sensitivity of different neutrino detectors (figurefrom [91] cAAS. Reproduced with permission).Figure 6.2: Ratio of observed to predicted event rate for the neutrino sourceexperiments at SAGE and GALLEX. The results of the two 51Cr exper-iments at GALLEX and both the 51Cr and 37Ar experiments from SAGEare shown. The the weighted average (solid) and the its uncertainty(dashed) of the four results (data from Ref. [27]).77These results have eliminated any uncertainty in the nuclear structure of the de-tector material at the level required to resolve the gallium anomaly. However, un-certainty in the neutrino source material remains. The 51Cr(e,ne)51V Q-value of752.63(24) keV, as reported in the Atomic Mass Evaluation 2012 (AME12) [97],is dominated by the result of a single reaction-based measurement [98]. Accu-rate knowledge of this value is of great importance as it determines the probabilitythat a neutrino will be captured into an excited state in 71Ge. If the value in theAME12 is artificially inflated by 14 keV or more due to an erroneous measure-ment, then the predicted event rate would have falsely included neutrino captureinto the 499.9 keV excited state and been overestimated by 4.5卤0.4% [96]. Thispotential correction to the gallium anomaly has motivated an independent check ofthe 51Cr(e,ne)51V Q-value using the TITAN facility [4].6.2 Experiment DetailsA review of the TITAN experimental setup can be found in Chapter 3. All three iontraps, the RFQ, the EBIT, and the MPET, were used for the 51Cr electron-captureQ-value measurement. The 51Cr and 51V nuclides were produced by impinging a480 MeV, 10 碌A proton beam from the TRIUMF main cyclotron on a UO2 targetat ISAC. The beam was ionized by a FEBIAD ion source [61] and extracted fromthe target station as a 20 keV continuous ion beam.The ion bunches out of the TITAN RFQ were sent to the EBIT for charge breed-ing by an electron beam with current Ie = 89 mA, and energy Ee = 2.55 keV.The magnetic field strength was 4.5 T and charge-breeding times of 2 and 3 mswere used to optimize the number of ions in charge states 5+ and 6+, respec-tively. The desired charge state was selected by the BNG for injection into theMPET. Additionally, 39K+ ions were delivered from the TITAN off-line ion sourceintermittently between 51Cr and 51V measurements and measured in the 4+ chargestate to obtain a similar m/q-ratio. Resonances were taken with excitation timesof TRF = 60,66,160, and 166 ms, and an example of a 51Cr5+ resonance withTRF = 160 ms is shown in Figure 6.3. Due to the simultaneous delivery of 51Crand 51V, dipole cleaning [99] was required to remove the undesired species fromthe trap before implementing the TOF-ICR excitation. Dipole excitations were ap-78 32 34 36 38 40 42-15 -10 -5  0  5  10  15Time - of - Flight  (碌s)谓RF - 5575115 (Hz)51Cr5+ Figure 6.3: A TOF-ICR resonance for 51Cr5+ with a TRF = 160 ms excitation.The solid line is a fit of the theoretical line shape [42] to the data.plied for 36 ms on ions in charge state 5+ and 30 ms on ions in charge state 6+.6.3 Analysis and ResultsFrequency measurements on the isotopes of interest, 51Cr5,6+, 51V5,6+, and 39K4+,were performed in alternation. Different reference ion species were chosen forthe direct Q-value measurement (51V), and for the mass measurements (39K). Theknown mass and measured frequency of the reference ion were used in the calcu-lation of either the Q-value or the mass M. The frequency measurements of thereference ion were linearly interpolated to account for first order drifts in the mag-netic field [63]. The ratio of this interpolated frequency enc and the frequency ofthe ion of interest nc is then independent of the MPET magnetic field, and it is theprimary result of this experiment. For the direct Q-value measurement:RQ = enc(51VqV+)nc(51CrqCr+) = m(51CrqCr+)m(51VqV+) qVqCr , (6.1)79and for the mass measurement:RM = enc(39KqK+)nc(X) = m(X)m(39KqK+) qKqX , (6.2)where X represents either 51Crq+ or 51Vq+.The Q-value and the mass M are calculated directly from the weighted averageof all measured ratios RQ or RM, respectively:Q = 鈬Q qCrqV 1鈱楳V RQ1 qCr me+RQ qCrqV Be(51VqV+)Be(51CrqCr+) (6.3)MX = RM qXqK MKqK me +Be(39KqK+)+qX meBe(51XqX+) (6.4)where M is the atomic mass, me is the electron mass, and Be is the sum of atomicbinding energies for all electrons missing from the highly charged ion. The refer-ence