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K2K near detector laserball calibration : manipulator motivation, design and results 2006

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K 2 K Near Detector Laserball Cal ibrat ion: Manipulator Motivation, Design and Results by Frank Olaf Berghaus B . S c , Saint Mary ' s University, 2003 A T H E S I S S U B M I T T E D I N P A R T I A L F U L F I L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F Master of Science in The Faculty of Graduate Studies (Physics) The University Of Br i t i sh Columbia A p r i l 18, 2006 © Frank Olaf Berghaus 2006 11 Abstract The K 2 K experiment uses a muon neutrino (v^) beam generated at the K E K accelerator facility, aimed at Super-Kamiokande (Super-K) detector 250 k m away, to measure oscillations first seen from atmospheric u's at Super-K. The measurement is done using two detectors. The near detector measures the flux 300 m from the origin of the neutrino beam. The far detector (Super-K) measures the neutrino flux 250 k m downstream. One main source of error in the oscillation measurement is the understanding of the near de- tector. After some optical calibrations along the vertical axis of the One K i l o Ton (1KT) detector found problems wi th the position reconstruction a manipulation system was built. The goal of this manipulation system was to allow exploration of the entire 1 K T volume wi th a calibration source. The design required the manipulation system to place the calibration source to ~1 cm accuracy in the 1 K T , and to avoid all contact wi th the photomultiplier tubes monitoring the tank volume. This manipulation system was built and tested at T R I U M F (Tri-University Meson Facility) and deployed in the 1 K T detector at K E K . The results of the optical position reconstruction indicate a reconstruction bias of unknown origin at high occupancy. i i i Contents A b s t r a c t i i C o n t e n t s i i i L i s t o f T a b l e s . . . v i L i s t o f F i g u r e s v i i i A c k n o w l e d g e m e n t s x i I Thesis xii 1 I n t r o d u c t i o n 1 1.1 Neutrinos 1 1.1.1 Problems 2 1.1.2 Theory 5 1.1.3 Extension to Three Neutrinos 8 1.1.4 Previous Experiments 9 1.2 The K 2 K Experiment 9 1.3 The K E K Proton Synchrotron A n d Beam Line 12 1.3.1 The Neutrino Beam 13 1.4 Near Detector 16 1.4.1 One Ki lo ton Water Cerenkov Detector 17 1.4.2 The Fine Grained Detector 25 1.5 The Super-Kamiokande Detector 27 1.6 The Global Positioning System . . . 28 2 1 K T E x p l o r a t i o n W i t h A Di f fuse r B a l l O n A S t r i n g . . . . 30 2.1 Detector Setup for Opt ica l Cal ibrat ion 31 2.1.1 Laserball Da ta 33 Contents iv 2.2 Opt ical fit for Laserball Position 33 2.3 Position Bias and the Time Charge Correction 38 2.3.1 W i d t h of the Integration Gate 38 2.3.2 Time Charge Correction Problem 38 2.3.3 Reconstruction Bias 40 2.4 Conclusion on Laserball Study 42 3 Manipulator Construction 44 3.1 Motivat ion 44 3.2 Hardware 44 3.3 Electronics 48 3.3.1 L i m i t and Safety Systems 51 3.3.2 The Manipulator Coordinate Systems 54 3.3.3 Manipulator Position 54 3.3.4 The Manipulator G U I 59 3.4 Construction and Assembly 62 3.5 Cal ibrat ion 62 3.5.1 Wobble 65 3.5.2 Total Station 65 3.6 Manipulator Setup A t The 1 K T 69 4 Manipulator Data and Analysis 74 4.1 Da ta Taken In Japan 74 4.1.1 Reconstruction Bias and Fiducia l Volume Study . . . . 75 4.1.2 U p / D o w n Asymmetry and Energy Scale 75 4.1.3 Scattering and Particle Identification 76 4.2 Reconstruction 76 4.2.1 Saturation C u t 78 4.2.2 Geometrical Shadow Cut 78 4.2.3 T iming and Outlier Cut 78 4.2.4 Nominal Laserball Position 81 4.2.5 Results of the Reconstruction 81 4.3 Discussion 87 5 Conclusion 92 Bibliography 93 Contents . v A D a t a W i t h L a s e r b a l l O n A S t r i n g . 96 B M a n i p u l a t o r D a t a 100 C A n a l y s i s C o d e 119 C . l Ntuple Generator 119 C.2 Position Reconstruction 121 v i List of Tables 1.1 K E K Beam Accelerator Components [1] 13 1.2 v Beam Composition A t Origin [2] 14 1.3 G P S Survey of K 2 K Target and Far Detector 15 1.4 Properties of the 20-inch Hamamatsu Photomultiplier Tubes ( P M T s ) used in the 1 K T [1] and [3] ' . 19 1.5 Basic Information on the Super-Kamiokande Detector 28 3.1 Manipulator drive motor specifications 49 3.2 Boundaries for the Manipulator L imi t A n d Safety Systems [4] 58 4.1 Solid angle subtended by more and less responsive areas of the photodiode as seen by the laserball as it moves close to the P M T . The photodiode is modeled as a hemisphere. The central part is 0° to 2° from the top of the of the hemisphere. The middle part is defined as 2° to 10° from the top of the hemisphere. The rest is qualified as the Outer part 91 A . l Da t a Taken W i t h Laserball on String 97 A . 2 Da ta Taken W i t h Laserball on String Part 2 98 A . 3 Da ta Taken W i t h Laserball on String Part 3 99 B . l Summary of manipulator runs taken at K E K 101 B.2 Manipulator runs table 2 102 B .3 Manipulator runs table 3 103 B.4 Manipulator runs table 4 104 B.5 Manipulator runs table 5 105 B.6 Manipulator runs table 6 106 B.7 Manipulator runs table 7 107 B.8 Manipulator runs table 8 108 B .9 Manipulator runs table 9 109 B.10 Manipulator runs table 10 110 List of Tables v i i B . l l Manipulator runs table 11 I l l B.12 Manipulator runs table 12 112 B.13 Manipulator runs table 13 113 B.14 Manipulator runs table 14 114 B.15 Manipulator runs table 15 115 B.16 Manipulator runs table 16 116 B.17 Manipulator runs table 17 117 B.18 Manipulator runs table 18 118 Vll l List of Figures 1.1 Generations of Matter 2 1.2 Energy spectra of neutrinos emitted by the sun and labeled by the reactions that produce those neutrinos [5] 3 1.3 Results of the Super-K neutrino oscillation measurement. This zenith result comes from investigating the muon neutrino anisotropy [6] 1.4 v Propagation and Oscillation 8 1.5 Solar Neutrino Results 10 1.6 Atmospheric Neutrino Results 11 1.7 K 2 K Layout 12 1.8 v Beam Schematic 13 1.9 Beam M C without Oscillation . 15 1.10 Near Detector 16 1.11 1 K T Schematic 18 1.12 Schematic of 20in P M T 20 1.13 1 K T Water Purification System 21 1.14 1 K T Data Acquisi t ion System . . 23 1.15 1 K T Coordinate Systems 24 1.16 1 K T Fiducia l Volume 26 1.17 The Super-Kamiokande Detector 29 2.1 Laser Cal ibrat ion Setup 32 2.2 Finding the t iming peak 35 2.3 Opt ica l F i t t ing for the Laserball Position 36 2.4 Error on Fi t ted Laserball Position 37 2.5 Laserball Reconstruction wi th 10ns Gate 39 2.6 Laserball Position wi th new T Q - M a p 41 2.7 Laserball Monte Carlo Results 43 3.1 Manipulator in 1 K T 46 3.2 Support of the manipulator 47 List of Figures i x 3.3 Manipulator Joints 48 3.4 Schematic of the Manipulator Control System [4] 50 3.5 Inclinometer Board 53 3.6 Side view of manipulator coordinate system 55 3.7 Top view of the manipulator coordinate system 56 3.8 Manipulator Coordinate System 57 3.9 Manipulator G U I 60 3.10 Manual Control G U I 61 3.11 Manipulator Support Test Setup 63 3.12 Test setup of the Manipulator 64 3.13 Manipulator Vertical Section Wobble 66 3.14 A - A r m L i m i t Inclinometer Correction 67 3.15 B - A r m L i m i t Inclinometer Correction 68 3.16 Manipulator Insertion step one 70 3.17 Manipulator insertion step two 71 3.18 Manipulator insertion last step 72 3.19 Canadian Group at K E K with the Manipulator 73 4.1 Time distribution from a run using the bal l on a string. Note that al l P M T s gave mean times wi thin a window less than 3ns wide 77 4.2 A D C Saturation 79 4.3 Manipulator shadow as determined by geometrical ray tracing. The crooked line in the middle represents the location of the arms 80 4.4 Uncorrected Position Offsets 82 4.5 G o o d agreement between nominal and fit positions for the low occupancy data wi th al l cuts and corrections 83 4.6 The nominal and fit positions for the high occupancy data disagree even after al l cuts and corrections are applied 84 4.7 Uncorrected Position Bias 85 4.8 Manipulator Reconstruction Bias 86 4.9 Manipulator Opt ical F i t Accuracy 88 4.10 Position reconstruction bias between high and low occupancy data 89 4.11 Average P M T t iming differences between high and low occu- pancy as a function of distance between P M T and laserball. . 90 List of Figures x C . l F low chart of analysis code used for the manipulator 120 x i Acknowledgements I would like to thank my supervisor Dr . Scott Oser, who motivated this work and greatly supported the work on the manipulator project. I would also like to thank Dr . Richard Helmer, the supervisor of the manipulator project at T R I U M F . The project of course would not have been possible without the hard work of the designers David Morris ( T R I U M F ) , and M a r k Lenkowski (University of Victor ia) . I would also like to thank Dr . Peter Ki tch ing , Dr . Shaomin Chen, Dr . A k i r a Konaka and Dr . Issei Ka to for their assistance and knowledge about the details of the 1KT and the K2K experiment. F ina l ly I would like to thank K e i t h Hoyle ( T R I U M F ) who was of great help in the final assembly of the manipulator. I would like to acknowledge Rich Helmer for upgrading my flight from Tokyo to Vancouver to first class, allowing me to beat Zelda in flight as well as Cadbury Schweppes for their Japanese distribution of Dr . Pepper. Part I Thesis Chapter 1 i Introduction Firs t I wi l l talk about the history of neutrinos from the first predictions to their current place in the Standard Model of particle physics. I wi l l also give a short introduction to the experiments that uncovered the rich field that neutrino physics is today. Next I wi l l discuss the K 2 K ( K E K to Kamioka) experiment and the results of its data run. F ina l ly the near detector system, which the rest of this work wi l l be on, is discussed. 1.1 Neutrinos In 1931 German physicist Wolfgang Paul i postulated a uncharged particle to save conservation of energy in nuclear beta decay [7]. Enrico Fermi took Pauli 's idea and used it in his theory of nuclear decays and dubbed the particle "neutrino" (Italian for "little neutral one"). Un t i l 1953 neutrinos were only needed as a tool to explain missing energy and momentum in beta decays (n^ decays for example). Clyde L . Cowan, Jr and Frederick Reines first observed neutrinos by this reaction [8]: P + p + ^ P + + n° (1.1) Figure 1.1 shows where neutrinos fit into the current picture of the con- stituents of matter. The first piece of information to take from Figure 1.1 is that we have two different types of matter, quarks, which make up hadrons, and leptons. The quarks and leptons are further separated in two rows: quarks wi th charge q = + | are in the top row, those wi th q = — | are placed in the second row. The chargeless leptons (neutrinos) are in the thi rd row, and charged leptons in the last row. Furthermore the particles are organized in three columns by their "flavor". For example the first pair of leptons, the e and ue, are of electron flavor. Interactions of leptons conserve the total number of leptons as well as lepton flavor. Thus the two quarks (or leptons) of each flavor are associated, meaning that if you see one in a reaction, you Chapter 1. Introduction 2 Q ua rk s up charm top Q ua rk s H s b bottom L ep to ns  Ve electron neutrino V H II muon tau neutrino! 1 neutrino L ep to ns  electron |̂  1  ,\t I T 2 photon j \g gluon Vaal |Z O w Z Boson XL Figure 1.1: Matter consists of either hadrons (quarks) or leptons. Each comes in three flavor generations. The first generation holds the lightest and thus stable fundamental particles while the second and third generations hold the heavier counterparts which decay. wi l l likely see the other. Quarks do not conserve flavor, as described by the C K M matrix described in the next section. Antimatter is organized in the same way, just that the internal quantum numbers (like charge, or lepton number) are reversed. For example in beta decay an electron is produced and to balance the total number of leptons and the total number of electron- like particles an electron anti-neutrino is produced as an up quark changes into a down quark (eg. Equation 1.2). d —* uei>e (1.2) Cowan and Reines observed the anti-neutrino associated wi th the electron. In 1962 the Brookhaven National Laboratory ( B N L ) and C E R N reported that neutrinos created in muon decays behave differently from neutrinos produced in beta decays [9] establishing the existence of a second kind of neutrino, called v^. To finish off our current picture the D O N U T experiment found the r neutrino [10], thus giving an uncharged partner to every charged lepton. 1.1.1 Problems Solar Neutrinos The Sun is a natural source of neutrinos, which are produced in the fusion reactions fueling the Sun. Figure 1.2 shows the energy spectra of neutrinos emitted by the Sun. These spectra are calculated using measurements from Chapter 1. Introduction 3 Figure 1.2: Energy spectra of neutrinos emitted by the sun and labeled by the reactions that produce those neutrinos [5]. Chapter 1. Introduction 4 helio-seismology as constraints on the standard solar model. This allows the calculation of the rates for the reactions producing neutrinos in the Sun. Ray Davis d id the first experiment looking at solar neutrinos at Home- stake in 1964 [11]. The number of neutrinos observed by Davis d id not agree wi th the flux predicted using helio-seismology and the standard solar model [12]. In fact Davis observed about a third of the neutrinos that were expected using the solar model. Later the Kamiokande, Sage and G A L L E X experiments also saw fewer solar neutrinos than predicted. The inspiration to explain this problem came from quark flavor mixing. In the decay shown in Equation 1.3 a strange quark turns into a down quark: A° -> pir~ (1.3) This means that the flavor in quarks is not conserved as it is in leptons. The Cabibbo-Kobayashi-Maskawa ( C K M ) matrix describes this "mixing" of quark flavors: f d'\ s' Vud Vcd vtd Vt ta vub vtb s J V b ) (1.4) where the V-mat r ix is the C K M matrix. The u, c and t are coupled in C C interactions to d', s' and b' respectively, rather than the original d, s and b quarks. This allows reactions in which quark flavor changes. The inconsistency between neutrino observations and the solar model prediction can be explained by neutrino oscillations which follow from a sim- ilar mixing to the quark mixing described in Equation 1.4 [13]. Neutrino oscillation wi l l be discussed in Section 1.1.2. Atmospheric Neutrinos Neutrino oscillations were first observed with the Super-Kamiokande exper- iment. The Super-Kamiokande experiment now is the far detector for the K 2 K experiment. Atmospheric neutrinos are produced in hadronic showers caused by cosmic rays entering the atmosphere. Most cosmic rays are pro- tons or light nuclei. When these hit the upper atmosphere a hadronic shower composed of pions and a few other light hadrons is caused. Since over 95% of a l l neutrinos below lOOGeV come from the (charged) pion decay chain and Kamiokande and Super-Kamiokande are sensitive to neutrinos wi th less Chapter 1. Introduction 5 energy than 8 G e V , we can ignore the other hadron decay chains [14]. Equa- t ion l .5 shows the relevant decays: p± -y e± + ue(ue) + vJyVy) The final state electron quickly dissipates in the atmosphere only leaving some photons. So we expect to see two muon-(anti)neutrinos for every elec- tron (anti)neutrino. The Kamiokande and S K detector cannot tell the matter and antimatter states apart, thus we sum over the two. This ratio holds even when considering a large range of other particles in the hadronic showers and a larger window of neutrino energies [14, 15]. Furthermore the cosmic radiation incident upon the atmosphere is isotropic, and neutrino interactions wi th matter are negligible. Thus we expect to see an isotropic distribution of neutrinos from the Super-Kamiokande experi- ment. Super-K found that neutrinos oscillate by observing an anisotropic muon neutrino flux and by comparing theoretical and experimental ratios of muon to electron neutrinos. Figure 1.3 shows the results of the Super-K experiment. 1.1.2 Theory Since neutrinos are chargeless leptons they only feel the weak force (neglect- ing gravity). A s such neutrino interactions are lumped into two categories: Charged Current (CC) when the weak force mediator is a W± and Neutral Current (NC) when the weak force is mediated by the Z ° . To observe the neutrino oscillations I talked about in the last section we have to assume that the flavor (interaction) and mass (propagation) eigenstates of neutrinos are not the same. Two Neutrino Oscillation To simplify this explanation let us consider a model where only two v exist and oscillate. Equation 1.6 shows a just after it is created. Here is the interaction eigenstate that couples to the muon and z/2 and v3 are the two mass eigenstates. Since both interaction and mass eigenstates form a complete basis for al l neutrinos we can write one as a linear combination of the other. = cos flu | vi) +sinc9 1 2 |^ 2 ) \vT) = - s i n 0i21 i^i) + c o s 0 i 2 | f 2 ) Chapter 1. Introduction 0 Figure 1.3: Results of the Super-K neutrino oscillation measurement. This zenith result comes from investigating the muon neutrino anisotropy [6] Chapter 1. Introduction 7 Equat ion 1.7 adds time dependence to the as predicted by quantum me- chanics: \ur(x,t)) = - e - l ( £ l f - p l 5 ) sin ^ l ^ i ) + e ^ 2 ' - ^ c o s r ? ^ ) (1.7) Note from Equation 1.7 that neutrino oscillation only occur if the propagation eigenstates of the neutrinos have different masses. If we express the mass eigenstates in terms of flavor states by solving Equation 1.6 for the mass states we have: e-t{Eit-pi-x) Q 0 e-t(.E2t-p2-x) Where X(6) is the rotation matrix: (1.8) cos 6 sin 6 — sin 0 cos 9 Now assuming we start of wi th a muon neutrino, as we do at K 2 K we obtain the probability of observing a tauon neutrino by Equation 1.9: <i /> r (x, t)) = Pv^Vr = s i n 2 ( 2 g 1 2 ) s i n 2 ( L 2 7 ^ m i 2 L ) E (1.9) Here A m 2 2 = m i — m 2 1 S ^ n e mass squared difference in eV, L is the distance traveled (in km), and E is the total energy of the neutrino (in G e V ) . Now you can see that we should only observe neutrino oscillations if neutrinos have mass and those masses differ between the different neutrino mass eigenstates. From the results of the Super-K experiment [6] we take an estimate of A m 2 2 and tune E such that knowing L we measure A m f 2 precisely. Note that if: 1 . 