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Neutron Multiplicity Counter Design Without Helium-3

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Title:
Neutron Multiplicity Counter Design Without Helium-3
Physical Description:
1 online resource (172 p.)
Language:
english
Creator:
Lintereur, Azaree T
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Biomedical Engineering
Committee Chair:
Gilland, David R
Committee Members:
Bolch, Wesley Emmett
Hintenlang, David Eric
Mair, Bernard A

Subjects

Subjects / Keywords:
detector -- mcnpx -- multiplicity -- neutron -- radiation
Biomedical Engineering -- Dissertations, Academic -- UF
Genre:
Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Neutron multiplicity counters are used to quantify the mass of a fissile isotope in a sample with undefined parameters.  Isotopes that decay through fission emit unique neutron multiplicity distributions. The first three factorial moments of the detected distribution can be used to identify one, two or three unknown assay variables.  Neutron multiplicity counters are complex systems that require a high neutron detection efficiency, a short neutron life-time in the counter (die-away time), and minimal gamma ray sensitivity.  Traditional multiplicity counter designs have relied upon the use of 3He filled proportional counters for neutron detection.  The availability of 3Hehas decreased, which has produced a need to develop a multiplicity counter configuration without 3He.  The complexity of multiplicity counter systems requires that several performance parameters be optimized simultaneously.  In this work, the best performing configurations,within specified physical dimensions, were identified for three currently commercially available thermal neutron detectors with the use of the Monte Carlo transport code, MCNPX.  The designs for the maximum efficiency and minimum die-away time were determined.  The simulated system with the highest performance capability was identified as the one designed with 6LiF/ZnS scintillating sheets inter-layered with plastic light guides.  A bench-top test unit based on the simulated 6LiF/ZnS sheet design was constructed. Measurements were performed with the bench-top test unit to establish the appropriate configuration for a small-scale system assembly, and to validate the simulation predictions.  Two different types of plastic light guides were measured: a wavelength shifting plastic, and non-scintillating polymethyl methacrylate. The configuration selected for a future complete bench-top construction consisted of 0.7-cm thick wavelength shifting plastic light guides with a photomultiplier tube coupled to each end with a tapered light guide. The 6LiF/ZnS sheets and plastic light guides have a higher inherent gamma ray sensitivity than 3He filled proportional counters.  Thus, the detected distribution will not be solely dependent upon the neutron multiplicity distribution.  The detected gamma ray signals were separated from the detected neutron signals by applying pulse shape discrimination algorithms.  The effect of gamma ray misidentifications on the measured parameters was considered by including the correlated gamma ray multiplicity distributions associated with a spontaneous fission event in the formulas for the unknown sample parameters.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Azaree T Lintereur.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Gilland, David R.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-08-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045906:00001

MISSING IMAGE

Material Information

Title:
Neutron Multiplicity Counter Design Without Helium-3
Physical Description:
1 online resource (172 p.)
Language:
english
Creator:
Lintereur, Azaree T
Publisher:
University of Florida
Place of Publication:
Gainesville, Fla.
Publication Date:

Thesis/Dissertation Information

Degree:
Doctorate ( Ph.D.)
Degree Grantor:
University of Florida
Degree Disciplines:
Biomedical Engineering
Committee Chair:
Gilland, David R
Committee Members:
Bolch, Wesley Emmett
Hintenlang, David Eric
Mair, Bernard A

Subjects

Subjects / Keywords:
detector -- mcnpx -- multiplicity -- neutron -- radiation
Biomedical Engineering -- Dissertations, Academic -- UF
Genre:
Biomedical Engineering thesis, Ph.D.
bibliography   ( marcgt )
theses   ( marcgt )
government publication (state, provincial, terriorial, dependent)   ( marcgt )
born-digital   ( sobekcm )
Electronic Thesis or Dissertation