masses of 51V and 39K were obtained from the AME12 [100], and the bind-ing energies were taken from Ref. [77], with estimated uncertainties in the 10 eVrange. The uncertainty of the Q-value and masses were obtained from propagationof errors, with the primary contribution coming from uncertainty of the measuredratio dR. Since the ratio contains the ionic masses, the analysis was carried out on5+ and 6+ charge states independently.In the direct Q-value measurement, the achieved statistical precision for the fi-nal ratio was dR5+stat = 12.7 ppb and dR6+stat = 21.5 ppb, which was added in quadra-ture to any uncertainty resulting from systematic effects (discussed below). Manyof them/q-dependent systematic uncertainties common to Penning-trap mass spec-trometry, including spatial magnetic field inhomogeneities, harmonic distortions ofthe electrode structure, misalignment between magnetic field and trap axes, and rel-ativistic effects, became negligible [63] by measuring the ratio in an m/q-doublet(i.e., 51Cr5+ with 51V5+, and 51Cr6+ with 51V6+). Along with fluctuations in thetrapping potential, these are all sub part-per-billion (ppb) effects, which is signif-icantly smaller than dRstat . Magnetic field drifts, which have been measured at80Table 6.1: Results for the Q-value determination of the 51Cr(e,ne)51V reac-tion. Both the measured frequency ratio and the resulting Q-value arereported with their total uncertainties.Ion Ref. R = encV / nCrc Q-value (keV)51Cr5+ 51V5+ 1.000015851(14) 752.14(64)51Cr6+ 51V6+ 1.000015827(23) 751.05(108)Average Q-value: 751.86(55)0.04(11) ppb per hour [101], were also neglected as the spacing between referencemeasurements was only 30 to 90 minutes. The frequency measurements were alsoanalyzed with mixed charge-state pairings (i.e., 51Cr5+ with 51V6+, and 51Cr6+with 51V5+), and this variation in m/q produced Q-values all within 1s agree-ment. This consistency suggests that there are no m/q-dependent shifts that wereunaccounted for in the analysis at the desired level of precision.Systematic shifts in the measured cyclotron frequency can be caused by thepresence of contaminant ions in the MPET [102]. Although dipole cleaning wasimplemented on either 51Cr or 51V, there was a risk of non-unity efficiency inthe dipole cleaning, charge exchange with residual gas, and unidentified contam-ination. With a typical measurement consisting of 0-2 detected ions per cycle,possible shifts were accounted for by performing a count-class analysis [103] onall data sets. Measurements with only 1-2 detected ions after extraction fromthe MPET were also analyzed without count-class analysis, and the results werewithin 1s agreement. Finally, a small systematic uncertainty of dR5+sys = 4.6 ppband dR6+sys = 7.4 ppb was introduced by neglecting time-correlations [66] betweenneighbouring ratios. The resulting total uncertainty is thus dR5+ = 13.6 ppb anddR6+ = 22.5 ppb.The results of all ratio measurements are shown in Figure 6.4 for the two chargestates and various excitation times: 61, 66, 160, and 166 ms. The final weightedaverage of the ratios and the resulting Q-value are summarized in Table 6.1. Theresulting Q-value from all data sets is 751.86(55) keV. Furthermore, the absolutemasses of 51Cr and 51V were measured using 39K4+ as a reference ion (see Table81 14800 15000 15200 15400 15600 15800 16000 16200 16400 0  10  20  30  40  50  60R - 1 [ppb]Measurement Number5+; 61 ms 5+; 160 ms 6+;66 ms 6+; 166 msFigure 6.4: Cyclotron frequency ratios between 51Vq+ and 51Crq+ for differ-ent excitation times and charge states. Each point represents the ratioresulting from a single 51Crq+ resonance and its neighbouring 51Vq+resonances. The blue (left) and red (right) lines show the 1s error bandfor all 5+ and 6+ ratio measurements, respectively.6.2). All results are within 1s agreement with the AME12 values, and improve theprecision in the AME12 by a factor of 1.6 and 1.8 for 51Cr and 51V respectively.The Q-value was also derived from the absolute mass difference and the resultagrees with the direct Q-value measurement.6.4 SummaryThe first direct Q-value measurement of the 51Cr(e,ne)51V reaction was made atTITAN. The result, QEC = 751.86(55) keV, is in agreement with the reaction-basedmeasurements summarized in the AME12, differing by 1.3s . The neutrino energyused in the calculations of the predicted event rate for