2 7 A m 2 L 2nE » 1 (1.10) the probability of finding either flavor averages to 5, if s in 2 2#i2 = 1. Figure 1.4 shows the probability to observe the neutrino of the original flavor (PVii-*Ut = 0) or the neutrino of the oscillated flavor (PVli->uT = 1) depending on when you observe the neutrino. Chapter 1. Introduction 8 Figure 1.4: The probability for a neutrino of flavor p to oscillate into neutrino of flavor r after traveling a distance L (km) at energy E (GeV) . The mass squared difference was taken to be A m 2 = 3 • 1 0 - 3 eV2 for s in 2 29 = 1 as taken from the latest K 2 K results [16]. 1.1.3 Extension to Three Neutrinos Since we have three generations of neutrinos we must do this for each of the three possible combinations. Doing this we obtain Equation 1.11. (1.11) Here I is the lepton (e, r ) associated wi th v\ and the Vi are the neutrino mass eigenstates. U is the Maki-Nakagawa-Sakata (MNS) matrix [17] de- scribing neutrino mixing and is analogous to the C K M matr ix describing quark mixing. It is more convenient to look at the M N S matrix broken into three ma- trices each describing oscillations involving two of the three neutrino mass eigenstates. U = Here s 1 0 0 0 023 -S23 0 C23 Cl3 0 -elSs13 -iS Sl3 Cl2 - S l 2 0 Sl2 Cl2 0 0 0 1 0 1 0 0 c 1 3 ij — sin 9ij and = cos 6ij and 8 is a phase factor that introduces C P violation for the neutrino sector. The first matrix (23-mixing) is maxi- mal (ie 023 ~ | ) and can be investigated by atmospheric and long baseline Chapter 1. Introduction 9 neutrino experiments. In the second matrix (13-mixing) the mixing angle is small (similar to quark mixing) wi th #13 < ^ . Solar neutrino experiments found the last matrix (12-mixing) to show large but non-maximal mixing wi th 0i2 « § [18]. 1.1.4 Previous Experiments Since the discovery of neutrino oscillation in 1998 the mixing angles of the M N S matr ix have been investigated thoroughly. The Super-K group mea- sured the disappearance interpreted as u^ *-* uT oscillation by observ- ing atmospheric neutrinos. This observation gives the mixing angle 023 as s in 2 20 > 0.92 and 1.5 • 10~ 3 < A m ^ 3 < 3.4 • 10" 3 eV2 (at 90% confidence) for the associated mass eigenstates [6]. Together the S N O and K a m L A N D experiment have measured ue <-> i / M / T mixing, which allows the measurement of flu = 33.911:2 a n d A m i 2 = (S-O-cL) • 1 0 - 5 e V 2 u s i n g neutrinos produced in the Sun [19] or in reactors. The allowed mass squared differences and mix- ing angles for the neutrino mass eigenstates are summarized in Figure 1.5 for the results from solar neutrinos and Figure 1.6 for long baseline neutrino experiments. 1.2 The K 2 K Exper iment The K E K to Kamioka ( K 2 K ) is the first accelerator-based long-baseline neu- trino oscillation experiment, and measures the same oscillation as atmo- spheric neutrino experiments such as Super-K. The K 2 K experiment con- firmed Up <-> uT oscillation seen by experiments like Super-K [6] at greater than 4fj significance [16]. The K 2 K measurement uses an accelerator-made neutrino beam and mea- sures the energy-dependent difference between the u^ flux measured at near (300 m from the beam origin) and far (250 km) detectors. The neutrino os- cil lation parameters are fitted by predicting the neutrino flux and spectrum for the far detector based upon the measurement from the near detector. To measure u^ <-> uT oscillation K 2 K uses a muon neutrino (u^) beam made at the K E K accelerator site that is aimed at the Super-K detector in Kamioka. The neutrino beam is made by scattering 12 G e V protons off an aluminum target and focusing the produced n+ into a decay pipe using two horn magnets. The pions decay to give a 98% pure muon neutrino Chapter 1. Introduction 10 Figure 1.5: The allowed region for mass squared difference and mixing an- gle for the solar neutrino sector. Da ta from S N O , K a m L A N D , Gallex, and S A G E [19]. Chapter 1. Introduction 1 1 Figure 1.6: The allowed region in mass squared difference and mixing an- gle for the atmospheric neutrino sector according to the K2K long baseline experiment. Chapter 1. Introduction 12 Figure 1.7: The K 2 K experiment fires a beam made at the K E K accelera- tor at the Super-Kamiokande detector through 250 k m of earth. The near (or front) and Super-Kamiokande (or far) detector measure the muon neutrino flux. Neutrino oscillation is measured through disappearance [20]. beam. The neutrinos travel a distance of L = 250 k m wi th mean beam energy E = 1.3 G e V through the island of Honshu in Japan as displayed in Figure 1.7. 1.3 The K E K Pro ton Synchrotron A n d Beam Line The v beam is produced at K E K by a synchrotron that accelerates protons to 12 G e V ( K E K - P S ) . The protons are accelerated step by step as summarized in Table 1.1. Protons are inserted into the accelerator in spills which occur every 2.2 s. Each spill carries 7 • 10 1 2 protons in nine "bunches" separated by 120 ns. In total then a spill of protons (from first to ninth bunch) lasts 1.1 ps. To accelerate the protons in a spill to 12GeV they must go through the M a i n Ring . After one cycle in the main ring the protons are extracted though a beam pipe leading to the target. O n the way to the target the beam profile Chapter 1. Introduction 13 Table 1.1: K E K Beam Accelerator Components [1] Accelerator Component Final Proton Energy Pre-injector 750 keV L I N A C 40 M e V B O O S T E R 500 M e V M a i n Ring 12 G e V «•! -+ 250km 300m 200m Figure 1.8: Schematic of the K 2 K neutrino beam generation and travel. and intensity are carefully monitored. The position of the proton beam needs to be known accurately such that the final neutrino beam is properly directed at the far detector. F ina l ly the spill of protons hits the target. A t this point about (5 — 6) • 10 1 2 protons are left in the nine bunches. 1.3.1 The Neutrino Beam Figure 1.8 shows a schematic of the K 2 K experiment. The proton beam hits the aluminum target creating a pion beam. The target is a 66cm long cylinder wi th a 3cm diameter. It is made of 6061-t aluminum alloy [1]. The Horn Magnets Two so-called "horn magnets" are cylindrically symmetric magnets that cre- ate a toroidal magnetic field. They function on a 250 k A current pulse lasting for 2 msec on a 2.2 s cycle. This pulse current is synchronized wi th the beam spills. The horn magnets operate on this pulsed current to prevent overheat- ing. The target is inside the first horn magnet forming the conductor core for the magnet. The second magnet is placed 10.5 meters downstream. The Chapter 1. Introduction 14 Table 1.2: v Beam Composition A t Origin [2] Particle Source Fraction of Beam Low Energy: ix+ - 97.3% High Energy: K+ 1.3% v» 7T~ —• or decay 1.5% 0.018% toroidal magnetic field created by the horn magnets focuses positive particles (mostly 7 r + ) created at the target down the decay pipe. The horn magnets effectively reduce the transverse momentum of positive particles by 100 M e V per meter of longitudinal travel though the magnet [2]. Negative particles produced at the target are dispersed by the magnetic field. Decay Volume The decay volume starts 19 m downstream of the target. The decay volume is a 200 m long cylindrical tunnel. The diameter of the tunnel is 1.5 m, 2 m and 3 m for the following 10 m, 90 m and 100 m sections respectively. 7 r + entering the tunnel have a momentum of 2-3 G e V / c . Whi le traveling through the decay volume the 7 r + ' s decay as displayed in Equation 1.12: 7 T + - + U+V^ (1.12) The transverse momentum of the p and the after the decay are small com- pared to the momentum of the pion. Thus the neutrino is emitted wi th in a few 10 mrad from the forward direction (toward Super-K). Table 1.2 sum- marizes the beam composition just after the decay volume according to the beam Monte Carlo. The muons produced in the pion decay are detected by the M U M O N detector at the beam dump. This muon monitor measures whether the beam is on target. Beam Aim Figure 1.9 shows the neutrino flux and neutrino energies off the beam axis. A s you can see from Figure 1.9 it is imperative that the beam is aimed at Chapter 1. Introduction 15 R[km| E,"(G»V) Figure 1.9: Monte Carlo simulation of the K 2 K neutrino beam without neu- trino oscillation. The left gives the neutrino flux 250km downstream of the target at some transverse distance R from the Super-K detector. The right display gives the neutrino energy distribution on the beam axis and 4mrad, 8mrad and 12mrad off the axis [1]. Table 1.3: G P S Survey of K 2 K Target and Far Detector K 2 K Component Latitude Longitude Al t i tude Target Super-K Center 36°09'14.9531"iV 36°25'32.5867"iV 140°04'16.3303"£ 137°18'37.1214"£ 70.218 m 371.839 m Super-K to wi th in a mill iradian to properly understand the flux and energy spectrum of the beam neutrinos. This has been accomplished through a G P S survey. Table 1.3 gives the locations of the target and the center of the far detector according to a G P S survey. Using this survey the required beampipe direction is determined to an accuracy of O.Olmrad [21]. The components of the K 2 K beam were aligned such that the beam is pointing at the center of the Super-K detector wi th an accuracy of O.lmrad. The M U M O N confirms the beam is lined up. Chapter 1. Introduction 16 SciFi Detector Figure 1.10: The Near Detector consists of four detector systems: The 1 K T water Cerenkov detector, the Sc iF i , SciBar and M R D detectors [20]. The Sc iF i , SciBar and M R D together constitute the F G D system. 1.4 Near Detector The near detector measures the i / M flux 300m from the production target along a line between the target and Super-K. Figure 1.10 shows the near detector components. The first part of the near detector heading along the particle beam is the 1 K T water Cerenkov detector. Next is the S c i F i de- tector, which is a water-based scintillating fiber detector. After the S c i F i detector the neutrino beam moves through SciBar, a fine segmented, fully active scintillation tracker. Originally K 2 K was using a lead-glass calorime- ter instead of SciBar. Last the neutrinos pass the M u o n Range Detector ( M R D ) . The Sc iF i , SciBar (previously Lead Glass Calorimeter) and M R D together are referred to as the Fine-Grained Detector system ( F G D ) . This thesis concerns the calibration of the 1 K T detector, thus I w i l l focus on the 1 K T here. Chapter 1. Introduction 17 1.4.1 One Kiloton Water Cerenkov Detector The 1 K T detector is a smaller replica of the Super-Kamiokande (far) detector. The 1 K T and the Super-K detectors measure the flux and energy spectrum at both ends of the beam which are used to infer the oscillation parameters. Using the 1 K T for the flux normalization is advantageous since the greatest uncertainties in the absolute flux measurement arise from the interaction cross-section for neutrinos wi th the detector material. Since the 1 K T and the Super-K detector both use H 2 0 for the detector bulk this uncertainty cancels. The 1 K T detector also gives a good high statistics measurement of neutrino-water interactions. Physical Design Figure 1.11 shows a schematic of the 1 K T tank. The 1 K T is a cylinder 10.8 m high and 10.8 m in diameter. Black and Tyvec sheets covering the metal support frame for the photomultiplier tubes separate the 1 K T detector into two optically isolated parts: • The Inner Detector (ID) is the volume inside the support frame. The ID forms a cylinder of 8.6 m in height and diameter. The ID is monitored by 680 20-inch R3600 Hamamatsu Photomultiplier Tubes. Table 1.4 summarizes the properties of the 20-inch P M T s used in the ID . F i g - ure 1.12 gives a schematic view of a P M T . The 680 P M T s are arranged along the top, bottom and wall of the support frame on a grid spacing the centers of the P M T s 70 cm apart. The wall of the 1 K T carries 456 P M T s organized in 38 columns of 12 P M T s each. The top and bottom are covered in 112 P M T s each. • The Outer Detector (OD) is the water region between the support frame and the outer wall of the 1 K T detector. This region is 1 m thick along the barrel and 0.6 m thick at the bottom of the tank. The O D is monitored by 68 8-inch P M T s that provide a veto against cosmic muons. Downgoing muons are rejected by the signal in the P M T s at the bot tom of the 1 K T . The P M T arrangement in the inner detector is the same as in the Super-K detector giving a 40% optical coverage along the walls. Chapter 1. Introduction 18 Figure 1.11: The 1 K T is a water Cerenkov detector containing approximately 1000 tons of H 2 0 . Its inner volume is monitored by 680 20-inch Photomul- tiplier Tubes (PMTs) .The outer detector volume is monitored by 68 smaller (8-inch) outward looking P M T s . The outward looking P M T s are mounted on the front th i rd of the barrel (facing into the beam) and on the bottom of the support frame facing downward. Chapter 1. Introduction 19 Table 1.4: Properties of the 20-inch Hamamatsu Photomultiplier Tubes ( P M T s ) used in the 1 K T [1] and [3] P M T Property Value Photo-cathode Area 50cm Diameter Shape Hemispherical Window Mater ia l Pyrex Glass 4-5mm Photo-cathode Mater ia l Bialkal i (Sb-K-Cs) Dynodes 11 stages, Venetian bl ind style Quantum efficiency 22% at A = 390nm Sensitive Wavelength 300 to 600nm, peak at 390nm Typica l G a i n 10 7 at ca. 2 k V Dark Current 200 n A at 10 7 gain Dark Pulse Rate 3kHz at 10 7 gain Cathode non-uniformity < 10% Anode non-uniformity < 4 0 % Manufacturer Hamamatsu Photonics Corporat ion Time Resolution for Single P . E . ~3ns Time Resolution for Many P . E . ~0.5ns Chapter 1. Introduction 20 < <> 520 photosensitive area > § 460 l B - 7 0 0 0 0 3 Figure 1.12: Schematic of the 20in P M T used in the 1 K T detector Chapter 1. Introduction 2 1 fast recirculation Figure 1.13: Schematic of the 1 K T water purification system. Water is pumped through these filters at a rate of 20 tons per hour. Dotted lines are optional water pipes [1]. The Earth 's magnetic field affects the P M T response. To cancel the geomagnetic field nine horizontal and seven vertical Helmholtz coils have been set up around the 1 K T detector. Figure 1.11 shows the room above the inner detector. This cavity permits access to the detector through a small ~1 m by 1 m hatch on the side of the upper deck. The Water System Particles dissolved in the detector's water volume wi l l scatter the light trav- eling in the tank. Since scattering wi l l change the t iming signal from the P M T s in the 1 K T the water must be as pure as possible. To ensure water quality the water in the 1 K T is pumped through a series of filters at a rate of 20 tons per hour. Figure 1.13 is a schematic of the 1 K T water purification system. A pump next to the 1 K T in the near detector pit pumps the water out of the 1 K T into the filter system. First the p re -UV and ultraviolet ( U V ) filters k i l l any bacteria in the water. Next metallic ions in the water are removed by a deionizer. Then a filter removes al l particles larger than about 1 / im in diameter. F ina l ly the ultra-filter removes particles larger then 10 nm i n diameter. After the filtering process the chiller cools the water to 10°C. The water purity is monitored by measuring the water's electrical resis- tivity. For regular operation the resistivity of the water is kept to 10 MQ/cm. Chapter 1. Introduction 22 The attenuation length of the water under these conditions was determined to be A = 50 m using Cerenkov light (wavelength ~390 nm) from cosmic rays [1]. The l K T ' s Data Acquisition System Figure 1.14 displays the general data flow for the data acquisition system of the 1 K T detector. The raw signal from each P M T is transferred though a coaxial cable from the 1 K T detector to an electronics hut. Sine the operation of the electronics is dependent on their temperature the electronics hut is always air-conditioned to keep the temperature below 25°C. P M T s are put into groups of 12. Next the signal from each P M T is split into four. The four signals lead into: • Two independent analog-to-digital converters ( A D C s ) . The conversion for the A D C s is 0.15 pC/count . • A discriminator which sends its output to two time-to-digital convert- ers. This discriminator also provides the timeout signal for the analog to digital conversion in the A D C s and T D C s . The discriminator thresh- old is set to a voltage corresponding to 0.3 photoelectrons, and the T D C conversion factor is 0.4 ns/count. • The P M T S U M , which determines the analog sum of each P M T in a group of 12. A l l P M T S U M signals are added and sent to one Flash A n a - log to Digi ta l Converter ( F A D C ) wi th a 500 M H z sampling frequency and 8 bit resolution. The number of events in a spil l are recorded by counting the number of peaks in the signal shape read out by the F A D C . The two A D C s and T D C s for each P M T channel are organized on Analog T iming Modules ( A T M s ) originally developed for Super-K. Each A T M holds the A D C s as well as T D C s for twelve P M T s and First In First Out (F IFO) data storage for each. The A T M s are organized into T K O modules as dis- played in Figure 1.14. The T K O modules also hold a Super-Control-Head (SCH) data storage for the A D C and T D C signals from each A T M . Further- more the T K O module has a G o / N o t G o ( G O N G ) module which tells the A T M s to store their data to the S C H if it receives a trigger 1.1 ps after the A T M gets hit wi th data