Simulation of the Sudbury Neutrino Observatory Neutral Current Detectors Hok Seum Wan Chan Tseung Wadham College, Oxford Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at the University of Oxford Trinity Term 2008 Simulation of the Sudbury Neutrino Observatory Neutral Current Detectors Hok Seum Wan Chan Tseung Wadham College, Oxford Thesis submitted in partial fulfilment of the requirements for the degree of Doctor of Philosophy at the University of Oxford Trinity Term 2008 Abstract The Sudbury Neutrino Observatory (SNO), a heavy water Cherenkov experiment, was designed to detect solar 8B neutrinos via their elastic scattering interactions on elec- trons, or charge current and neutral current (NC) interactions on deuterium. In the third phase of SNO, an array of 3He proportional counters was deployed to detect neutrons produced in NC interactions. A simulation of the current pulses and energy spectra of the main kinds of ionization events inside these Neutral Current Detectors (NCDs) was developed. To achieve this, electron drift times in NCDs were evaluated with a Monte Carlo method, and constrained by using wire alpha activity inside the counters. The pulse calculation algorithm applies to any ionization event, and takes into account processes such as straggling, electron diffu- sion, and propagation through the NCD hardware. A space charge model was developed to fully explain the energy spectra of neutron and alpha events. Comparisons with data allowed the various classes of alpha backgrounds to be identified, and gave evidence for the spatial non–uniformity of 238U and 232Th chain nuclei in the counter walls. The simulation was applied to determine the fractional contents of the main types of alpha backgrounds in each NCD string. The number of neutron capture events in the array was extracted via a statistical separation, using Monte Carlo generated alpha background pulse shape parameter distributions and minimal energy information. The inferred total 8B solar neutrino flux is: Φ =5.74 0.77 (stat.) 0.39 (sys.) 106 cm−2s−1 NC ± ± × in agreement with Standard Solar Model predictions and previous SNO results. To my parents Acknowledgements I am greatly indebted to the Oxford SNO group: Profs. Nick Jelley and Steve Biller, Dr. Simon Peeters, Dr. Nick West, and my office-mates over the years: Drs. Jeanne Wilson, Jessica Dunmore, Charlotte Sims, James Loach, Helen O’Keeffe and Gabriel Orebi-Gann. It has been an immense pleasure to be part of the SNO collaboration and the NCD group, and to work with Noah Oblath, Prof. Hamish Robertson, Prof. Hans Bichsel, Drs. Sean McGee, Keith Rielage, Jocelyn Monroe, Gersende Prior and Berta Beltran on NCD simulation. I am grateful to the many friends who helped me during my time as a graduate student, in particular: Chen-Chi Lin, Ryan Wei, Matthew Bladen, Merim Bilalic, Mrs. Gilbert, Melin Huang, Adam Cox and Charles Duba. Most of all, I thank my family for their unwavering support. This work was sponsored by the Oxford University Press and Wadham College through a Clarendon Fund Scholarship, an ORS award, and the University of Washington through a visiting studentship. Contents 1 Introduction 1 1.1 Summaryofneutrinoproperties . 1 1.2 Neutrinooscillations . 1 1.3 Solarneutrinos ................................. 3 1.4 TheSNOexperiment .............................. 4 2 Neutral Current Detectors 8 2.1 Counterproperties ............................... 8 2.2 Electronics.................................... 12 2.3 Calibration ................................... 13 2.4 Signals...................................... 13 2.5 Aimsandoutlineofthisthesis. 16 3 Electron Transport in NCDs 19 3.1 Simulationmethod ............................... 21 3.1.1 Differenceequations . 21 3.1.2 Null collision technique . 22 3.1.3 Kinematics of isotropic collisions . .... 24 3.1.4 Anisotropiccollisions . 25 3.2 Implementation and benchmarking . 25 3.2.1 Driftspeedsatconstantfields . 27 4 3.2.2 Diffusion coefficients in He and CF4 at constant fields . 30 3.3 Results...................................... 32 3.3.1 Drift and time resolution in NCD counters . 32 3.3.2 Correcteddriftcurve . 36 3.3.3 z resolution ............................... 37 3.3.4 Chargedistributions . 37 3.4 Summary .................................... 41 4 Simulation of NCD Pulses 43 4.1 Method ..................................... 43 4.2 Currentfrompointcharges. 46 4.3 Protons,tritonsandalphasinNCDs . 48 4.3.1 StoppingandrangeofionsinNCDgas . 48 iv CONTENTS v 4.3.2 Proton, triton and α particletracks . 50 4.3.3 Straighttrackapproximation . 53 4.3.4 EnergystragglingofionsinNCDgas . 54 4.4 β particles.................................... 55 4.5 Hardwaremodel................................. 56 4.5.1 Pulsereflections............................. 