Notes

Abstract:
Neutron multiplicity counters are used to quantify the mass of a fissile isotope in a sample with undefined parameters.  Isotopes that decay through fission emit unique neutron multiplicity distributions. The first three factorial moments of the detected distribution can be used to identify one, two or three unknown assay variables.  Neutron multiplicity counters are complex systems that require a high neutron detection efficiency, a short neutron life-time in the counter (die-away time), and minimal gamma ray sensitivity.  Traditional multiplicity counter designs have relied upon the use of 3He filled proportional counters for neutron detection.  The availability of 3Hehas decreased, which has produced a need to develop a multiplicity counter configuration without 3He.  The complexity of multiplicity counter systems requires that several performance parameters be optimized simultaneously.  In this work, the best performing configurations,within specified physical dimensions, were identified for three currently commercially available thermal neutron detectors with the use of the Monte Carlo transport code, MCNPX.  The designs for the maximum efficiency and minimum die-away time were determined.  The simulated system with the highest performance capability was identified as the one designed with 6LiF/ZnS scintillating sheets inter-layered with plastic light guides.  A bench-top test unit based on the simulated 6LiF/ZnS sheet design was constructed. Measurements were performed with the bench-top test unit to establish the appropriate configuration for a small-scale system assembly, and to validate the simulation predictions.  Two different types of plastic light guides were measured: a wavelength shifting plastic, and non-scintillating polymethyl methacrylate. The configuration selected for a future complete bench-top construction consisted of 0.7-cm thick wavelength shifting plastic light guides with a photomultiplier tube coupled to each end with a tapered light guide. The 6LiF/ZnS sheets and plastic light guides have a higher inherent gamma ray sensitivity than 3He filled proportional counters.  Thus, the detected distribution will not be solely dependent upon the neutron multiplicity distribution.  The detected gamma ray signals were separated from the detected neutron signals by applying pulse shape discrimination algorithms.  The effect of gamma ray misidentifications on the measured parameters was considered by including the correlated gamma ray multiplicity distributions associated with a spontaneous fission event in the formulas for the unknown sample parameters.
General Note:
In the series University of Florida Digital Collections.
General Note:
Includes vita.
Bibliography:
Includes bibliographical references.
Source of Description:
Description based on online resource; title from PDF title page.
Source of Description:
This bibliographic record is available under the Creative Commons CC0 public domain dedication. The University of Florida Libraries, as creator of this bibliographic record, has waived all rights to it worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law.
Statement of Responsibility:
by Azaree T Lintereur.
Thesis:
Thesis (Ph.D.)--University of Florida, 2013.
Local:
Adviser: Gilland, David R.
Electronic Access:
RESTRICTED TO UF STUDENTS, STAFF, FACULTY, AND ON-CAMPUS USE UNTIL 2015-08-31

Record Information

Source Institution:
UFRGP
Rights Management:
Applicable rights reserved.
Classification:
lcc - LD1780 2013
System ID:
UFE0045906:00001


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1 NEUTRON MULTIPLICITY COUNTER DESIGN WITHOUT HELIUM 3 By AZAREE T. LINTEREUR A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 2013

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2 2013 A zaree T. L intereur

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3 For Angel, who t aught me the impossible can be achieved

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4 ACKNOWLEDGMENTS I owe an enormous debt of gratitude to Dr. James Ely and Dr. Richard Kouzes for giving me the opportunity to complete this dissertation, and providing guidance along the way. There have been more people than I can list who have supported this project, answ ered questions and suggested ideas, individually I am deeply grateful to all who contributed to this effort. In particular I would like to thank Dr. Mitchell Woodring for his incredible patience in the lab and Dr. Ed ward Siciliano for his guidance with the simulations My entire committee at the University of Florida, Prof. David Gilland, Prof. David Hintenlang, Prof. Wesley Bolch, and Prof. Bernard Mair has been tolerant of the time it took for me to complete this project and supportive of my efforts, and for that I thank them all. I would like to acknowledge all of my friends who have gone through th is process ; t hank you to everyone who has commiserated with me on the frustrations of completing a dissertation. I would particularly like to thank Crystal Thrall for all of her encouragement, especially when it seemed like finishing was impossible I would also like to recognize everybody who reminded me that life is about balance, so thank you to everyone who comp eted horses, ran races, went hiking and just generally helped me enjoy life despite the stress of graduate school. I especially want to thank Dr. Stacie Atria, who time and again has gone above and beyond the requirements of friendship. And she will alw ays be the first veterinarian I call I must also thank my family i n particular my mom, who taught me to always ask why, and my sister, for her unwavering support. Finally, without funding this work would not have been possible, s o I would like to acknowledge that t his project was supported by the United States Department of