from P M T s . F ina l ly each A T M module has a dis- criminator that generates a rectangular voltage pulse 200 ns long and 10 m V Chapter 1. Introduction 23 Figure 1.14: A flow chart displaying the data flow from the P M T s to the readout electronics [1]. Chapter 1. Introduction 24 y X y neutrino z beam x Beam Coordinates Tank Coordinates Figure 1.15: The beam and tank coordinate systems are important when working wi th the 1 K T detector. In the figure the x-axis on the left and the y axis on the right point into the page. high for each P M T that records a hit. This pulse is called the H I T S U M and the combined H I T S U M from all A T M s gives the number of hit P M T s (also called the occupancy) of the event. For usual operation beam timing provides an enable signal synchronized wi th the beam spills letting the T K O modules (four crates containing the A T M modules for al l the P M T s in the 1 K T ) receive data for 1.3 LIS. The data taken for this thesis is all calibration data, and the beam t iming signal is replaced by a trigger created by a photo diode pulsed by the calibration laser. Four V M E crates (one for each T K O module) are used to record the data from the S C H in the T K O modules. Finally, if more then 40 P M T s were hit the trigger crate enables the data read out and the computers read in the events. Since we may want to read out events wi th less than 40 hit P M T s for the optical calibration this trigger is not used here either, and instead al l triggered events are read out. 1KT Coordinate Systems Figure 1.15 shows the two coordinate systems that are important in the 1 K T detector, the: Chapter 1. Introduction 25 • Beam Coordinate System, and • Tank Coordinate System The tank coordinate system is used for our calibration analysis. The beam coordinate system is used for the regular data analysis in the 1 K T tank and the official Monte Carlo. Fiducial Volume Figure 1.16 shows the three fiducial volumes that are used in the 1 K T neu- trino analysis: • Volume A is a large cylinder aligned wi th the 1 K T , 6m in height and 6m in diameter. Volume A is centered on the center of the 1 K T . • Volume B also is a cylinder centered on the center of the 1 K T , but the axis of the cylinder is aligned with the neutrino beam. Volume B is 4m in length and 4m in diameter. • Volume C is the upsteam half of volume B . For neutrino data in the 1 K T we consider events that have a vertex origi- nating in fiducial volume C . Volume A is used to measure the neutrino beam profile and volume B is used to ensure the stability of the neutrino event rate. 1.4.2 The Fine Grained Detector The fine grained detector ( F G D ) gives a neutrino flux and spectrum measure- ment independent of the 1 K T water Cerenkov detector. The basic concepts of the F G D wi l l be outlined here for completeness, but since the calibration of the 1 K T only marginally depends upon the F G D this description wi l l not be so detailed. The fine grained detector measures al l of the charged particles produced in neutrino interactions, which the 1 K T cannot do very accurately, since some of the heavier particles are below Cerenkov threshold in the 1 K T . The 1 K T measures the neutrino flux to compare to the flux at Super-K. This the 1 K T can do better than the F G D because the target material is the same as for Super-K thus cancelling the significant uncertainty in the neutrino interaction cross-section for the detector materials. Chapter 1. Introduction 26 Figure 1.16: Only neutrino events that reconstruct in fiducial volume C are considered for the neutrino flux and energy measurement used in the K 2 K analysis [1]. Chapter 1. Introduction 27 Scintillating Fiber Tracker The Sc iF i detector is composed of twenty 2.6 m by 2.6 m tracking modules containing two layers of horizontal and vertical scintillating sheets made of 0.692 m m fibers. The tracking layers are placed 9 cm apart. In between the 20 tracking layers 19 aluminum tanks contain a total of 6 tons of water. Charged particles produced in neutrino interactions are tracked using the scintillation light they cause in the fibers in the tracking layers. The scintillating fibers are read out by C C D cameras wi th image intensifiers. Scintillating Bar The Scintillating Bar (SciBar) detector was an upgrade to K 2 K replacing the lead glass calorimeter. A total of 14,848 scintillating bars, each 1.3 cm thick, 2.5 cm wide and 300 cm long, were produced at Fermilab [22] for use in the SciBar detector. Now they are arranged in 64 alternating layers of horizontal and vertical bars. This gives a 3 x 3 x 1.7 m fully active detector volume. Wavelength shifting fibers guide the scintillation light produced by charged particles traveling in the SciBar detector to multi-anode photomul- tiplier tubes ( M A P M T s ) that read out the signal. Muon Range Detector The M R D is a range calorimeter composed of 864 tons of iron intended to stop muons products of neutrino interactions in the previous detector systems, in order to get the muon energy by its range. The metal is arranged in twelve 7.6 m by 7.6 m by 10 cm thick sheets. Around the iron sheets are 13 sets of horizontally and vertically arranged drift tubes. The 6632 drift tubes are filled wi th a gas mixture containing 90% Argon (Ar) and 10% Methane (CH4). The drift chambers are read out by T D C s . 1.5 The Super-Kamiokande Detector Figure 1.17 shows the Super-K detector which is located 1 k m underground in the Mozumi mine of the Kamioka Min ing and Smelting C o [23]. Table 1.5 summarizes the information on the Super-K detector.Like the 1 K T the Super- K detector is a cylinder. The entire Super-K detector is 41.4 m high and 39.3 m in diameter. A cylindrical frame in the detector (36.2 m high and Chapter 1. Introduction 28 Table 1.5: Basic Information on the Super-Kamiokande Detector Detector Part Statistic Outer Dimensions 41.4m High, 39.3m Diameter Cylinder Inner Dimensions 36.2m High, 33.8m Diameter Cylinder Outer Water Mass 18,000 tons Inner Water Mass 32,000 tons Outer Monitor ing P M T s 1,885 Inner Monitor ing P M T s 11,146 P M T Readout T iming Resolution 0.40 ns (1.2 ps Range) P M T Readout Charge Resolution 0.2 p C (550 p C Range) Energy Range 5.7 M e V - 8 G e V Energy Resolution 2.5% (at 1 G e V ) 33.8 m in diameter) hold 11,147 P M T s looking inward into the inner detector volume. A similar but larger frame surrounding the first frame holds 1885 P M T s looking outward at the outer detector volume. Each of the two frames are covered in opaque sheets, optically isolating the inner and outer detector, but also creating a 55 cm dead region between the two. Super-K is sensitive to e~(vi,e~)vi and X(ui,l)X' interactions. 1.6 The Global Positioning System To distinguish K 2 K beam neutrino events from atmospheric neutrinos at the far (Super-K) detector the G P S system is used to provide an accurate time stamp between Super-K and K E K . A 1 Hz t iming signal from the G P S system is sent to calibrate a local clock at both K E K and Super-K. The local clocks operate at 50MHz giving a 32-bit time signal that is used as a time stamp on the recorded events. This time stamp is used in the analysis to tell beam events from atmospheric events, relying on the spill times at K E K to predict the neutrino arrival time at Super-K. Figure 1.17: The Super-Kamiokande Detector 30 Chapter 2 1KT Exploration With A Diffuser Ball On A String The 1 K T detector has previously been calibrated using a • Laser diffuser ball to get the T Q - M a p , • Xenon lamp diffuser ball to equalize the P M T Gain , • Comic ray muons to determine the energy scale, • Nickel source to measure quantum efficiencies, and • Laser beam to calibrate for scattering and reflection. The TQ-map is a time correction for each P M T that is supposed to correct differences in the time signal arising from signal travel time in the P M T s and wires as well as any effects the charge deposited in the P M T may have on the measured time. The setup to generate the TQ-map is the same as for this laserball study (and wi l l be described in Section 2.1). For the TQ-map the laserball is kept at the center of the 1 K T . In the 2003 TQ-map it was noticed that the laserball seemed to be shifted by a few centimeters in the z-coordinate (tank system). One motivation for this laserball study is to find out whether this is a problem wi th the reconstruction or wi th the laserball placement. The xenon lamp study uses a setup similar to the laserball, just that instead of the laser a xenon lamp is mounted on the optical table and a dif- ferent diffuser bal l is used. To be able to calibrate the P M T gain throughout the 1 K T , first 103 of the 680 P M T s in the inner detector had their voltage supply calibrated to give the same gain before they were installed. A ratio of the charge signals from the uncalibrated P M T s over the calibrated P M T s is used to adjust the P M T voltage to set all P M T s to the same gain. Muons from cosmic rays are put in two categories for the cosmic ray calibration. Vertically travelling muons are tagged by the coincidence of Chapter 2. 1KT Exploration With A Diffuser Ball On A String 31 two scintillator pads set up above the 1 K T (over the C R P described in Sec- t ion 3.2). Horizontally travelling muons are identified by a coincidence be- tween a signal in the upsteam part of the outer detector and a veto trigger plane set up downstream of the 1 K T . The laser described in the next section was used to shine a laser beam down the Cosmic Ray Pipe parallel to the central axis of the 1 K T . From comparing the data to the 1 K T Monte Carlo simulation of a light beam, Rayleigh scattering and the reflection of the P M T s and the black sheets isolating the inner and outer detectors are inferred. Further investigation of the t iming of M C events as compared to real data reveals a t iming difference between the top and bottom P M T s [24]. The observed t iming difference motivated this laserball study to determine what the impact on the optical position reconstruction was. 2.1 Detector Setup for Optical Calibration To take calibration data using the diffuser ball (or laser ball) an optical table is set up in the 1 K T control room at K E K . Figure 2.1 shows a schematic of the laser setup for optical calibration using the laserball. A VSL-337 air cooled nitrogen laser is set up on the optical table. The laser receives a 10Hz external trigger signal and fires a 4 ns pulse of light at A = 337 nm [25]. A laser dye is used to tune the wavelength of the laser-light to 390 nm. The laser light is sent though a beam splitter that sends half the laser light through a fiber-optic cable into a photo diode wi th a fast response to the laser light. The signal from the photo diode is sent to trigger electronics of the 1 K T to supply a t iming reference and start the data collection. The other half of the laser light goes through a series of filters and though a 200 m long fiber optic umbilical cord into the diffuser ball . The diffuser ball or laserball scatters the light isotropically through the tank. The diffuser bal l is a glass sphere of approximately 3 cm diameter that contains M g O impurities and silica gel to scatter the light from the laser isotropically. The fibre optic umbilical enters the laserball through a 2.5 cm deep and 4 m m wide hole, and is held there by transparent, waterproof glue. Chapter 2. 1KT Exploration With A Diffuser Ball On A String 32 Aluminium Box Half Mirror Variable ND Filter * 20inch PMTs Fiber Diffuser Ball Trigger Detector Figure 2.1: The setup for the optical calibration using a laserball. Laser light passes through a beam splitter, letting half the laser light go into the 1 K T tank and reflecting the other half into the photodiode, which provides the t iming trigger. The photo diode is labelled P . D . in the figure. Chapter 2. 1KT Exploration With A Diffuser Ball On A String 33 2.1.1 Laserball Data While the beam was shut down for the K 2 K experiment in October 2003, Ju ly 2004 and June 2005, the Canadian K 2 K group took some data using the above setup. In October 2003 only two runs were taken, one at the center and one close to the top of the 1 K T . The data in Ju ly 2004 was taken at al l locations the bal l on a string could reach. Various runs were taken along the entire vertical axis of the 1 K T . The position of the laserball was also measured more carefully since the uncertainty in the nominal position of the previous data made further conclusions about the optical reconstruction impossible. The final set of laserball runs were taken after the manipulator data run to provide an absolute positioning reference for the manipulator bal l positions. For the 2004 and 2005 laserball data we took multiple runs at each posi- t ion in the 1 K T using different filters for the laser light. Using these filters the laser light intensity was varied between: • Low occupancy: Most P M T s are not hit, and those P M T s that are hit usually see a single photoelectron. For this analysis any run wi th P M T S U M signaling less than 110 P M T s is considered low occupancy. That corresponds to less than 120 photoelectrons (pe's) in the 1 K T . • Medium occupancy: Most P M T s in the 1 K T are hit by at least one photon (110 < PMTSUM < 390 that is 120 to 580 pe's) . • High occupancy: A l l P M T s in the 1 K T are hit wi th many photons (PMTSUM > 390 that means 580 or more pe's). A l l data taken is summarized in Appendix A . Note that the high occupancy runs wi th the given cut on P M T S U M have an average number of hits of 500 to 680 P M T s in an event. 2.2 Optical fit for Laserball Position The position of the laserball is determined run by run. A t iming histogram integrating over the entire run is formed for each P M T . Since the P M T s vary in their distance from the ball we subtract an estimated time of flight for light to go from the nominal position of the bal l to the P M T . This localizes al l Chapter 2. 1KT Exploration With A Diffuser Ball On A String 34 the t iming peaks around 1000ns. The assumed speed of light in water is 21.66 cm/ns at A = 390 nm. The histograms record the t iming information in 0.1 ns bins from 900 ns to 1100 ns. A n integration gate 4 ns wide is slid across the histogram to find the t iming window with the largest number of hits inside the integration gate. The peak is then determined by taking the mean of the channels in the integration gate. A n uncertainty on this mean is estimated by taking the width of the peak inside the window as measured by the standard deviation over the square root of the number of events in the time window. Figure 2.2 shows an example using a 10 ns wide integration gate. Integration gates of different widths were tested. In Section 2.3.1 the effect of the width of the integration gate wi l l be discussed further. Once the t iming peaks for each of the histograms are determined we add the estimated time of flight back to the result. Now a x2 minimization is run to fit the bal l position to the set of 680 P M T times for the run. Figure 2.3 shows that the time of flight from the ball to each P M T is given by: - * • / / = - = L i - ^ [ (2- 1) where Xbau is the fit position of the ball , XPMT is the position of the P M T under consideration and v — 21.66 cm/ns is the group velocity of light wi th wavelength 390 nm traveling through water, tf1 is the time expected for P M T number i to be hit and t0ff is the time offset between the photodiode trigger and the point at which the laser light leaves the laserball. Hence we minimize: Npmt /.pmt _ .th \ 2 x 2 = E (h—k.) ( 2 . 2 ) i = l \ °% ) by varying x^ali and taff. Here Npmt is the number of P M T s used in the fit, t f m t is the time measured by the P M T and of is the sum of the variance in the mean of the t iming peak of the P M T plus a systematic error in the time charge correction: a1 • 2 _ upmt,i 9 Where asys = 0.4 ns is estimated by looking at the variance of the P M T times during one run. To find the error in the reconstructed position, we divide the 680 tubes into N non-overlapping subgroups selected isotropically thoughout the 1 K T tank, where N = 2, 3, 4 ... 40. We fit the bal l position Chapter 2. 1KT Exploration With A DiSuser Ball On A String 35 Figure 2.2: A 10ns wide integration gate slides across the histogram contain- ing al l the time-of-flight-adjusted P M T times in the run for a single P M T . In the time range wi th the largest number of events inside the gate we calculate the mean and of y/N to be the time and uncertainty on that t ime estimate. The picture shows normalized high and low occupancy t iming histograms. CiJOOO C O •§800 (5 s H600 400 200 Q Example Of Integration Gate Function I I I—I I T I I I I I I I l * T I I I I I I I I I I I I I I I I J—I I I I l _ i I I 1 -• High OccupancyJ Low OccupancyJ 1 1 1 1 i i 980 985 990 995 1000 1005 1010 1015 1020 PMT-Time - Time-Of-Flight (ns) Chapter 2. 1KT Exploration With A Diffuser Ball On A String 36 Figure 2.3: Opt ical F i t t ing for the Laserball Position L a s e r b a l l ' o s i t i o n = ( t , x , y , z ) t p - t = d / v P M T P o s i t i o n = ( t „ x „ y p , Zp) using the N subgroups, then calculate the variance of the N fitted positions. Next we fit the plot of the fitted position variance versus N to the function: o(N) - OOVN (2.3) where N is the number of groups, and o0 is the uncertainty for a single group of 680 P M T s (the result used for the ball position). The uncertainty on the variance at the value of N is given by: Ao{N) = o(N) - 1) Figure 2.4 shows cr(N) for one sample run. The results from using every 12th, 24th, or 36th P M T are anomalous because this selects exactly one ring of P M T s along the 1 K T wall, and so do not give isotropic subgroups. Thus we ignore the results from using 12, 24, and 36 subgroups (by assigning them a very large error). Once we understand this anomalous behavior Equat ion 2.3 fits the data exceptionally well. Chapter 2. 