56 4.5.2 PropagationalongNCDwires . 59 4.5.3 ElectronicsandDAQ . 59 4.5.4 Simulation of NCD baseline noise . 61 4.6 Data-MonteCarlocomparisons . 67 4.6.1 Neutron pulse shape parameter distributions . ...... 68 4.6.2 Low energy α pulse shape parameter distributions . 70 4.7 Non-standard α pulses ............................. 73 4.7.1 Wire α events.............................. 73 4.7.2 End-effect α events........................... 74 4.8 Summary .................................... 77 5 Simulation of NCD Energy Spectra 79 5.1 Gasgain..................................... 80 5.2 Simulationofspacechargeeffects . .... 80 5.2.1 Motivation................................ 80 5.2.2 Simulationmethod . .. .. 83 5.2.3 Modeloptimization. 85 5.2.4 Modelpredictions. 87 5.3 Energyresolution ................................ 90 5.4 Straggling of α particlesinnickel . 90 5.5 Alphaenergyspectra .............................. 92 5.5.1 210Pospectrum ............................. 92 5.5.2 Bulkspectra............................... 93 5.6 BackgroundcontentofNCDstrings . 98 5.7 β energyspectrum ............................... 102 5.7.1 Estimation of the β eventrate..................... 102 5.7.2 Simulationmethod . .. .. 103 5.8 Summary .................................... 106 6 Separation of Neutrons and Alphas 108 6.1 Representationofalphasbelow1MeV . 109 6.2 Alpha R10,40 parameterdistributions . 112 6.2.1 Instrumentalsystematics . 113 6.2.2 Physics model uncertainties . 116 6.2.3 Wire, end-cap and other neutron-like alphas . ..... 116 6.2.4 Comparisons with α data ....................... 117 6.3 Extractionofneutrons . .. .. 117 6.3.1 Fitprocedure .............................. 117 CONTENTS vi 6.3.2 Results.................................. 119 6.4 Theneutralcurrentflux ............................ 120 6.4.1 Discussion................................ 122 7 Summary and Conclusions 124 A String-by-string differences 126 B 238U and 232Th chains 128 C Semi-analytic pulse calculation 129 D Pulse shape parameters 131 E Software implementation 133 F Low energy bulk α spectra 134 G Coincidence events 135 H List of neutron-like alpha pulses 136 Bibliography 138 List of Figures 1.1 Solar neutrino energy spectra, and MSW electron neutrino survival proba- bility as a function of energy for 8Bneutrinos ................ 3 1.2 Neutrino fluxes from the SNO salt phase . 5 1.3 SchematicoftheSNOdetector . 7 2.1 SchematicofanNCDstring . 10 2.2 TheNCDarrayconfiguration . 11 2.3 The NCD Electronics and DAQ system . 14 2.4 Example NCD shaper ADC spectra and pulses . 17 3.1 Describing the path of an electron in NCD gas . ..... 22 3.2 Flow diagram for e− transportMC ...................... 26 3.3 Calculation of e− driftspeedsinAr ...................... 28 − 3.4 Calculation of e drift speeds in CH4 ..................... 29 3.5 Calculation of e− driftspeedsinHe ...................... 29 − 3.6 Calculation of e drift speeds in CF4 ..................... 30 − 3 3.7 Calculations of e drift speeds in 80:20 and 90:10 He and CF4 mixtures . 31 3.8 Calculations of DT /µe, the transverse diffusion coefficient to mobility ratio in CF4 andHeforelectrons .......................... 31 3.9 Calculated e− drift times in NCD gas, with experimental constraints . 34 3.10 pw30vsEnergyscatterplotsforalphas . 35 3.11 Predicted time resolution due to e− diffusion, and calculated z distributions ofavalancheelectronsattheNCDanode . 35 3.12 Scaling of e− drift times using wire α events ................. 37 3.13 An example simulated e− avalancheattheanode . 39 3.14 Simulated z-profile of electrons at the anode in multiple avalanches . 40 4.1 Steps in the calculation of Itrack for a p-t event................ 45 4.2 Example simulated NCD events: p-t, α and β ................ 47 4.3 Stopping powers and ranges of protons, tritons and alphas in NCD gas . 51 4.4 Simulated proton and α particletracksinNCDgas . 53 4.5 LateralstragglingofalphasinNCDgas. ..... 54 4.6 Definition of track parameters for straight line travel . ........... 55 4.7 Simplified electronics model . 57 4.8 Average micro-discharge pulse from string 27, compared with simulation . 59 vii LIST OF FIGURES viii 4.9 EffectsofNCDhardwareonpulseshape . 60 4.10 Validation of noise simulation technique . ........ 64 4.11 Plot of µe vs σg forNCDnoise......................... 65 4.12 Baseline NCD noise spectra from electronic calibrationruns ........ 66 4.13 Variation of baseline noise RMS with time, and stability of noise power spectra...................................... 66 4.14 An example simulated baseline noise train . ....... 67 4.15 Comparisons of simulated neutron pulse width distributions with data . 69 4.16 Comparisons of simulated neutron pulse shape moment distributions with data ......................................