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5 Energy NNSA, Office of Nonproliferation and Verification Research and Development (NA 22). I am also grateful to the Next Generation Safeguards Initiative, Of fice of Nuclear Safeguards and Security, National Nuclear Security Administration for partially supporting my time on this project The Pacific Northwest National Laboratory release number for this document is PNNL 22572.

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6 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ .. 4 LIST OF TABLES ................................ ................................ ................................ ............ 8 LIST OF FIGURES ................................ ................................ ................................ .......... 9 LIST OF ABBREVIATIONS ................................ ................................ ........................... 13 ABSTRACT ................................ ................................ ................................ ................... 15 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .... 17 Sample Analysis ................................ ................................ ................................ ..... 18 Neutron Detection Basics ................................ ................................ ....................... 21 Helium 3 Shortage ................................ ................................ ................................ .. 24 Helium 3 A lternatives ................................ ................................ .............................. 26 Objectives of this Work ................................ ................................ ........................... 30 2 MULTIPLICITY COUNTERS ................................ ................................ .................. 31 Principles of Operation ................................ ................................ ............................ 31 Mult iplicity Counter Designs ................................ ................................ .................... 43 3 COUNTER MODEL AND SIMULATIONS ................................ ............................... 51 MCNPX Simulation Methodology ................................ ................................ ............ 52 ENMC Template ................................ ................................ ................................ ..... 55 Boron 10 Based Detector Simulations ................................ ................................ .... 61 10 B Lined Plate Configuration ................................ ................................ ................. 71 6 LiF/ZnS Based Detector Simulations ................................ ................................ ..... 72 Model Validation ................................ ................................ ................................ ..... 73 Performance Comparison ................................ ................................ ....................... 79 4 BENC H TOP SYSTEM DESIGN ................................ ................................ ............ 83 6 LiF/ZnS Physics ................................ ................................ ................................ ..... 83 Light Transm ission ................................ ................................ ................................ .. 85 Configuration ................................ ................................ ................................ .......... 89 Data Acquisition ................................ ................................ ................................ ...... 92 Pulse Shape Discrimination ................................ ................................ .................... 94

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7 5 MEASUREMENT RESULTS ................................ ................................ .................. 97 Neutron Measurements ................................ ................................ .......................... 98 Gamma Ray Measurements ................................ ................................ ................. 106 Trace Variations ................................ ................................ ................................ .... 116 Model Vali dation ................................ ................................ ................................ ... 121 6 THEORETICAL CONSIDERATIONS: GAMMA RAY EFFECTS .......................... 126 Neutron Moments ................................ ................................ ................................ 127 Gamma Ray Moments ................................ ................................ .......................... 130 Joint Dist ributions ................................ ................................ ................................ 134 Final Formulas ................................ ................................ ................................ ...... 136 Assay Affect ................................ ................................ ................................ .......... 1 38 7 SUMMARY AND FUTURE WORK ................................ ................................ ....... 144 APPENDIX A DERIVATION OF EQUATIONS ................................ ................................ ............ 147 B SAMPLE PARAMETER EFFECT ON THE CALCULATED MASS ....................... 160 C VIRTUAL LIST MODE SHIFT REGISTER ................................ ............................ 163 LIST OF REFERENCES ................................ ................................ ............................. 167 BIOGRAPHICAL SKETCH ................................ ................................ .......................... 172