1KT Exploration With A Diffuser Ball On A String 37 Figure 2.4: The error on the laserball position is calculated by fitting to the variance of position fits using subgroups of P M T s . The error is given by the fit parameter cr0 — -PI, which is the extrapolated uncertainty for a single subgroup of 680 P M T s . Chapter 2. 1KT Exploration With A Diffuser Ball On A String 38 2.3 Position Bias and the Time Charge Correction 2.3.1 Width of the Integration Gate To choose the proper size for the integration gate we must look at the time histograms used to determine the P M T t iming peak. Figure 2.2 shows the t iming histograms for a low and a high occupancy run. The figure also shows a 10 ns integration gate. The high occupancy peak does not show a scattering ta i l while the low occupancy peak does. This is expected since in a high occupancy run each P M T gets hit by many photons and the electronics wi l l register the first hit as the time on the P M T . Thus it is likely that in a high occupancy run the P M T s get hit by light that has not been scattered. In a low occupancy run each P M T is hit by about one photon, thus for some fraction of the P M T hits we should see scattered light only. The scattered light w i l l not travel a straight path to the P M T but wi l l hit the P M T a few nanoseconds after direct light. Thus the large integration gate wi l l be pulled to a higher time by the scattering tai l in low occupancy runs. A small integration gate wi l l be influenced by statistical fluctuation, especially in the low occupancy regime. The integration gate used init ial ly was taken to be 20 ns wide. This resulted in a strong scattering effect for low occupancy data. Using the 10 ns gate displayed in Figure 2.3 reduced this effect. After closer examination of the P M T histograms a 4 ns gate was used which eliminated the scattering ta i l completely, but is unaffected by statistical fluctuations which are of the order of a few 0.1 ns. 2.3.2 Time Charge Correction Problem Ear ly analysis of the t iming calibration data encountered many problems. Figure 2.5 shows the results of the first reconstruction using the 10 ns gate. The most obvious result is that the ball reconstructs 10 cm higher than we measured. The next is that the medium and high occupancy data show a significant (ca. 2%) slope. The offset could be explained by a simple mismea- surement of the reference mark on the wire suspending the bal l (Appendix A explains how the nominal position is determined). The slope in the line fitted to the reconstructed positions shows that the fitted bal l position is in fact closer to the center than it should be. Since this slope only depends on how Chapter 2. 1KT Exploration With A Diffuser Ball On A String 39 Figure 2.5: When comparing the position fitted using the 10ns gate to the nominal position we find that all measurements are displaced by approxi- mately 10cm. Med ium and high occupancy data also shows a slope. The data plotted here is from the 2004 data set wi th the old T Q - m a p . Chapter 2. 1KT Exploration With A Diffuser Ball On A String 40 the nominal position measurements are done relative to each other there is no simple explanation for the slope. Since the charge deposited in P M T s closer to the laserball is greater than in those far away the slope suggests a problem wi th the time-charge correction for the 1 K T detector. This prompted Dr . Shaomin Chen, who is in charge of the time charge correction for both the Super-K and the 1 K T detector, to redo the T Q - map in 2004. The TQ-map is a correction to the P M T t iming signals that incorporates P M T to P M T differences in signal travel time (due to cable length differences) and effects on the measured time from the amount of charge deposited in the P M T . The P M T times are measured in a similar way to the method used for this analysis. The TQ-map uses a 100 ns integration gate to find the mean and R M S of the t iming peak. The final P M T time is measured by taking the mean of al l events within a ^%cr window around the previous mean. The new TQ-map uses a 50 ns window for this calculation. Furthermore the new TQ-map restricts the charge bin measured in different runs to be similar to the average charge deposited in the 1 K T . Using this cut avoids using P M T s that have a high fluctuation of the secondary electrons produced in the low occupancy runs in the high charge correction from the TQ-map . It is important to do this since, as explained before, the high occupancy data is not as affected by scattering as the low occupancy data. F ina l ly a new pedestal correction was used in the TQ-map generation to eliminate some low charge anomalies in some P M T s . A long wi th the revision of the TQ-map the constant characterizing the buffer amplification for the P M T s was corrected as well. Figure 2.6 shows the result of the position reconstruction wi th the new T Q - M a p and the corrected buffer amp constant. The low and high occupancy runs now agree relatively well wi th the nominal position. The medium occupancy runs however show a significant slope. 2.3.3 Reconstruction Bias Even wi th the reworked TQ-map and the corrected buffer amp constant, Figure 2.6 shows some anomalies. The medium occupancy data has a strong (1%) slope indicating that the data reconstucted closer to the center than it should have. The low and high occupancy data agree and show an insignif- icant (0.2%) slope in the opposite direction of the medium occupancy data (ie. the fitted positions are closer to the wall then they should be). To see if the bias in the results from the laserball study can be explained, Chapter 2. 1KT Exploration With A Diffuser Ball On A String 41 ^25 s o ^20 I I 15 o £ 10 N Laserball Reconstruction with Fixed TO-Map ~i I I i i i I i i—i—i—I—i—i—i—i—I—i—i—i—i—I—i—i—i—i—I 1 i—i—r«T—r • Low Occupancy ° Med Occupancy * High Occupancy 0 -5 •10 •15 h -20 P -25 J—i—i—i—i—i i i i i i i i i i i_ -300 -200 -100 0 100 200 300 Nominal_z (cm) Figure 2.6: The reconstruction as in Figure 2.5 but using the new T Q - m a p and new buffer amp constant, for the data from Spring 2004. The slope seen in the medium occupancy data here is different from what we see in the manipulator data later; this may be because we changed what we call low, medium and high occupancy. 42 the full 1 K T Monte Carlo was run at the positions we placed the laserball. Figure 2.7 shows the results of running the position reconstruction on data generated wi th the 1 K T Monte Carlo. Here the nominal bal l positions are exact, so any deviation is due to problems in the reconstruction. In the first laserball simulation we suppressed scattering and absorption, thus the mean times for each of the P M T s should not be pulled by scattering. Later we turned on scattering and eventually a slope similar to the one seen in the medium occupancy data can be observed. A l l the M C data was run sim- ulating low occupancy which should be more sensitive to scattering. That is, in medium and high occupancy runs the P M T s are struck by many pho- tons, thus chances are that the P M T wi l l be hit by at least one unscattered photon in each light pulse. Since the T D C wi l l record the arrival time of the first signal, our analysis should effectively eliminate scattering for high occupancy and reduce it for medium occupancy. However the slope in the medium occupancy data is opposite to what can be explained by scattering. Furthermore if scattering was the problem it should be most prominent in the low occupancy data not medium occupancy. Running the M C on posi- tions throughout the entire tank volume showed that bal l positions along the x and y axis of the tank coordinate system reconstruct well (ie. there is no slope or offset in plots similar to Figure 2.7 for the x and y axis). 2.4 Conclusion on Laserball Study Since the Monte Carlo position reconstruction does not match the data from the laserball either the analysis is flawed or we cannot trust the Monte Carlo results. This means it would be of interest to study the entire detector volume (x, y and z axis) for the bias effect seen in Figure 2.6 to see how the Fiducia l Volume of the 1 K T is affected. Furthermore the uncertainty in the position reconstruction is around 1cm in the x, y and z directions, so to make any further conclusion we need to locate the laserball wi th a precision of 1cm in each direction. Chapter 2. 1KT Exploration With A Diffuser Ball On A String 43 Figure 2.7: Results of the laserball position reconstruction using the 1 K T Monte Carlo. Amount of scattering is varied. The bal l positions are known precisely. 44 Chapter 3 Manipulator Construction The manipulator is a robotically controlled arm that maneuvers the laserball throughout the 1 K T tank, including off axis positions. 3.1 Motivation The study of the 1 K T tank using the laserball deployed along the central axis showed unexpected reconstruction biases as evidenced by the slope in the position reconstruction. We need to understand the effect on the fiducial volume of the 1 K T since the fiducial volume error is one of the major errors on the far-near extrapolation. Section 2.4 described the basic goals for the construction of the manipulator arm, which are: • Reach the entire 1 K T tank volume, • Locate the laserball to wi thin l -2cm in each dimension, and • Do not touch the any P M T s in the 1 K T . Whi le making all this possible we cannot change anything in the l K T ' s cur- rent setup. 3.2 Hardware A s displayed in Figure 1.11 the only access to the 1 K T tank is from above the detector volume. The 1 K T detector volume itself has two possible access points from the access room above the detector: • The central laserball access hole (center of the tank), and • The cosmic ray pipe access port ( C R P ) (x = -70 cm ,y = 70 cm in tank coordinates). Chapter 3. Manipulator Construction 45 Due to the lack of access points along the side of the 1 K T a setup using three wires controlling the bal l from three points around the top of the tank is impossible. The remaining option is an arm wi th mobile sections inserted in one of the access points. This means the central laserball access hole cannot be used since it leads though a curved pipe. Hence we must lower our assembly into the tank through the C R P access port. Figure 3.1 shows a schematic of the manipulator when deployed in the 1 K T tank. The manipulator is lowered into the 1 K T tank from the cavity above the detector volume through the C R P access hole. The first problem is that the 1 K T tank is 8.6 m deep and has a diameter of 8.6 m, thus the manipulator needs to be long so that it can explore the detector volume. The manipulator also needs to be rigid so we can achieve the desired 1cm position resolution in each direction. Bu t the room above the 1 K T is 1.35 m high along the outside of the cavity and 2.7 m high at the center of the room. Furthermore the C R P port lies beneath a support structure holding up the roof of the 1 K T tank, where a pipe in the center of the cavity supports the roof through a number of small pipes. The C R P access port itself is 1.5 m long and 0.30 m in diameter. That means the longest section of the manipulator can only be about 2 m long to fit into the 1 K T . To meet the above challenges we use this design for the manipulator arm: • A 5 m long x 15 cm wide vertical section (VS) . To be able to insert the vertical section into the 1 K T though the C R P port under the roof and roof support the 5 m V S needs to be divided into three parts, that are connected through hinges, such that the V S may bend. To allow the V S to be rigid during the operation of the manipulator the three sections are clamped together once in place • Three moving sections: — A - A r m : 2.00 m long x 8 cm wide rigid section, attached to V S , that may rotate through 360° in a vertical plane — B - A r m : 1.50 m long x 5 cm wide rigid section, attached to A-a rm, that may rotate through 360° in a vertical plane — C - A r m : 0.20 m long x 5 m m wide rigid section, attached to B-arm, that may rotate through 360° and holds the laserball The entire manipulator arm is held by a turntable, which may rotate through 360° in azimuth. The manipulator and turntable are held by a structure Chapter 3. Manipulator Construction 4 6 ' circles denote travel of individual arms and the total combined reach * preliminary length of inner arm » 1500mm * preliminary length of centre arm = 1370mm * preliminary distance from outer arm hinge centre to outside of laser boll = 130mm Figure 3.1: A schematic of the manipulator arm deployed in the 1 K T tank. Chapter 3. Manipulator Construction 47 Figure 3.2: Concept drawing of the manipulator support structure while the manipulator is being inserted. clamped onto the support beam for the roof of the 1 K T and a cage that has already been set up to hold equipment for the C R P . Figure 3.2 shows how this support is set up in the cavity above the 1 K T detector. The fact that the vertical section is cut into three pieces that have to be attached rigidly to each other causes some issues that wi l l be addressed further in Section 3.5. Since the manipulator wi l l operate in ultra pure water the arms are made of stainless steel. To make it possible to drive the arms they are designed wi th waterproof cavities such that the arms are neutrally buoyant. A G a l i l motor controller drives two large and one small P i t tman brushed D C motors wi th optical encoders, and output shaft gearboxes supply the driving force for the A , B , and C arms. The motors are mounted on the turntable above the water. The small motor drives the C-arm. The driving force from the motors is transmitted down the manipulator using a polyurethane chain. To minimize backlash the polyurethane chain is used only around the sprockets that pass Chapter 3. Manipulator Construction 48 C-Arm \ \ J*L:--; 1 Figure 3.3: The joints between the moving sections of the manipulator arm are shown wi th the sprockets that are used to drive the arm wi th polyurethane chain supplying the drive force from the motors. on the force from the chain. These sections of chain are linked by stainless steel wires. Linked sprockets are used to move the driving force down the manipulator. Figure 3.3 shows the sprockets used at the manipulator joints to transmit the driving force to the arms. Fina l ly the turntable is driven by a large P i t tman motor mounted on the turntable support. To reduce reflection off of the arms the A , B , and vertical section of the manipulator are wrapped in black plastic. Strips of the plastic are wrapped around the A and B arms under the drive chains and secured wi th th in nylon rope. Each of the three pieces of the vertical section are also wrapped in black plastic sheets secured using white plastic tie wraps. 3.3 E l e c t r o n i c s Figure 3.4 displays the organization of the control system for the manipula- tor. We interact wi th the manipulator through a Graphical User Interface Chapter 3. Manipulator Construction 49 Table 3.1: Specifications for the P i t tman motors used to drive the manipu- lator. Encoder Accuracy is given in counts per turn. Property Large Motor Small Motor Model number GM9234S033-R1 GM8724S029-R1 Dr iv ing voltage 24V, D C 24V, D C Gear ratio 218.4:1 187.7:1 Encoder accuracy 500 500 (GUI) designed wi th Mat lab . The G U I communicates wi th a M a x i m u m Integrated Da ta Acquisi t ion System ( M I D A S ) online database ( O D B ) [26]. The database can also be accessed directly through a database editor. Two front end programs continually scan the O D B for updates. The motor con- troller front end (feMotor) looks for updates to the manipulator destination in the database and communicates these to the G a l i l motor controller. The motor positions are determined though the internal motor encoders. For the motors driving the A , B , and C arms an auxiliary encoder is installed on the sprocket attached to the motors. The auxiliary encoder for the turntable motor is attached at the top of the tr ipod, above the ball bearing holding the manipulator. The auxiliary encoders provide a second measurement of the arm positions that does not suffer from backlash wi thin the motors, but is affected by backlash in the polyurethane chains. B o t h sets of encoder mea- surement are read into the M I D A S O D B through the motor controller and then the motor front end. In total four systems are used to track the manipulator position, to be absolutely sure of the manipulator position: • Motor encoders, • Aux i l i a ry encoders, and • Two inclinometer systems. The inclinometer systems denoted L imi t and Safety are described in the next section. The motor encoders are quadrature encoders that record the motor position wi th four disks having 500 counts per turn giving a total of 2000 steps every 360°. The motor encoders suffer from motor and chain backlash. The auxiliary encoders are attached to the sprockets on the motor drive shaft. That means they only suffer from chain backlash. The auxiliary encoders Chapter 3. Manipulator Construction 50 - Monitor ODB for move reqs -Update motor k̂ j limits and positons Contn>U.rfDri,er T^™*—j rl 1 Limits Computer r ^ - •RS232 Console - Safety Computer T Figure 3.4: Schematic of the Manipulator Control System [4] Chapter 3. Manipulator Construction 51 have an index mark recorded in the database, thus they provide an absolute measurement wi th 2,500 counts per turn per disk or 10,000 steps for 360°. The index mark is measured during the calibration and was to be used to set the angle on the motor encoders after the setup at K E K . However the record of the index mark was lost during the travel to Japan. To use the encoders we set the encoder angle using the l imit inclinometer readout. Ten accelerometers are used as inclinometers in two positioning systems described in the next section, independent of the motors. Pairs of inclinome- ters are placed on electronics chips that are attached to the manipulator. Three