the calibration experimentsat SAGE and GALLEX has thus been verified at this level. As a consequence, theaccessible states of 71Ge in the neutrino capture reaction will remain unchangedin the calculations, and the predicted event rate from the 51Cr neutrino source has82Table 6.2: Measured cyclotron-frequency ratios and calculated mass excesses of 51Cr and 51V. The ratio R(q) =encref/n ionc was measured in two charge states and the average mass excess ME of the neutral atom is tabulated.The results are compared to the AME12 [97].Ion Ref. R(q = 5) R(q = 6) METITAN MEAME DTITAN-AME51Crq+ 39K4+ 1.045996804(16) 0.871654613(20) 51451.71(61) 51451.05(88) 0.66(107)51Vq+ 39K4+ 1.045980222(15) 0.871640810(17) 52203.69(54) 52203.69(88) 0.00(103)83not been overestimated as a result of an erroneous 51Cr electron-capture Q-value.When combined with the results of measurements on the 71Ga neutrino capturereaction, these precision measurements have eliminated uncertainty in the nuclearstructure that could have been responsible for the gallium anomaly, leaving otherpossibilities including new physics and the sterile neutrino hypothesis to explore.84Chapter 7Conclusions and OutlookPenning-trap mass spectrometry (PTMS) is used for the most precise measurementsof atomic masses to date. With measurements on stable nuclides and fundamentalparticles made to within 1 part in 1011, and with measurements on exotic, short-lived nuclides made to within a few parts in 109, PTMS is at the frontier of pre-cision measurements. Performing precision measurements on exotic nuclides istechnically challenging, but as the mass is a fundamental property unique to eachnuclide, accurate and precise knowledge plays a critical role in the advancement ofboth theories and applications of nuclear and particle physics. The first PTMS mea-surement of the mass difference (Q-value) between 51Cr and 51V was provided asa part of this work, along with a novel optimization of charge-breeding techniquesfor Penning-trap mass measurements on highly charged, radioactive ions.Neutrinos are a fundamental particle in the Standard Model, and yet long-standing anomalous results pervade the field of neutrino physics [27]. One suchexample is the gallium anomaly, which arose from measurements made at the so-lar neutrino experiments SAGE and GALLEX. Despite its successes, the theory thatwas used to confirm the solar neutrino deficit was found to be incompatible with theresults of the calibration measurements. A measurement of possible neutrino ener-gies from the source materials that were used in the calibration was carried out byperforming the first direct Q-value measurement of the 51Cr(e,ne)51V reaction.Measurements were made with highly charged ions in the 5+ and 6+ charge states,and a Q-value of QEC =751.86(55) keV was obtained. This result verified the neu-85trino energy used in theoretical calculations at SAGE and GALLEX and was foundto be in agreement with previously made reaction-based measurements. Taken to-gether with measurements of the 71Ga neutrino capture Q-value, this measurementhas eliminated uncertainty in the nuclear structure that could have been responsiblefor the gallium anomaly.The advantage of charge breeding prior for a Penning-trap mass measurementlies in the attainable precision of a measurement: by making use of the time-of-flight ion-cyclotron-resonance (TOF-ICR) technique, the precision scales linearlywith the charge state of an ion. In order to take advantage of this potential gain,the TITAN collaboration operates the only Penning-trap at a rare isotope facilitythat is coupled to an electron beam ion trap (EBIT) charge breeder. This thesis hasaddressed the concerns raised by implementing an additional stage in beam prepa-ration on low yields of short-lived isotopes and has provided a systematic methodof optimization. This optimization will determine which charge state to use, howlong the process will take, and whether or not the losses due to radioactive decayand efficiencies will be worth the precision gained for the mass measurement.The ratio between the attainable precision for a measurement made with highlycharged ions to one made without charge breeding was defined. This factor, GHCI ,reflects the linear increase with the charge state as well as accounts for all param-eters that would affect the statistical precision of a measurement. It was