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8 LIST OF TABLES Table page 1 1 Neutron capture properties for select materials. ................................ ................. 26 2 1 Spontaneous fission and ( ,n) yields for uranium and plutonium isotopes. ........ 50 2 2 Gamma ray yields for uranium and plutonium isotopes. ................................ ..... 50 3 1 Tube diameter and pressure combinations to achieve the same number of 10 B atoms in a system designed with BF 3 filled proportional counters as 3 He atoms present in the ENMC. ................................ ................................ .............. 64 3 2 Tube diameter variations and the required number to achieve the same number of 10 B atoms as 3 He atoms in the ENMC, assuming a lining thickness of 2.5 m. ................................ ................................ ................................ ........... 67 5 1 Test unit measurement configuration summary.. ................................ ................ 97 5 2 Results from the 252 Cf measurements with the 0.7 cm thick PMMA and WLSP with a single PMT coupled directly to the end of the detector. ............... 101 5 3 PMMA and WLSP coincident PMT measurement results with a 252 Cf source centered on the detector. ................................ ................................ .................. 103 5 4 Measurement summary for a single PMT coupled directly to the detector with the three di fferent WLSP thicknesses tested. ................................ ................... 105 5 5 PMMA and WLSP (0.7 cm thick) measurement results with a 2.7 Ci 60 Co gamma ray source. ................................ ................................ ........................... 107 5 6 Measurement summary with the 0.7 cm thi ck PMMA and 0.7 cm thick WLSP 116 5 7 Validation correction factors for the different bench top test units measured. .. 122 C 1 Example distribution from a JSR shift register in multiplicity mode and the corresponding factorial moments and singles, doubles and triples ................... 164 C 2 Probability distributions generated with a virtual shift register. ......................... 165

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9 LIST OF FIGURES Figure page 1 1 Helium 3 neutron reaction cross section. ................................ ........................... 23 2 1 Neutron multiplicity distribution for the spontaneous fission of 252 Cf and 240 Pu. .. 32 2 2 Neutron multiplicity distribution for the spontaneous fission of 240 Pu and the induced fission of 239 Pu. ................................ ................................ ..................... 33 2 3 Neutron distribution for a counter with a single exponential die away time. ....... 34 2 4 The two neutron source events that correspond to the two terms in Equation 2 8. ................................ ................................ ................................ .................... 39 2 5 The possible combinations of neutron source events that would result in double detections that correspond to the three terms in Equation 2 9. .............. 39 2 6 The possible combinations of neutron source events that would produce the triple detection combinations that correspond to th e six terms in Equation 2 12 ................................ ................................ ................................ ...................... 40 2 7 Comparison of the results from a conventional assay and a multiplicity assay for samples with different amounts of effec tive 240 Pu (adapted from Figure 7.3 Ensslin et al. [6]). ................................ ................................ .......................... 45 2 8 The ENMC shown with a sample being inserted into the chamber (photo courtesy of Dr. Henzlova). ................................ ................................ .................. 47 2 9 Prototype LANL developed 6 LiF/ZnS well counter (photo courtesy of Dr. Swinhoe). ................................ ................................ ................................ ........... 49 3 1 Illustration of the two scenarios simulated in this work. ................................ ...... 53 3 2 ENMC MCNPX model used as the template for the 3 He alternative configurations. ................................ ................................ ................................ .... 56 3 3 Example simulated spectrum from a 3 He filled proportional counter and a 10 B lined proportional counter. ................................ ................................ .................. 59 3 4 Die away time fit for the baseline 3 He system. ................................ ................... 61 3 5 The original ENMC footprint, with 121 2.54 cm diameter 3 He tubes, compared to the final BF 3 system footprint, with 155 5.08 cm diameter BF 3 tubes. ................................ ................................ ................................ .................. 64