pairs read out the angles of the A , B and C arms. Two boards are placed on the vertical section to determine its orientation. One of these boards reads the angle in the plane of swing of the arms, the other records the angle perpendicular to it. 3.3.1 Limit and Safety Systems The inclinometers are M E M S I C M X S 2 0 2 0 E L accelerometers. They provide an absolute orientation wi th respect to the direction of gravity. The in- clinometers are read out by 8051-based microprocessors that compute the position of the arm. If at any point the arm leaves a set of boundary condi- tions set in the O D B the l imit computer wi l l send a stop signal to the motor controller. The boundaries for the safety system are less stringent than those for the l imit system, however if the safety system triggers on a boundary violation it shuts down power to the motors. The accelerometers use an electric heat source and four thermocouples arranged in a plane around the heat source inside an air cavity. Under no acceleration the temperature of the air in the cavity decreases radially outward from the heat source and al l the thermocouples read the same. If accelerated the heat gradient in the air cavity changes, and thus do the readings of the different thermocouples. The thermocouples modulate the peak width of a 100 Hz square wave. The width of the pulse on the square wave encodes the acceleration between two thermocouples. We have such a set of thermocouples monitoring the heat source along two perpendicular axis (x and y) . First we need to determine the acceleration in each direction from the square wave: n = Ax. x L (3-1) v ~ p Chapter 3. Manipulator Construction 52 Here ax and ay are the acceleration in the x and y direction measured in relative units. Ax and Ay are the widths of the two output square wave peaks, and P is the period of the square wave (all measured in fj,s). Thus a vertical inclinometer can measure its absolute orientation by measuring the x and y component of the gravitational acceleration it feels. The inclinometer readout is a function of the ambient temperature. This can be corrected wi th a calibration [27]. Since the temperature for running in the 1 K T is very stable the temperature calibration is not necessary. The calibration is done using Equation 3.2: a? = An _ _ T C • A T ax ix nc — dx _ i b t _ Tc • AT uy — p po J-y ^ Here A° and P° are an offset intrinsic to each inclinometer and the period at 25°C. The second term accounts for slight differences in inclinometer chips. T? are correction constants that must be measured for each inclinometer and A T is represents a temperature difference that manifests itself as a change in the pulse period. A T is given by Equation 3.3: A T = 0.13 • (P — P°) (3.3) The details of this procedure and the code for the inclinometer readout are available from M E M S I C [27]. F ina l ly the angle of the inclinometer makes wi th respect to gravity is given by Equation 3.4: ac 9 = arctan (3.4) To get a measurement of the arm position then we mount an inclinometer on the A , B , and C arms in the plane of swing of the arm. Figure 3.5 shows the M E M S I C accelerometers mounted on the arm. Equation 3.4 only works if the inclinometer x and y axes are perpendicular and parallel to the arms central axis and in the plane of the arms swing respectively. To do this the mounts for the inclinometers are designed to be parallel to the central axis of the arm and parallel to the plane of swing for the arm. Section 3.5 explains how to correct for any error in the inclinometer chip alignment. The boards are waterproofed using polyurethane coating. Y o u can see four sets of wires leading the Ax and Ay signals from the two chips to the l imit and safety computers. The resolution of the inclinometers is less than one milli-gravity, which works out to be 0.09° in arm inclination [4]. The angle of the turntable for the L imi t and Safety systems is read out by a double potentiometer. Chapter 3. Manipulator Construction 53 Figure 3.5: The inclinometer board holding the L imi t and Safety inclinome- ters for the B - A r m . The board is mounted on a holder welded to the arm. The board is coated wi th polyurethane to make it water resistant. Some extra epoxy coating was added for additional safety. Chapter 3. Manipulator Construction 54 3.3.2 The Manipulator Coordinate Systems We use three coordinate systems to keep track of the manipulator in the 1 K T tank. Firs t we use a two-dimensional coordinate system in the plane of swing of the A , B , and C arm. The line in this plane parallel to the 1 K T A x i s is the vertical height axis. The origin of this axis is at the height of the bot tom of the vertical section. The horizontal in the arm plane is measured from the projection of the 1 K T axis onto the plane containing the manipulator arms. The height in this coordinate system is the z coordinate in the tank coordinate system. Figure 3.6 and 3.7 show the top and side view of this coordinate system in the 1 K T . To transform the bal l position (ie. the t ip of the C-Arm) into a point in the primed coordinate system (x',y') we use Equat ion 3.5. This primed coordinate system is a calculation tool to ease the transformation from (r, h, 9) coordinate to tank coordinates. F ina l ly we transform into the Manipulator Coordinate system displayed in Figure 3.8. The h axis for the manipulator and z axis of the detector coordinates are the same, and the x and y axis of the manipulator coordinate system are in equal but opposite direction as those in the detector coordinate system. 3.3.3 Manipulator Position The following algorithm to calculate the position of the joints of the manip- ulator arms is used by both the encoder and the inclinometer systems. The computers find the angles 0j from the encoder or inclinometer output and use the lengths (L{) of the manipulator sections (VS and Arms A , B and C) supplied by the O D B to calculate the arm position using equations 3.6: Tj =r0 + T,i=1 (L{ cos 9i) hj = h0 + YH=I (Li sin 6>j) (3.6) Here rQ is distance of the vertical section from the center of the 1 K T along the line in which the moving arms of the manipulator are pointing (see Figure 3.7 Chapter 3. Manipulator Construction 55 h \ r (r„. h o ) V / 0 i ft, h,) Safety Figure 3.6: Side view of manipulator coordinate system. The origin is defined by the finding the projection of the 1 K T axis onto the manipulator's plane of swing, and finding the height on the projected axis at the same hight as z = 0 m in t h e l K T . The positive r direction defines 0$ = 0. Chapter 3. Manipulator Construction 56 K T W a l l Figure 3.7: Top view of the manipulator coordinate system. The primed coordinate system is a temporary x and y axis used only to ease the calcula- tions. R0ff = 1.03 m is the distance between the center of the 1 K T and the insertion hole. The coordinates of the insertion hole in the tank coordinate system are x = 0.75 m and y = 0.705 cm. Chapter 3. Manipulator Construction 57 kmanip Figure 3.8: Top view of the Manipulator coordinate system. The z-axis is the same as the z-axis in tank coordinates (out of the page in this figure). Here 6 is the azimuthal angle in the manipulator coordinate system used for in the G U I which is described in Section 3.3.4 Chapter 3. Manipulator Construction 58 Table 3.2: Boundaries for the Manipulator L imi t A n d Safety Systems [4] Rule Boundary L i m i t Safety Roof B or C t ip Approaching Top \h\ <3.3 m \h\ <3.5 m Floor B or C tip Approaching Bot tom \h\ <3.3 m \h\ <3.5 m Center B or C tip Approaching V S 0.20 m 0.18 m Radia l B or C t ip Approaching W a l l \r\ <3.3 m |r | <3.4 m V A M i n i m u m Angle Between V S and A 40° 38° A B M i n i m u m Angle between A and B arms 15° 12° B C M i n i m u m Angle between B and C arm 15° 12° Turntable Over-rotation of the Turntable 5° 10° for clarification) and hQ is the height of the bottom of the vertical column along the central axis of the 1 K T (the same as the z-coordinate in the tank coordinate system). r0 depends on the orientation of the manipulator as described in Equation 3.7. 7 j and hj are the radial distance from the central axis and height along the central axis of the 1 K T of the t ip of the jth arm respectively (Figure 3.6 gives an illustration): rQ = Roffcos(j) (3.7) A s shown by Figure 3.7 RQff is the distance from the axis of the 1 K T to the insertion hole. 4> is t h e angle between the manipulator arms and the line from the top center of the 1 K T through the insertion hole. The manipulator is designed to make hQ = 0 cm, and this is what the encoder system uses. The inclinometer systems use the angle read out by the V S inclinometer in the plane of swing of the manipulator arms to determine rQ and hQ as described in Equat ion 3.8: ro = L0 cos 0O o\ / i o = L o ( l - s i n 0 o ) Here 0O is the angle of the vertical section in the plane of the arms (ideally 60 = 0°). The coordinate systems used to locate the manipulator are ex- plained further Section 3.3.2. After this computation the l imit computers check whether any of the manipulator's parts violate the boundary condi- tions summarized in Table 3.2. Determining the wall l imit is nontrivial since the manipulator is offset from the center of the 1 K T tank. The allowed radii in the coordinates calculated by the l imit and safety computers are given by Chapter 3. Manipulator Construction 59 Equat ion 3.9. Tsafe = Roff C O s ( ? T - <f>) ± \J' R2afe ~ R2offSm2(7T - (j)) (3.9) Figure 3.7 explains the meaning of the values needed in for this calculation. These were measured on site due to lack of structural drawings and then entered into the O D B . 3.3.4 The Manipulator GUI The main tool used to control the manipulator is the Mat lab G U I created to communicate wi th the O D B . Figure 3.9 shows how this G U I displays the current position of the manipulator according to al l three positioning systems. The graph in the left shows the height-radius coordinate system of the arm position in the plane of swing of the arms. O n the right you can see the position of the laserball from the top (the view is similar to the one outlined in Figure 3.7). The display is color-coded to show the position according to the inclinometer or encoder systems. The bottom left shows the angles read out from the four position systems. The G U I wi l l also indicate if a l imit is triggered and which further motion is prohibited. In the low center you can read the position of the bal l in the manipulator coordinate system. Another display shows the current status of the front end programs running on the control computer. In the bottom right you may enter the desired position of the manipulator. The control code computed the arm positions necessary to reach the given coordinate wi th the bal l given the desired concavity. The movement of the A , B and C arms is divided into a number of continuous steps. Before the arm moves, each of the positions the bal l should arrive at is checked for l imit violations. If any are found the move is not allowed and the position has to be reached using the manual control G U I . Sometimes it may be advantageous to order one arm of the manipulator to move to a specific angle (especially for the turntable). To do this the manual control G U I was developed. The manual menu in the main G U I opens the window displayed in Figure 3.10. The primary and secondary fields show the reading from the motor and auxiliary encoders. The Destination field lets you enter a target angle for the motors. The last stop indicates why that particular arm stopped moving last. If the arm hit a l imit the checked boxes wi l l indicate which way the arm may not move. Figure 3.9: Screen-shot of the M a i n Graphical User Interface for the manip- ulator arm. Chapter 3. Manipulator Construction 61 'Student Version' : LBNO LaserBall Manual Control Pile Arm A Degrees -30.07 3»c?firt»ry -30.40 Destination Last Stop Move Unknown Stop \ Punitive Lifnit | Negative Limit I Index Arm B Degrees Prirroiy Destination Last Stop -31.01 -39 34 -91. Unknown j Negative Limit i Index Move Stop Arm C Degrees Turntable Degrees Prtnary Destination Last Stop j Positive Umit i Index -8736 -87.05 -87.4| Move Unknown Stop Primary S e e m da i y Destination Last Stop 18C.49 179 4S Unknown itive Limit ;ative Limit Move Stop Figure 3.10: The Manual Control G U I for the Manipulator. This G U I allows the user to move one arm to a specific angle. Chapter 3. Manipulator Construction 62 3.4 Construction and Assembly The design drawings for the manipulator were done professionally by M a r k Lenckowski of the University of Vic to r i a design workshop and Corrie Holm- berg from the T R I U M F design workshop. The parts of the arm were ma- chined at the machine shops at T R I U M F , the University of Br i t i sh Columbia Physics department, and the University of Vic tor ia . Most of the machining required very precise work and was done by professionals, while a few parts requiring less accuracy were machined by me. A l l the parts from the differ- ent machine shops were assembled at T R I U M F by Rich Helmer, K e i t h Hoyle and myself for calibration. Some problems, such as the stability of the t r ipod supporting the turntable, were recognized and fixed during the test assembly at T R I U M F . The final assembly was carried out by the entire K 2 K Canada group, wi th help from K e i t h Hoyle, Mark Lenkowski and David Morris . 3.5 Calibration Before the manipulator was deployed in the 1 K T it was tested and calibrated at T R I U M F . The robot arm was suspended from the roof of the proton hall . Figure 3.11 shows the imitation of the 1 K T access that was set up at T R I U M F on the roof of the proton hall . Figure 3.12 shows the manipulator setup in the proton hall at T R I U M F . Since the manipulator is not in water the A and B arms are not neutrally buoyant. So to allow the A and B arms full range of motion, pipe counterweights were used. The counterweight on the A - a r m did not properly balance and it was only possible to move the A - a r m though small angles at a time for the calibration of the manipulator. The angle between the vertical section and the turntable was tested to be perpendicular wi th a carpenters edge around its circumference of the vertical section. A luminum spacers were placed between the vertical section mounts and the turntable unti l the angle between the turntable and the vertical section was perpendicular. Using the carpenters level this measurement is probably accurate to 0.4°. Next the turntable supporting the manipulator was adjusted unti l a machinist's level set on the turntable supporting the vertical section read level. Chapter 3. Manipulator Construction 6 3 Figure 3.11: Mockup of the 1 K T access at T R I U M F . The support structure for the manipulator is set up on imitations of the roof support beam and the C R P cage. The weight of the Manipulator is on the joint at the top of the t r ipod. The t r ipod holds the turntable and manipulator in place. Chapter 3. Manipulator Construction 64 Figure 3.12: View of the manipulator suspended from the ceiling of the proton hall at T R I U M F Chapter 3. Manipulator Construction 65 3.5.1 Wobble Due to the length of the vertical section and the fact that it is composed of three sections the bot tom of the vertical section moves in a small circle as the turntable rotates. This motion is reproducible, thus we measured the rotation of the bottom of the vertical section. This was accomplished by mounting two plumb bobs on opposing sides at the bottom of the vertical section and recording their positions throughout one rotation. The center point between the two plumb bob locations was taken to be the center of the manipulator. A reading from the auxiliary encoder for the turntable was taken wi th each position, however we needed to change the index position when we set the manipulator up at K E K . This means that we need to rotate the position of the circle. Figure 3.13 shows the result from these measurements. The wobble of the bottom of the main section is caused by two problems wi th the manipulator set up. First the vertical section of the manipulator may not be perpendicular to the turntable. This would cause the bottom of the vertical section to describe a circle centered on the center of the turntable. The second problem is that the turntable may not be perfectly level. This means that the center of the bottom of the vertical section may not coincide wi th the center of the turntable, thus causing the vertical section to wobble about a point not below the center of the turnable. 3.5.2 Total Station The A and B arms were taken though their entire range of motion while monitored wi th a Leica 5005 Total Station. The total station uses two small targets that were attached to the A and B arms and measures the positions of these targets relative to the total station by lining up its sights wi th marks on the targets. Using the position information of the two targets on each arm the orientation of the arms in space can be measured wi th an accuracy of 0.33 arc-seconds. The readout of al l the manipulator position systems was taken as each arm was rotated through 360°. It was expected that the in- clinometer chips were not perfectly aligned wi th the plane of motion of the arms. This would result in a sinusoidally varying offset of the inclinometer angle from the real angle. Figure 3.14 shows the result for the A - a r m cor- rection and Figure 3.15 shows the result for the B-arm correction. The best approximation to the real offset was taken sine fit for the A - a r m and a to be a linear interpolation between data points for the B-arm. Chapter 3. Manipulator Construction 66 6 5 4 3 ^ 2 E o 1 0 -1 -2 -3 Manipulator VS Wobble Manipulator Coordinate System, Centered on Insertion Hole ~i r- ~i r- . - X — - ~ x ~ • • . x ^ • • X X y / / \ \ ' ' X ' " / / \ \ X \ I Ix \ + I X I X • . . \ * / . . x . . . . \ \ s. / / y : X • - X u • -u.'X-~ • • -3 -2 -1 0 1 x (cm) Figure 3.13: The circle traced out by the bottom of the vertical section of the manipulator in the manipulator coordinate system. The origin of this plot lies below the turntable center. Chapter 3. Manipulator Construction 07 A-Arm Limit Inclinometer Correction 8r -250 -200 -150 -100 -50 0 50 9limit ( 0 ) Figure 3.14: The correction for the limit inclinometer on the A-a rm. Chapter 3. Manipulator Construction B-Arm Limit Inclinometer Correction 0.5 - 0 . 