foundthat for sufficiently high yields (i.e., able to fully compensate for radioactive decayand efficiency losses and still result in one trapped ion each measurement cycle)the full factor of q could be exploited. Otherwise, the additional losses that wouldoccur during the charge breeding would reduce the attainable statistical precisionas compared to a measurement without charge breeding. The equations and sam-ple calculations from Chapter 4 fully determine the benefit of charge breeding forPTMS with radioactive ions.Simulations of the charge-state evolution from CBSIM were used to explorethe phase space of charge-breeding conditions and optimize GHCI . The procedurefor identifying the optimal electron-beam energy, electron-beam current density,charge-breeding time, and charge state was provided with an example on the ex-otic nuclide 74Rb (t1/2 = 65 ms). It was found that the optimal electron-beamenergy was for a closed-shell electronic configuration, although variations in the86electron-beam energy did not have a large influence on the maximum attainableprecision. The electron-beam current density, however, was found to play a largerole in obtaining the maximum precision gain. Since increasing the electron-beamcurrent density increases the rate of interaction between ions and electrons in thebeam, it effectively speeds up the charge-breeding process, reducing losses causedby radioactive decay during the charge breeding. As a result, the optimal charge-breeding time was found not to exceed two half-lives.The theoretical foundations used to develop CBSIM were investigated using theTITAN EBIT. The studies focused on the effect of changing electron-beam currentdensity on charge breeding stable Rb ions by making systematic changes to theelectron-beam current and magnetic field in the trapping region. A single testableprediction was defined, which stated that a unique charge-state distribution is pro-duced for a unique combination of electron-beam current, magnetic field strength,and charge-breeding time. Although changes in either the electron-beam currentor charge-breeding time changed the resulting charge-state distribution in a pre-dictable fashion, no other expected trends were confirmed with this experimentalsetup. These results indicate that the idealistic assumption of perfect overlap be-tween the electron beam and the ion bunch is not valid in our studies. Alignmentstudies revealed an offset between the electron collector assembly and the beamline axis that could have been responsible for the trends that were found to beincompatible with the theory. The electron collector assembly, the electron gun as-sembly, and the beam line were all realigned with the magnetic field axis, bringingthe experimental conditions closer to what can be accurately described by theory.Additional tests with the enhanced charge-breeding setup have been recommended.Once a reasonable theoretical description of the experiment has been achieved,the systematic optimization of charge breeding for PTMS with highly charged, ra-dioactive ions can be directly applied. This optimization provides the ideal charge-breeding conditions and reduces the amount of experimental effort required to pre-pare for a high-precision mass measurement. Furthermore, it provides a quanti-tative estimate of the benefit of charge breeding for PTMS by accounting for allrelevant variables in the determination of the attainable precision. This work canbe applied to all future mass measurements at TITAN when determining whether ornot charge breeding is advantageous for a high-precision mass measurement.87Bibliography[1] E. Haseltine. The 11 Greatest Unanswered Questions of Physics. Discover.1 February 2002. Print. ! pages 1[2] Y. Blumenfeld, T. Nilsson, and P. Van Duppen. Facilities and methods forradioactive ion beam production. Physica Scripta, T152:014023, 2013. !pages 1[3] K. Blaum, J. Dilling, and W. No篓rtersha篓user. Precision atomic physicstechniques for nuclear physics with radioactive beams. Physica Scripta,T152:014017, 2013. ! pages 1, 11, 75[4] J. Dilling, P. Bricault, M. Smith, and H.-J. Kluge. The proposed TITANfacility at ISAC for very precise mass measurements on highly chargedshort-lived isotopes. Nuclear Instruments and Methods B, 204:492 鈥 496,2003. ! pages 2, 78[5] J. Dilling and R. Baartman, et al. 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