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10 3 6 The range of alpha particles in several possible compositions of the lining for 10 B lined proportional counters, and the range of the 7 Li ions in the same linings. ................................ ................................ ................................ ................ 66 3 7 Four tubes with a diameter of 0.8 cm occupy the same area as one tube with a diameter of 2.0 cm. ................................ ................................ .......................... 67 3 8 FOM space mapped out with the simulated 10 B lined proportional counter configurations. ................................ ................................ ................................ .... 69 3 9 Surface contour of the FOM space mapped with the simulated 10 B lined proportional counter configurations. ................................ ................................ ... 70 3 10 The original ENMC footprint, with 121 2.54 cm diameter 3 He tubes compared to the final 10 B lined system footprint, with 4725 0.40 cm diameter 10 B lined tubes. ................................ ................................ ................................ .................. 71 3 11 The original ENMC footprint, with 121 2.54 cm diameter 3 He tubes compared to the final 6 LiF/ZnS system footprint, with 20 6 LiF/ZnS screens. ....................... 73 3 12 Model and measurement configuration for the 10 B lined proportional counter model validation. ................................ ................................ ................................ 74 3 13 The neutron capture efficiency and counting efficiency as a function of 10 B lining thickness. ................................ ................................ ................................ .. 76 3 14 Measured pulse height spectrum obtained with a 252 Cf source located 25 cm from a 10 B lined proportional counter. ................................ ................................ 77 3 15 Simulated pulse height spectra for three different lining thickness. .................... 78 3 16 The effect of the tube lining thickness on the FOM of a system simulated with various numbers of 4.0 mm diameter 10 B lined proportional counters. ............... 80 3 17 Final FOM comparison for the 3 He a lternative multiplicity counter configurations shown with the ENMC and the PCMC. ................................ ........ 82 4 1 Magnified (50x) view of a section of a 6 LiF/ZnS sheet. ................................ ....... 84 4 2 The WLSP and PMMA sheets used for the bench top test system. ................... 86 4 3 Emission Spectrum for the 6 LiF/ZnS screens and the absorption and emission spectra for the WLSP. ................................ ................................ ......... 87 4 4 Refracted light between two media. ................................ ................................ .... 89 4 5 6 LiF/ZnS system and a modified concept for the construction of the initial systems with the bench top test unit equivalent marked. ................................ ... 90

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11 4 6 Bench top test unit assembled on a support structure with two PMTs and no tapered light guides. ................................ ................................ ........................... 91 4 7 Test unit with a tapered light guide attached (photo taken by the author). ......... 92 4 8 Neutron and gamma ray digitized traces illustrating the regions of charge integration for the PSD methodology applied. ................................ .................... 94 4 9 Histogram illustrating the charge ratio region from the 60 Co gamma ray traces and the 252 Cf neutron traces. ................................ ................................ .............. 95 4 10 Parameters for a standard FOM calculation illustrating gamma ray and neutron separation. ................................ ................................ ............................. 96 5 1 Horizontal source positions for the bench top test unit measurements. ............. 99 5 2 Example gamma ray and neutron traces recoded with the Pixie 500. ................ 99 5 3 Charge ratio histogram of the traces collected with the 0.7 cm thick WLSP and the 0.7 cm thick PMMA in response to a 252 Cf source. .............................. 100 5 4 Charge ratio histogram of the traces collected with a 252 Cf source in the center of the detector constructed with the 0.7 cm thick PMMA ...................... 103 5 5 Charge ratio histogram of the traces collected with a 252 Cf source positioned in the center of the detector constructed with t he 0.7 cm thick WLSP. ............. 104 5 6 PMMA response with a single PMT to a gamma ray flux of 5.9x10 7 /s and 8.5x10 6 /s. ................................ ................................ ................................ ....... 109 5 7 WLSP response with a single PMT to a gamma ray flux of 5.9x10 7 /s and 8.5x10 6 /s. ................................ ................................ ................................ ....... 109 5 8 Trace examples showing the system response to a high gamma ray rate. ...... 110 5 9 PMMA response to a gamma ray flux of 5.9x10 7 /s with a single PMT and with two PMTs in coincidence. ................................ ................................ .......... 110 5 10 WLSP response to a gamma ray flux of 5.9x10 7 /s with a single PMT and with two PMTs in coincidence. ................................ ................................ .......... 111 5 11 Charge ratio histograms with the 0.7 cm thick PMMA and a single PMT in response to a 252 Cf source and an incident gamma ray flux. ............................ 112 5 12 Charge ratio histograms with the 0.7 cm thick PMMA and two PMTs in coincidence in response to a 252 Cf source and an incident gamma ray flux. .... 113 5 13 Charge ratio histograms with the 0.7 cm thick WLSP and a single PMT in response to a 252 Cf source and an incident gamma ray flux. ............................ 115