5 - 1 / / / / / / / / > i i \ \ / -J I 1- - 2 5 0 - 2 0 0 - 1 5 0 - 1 0 0 - 5 0 0 5 0 limit Figure 3.15: The correction for the B-arm l imit inclinometer. Chapter 3. Manipulator Construction 69 3.6 Manipulator Setup At The 1KT After testing at T R I U M F the manipulator was taken apart and shipped to Japan. It arrived on A p r i l 21, 2005. The first data was taken A p r i l 30, 2005 and the 1 K T was collecting calibration data only interrupted by a few problems wi th the 1 K T D A Q until it was taken down on June 14, 2006. The manipulator was taken apart and shipped back to Canada two weeks later. The manipulator was assembled inside the free room above the 1 K T since it could not fit inside the front door of the 1 K T fully assembled. We could fit the moving sections and the first vertical section into the 1 K T at the same time as long as the chains were not hindering the full range of motion of the arms. So once this first part of the manipulator was inside the 1 K T the chain drives and the black plastic coat were installed. Since the entire manipulator is too large to fit into the room above the detector volume and too large to easily fit through the C R P we need to lower the manipulator section by section starting wi th the B and C arm and moving on toward the vertical sections. Once the A , B and C arms were in the detector volume there was enough room to fit the last two parts of the vertical section. The joints and chain drive along the vertical section were assembled in the tank. F ina l ly the vertical section was lowered in the 1 K T piece by piece. When the second and th i rd parts of the V S were lowered into the 1 K T the brackets fastening the V S parts together in a solid section needed to be tightened before the section was lowered into the detector. Figures 3.16 to 3.18 display this step-by-step procedure showing the insertion of the second part of the vertical section. After the manipulator on its turntable was put into the 1 K T the support structure was finished and its position aligned to match the calibration setup at T R I U M F . The machinist's level we used to ensure that the turntable was horizontal turned out to be broken when we used it at K E K , which made it impossible to exactly recreate the setup at T R I U M F . Thus another level was used and we recorded the setup at K E K which we later reproduced to perform a back calibration of the manipulator at T R I U M F . Another problem we encountered was that we lost the booklet which had the recorded index marks on the auxiliary encoders used at T R I U M F to set the motor encoder angles. Since the 0° reading of the l imit inclinometers was known to be good, we set the motor and auxiliary encoders using the l imit inclinometer reading. Because of this we use the l imit inclinometer to give us the nominal position of the laserball for the manipulator analysis. W i t h the corrections from the total station the inclinometer readings are precise Chapter 3. Manipulator Construction 70 Figure 3.16: Example of the step-by-step insertion procedure used to fit the manipulator into the 1 K T . Here the second part of the vertical section is lifted off the makeshift assembly table, before it can be lowered into the detector. Chapter 3. Manipulator Construction 71 Figure 3.17: The stage of the manipulator insertion that is most crit ical, fitting the V S pieces into the C R P under the roof support. Chapter 3. Manipulator Construction 72 Figure 3.18: Before lowering part 2 of the V S into the 1 K T the clamp holding parts one and two straight must be fastened. 73 Figure 3.19: The manipulator group just after the manipulator assembly and insertion had been completed. From left to right: Mark Lenckowski, R i ch Helmer, Scott Oser, Frank Berghaus, A k i r a Konaka, and David Morris to 0.3° which translates into an 1cm uncertainty in the ball position, thus matching our design goals. The manipulator was covered in black tarp to minimize reflection except for the joints attaching the polyurethane chains to the stainless steel sections. Figure 3.6 shows the Canadian group around the manipulator fully assembled and inserted into the 1 K T tank. 74 Chapter 4 Manipulator Data and Analysis 4.1 Data Taken In Japan Data was collected by the manipulator in order to study: • Posit ion reconstruction throughout the 1 K T , • Effect of the manipulator shadow on the reconstruction, • Posit ion reproducibility, • F iducia l volume error, • Opt ical parameters: — Attenuation length, and — Angular response of the P M T s , • Detector asymmetry from: — Vertical position, and — Magnetic fields in 1 K T , and • Effects of laserball orientation. To achieve al l this we took data using the manipulator wi th these motions: • B a l l rotation and flips to study: — Laserball asymmetry, and — Shadow effects • Swings of a single moving arm to study: — Manipulator position accuracy, and Chapter 4. Manipulator Data and Analysis 75 — Position reconstruction • Scans along the different axes in the 1 K T to study: — Position reconstruction, and — P M T Acceptance and optical properties • Tracing out hexagons at different heights to study: — Detector asymmetry, and — Position reconstruction • A G r i d through the F V to study: — Position reconstruction, and — P M T acceptance, and • Off center TQ-map data. Appendix B summarizes al l the data that was taken wi th the manipulator. 4.1.1 Reconstruction Bias and Fiducial Volume Study The error in the fiducial volume is the dominant uncertainty in the 1 K T measurement for the far/near ratio. To know the flux measurement of the 1 K T we need to be able to correctly identify the volume of the 1 K T we are considering for fully contained (FC) events. A F C event has a neutrino interaction vertex in the 1 K T and al l light detected during the event must be in the inner detector volume. 4.1.2 Up/Down Asymmetry and Energy Scale Some of the manipulator data is specifically designed to study the up-down asymmetry in the 1 K T . A 1.7% horizontal-vertical asymmetry in the energy of muons stopping in the detector can be observed using cosmic rays [28]. The axis scans done wi th the manipulator may be able to characterize this asymmetry more. Chapter 4. Manipulator Data and Analysis 76 4.1.3 Scattering and Particle Identification Scattering and reflections inside the 1 K T have a strong effect on particle identification (PID) and R ing counting in the 1 K T . This effect is particularly- strong on multi-ring electron-like events. The data throughout the 1 K T taken wi th the manipulator wi l l aid the understanding of scattering of light in the 1 K T tank. 4.2 Reconstruction In this thesis we wi l l only be studying the effects revealed by the position reconstruction. The basic algorithm for the laserball reconstruction is the same as described in Section 2.2. When making the P M T s t iming histograms we started by excluding P M T events on which the A D C saturates, since the time and charge reading on these events are inaccurate. The presence of the manipulator requires that the shadow it casts on the P M T s must be taken into account. We also need to find P M T s that are hit by light from grazing reflection of the manipulator. Three methods are used to identify shadowed P M T s and exclude them from the fit. We cut P M T s using: • Geometrical location of the manipulator shadow, • A t iming cut: \tpmt ~ tof - t^t\ > 20 ns (4.1) where tpmt is the time measured by the P M T , tof is the time of flight, and tpmt is the average tof-corrected time over al l P M T s , and • A n outlier cut: P M T s wi th 5a and larger fit residuals. The t iming cut identifies P M T s that have times very far away from the mean time-of-flight corrected time: most likely a bad P M T , or one measuring a lot of reflected/scattered light. Figure 4.1 shows the distribution of P M T times for a run wi th the laserball on a string. So al l P M T s wi th a time of more then 20ns from the mean can be regarded as broken or seeing a lot of light from reflection off of the manipulator. This cut allows a lot of room for outlying P M T s . These wi l l show up wi th large fit residuals since their time wi l l be very different from the mean times of surrounding P M T s . These outlying P M T s wi l l get tagged by the outlier cut. Chapter 4. Manipulator Data and Analysis 77 tof Corrected PMT Time Distribution T — i — i — i — | - 1 — i — i — r - | — i i i — i — | — i i i — r - | — 1~ ib 1 1 1 1 1 1 Entries 680 ; Mean 1001. - R M S 0.2925 - • • • i i • i • • n P., r / Hi J 1—1 ' ' ' I I I I L HMMl/l nr, ' i i i i _ 999 999.5 1000 1000.5 1001 1001.5 1002 1002.5 1003 t-tof (ns) Figure 4.1: T ime distribution from a run using the ball on a string. Note that al l P M T s gave mean times within a window less than 3 ns wide. Chapter 4. Manipulator Data and Analysis 78 4.2.1 Saturation Cut Since no documentation on the A D C saturation signal for the 1 K T P M T s exists we scanned the two A D C channels of the P M T s for al l P M T s in a high occupancy run looking for a cutoff. The A D C saturation spike is clearly visible at the right hand of Figure 4.2. The A D C output channel for a saturated P M T is 1166012416. Considering the P M T s are read out by 12-bit A D C s this value makes little sense, and no clarification has been forthcoming. The meaning of the spike on the plot is clear enough though. Thus any P M T events wi th a raw A D C output equal to 1166012416 in either channel from the P M T are cut. 4.2.2 Geometrical Shadow Cut To explain how the location of the shadow of the manipulator is determined first consider any point on the wall , top or bottom of the 1 K T . Knowing the bal l position we calculate the vector from the laserball to that point on the wall . This gives us the line from the laserball to the point on the wall , let's call it the light ray. Knowing the position of the beginning and end of each arm we can draw a line along the central axis of the arm. Next we determine the point on the light ray and the point on the arm that are the closest to each other. If the distance between those points is less than the radius of the arm being considered we call the point on the 1 K T shadowed. Figure 4.3 shows the shadowed region of the 1 K T as calculated by this routine for one run. We flag any P M T as shaded if the shadow reaches anywhere wi thin 10 cm of the edge of the P M T . The loose requirement for the shadow is motivated the limitations on the knowledge of the absolute position of the manipulator in the 1 K T . This cut is responsible for almost al l excluded P M T s . 4.2.3 Timing and Outlier Cut To identify P M T s wi th unreasonable times we determine the mean of the time-of-flight corrected P M T times. Then al l P M T s are scanned, and P M T s that are 20 ns from the mean are flagged. This removes P M T s that see mostly light reflected off of the manipulator. To determine any left-over outliers the fit is run once. A n y P M T wi th a fit residual greater than five times the error on the P M T mean time (5cr) is flagged. Almost no P M T s are flagged by this last cut. This cut removes Chapter 4. Manipulator Data and Analysis 79 ADC Saturation Spike 1 tL-r— Figure 4.2: The A D C cutoff is clearly visible wi th the spike at channel 1166012416. The multiple peaks represent the two channels of raw A D C output from the P M T . A l l A D C s seem to saturate at the same raw A D C output value. Chapter 4. Manipulator Data and Analysis 80 Area Shaded by Manipulator X(cm) Figure 4.3: Manipulator shadow as determined by geometrical ray tracing. The crooked line in the middle represents the location of the arms. Chapter 4. Manipulator Data and Analysis 81 P M T s that are passed by the P M T timing cut, but have very different times from their neighbors. This would be caused reflection effects of the manipu- lator. 4.2.4 Nominal Laserball Position The nominal position of the laserball is determined using the information from the l imit inclinometer system. We use the fits displayed in Figures 3.14 and 3.15. These corrected angles are used to determine the nominal position of the laserball using the algorithm outlined in Section 3.3.3. The correction for the vertical section wobble is not properly understood, since it was difficult to properly relate the orientation of the wobble as measured at T R I U M F to the manipulator position in the 1 K T detector. Therefore the wobble correction was not applied. 4.2.5 Results of the Reconstruction Before applying the inclinometer position correction and the cuts for shadow and reflections our reconstructed positions agree wi th the nominal positions to about 6 cm. Figure 4.4 shows this agreement between uncorrected nominal and fit positions. Figure 4.5 shows that the fitted position agrees wi th the nominal position better than 3 cm for low occupancy data after accounting for shadows, scattering, inclinometer offsets, and saturation. Figure 4.6 shows that the high occupancy data has a large spread between the nominal and fitted positions even after al l the corrections. The offsets in the x, y and z positions are due to our uncertainty in placing the manipulator relative to the 1 K T tank. Since no design drawings of the 1 K T were available it is expected that the positions are off by a few centimeters. The variance of the difference between fitted and nominal ball positions represents how well we understand the positions of the manipulator relative to each other, thus it is the interesting number to look at. Since the problems wi th the position reconstruction of the high occupancy runs were not resolved by the saturation cut, the error in the reconstruction of the high occupancy data may be the result of another systematic effect. Figures 4.7 and 4.8 show the laserball position reconstruction throughout the tank volume without and wi th al l corrections respectively. The most curious feature of Figure 4.8 is the consistent agreement between low and medium occupancy, while the high occupancy data always seems different. Chapter 4. Manipulator Data and Analysis 82 Sum of High, Medium and Low Offsets 0 5 10 15 20 fit - nominal x (cm) CD a 1*3 c I-C <u JO e -20 -15 -10 -5 0 5 10 15 20 fit - nominal y (cm) 20 P 15 10 5 0 _ l I I I I I I I 1—1 I I I I I I I I l _ L 20 -15 -10 -5 0 5 10 15 20 fit - nominal z (cm) Figure 4.4: Offset between uncorrected nominal and fitted positions for al l manipulator runs. Each 'event' in one of these histograms is one run. Y o u can see that nominal and fitted positions do not agree very well without any corrections or cuts. Chapter 4. Manipulator Data and Analysis 83 Low Occupancy Fit Offset - i i I I 1 1 1 ii.* — j i 1 1 1 1 1 1 1 1 1 c 12 IIDI ' ' ' 1 1 1 f l - Entries Mean -3.991. RMS 2.744- -20 -10 0 10 20 -20 -10 0 10 20 fit - nominal x (cm) fit - nominal y (cm) I I E M 1 1 I 1 1 1 M Entries 163 •0.1755J S 3.711J -20 -10 0 10 20 fit - nominal z (cm) Figure 4.5: G o o d agreement between nominal and fit positions for the low occupancy data wi th al l cuts and corrections. Chapter 4. Manipulator Data and Analysis 84 High Occupancy § 9 j * 8 Fit Offset -20 -10 0 fit - nominal x (cm) -10 0 10 fit - nominal y (c 12 10 8 6 4 2 0 i i i I i i i i w ' 1 1 1 1 1 hr Enlries Mean -2.30ll RMS 6.944- 20 -10 0 10 20 fit - nominal z (cm) Figure 4.6: The nominal and fit positions for the high occupancy data dis- agree even after al l cuts and corrections are applied. Chapter 4. Manipulator Data and Analysis 85 Position Fit Bias Profile Histograms i — i — i — I — i — i — i — i — I — i — i — i — i — I — i — i — i — i — I — i — i S- 1 i — I — i — r 100 200 300 nominal x (cm) -300 -200 -100 0 100 200 300 nominal y (cm) e -300 -200 -100 0 100 200 300 «1 nominal z (cm) «3 Figure 4.7: Wi thout corrections to the nominal positions and cuts to the data used in the fits the optical reconstruction shows significant deviations throughout the tank. The results along the vertical axis show a very strong slope. Chapter 4. Manipulator Data and Analysis 86 Reconstruction Bias Profile ram -300 -200 -100 i 4-1 ? 100 200 300 nominal x (cm) 0 -5 t- 10 'r pr—I—|—I—I—I—I—|—I—i—i—I—|—I—I I i—|-1—I—i—i—r—I—I I I—|—I I I I | ..J..-4J c -300 -200 -100 0 100 200 300 nominal y (cm) f 10 3 5 " 0 1 -5 1-10 _i i i i I i i I i i i i 1 i i i i L -300 -200 -100 0 100 200 300 nominal z (cm) Figure 4.8: Offset between fitted and nominal (real) laserball position for the manipulator data. Black and solid represents low, blue and dashed medium and red or dotted high occupancy. The lines are a log likelihood fit to the points, which are the average of all the manipulator positions in their vicin- ity. The error bars represent the variance of the laserball positions used to determine the point. Chapter 4. Manipulator Data and Analysis 87 Since the low and medium occupancy data agree well wi th the nominal bal l positions and the high occupancy data does not we can conclude that there is a problem in the high charge and occupancy regime. Figure 4.9 displays the fit agreement wi th the nominal position for al l the manipulator data. Considering this consistent difference between low and high occupancy data we would like to investigate whether there is a relation between the positions the high and the low occupancy data fit. Figure 4.10 shows that the high occupancy data consistently constructs ~ 3% further outward than the low occupancy data. To figure out why the high occupancy fit so disagrees wi th medium and low occupancy we investigate the t iming over all the P M T s in the 1 K T tank. Figure 4.11 shows the P M T times for high and low occupancy runs as a function of the distance from P M T to the laserball. This effect seems to be consistent wi th a higher effective speed of light for the high occupancy data. 4.3 Discussion Further investigation into the construction process of the TQ-map revealed that it uses a larger integration gate than the ± 2 n s gate in our analysis (see Figure 2.2). This means that the low occupancy data for the T Q - m a p should be affected by the scattering. In fact the scattering ta i l would have the TQ-map believe that al l the P M T s are slow in low occupancy runs, thus subtracting from the time signal of low charge P M T s . This would effectively pul l the optical fit toward the low charge P M T s since their time is wrongly corrected to an earlier value than it should be. This means that in high occupancy data the bal l should reconstruct closer to the center of the 1 K T since the P M T s on the side far from the laserball have a lower time than they should. This is precisely opposite to the effect displayed in Figure 4.8. Another possible explanation is that the P M T s respond faster to photons that hit the central area of the photocathode. This is known to happen wi th the 20-inch Hamamatsu P M T s used in the 1 K T . P M T s that are hit in a high occupancy run would alway respond to the first signal they see, which comes from that central region. For low occupancy runs only a fraction of al l events hit the photocathode close to the center. The TQ-map should take out this effect, but since TQ-map only uses data from runs wi th the laserball in the center of the 1 K T it may not correctly identify this effect for off-center low Chapter 4. Manipulator Data and Analysis 88 1 c a 14 12 10 8 6 4 2 0 12 10 8 6 4 2 0 Position Fit Offset 1 1 I 1 1 1 '-I «3 • • I HIM:,:::: , § 12 E 10 o j <5 8 i f 6 -fc 4 f- 2 r 20 -10 0 10 20 fit - nominal x (cm) i i 1111 i i 1 1 1 1 1 1 1 1 1 1 1 1 20 -10 0 10 20 fit - nominal z (cm) 0 i i i i I i I,, i i T — i i i i i — i r -20 -10 0 10 20 fit - nominal y (cm) Figure 4.9: Agreement between fit and nominal positions for al l manipulator data. Black and solid is low, blue and dashed is medium and red and dotted is high occupancy. Note that the high occupancy histogram is much wider than the black or blue histograms. Chapter 4. Manipulator Data and Analysis 89 Figure 4.10: Posit ion reconstruction bias between high and low occupancy data Chapter 4. Manipulator Data and Analysis 90 100 200 300 400 500 600 700 800 900 Distance to Ball, R (cm) Figure 4.11: Average P M T timing differences between high and low occu- pancy as a function of distance between P M T and laserball. 91 Table 4.1: Solid angle subtended by more and less responsive areas of the photodiode as seen by the laserball moving closer to the P M T . The photo- diode is modeled as a hemisphere. The central part is 0° to 2° from the top of the of the hemisphere. The middle part is defined as 2° to 10° from the top of the hemisphere. The rest is qualified as the Outer part. Distance Fraction of Solid Angle to bal l Central Middle Outer 430 cm 0.0031 0.0731 0.9238 330 cm 0.0031 0.0742 0.9227 230 cm 0.0032 0.0762 0.9205 130 cm 0.0035 0.0824 0.9141 30 cm 0.0086 0.1811 0.8103 occupancy runs. It is more likely for photons from the laserball to strike the P M T s in the central area of the photocathode if the laserball is closer to the P M T s . Table 4.1 shows the solid angle subtended by the sensitive areas of the P M T as the bal l approaches the P M T . The quickly responding central area only becomes significant in size as the laserball gets much closer to the P M T s than we allowed the manipulator to get. Thus this effect cannot be responsible for the difference between high and low occupancy we see here. The laserball fluoresces when excited by the large number of photons traveling though it during a high occupancy run. Thus we could have light of different wavelength in the 1 K T . This could cause a different effective speed of light. Bu t for this to be true the P M T s should respond at a different time for a high occupancy run than low occupancy run since for the bal l in the center the light from the fluorescence line wi l l travel at a different speed then the laser light. However if the light from the fluorescence were faster then the laser light we would get a slope opposite to what we see in figures 4.8 and 4.10. If the fluorescence light is slower than the laser light the P M T wi l l record the time it was hit by the laser light, thus negating the effect. Chapter 5 Conclusion 92 A diffracting bal l suspended by a string in the 1 K T tank of the K 2 K ex- periment was used to demonstrate a problem wi th the understanding of the t iming reconstruction of the 1 K T . A n optical position reconstruction revealed that the positions of the laserball were reconstructed about 3 cm too low, and for medium occupancy wi th a significant bias, pulling the position fit out- ward. These problems motivated the construction of the manipulator arm which allowed the exploration of the entire 1 K T volume wi th the laserball. The positioning accuracy reached in this study is ~3 cm, but there are st i l l some unresolved issues in the calibration of the manipulator. The optical reconstruction of the laserball on the manipulator was possible after shad- owing, scattering and reflections caused by the manipulator were identified. We find the high occupancy data reconstructs further away from the center than expected. This reconstruction bias is consistent wi th a lower effective speed of light in high occupancy data but the cause for this effect has not been identified. 93 Bibliography [1] Issei Ka to . Indications of Neutrino Oscillation in K2K Experiment. P h D thesis, Kyo to University, Ju ly 2005. [2] The K 2 K Collaboration. A measurement of neutrino oscillations by the k2k experiment (tenative title). Phys. Rev. Letters, 2006. [3] The K 2 K Collaboration. tdcres.dat. Code in k2k04a/skam/const/tdcres.dat, 2004. [4] David Morr is et al . A n optical calibration manipulator system. Technical report, T R I U M F , 2006. Accepted for publication. [5] John N . Bahcal l , A ldo M . Serenelli, and Sarbani Basu. 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[28] Shunichi Mine . Energy scale. K 2 K Collaboration Meeting, 2005. 96 Appendix A Data With Laserball On A String The setup for collecting the optical calibration data using the laserball is de- scribed in Section 2.1. The laserball data taken is summarized in tables A . l , A . 2 and A . 3 . The laserball could be positioned accurate to 10 cm for the data taken in October 2003, 5 cm for the data taken in Spring 2004 and about 3 cm for data taken in the Summer of 2005. The nominal position of the laserball is determined by measuring the desired height from a piece of tape on the wire holding the bal l in the tank that indicating where to put the bal l to suspend it in the center of the tank. Then the wire is fixed at the measured position. Note that for runs 613342 to 98 the voltage supply to the photo-diode was turned off. This means the t iming signal supplied by the photo-diode is unstable making the position reconstruction for these runs very inaccurate. Appendix A. Data With Laserball On A String 97 Table A . l : Summary of data taken wi th laserball on a string. Height in tank is the z position of the bal l in the tank coordinate system (see Figure 1.15) R u n Number Height (cm) Occupancy Events Notes October 2003 Data: 603039 0 45 13,000 603041 300 45 25,000 Spring 2004 Data: 602960 0 57 20,000 602963 0 79.5 20,000 602964 0 140 20,000 602965 0 200 20,000 602966 0 300 10,000 602969 0 400 10,000 602972 0 500 10,000 602973 0 580 5,000 602974 0 600 5,000 602975 0 605 5,000 602976 0 619 5,000 602978 0 650 5,000 602980 0 675 3,000 602981 0 675 3,000 602983 0 675 3,000 602984 0 675 3,000 602985 0 675 3,000 602986 0 675 3,000 602987 0 675 2,000 602988 0 675 2,000 602989 0 675 2,000 602993 0 680 2,000 602994 0 680 2,000 602995 0 680 2,000 602996 0 680 2,000 602997 0 680 2,000 602998 0 680 2,000 603000 -200 678 5,000 Problems wi th t iming 603002 -200 60 40,000 603004 -200 160 29,000 603039 0 45 12,000 603041 300 45 20,000 603045 0 150 603047 0 150 10,000 Appendix A. Data With Laserball On A String 98 Table A . 2 : Da ta taken wi th laserball on string Part 2 Height (cm) Occupancy Events Notes Ju ly 2004 Data: 603050 -200 250 7,000 603051 200 250 10,000 613342 -300 45 20,000 Photo diode Voltage is off 613346 -300 375 3,000 Photo diode Voltage is off 613348 -300 300 4,500 Photo diode Voltage is off 613350 -300 25 30,000 Photo diode Voltage is off 613351 -300 50 40,000 Photo diode Voltage is off 613352 -300 100 Photo diode Voltage is off 613353 -300 190 16,000 Photo diode Voltage is off 613354 -300 230 2,000 Photo diode Voltage is off 613356 300 150 6,000 Photo diode Voltage is off 613364 300 low Photo diode Voltage is off 613374 300 30 Photo diode Voltage is off 613389 300 400 25,000 Photo diode Voltage is off 613391 300 180 30,000 Photo diode Voltage is off 613393 300 25 67,000 Rotate bal l by 180° Photo diode Voltage is off 613396 200 420 Rotate bal l back Photo diode Voltage is off 613398 200 200 Photo diode Voltage is off 613399 200 200 --> 70 613401 200 30 613402 200 30 Rotate bal l by 180° 613405 100 200 -• 150 Rotate bal l back 613408 100 600 613410 100 .25 613412 100 25 Rotate bal l by 180° 613414 0 580 Rotate bal l back 613417 0 25 613419 0 25 Rotate bal l by 180° 613421 -100 520 Rotate bal l back 613423 -100 200 613425 -100 25 Appendix A. Data With Laserball On A String 99 Table A . 3 : Da ta taken wi th laserball on string Paxt 3 R u n Number Height (cm) Occupancy Events Notes June 2005 Data: 615632 0 20 5,000 615633 0 500 5,000 615634 0 679 20,000 615636 -298 680 5,000 615637 -298 500 5,000 615638 -298 20 20,000 N 615641 -170 20 20,000 615642 -170 500 5,000 615643 -170 680 5,000 615645 127 680 5,000 615646 127 500 5,000 615647 127 20 20,000 615649 273 680 5,000 615650 273 500 5,000 615651 273 20 20,000 100 Appendix B Manipulator Data The laser setup for the these runs using the manipulator is the the same as the setup for the laserball on a string described in Section 2.1. The Manipulator and its operation is described in Chapter 3. The runs here were taken between A p r i l 25, 2005 and June 14, 2005. The bal l position is given in the tank coordinate system. In low occupancy runs 20, medium occupancy runs 480 and high occupancy runs 680 P M T s are hit on average. The nitrogen laser broke during run 615550 and was replaced. The missing runs between 615550 and 615597 were used find the problem and test the replacement laser. The data from the online database summarizing the complete manipula- tor status during each run is available at: ht tp: / / t rshare. t r iumf.ca/~berghaus/work/manipulator/online/odb/ Sketches of the manipulator orientations in each of the run plan sections are available at: http://phys01.comp. uvic .ca:8080/ t2k/Members/frank/Runplan/view/ Appendix B. Manipulator Data 101 Table B . l : Summary of manipulator runs taken at K E K R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy A 3 615026 -77.50 73.28 -301.34 low A 3 615027 -77.50 73.28 -301.34 medium A 3 615028 -77.50 73.28 -301.34 high A 4 615029 -76.27 71.90 -296.18 high A 4 615030 -76.27 71.90 -296.18 medium A 4 615031 -76.27 71.90 -296.18 low A 5 615032 -72.64 67.95 -296.75 low A 5 615033 -72.64 67.95 -296.75 medium A 5 615034 -72.64 67.95 -296.75 high A 6 615035 -71.70 66.98 -304.18 high A 6 615036 -71.70 66.98 -304.18 medium A 6 615037 -71.74 66.96 -304.01 low B l 615038 172.90 -199.58 -127.81 high B l 615039 172.90 -199.58 -127.81 medium B l 615040 172.90 -199.58 -127.81 low B l 615041 172.90 -199.58 -127.81 low B 2 615043 -76.32 71.94 -132.60 high B 2 615044 -76.32 71.94 -132.60 medium B 2 615045 -76.32 71.94 -132.60 low B 3 615046 47.26 -60.05 -311.38 high B 3 615047 47.26 -60.05 -311.38 medium B 3 615048 47.26 -60.05 -311.38 low B4 615049 173.43 -200.11 -128.46 low B4 615050 173.43 -200.11 -128.46 medium B4 615051 173.43 -200.11 -128.46 high B5 615052 65.88 -81.42 -201.64 high B 5 615053 65.88 -81.42 -201.64 medium B 5 615054 65.88 -81.42 -201.64 low B6 615055 41.50 -54.31 -93.42 low B6 615056 41.95 -54.37 -93.48 medium Appendix B. Manipulator Data 102 Table B.2: Manipulator runs table 2 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy B6 615057 40.78 -55.19 -93.57 high B 7 615058 45.87 -60.72 -311.89 high B 7 615059 46.63 -60.25 -311.61 medium B 7 615060 46.53 -60.13 -311.85 low C I 615061 99.34 -204.60 -198.20 low C I 615062 99.34 -204.60 -198.20 medium C I 615063 99.34 -204.60 -198.20 high C2 615064 -133.41 -195.40 -197.01 high C2 615065 -134.27 -195.41 -197.01 medium C2 615066 -133.41 -195.42 -197.13 low C 3 615067 -243.27 10.47 -198.27 high C 3 615068 -242.96 10.38 -198.22 medium C 3 615069 -243.03 10.56 -198.05 low C4 615070 -120.17 204.17 -199.87 high C4 615071 -120.01 204.09 -200.05 medium C4 615072 -119.82 203.87 -199.75 low C 5 615073 110.79 198.14 -196.13 high C 5 615074 110.79 198.01 -196.12 medium C 5 615075 110.91 197.63 -195.77 low C6 615076 220.54 -7.37 -196.81 low C6 615077 220.74 -7.35 -196.95 medium C6 615078 220.66 -8.33 -196.85 high C 7 615079 219.66 -7.14 207.20 high C 7 615080 219.78 -7.18 207.25 medium C 7 615081 220.04 -7.24 207.03 low C8 615082 109.71 198.95 206.31 high C8 615083 109.71 198.95 206.31 medium C8 615084 109.71 198.95 206.31 low C9 615085 -118.68 199.84 206.71 high C9 615086 -118.60 199.92 207.07 medium Appendix B. Manipulator Data 103 Table B .3 : Manipulator runs table 3 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy C9 615087 -118.71 199.91 206.85 low CIO 615088 -236.48 13.31 204.82 high CIO 615089 -236.43 13.33 204.64 medium CIO 615090 -236.50 13.61 204.61 low C l l 615091 -132.32 -186.29 207.34 high C l l 615092 -132.31 -186.59 207.35 medium C l l 615093 -131.18 -186.63 207.29 low C12 615094 94.46 -196.03 210.89 high C12 615095 94.52 -196.06 210.84 medium C12 615096 94.09 -196.32 211.04 low D l 615097 190.81 -218.11 13.19 high D l 615098 191.77 -217.18 13.38 medium D l 615099 191.28 -217.67 12.99 low D2 615100 183.62 -214.11 14.61 high D2 615101 185.03 -212.79 14.63 medium D2 615102 183.59 -214.08 14.46 low J l 615103 66.70 -83.91 220.43 medium J l 615104 66.70 -83.91 220.43 high J l 615105 65.88 -84.54 220.31 low J2 615106 65.83 -82.94 -202.03 high J2 615107 64.88 -83.44 -202.17 medium J2 615108 65.17 -83.23 -202.22 low J3 615109 170.18 -195.77 -144.71 high J3 615110 169.26 -196.51 -144.66 medium J3 615111 173.56 -192.36 -144.43 low J4 615112 -116.39 115.76 -150.52 high J4 615113 -116.18 115.67 -150.19 medium J4 615114 -116.45 115.81 -150.50 low E l 615115 -75.07 68.37 -296.46 high E l 615116 -75.09 68.00 -296.32 medium Appendix B. Manipulator Data 104 Table B.4: Manipulator runs table 4 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy E l 615117 -75.07 68.27 -296.38 low E2 615118 -76.42 70.56 -296.54 high E 2 615119 -76.24 70.55 -296.63 medium E 2 615120 -76.32 70.54 -296.61 low E3 615121 -74.91 72.39 -296.59 high E3 615122 -74.91 72.32 -296.30 medium E3 615123 -74.92 72.33 -296.52 low E4 615124 -72.21 70.39 -296.75 high E4 615125 -71.93 70.36 -296.83 medium E4 615126 -72.24 70.36 -296.75 low F l 615127 -283.86 81.40 -316.49 high F l 615128 -283.92 81.98 -316.56 medium F l 615129 -284.06 81.99 -316.49 low F l 615130 -295.62 82.86 -295.67 high F l 615131 -295.62 82.86 -295.67 high F l 615132 -295.59 81.87 -295.71 medium F l 615133 -188.94 76.45 -296.31 low F 2 615134 -189.14 76.58 -296.37 high F2 615135 -188.79 76.49 -296.27 medium F 2 615136 -189.17 76.31 -296.27 low F 3 615137 28.32 67.01 -296.96 high F 3 615138 28.32 67.01 -296.96 medium F 3 615139 28.32 67.01 -296.96 low F4 615140 28.21 66.46 -296.73 high F4 615141 28.33 66.48 -296.50 medium F4 615142 28.31 66.31 -296.76 low F 5 615143 122.87 63.48 -294.68 high F 5 615144 122.44 62.43 -294.95 medium F 5 615145 122.65 62.48 -295.13 low G l 615146 129.21 62.79 -297.51 high Appendix B. Manipulator Data 105 Table B.5: Manipulator runs table 5 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy G l 615147 129.15 63.95 -297.76 medium G l 615148 56.44 226.41 -297.99 low G 2 615149 -277.64 80.01 -298.58 high G 2 615150 -277.63 81.29 -298.55 medium G 2 615152 -277.37 81.15 -298.67 low G 3 615153 -278.71 81.22 -196.80 high G 3 615154 -278.71 81.70 -196.84 medium G 3 615155 -278.46 81.68 -196.38 low G 4 615156 130.01 62.24 -195.55 high G 4 615157 129.51 62.20 -195.72 medium G 4 615158 122.35 63.10 -88.87 low G 5 615159 121.95 62.95 -88.86 high G 5 615160 122.37 62.55 -89.11 medium G 5 615161 121.99 63.29 -88.74 low G6 615165 -271.51 81.30 -90.22 high G6 615166 -271.33 81.37 -90.17 medium G6 615167 -271.60 80.43 -90.22 low G 7 615168 -279.79 79.88 0.34 high G 7 615169 -280.11 81.42 0.33 medium G 7 615170 -279.87 80.71 0.14 low G8 615171 129.70 62.54 1.37 high G 8 615172 129.98 61.77 1.68 medium G 8 615173 129.85 61.90 1.44 low G 9 615174 129.33 61.69 102.57 high G9 615175 129.26 62.15 102.06 medium G 9 615176 129.16 62.27 102.18 low G10 615177 -279.69 81.53 101.16 high G10 615178 -279.74 81.62 101.11 medium G10 615179 -279.47 81.17 100.79 low G i l 615180 -275.84 81.32 206.95 high Appendix B. Manipulator Data 106 Table B.6: Manipulator runs table 6 R u n P l a n R u n Number X (cm) Y (cm) Z (cm) Occupancy G i l 615181 -275.55 81.39 206.82 medium G i l 615182 -276.03 81.55 206.54 low G12 615184 124.73 62.39 208.06 high G12 615185 124.75 60.58 208.27 medium G12 615186 124.53 61.78 208.19 low G13 615187 115.78 62.11 310.88 high G13 615188 115.61 62.44 311.11 medium G13 615189 115.60 62.71 311.05 low G14 615190 -267.10 80.53 310.06 high G14 615191 -267.09 80.20 309.94 medium G14 615192 -267.01 81.25 310.06 low H I 615193 -13.08 4.16 312.22 high H I 615194 -13.85 3.65 312.59 medium H I 615195 -12.96 4.50 312.76 low H2 615196 -7.76 -2.75 211.29 high H2 615197 -7.66 -2.61 211.13 medium H2 615198 -7.07 -2.29 211.25 low H3 615199 -5.25 -5.23 105.33 high H3 615200 -5.43 -5.54 105.61 medium H3 