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12 5 14 Example of the two neutron trace types collected with all of the systems measured. ................................ ................................ ................................ ......... 117 5 15 Emission spectrum of the 6 LiF/ZnS sheets from the time of excitation to 3.0 ms ................................ ................................ ................................ .................... 118 5 16 Emission spectra from the 6 LiF/ZnS without the polyester interface and from the polyester coated 6 LiF/ZnS for three different excitation wavelengths. ........ 120 5 17 Simulated bench top detector inside the light tight box and shown with components labeled in the cross section view. ................................ ................ 122 5 18 Gamma ray rejection and VCF for different pulse height thresholds applied to the 252 Cf and 137 Cs coincidence measurements. ................................ .............. 124 6 1 Single gamma ray sources for the first factorial moment of the gamma ray probability distribution. ................................ ................................ ...................... 132 6 2 Double gamma ray sources for the second factorial moment of the gamma ray probability distribution. ................................ ................................ ................ 133 6 3 Triple gamma ray sources for the third factorial moment of the gamma ray probability distribution. ................................ ................................ ...................... 134 6 4 The effect of the gamma ray efficiency on the calculated mass for a 10 g 240 Pu sample with different values of M and if the gamma ray distributions are not accounted for in the calculations for F, M and ................................ .. 139 6 5 Detail of the likely region of g amma ray efficiency of interest from Figure 6 4 for the 6 LiF/ZnS based bench top system. ................................ ........................ 141 B 1 The change in the calculated mas s if M is held constant (M=1) and alpha ( and the gamma ray efficiency ( ) are varied. ................................ ................... 161 B 2 The change in the calculated mass if alpha ( ) is held constant ( =0) and the Multiplication (M) and the gamma ray efficiency ( ) are allowed to vary. ......... 162 C 1 Shift register diagram. ................................ ................................ ...................... 163

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13 LIST OF ABBREVIATION S ANMC Alternative Neutron Multiplicity Counter BF 3 Boron Triflouride 252 Cf Californium 252 137 Cs Cesium 137 60 Co Cobalt 60 DA Destructive a nalysis Die away time eV Electron volt E NMC Epithermal Neutron M ultiplicity Counter FOM Figure of merit 3 He Helium 3 HEU Highly enriched uranium IAEA International Atomic Energy Agency 6 LiF/ZnS Lithium 6 fluoride zinc s ulfide LANL Los Alamos National Laboratory LEU Low enriched uranium MOX Mixed oxide fuel Neutron detection efficiency NMC Neutron m ultiplicity c ounter NDA Nondestructive a nalysis PMT Photomultiplier tubes Pu Plutonium PFPF Plutonium Fuel and Production Facility PMMA Polymethly Methacrylate

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14 PGF Probability generating f unction PH Pulse height (F8 ) tally PSD Pulse shape d iscrimination P C MC Pyrochemical Neutron Multiplicity Counter U Uranium VCF Validation correction f actor WLS P Wave l ength shifting p lastic

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15 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy NEUTRON MULTIPLICITY COUNTER DESIGN WITHOUT HELIUM 3 By Azaree T. Lintereur August 2013 Chair: David Gilland Major: Biomedical Engineering Neutron multiplicity counters are used to quantify the mass of a fissile isotope in a sample with undefined parameters. Isotopes that decay through fission emit unique neutron multiplicity distributions The first three factorial moments of the detected distribution can be used to identify one, two or three unknown assay variables. Neutron multiplicity counters are complex systems that requi re a high neutron detection efficiency, a short neutron life time in the counter (die away time) and minimal gamma ray sensitivity Traditional multiplicity counter design s ha ve relied upon the use of 3 He filled proportional counters for neutron detectio n. The availability of 3 He has decreased, which has produce d a need to develop a multiplicity counter configuration without 3 He. The complexity of multiplicity counter systems require s that several performance parameters be optimized simultaneously. In this work, the best performing c onfigurations within specified physical dimensions, were identified for three currently commercially available thermal neutron detectors with the use of the Monte Carlo transport code, MCNPX. The designs for the maximum efficiency and minimum die away time were determined The simulated system with the highest performance