615201 -5.50 -5.46 105.38 low H4 615202 -6.95 -2.90 4.31 high H4 615203 -6.95 -2.90 4.31 medium H4 615204 -7.25 -3.31 4.24 low H5 615205 -0.82 -9.23 -96.53 high H5 615206 -0.11 -8.44 -96.53 medium H5 615207 -0.65 -9.67 -96.83 low H6 615208 2.03 -12.86 -197.24 high H6 615209 1.97 -12.77 -196.94 medium H6 615210 1.89 -12.70 -196.95 low H7 615211 1.73 -12.53 -295.82 high Appendix B. Manipulator Data 107 Table B.7: Manipulator runs table 7 R u n P lan R u n Number X (cm) Y (cm) Z (cm) Occupancy H7 615212 1.48 -12.53 -295.83 medium H 7 615213 1.83 -12.35 -295.84 low L I 615214 3.77 268.28 -191.21 high L I 615215 4.26 268.09 -191.06 medium L I 615216 3.18 268.67 -191.33 low L 2 615217 1.71 199.09 -192.75 high L2 615218 1.62 199.10 -192.85 medium L2 615219 1.66 198.68 -192.73 low L 3 615220 -1.05 98.38 -196.34 high L 3 615221 -0.87 98.62 -196.00 medium L 3 615222 -0.56 98.81 -193.71 low L4 615223 -6.91 -3.19 -189.01 high L4 615224 -7.09 -3.23 -188.98 medium L4 615225 -6.81 -3.29 -188.78 low L5 615226 -13.50 -98.19 -183.57 high L5 615227 -13.52 -98.04 -184.89 medium L5 615228 -13.45 -98.32 -184.97 low L6 615229 -19.92 -195.88 -187.14 high L6 615230 -16.38 -195.04 -187.67 medium L6 615231 -16.27 -195.31 -187.86 low L 7 615232 -16.57 -272.90 -190.01 high L 7 615233 -21.24 -273.60 -189.96 medium L 7 615234 -20.06 -273.50 -189.66 low K l 615235 260.15 -13.49 -191.75 low K l 615236 260.74 -11.74 -191.51 medium K l 615237 260.39 -12.95 -191.44 high K 2 615238 189.56 -9.27 -187.05 high K 2 615239 190.04 -8.96 -186.68 medium K 2 615240 116.49 -18.15 -200.45 low K 3 615241 90.68 -6.93 -186.66 high Appendix B. Manipulator Data 108 Table B.8: Manipulator runs table 8 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy K 3 615242 91.13 -6.42 -187.44 medium K 3 615243 90.88 -6.30 -187.14 low K 4 615244 -7.63 -2.39 -185.20 high K 4 615245 -7.76 -2.50 -186.33 low K 4 615246 -7.91 -2.34 -186.24 medium K 5 615247 -108.56 2.16 -190.26 high K 5 615248 -107.78 1.81 -190.34 medium K 5 615249 -108.02 1.49 -190.49 low K 6 615250 -204.67 7.79 -189.12 high K 6 615251 -205.43 9.86 -189.52 medium K 6 615252 -204.51 8.22 -190.35 low K 7 615253 -270.36 12.05 -186.25 high K 7 615254 -269.80 12.11 -185.79 medium K 7 615255 -269.99 11.20 -185.85 low M l 615256 268.49 -13.81 6.02 high M l 615257 268.61 -13.84 6.10 medium M l 615258 268.72 -13.78 6.13 low M 2 615259 195.82 -10.20 5.95 high M 2 615260 195.45 -10.15 5.77 medium M 2 615261 195.86 -10.57 5.91 low M 3 615262 96.02 -7.85 2.41 high M 3 615263 95.66 -7.77 2.25 medium M 3 615264 96.27 -7.89 2.37 low M 4 615265 -3.88 -5.99 2.24 high M 4 615266 -4.31 -6.78 2.18 medium M 4 615267 -4.02 -6.56 2.19 low M 5 615268 -110.75 -4.22 2.22 high M 5 615269 -110.88 -3.51 2.26 medium M 5 615270 -111.03 -4.14 2.18 low M 6 615271 -210.95 3.61 2.33 low Appendix B. Manipulator Data 109 Table B.9 : Manipulator runs table 9 R u n P lan R u n Number X (cm) Y (cm) Z (cm) Occupancy M 6 615272 -211.34 4.37 2.40 medium M 6 615273 -211.38 4.06 2.46 high M 7 615274 -279.02 6.82 5.44 high M 7 615275 -279.36 7.85 5.17 medium M 7 615276 -279.13 6.78 5.49 low N l 615277 3.61 269.05 5.75 high N l 615278 2.00 269.71 6.02 medium N l 615279 3.51 268.81 5.73 low N2 615280 3.87 203.40 2.82 high N2 615281 3.44 203.69 2.88 medium N2 615282 4.04 203.33 2.74 low N3 615283 4.02 100.63 1.63 high N3 615284 3.60 100.44 1.74 medium N3 615285 3.56 100.58 1.61 low N4 615286 -3.79 -7.06 1.95 high N4 615287 -3.63 -7.00 1.83 medium N4 615288 -4.65 -5.66 1.55 low N5 615289 -11.21 -103.64 3.77 high N5 615290 -12.45 -103.81 3.72 medium N5 615291 -11.83 -103.60 3.97 low N6 615292 -13.99 -203.19 7.23 low N6 615293 -16.70 -203.89 7.30 medium N6 615294 -15.92 -203.49 7.27 high N7 615295 -18.24 -274.53 9.48 high N7 615296 -18.67 -274.68 9.78 medium N7 615297 -17.60 -274.38 9.95 low 0 1 615298 99.29 -9.51 -201.04 high 0 1 615299 99.53 -9.23 -200.97 medium 0 1 615300 99.39 -9.60 -201.48 low 0 2 615301 -10.59 -109.89 -201.72 high Appendix B. Manipulator Data 110 Table B.10: Manipulator runs table 10 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy 0 2 615302 -8.56 -109.33 -201.58 medium 0 2 615303 -10.93 -109.89 -201.67 low 0 3 615304 -112.54 -8.50 -208.69 high 0 3 615305 -112.63 -8.34 -208.56 medium 0 3 615306 -112.90 -8.30 -208.64 low 0 4 615307 6.86 102.00 -208.96 high 0 4 615308 7.07 101.87 -209.09 medium 0 4 615309 7.00 102.09 -208.89 low 0 5 615310 1.09 100.02 -109.47 high 0 5 615311 1.16 100.21 -109.65 medium 0 5 615312 1.16 100.21 -109.65 medium 0 5 615313 1.16 100.21 -109.65 low 0 6 615314 1.16 100.21 -109.65 high 0 6 615316 1.16 100.21 -109.65 low 0 7 615317 1.16 100.21 -109.65 high 0 7 615318 1.16 100.21 -109.65 medium 0 7 615319 1.16 100.21 -109.65 low 0 8 615320 94.17 -6.82 -100.76 high 0 8 615321 94.46 -7.10 -100.89 medium 0 8 615322 94.63 -6.30 -100.86 low 0 9 615323 93.52 -6.41 1.32 high 0 9 615324 93.16 -6.36 1.27 medium 0 9 615325 93.20 -6.34 1.33 low 010 615326 -13.11 -103.83 0.95 high 0 1 0 615327 -13.08 -103.84 1.11 medium 0 1 0 615328 -13.77 -103.84 1.02 low O i l 615329 -109.25 -3.17 -1.74 high O i l 615330 -109.82 -3.17 -1.57 medium O i l 615331 -109.24 -3.28 -1.59 low 0 1 2 615332 0.92 99.86 -1.24 high Appendix B. Manipulator Data 111 Table B . l l : Manipulator runs table 11 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy 0 1 2 615333 0.88 99.70 -1.30 medium 0 1 2 615334 0.66 99.53 -1.48 low 0 1 3 615335 -3.84 97.95 106.34 high 0 1 3 615336 -3.87 98.18 106.14 medium 013 615337 -3.89 98.27 106.32 low 014 615338 -108.53 1.65 106.00 high 014 615339 -109.01 1.83 106.35 medium 014 615340 -108.73 1.69 106.23 low 015 615341 -15.37 -99.20 101.02 high 015 615342 -14.84 -98.88 100.85 medium 0 1 5 615343 -14.29 -98.77 100.86 low 016 615344 88.82 -3.33 100.86 high 016 615345 88.83 -4.27 t 101.32 medium 016 615347 88.61 -3.90 100.68 low P I 615348 197.04 -17.13 -196.81 high P I 615349 197.89 -14.42 -196.99 medium P I 615350 58.80 243.34 -211.00 low P 2 615351 -17.35 -206.21 -198.29 high P 2 615352 -16.91 -206.23 -197.98 medium P2 615353 -16.98 -205.66 -198.19 low P3 615354 -214.06 0.88 -202.20 high P3 615355 -214.63 1.51 -201.98 medium P3 615356 -214.64 1.68 -202.16 low P4 615357 4.05 205.24 -201.87 high P4 615358 4.41 204.82 -202.00 medium P4 615359 4.00 205.16 -202.28 low P5 615360 1.72 202.26 -102.73 high P5 615361 1.97 201.54 -102.36 medium P 5 615362 2.18 201.89 -102.68 low P6 615363 -212.86 6.20 -103.31 low Appendix B. Manipulator Data 112 Table B.12: Manipulator runs table 12 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy P6 615364 -213.09 6.47 -103.33 medium P6 615365 -213.02 6.61 -103.30 high P 7 615366 -18.96 -202.58 -99.01 high P 7 615367 -19.42 -202.67 -98.85 medium P 7 615368 -18.52 -202.64 -99.01 low P8 615369 191.94 -10.45 -99.13 high P8 615370 191.74 -10.46 -98.79 medium P8 615371 191.83 -10.49 -98.76 low P9 615372 187.00 -8.96 1.52 high P9 615373 186.65 -9.46 1.40 medium P 9 615374 186.15 -9.25 1.17 low P10 615375 -12.26 -198.50 2.46 high P10 615376 -10.70 -198.56 2.45 medium P10 615377 -13.15 -198.84 2.42 low P l l 615378 -208.27 4.74 -1.75 high P l l 615379 -208.16 4.32 -1.93 medium P l l 615380 -207.98 5.07 -1.88 low P12 615381 1.24 197.97 -1.43 high P12 615382 0.73 198.43 -1.47 medium P12 615383 1.35 197.99 -1.44 low P13 615384 1.34 198.96 100.77 low P13 615385 1.27 199.00 100.60 low P13 615386 1.21 198.91 100.82 medium P13 615387 1.26 199.00 100.69 high P14 615388 -208.91 3.37 100.14 high P14 615389 -208.72 3.27 100.08 medium P14 615390 -209.15 3.45 100.42 low P15 615391 -20.80 -198.25 103.95 high P15 615392 -19.94 -198.10 103.84 medium P15 615393 -19.45 -198.13 103.82 low Appendix B. Manipulator Data 113 Table B.13: Manipulator runs table 13 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy P16 615394 188.09 -5.41 105.03 high P16 615395 188.48 -5.10 105.07 medium P16 615396 188.44 -5.16 104.80 low Q l 615397 172.77 -200.39 -121.59 high Q l 615398 171.97 -201.29 -121.21 medium Q l 615399 173.27 -199.98 -121.52 low Q2 615400 -76.37 72.01 -132.64 low Q2 615401 -76.40 72.03 -132.53 medium Q2 615402 -76.36 72.00 -132.45 high Q3 615403 46.22 -60.66 -311.68 high Q3 615404 46.36 -60.81 -311.26 medium Q3 615405 46.37 -60.81 -311.72 low Q4 615406 174.29 -199.22 -128.73 high Q4 615407 173.83 -199.64 -128.57 medium Q4 615408 174.80 -198.88 -128.41 low Q5 615409 50.92 -63.51 110.42 low Q5 615410 50.53 -63.96 110.41 medium Q5 615411 50.30 -64.17 110.35 high Q6 615412 49.57 -62.94 -311.90 high Q6 615413 49.40 -64.09 -310.56 medium Q6 615414 49.07 -63.29 -311.80 low Q7 615416 -0.79 -7.47 -298.56 high Q7 615417 -1.13 -8.10 -298.63 medium Q7 615418 -1.30 -8.19 -298.33 low Q8 615419 -54.00 48.01 -248.10 high Q8 615420 -53.91 48.07 -247.49 medium Q8 615421 -54.12 47.98 -247.98 low Q9 615422 -86.81 83.27 -170.06 low Q9 615423 -86.78 83.33 -170.13 medium Q9 615424 -86.99 83.34 -170.08 high Appendix B. Manipulator Data 114 Table B.14: Manipulator runs table 14 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy QIO 615425 -94.87 91.85 -97.76 high QIO 615427 -94.81 91.94 -97.75 medium QIO 615428 -94.90 91.74 -97.33 low Q l l 615429 192.45 -217.88 -99.14 low Q l l 615430 191.92 -218.32 -99.32 medium Q l l 615431 199.04 -211.62 -99.11 high Q12 615432 182.70 -209.22 -28.72 high Q12 615433 184.16 -207.99 -28.12 medium Q12 615434 184.09 -208.03 -28.52 low Q13 615435 149.97 -173.73 47.88 low Q13 615436 153.24 -170.72 47.76 medium Q13 615437 154.40 -169.63 48.22 high Q14 615438 99.07 -116.57 97.43 low Q14 615439 99.70 -115.99 97.25 medium Q14 615440 99.44 -116.34 97.33 high Q 3 R 615441 45.44 -60.69 -312.24 low Q 3 R 615442 47.15 -59.48 -312.02 medium Q 3 R 615443 46.66 -59.35 -312.01 high Q15 615444 64.69 -78.60 -201.83 high Q15 615445 64.78 -78.74 -202.00 medium Q15 615446 65.41 -77.90 -201.88 low Q16 615447 40.17 -54.96 -92.25 high Q16 615448 40.53 -54.92 -92.28 medium Q16 615449 42.48 -52.85 -92.08 low Q17 615450 -9.11 -1.03 -79.09 high Q17 615451 -7.68 -0.20 -79.28 medium Q17 615452 -8.03 -0.54 -79.29 low Q18 615453 -52.50 46.23 -41.18 low Q18 615454 -52.52 46.10 -41.23 medium Q18 615455 -52.24 46.04 -41.54 high Appendix B. Manipulator Data 115 Table B.15: Manipulator runs table 15 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy Q19 615456 188.49 -205.34 120.31 low Q19 615457 184.98 -208.88 119.98 medium Q19 615458 186.30 -207.54 120.01 high Q20 615459 177.31 -200.67 182.17 high Q20 615460 178.97 -198.89 182.44 medium Q20 615461 176.44 -201.54 182.15 low Q21 615462 136.64 -151.77 280.18 low Q21 615463 135.45 -152.65 280.34 medium Q21 615464 134.29 -153.67 280.40 high Q22 615465 91.83 -108.19 316.69 high Q22 615466 91.34 -108.24 316.96 medium Q22 615467 89.64 -110.06 316.69 low Q23 615468 42.23 -55.50 330.21 high Q23 615469 42.12 -55.79 330.06 medium Q23 615470 41.53 -56.08 330.18 low W l 615471 -13.60 -205.17 -266.51 high W l 615472 -11.48 -203.75 -267.14 high W l 615473 -11.35 -204.04 -266.91 medium W l 615474 -10.87 -204.02 -266.85 low W 2 615475 192.48 -8.28 -268.34 high W 2 615476 192.66 -8.33 -268.08 medium W 2 615477 192.67 -7.85 -268.19 low W 3 615478 192.09 -8.10 -215.51 low W 3 615479 191.96 -6.95 -215.85 medium W 3 615480 191.88 -7.97 -215.70 high W 4 615481 -13.16 -200.41 -216.11 high W 4 615482 -14.95 -201.02 -216.15 medium W 4 615483 -12.72 -200.23 -216.28 low W 5 615484 -14.64 -196.02 -111.81 high W 5 615485 -13.00 -195.78 -112.01 medium Appendix B. Manipulator Data 116 Table B.16: Manipulator runs table 16 R u n P l an R u n Number X (cm) Y (cm) Z (cm) Occupancy W 5 615486 -13.65 -196.17 -111.81 low W 6 615487 184.63 -6.38 -112.36 high W 6 615488 184.94 -6.54 -112.41 medium W 6 615489 184.56 -5.69 -112.31 low W 7 615490 193.02 -11.41 -17.37 high W 7 615491 192.99 -11.27 -17.51 medium W 7 615492 192.83 -11.35 -17.50 low W 8 615493 -14.17 -200.71 -16.46 high W 8 615494 -16.85 -201.18 -16.39 medium W 8 615495 -14.54 -200.71 -16.52 low W 9 615496 -13.49 -199.20 81.80 high W 9 615497 -14.73 -199.86 82.19 medium W 9 615498 -13.93 -199.38 81.79 low W 1 0 615499 191.32 -5.92 82.13 low W 1 0 615500 190.73 -8.19 82.32 medium W 1 0 615501 190.76 -6.53 82.28 high W I O 615503 190.72 -7.70 82.33 high W l l 615504 187.24 -6.74 189.07 low W l l 615505 187.45 -6.34 188.79 medium W l l 615506 186.58 -7.93 189.14 high W12 615507 -14.86 -195.50 188.42 low W12 615508 -15.10 -196.07 188.14 low W12 615509 -14.88 -195.42 188.41 medium W12 615510 -13.24 -195.21 187.96 high W 1 3 615511 -16.44 -186.70 292.58 high W 1 3 615512 -17.16 -186.92 292.52 medium W 1 3 615513 -16.77 -186.59 292.70 low W14 615514 176.02 -6.68 293.20 high W14 615515 176.26 -5.51 293.46 medium W14 615516 176.27 -5.76 293.23 low Appendix B. Manipulator Data 117 Table B.17: Manipulator runs table 17 R u n P lan R u n Number X (cm) Y (cm) Z (cm) Occupancy X I 615517 240.65 -12.10 5.98 high X I 615518 240.92 -11.03 6.10 medium X I 615519 240.46 -13.61 6.09 low X 2 615520 124.74 207.87 1.22 high X 2 615521 125.08 207.59 1.28 medium X 2 615522 125.72 207.63 1.66 low X 3 615523 -126.91 218.47 -1.14 high X 3 615524 -125.15 218.89 -1.26 medium X 3 615525 -125.41 218.93 -1.19 low X 4 615526 -255.29 6.42 1.48 high X 4 615527 -255.23 6.67 1.30 medium X 4 615528 -255.16 6.46 1.37 low X 5 615536 -145.51 -209.81 3.09 low X 5 615537 -145.08 -209.75 3.18 medium X 5 615538 -146.12 -209.53 2.73 high X 6 615539 105.50 -222.01 4.80 low X 6 615540 105.60 -222.17 5.08 medium X 6 615541 106.02 -221.75 4.90 high W l ' 615545 -16.92 -196.61 -283.38 high W l ' 615546 -15.90 -196.27 -283.50 medium W l ' 615547 187.22 -7.86 -283.19 low W 2 ' 615548 187.86 -6.71 -283.03 high W 2 ' 615601 186.62 -3.12 -285.56 high W 2 ' 615602 185.92 -6.03 -285.45 medium W 2 ' 615603 185.98 -5.28 -285.61 low Appendix B. Manipulator Data 118 Table B.18: Manipulator runs table 18 R u n P lan R u n Number X (cm) Y (cm) Z (cm) Occupancy W 6 ' 615604 202.13 -10.27 -141.71 high W 6 ' 615605 201.51 -11.62 -141.76 medium W 6 ' 615606 202.47 -8.18 -141.79 low W 5 ' 615607 -11.38 -210.58 -142.18 high W 5 ' 615608 -12.13 -210.75 -142.20 medium W 5 ' 615609 -11.79 -210.60 -141.93 low W 9 ' 615610 -13.08 -198.11 101.39 high W 9 ' 615611 -14.49 -198.32 101.37 medium W 9 ' 615612 -15.51 -198.71 101.15 low W 1 0 ' 615613 189.46 -7.07 101.67 low W 1 0 ' 615614 189.40 -6.50 101.57 medium W 1 0 ' 615615 189.26 -7.29 101.56 high W 1 4 ' 615616 208.18 -11.73 254.80 high W 1 4 ' 615617 208.17 -10.71 255.13 medium W 1 4 ' 615618 207.87 -12.25 255.07 low W 1 3 ' 615619 -10.74 -217.24 254.58 high W 1 3 ' 615620 -10.08 -217.22 254.68 high W 1 3 ' 615621 -9.67 -217.16 254.68 low W 9 " 615622 -14.10 -193.78 100.59 low W I O " 615623 185.20 -4.69 101.10 low W 6 " 615624 201.58 -10.62 -144.52 low W 5 " 615625 -12.38 -210.57 -144.76 low 119 Appendix C Analysis Code Figure C displays the basic data flow for the position reconstruction analysis. We have two sources of data: • Manipulator Systems, and • 1 K T Detector. The data from the manipulator positioning systems is held in the M I D A S O D B . W i t h each run we dump the O D B contents to a file. This file is scanned for the arm lengths and angles by read_odb, which also performs the con- struction of the nominal position described in Section 3.3.3. In addition the location and number of the odb files and run occupancy is fed to read.odb. read_odb.py generates four text files containing the location, number, and names of ofl files, run occupancy, as well as ball positions according to one of the four positioning systems (manJimits. txt , man_safety.txt, man_prima.txt and man_secon.txt for l imit and safety inclinometer and primary and sec- ondary encoder systems respectively). One of the four text files (usually the l imit positions) is read in by a Per l script called writeJb_script.pl. W i t h the data file to be read in the Per l script also takes a binary argument (0 or 1): • 0 means the scripts it generates are for scott_occ, and • 1 means the scripts are for the ofl to ntuple converter. Each script sets the necessary environmental variables for the K 2 K analysis and feeds the code the data it needs. C . l Ntuple Generator The ntuples generated from the laserball data contain only one event per spil l due to size limitations of the ntuple file format. These ntuples are used in the position reconstruction analysis performed by Shaomin Chen. Oq C a o -t S CO o O D_ C O l-i CO •5' K o 1-1 KT Sun Machine with k2k04a Framework RFM Data offline . p r o c e s s i n g ntuples uses scott occ creates [ | b 2 n t u p | e 1 executes lb######.sh run######.sh used for Shaomin's Analysis MIDAS ODB 4 read_odb.p^*- computes run######.txt I Manipulator man_limit man_safety man_prima man scon write_lb_script shdowflags Calculates shadow by ray tracing run######.dat fit_pos Fits Position Cut Outliers shex.res PAW offset bias plots Appendix C. Analysis Code 121 C.2 Position Reconstruction If the binary argument to writeJb_script.pl was 0 the scripts writeJb_script.pl generates run scott_occ. This wi l l perform the peak finder and saturation cuts explained in sections 2.2 and 4.2.1 respectively. scott_occ generates a file for each run containing the t iming peaks for each P M T , standard deviation of those peaks, time of flight to the P M T , P M T position and normals. This data is read in by the shadowflags code, which tags P M T s which are shaded according to the ray tracing algorithm. The files returned by shadowflags have the information from scott.occ, plus a flag of 0 for non-shaded and 1 for P M T s whose border is shaded and 2 for P M T s whose center is in the manipulator shadow. These files are read in by fit_pos, which scans for outlier P M T s in the time histogram and tags those wi th outliers by adding 4 to their shadow flag. Then the fit is run once, P M T s wi th large residuals are tagged by incrementing their flag by 8. The fit is run a final time ignoring al l P M T s wi th flags greater then zero. The result positions for all runs are put into a text file, together wi th run numbers, position uncertainties (algorithm described in Section 2.2), and the fits x2-

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