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16 capability was identified as the one designed with 6 LiF/ZnS scintillating sheets inter layered with plastic light guides. A bench top test unit base d on the simulated 6 LiF/ZnS sheet design was constructed. Measurements were performed with the bench top test unit to establish the appropriate configuration for a small scale system assembly and to validate the simulation predictions Two different typ es of plastic light guides were measured : a wavelength shifting plastic, and non scintillating p olymethyl methacrylat e. The configuration selected for a future complete bench top construction consisted of 0.7 cm thick wavelength shifting plastic light guid es with a photomultiplier tube coupled to each end with a t apered light guide The 6 LiF/ZnS sheets and plastic light guides have a higher inherent gamma ray sensitivity than 3 He filled proportional counters. Thus, the detected distribution will not be so lely dependent upon the neutron multiplicity distribution. The detected gamma ray signals were separated from the detected neutron signals by applying pulse shape discrimination algorithms. T he effect of gamma ray misidentifications on the measured parameters was considered by including the correlated gamma ray multiplicity distributions associated with a spontaneous fission event in the formulas for the unknown sample parameters.

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17 CHAPTER 1 INT RODUCTION Radiation detection is the measurement of the quanta emitted by a radionuclide or radiation producing source s Radiation detection has a variety of applications. The medical field utilizes radiation detection for diagnostic image formation and validation of radiation absorbed doses in cancer therapy [1] [2] Research applications, such as high energy physics, make use of radiation detection to probe some of the fundamental questions about matter and the universe. Material verification measurements rely on radiation detection to provide accurate sample quantif ication. The fundamentals of radiation detection apply to all of these applications; this work will focus on radiation detection for sam ple quantification nonetheless the detectors and detection techniques discussed could be applicable for other uses. Radiation can be classified as either ionizing or non ionizing. Ionizing radiation, as its name implies, carries with it sufficient energy to ionize an atom. Non ionizing radiation such as microwaves and radio waves, does not carry enough energy to i onize an atom, although it can deposit energy i n matter in the form of heat. Ionizing r adiation for energies of interest to nuclear radiation, can be placed into two general categories as defined by the International Commission on Radiation Units and Me asurements (ICRU) : directly and indirectly ionizing Directly ionizing radiation carries a charge, and can deliver energy directly to matter through Coulomb force interactions Indirectly ionizing radiation (which includes neutrons and gamma rays) does n ot carry an electric charge and transfers its energy through the production of secondary charged particles, which themselves are directly ionizing and thus able to deliver energy to matter as stated above [3] The presence of indirectly ionizing radiation is identified through the

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18 detection of the secondary products (energetic electrons or nucleons) produced by the interactions of indirect ionization in matter [4] Sample Analysis Measurement techniques for nuclear materials can be loosely grouped into two categories: destructive analysis (DA) and non destructive analysis (NDA). Destructive analysis is any technique that requires the destruction of the sample for the measurement to be performed. Some examples of DA measurements include mass spectrometry, gravimetry, and reduction oxidation tit ration techniques [5] Non destructive analysis methods do not affect the sample. N ondestructive g amma ray measurements are often used to identify th e presence o f a gamma ray source or verify the isotopic composition of a sample. Gamma rays can be shielded with materials that shield can be effectively assayed through gamma ray measurements to the outer layer of the sample. N eutron detection (if the sample is a neutron emitter ) can be a viable alternative (or addition) to gamma ray measurements for shielded samples Neutrons are highly penetrating, compared to gamma rays, through most materials (hydrogenous materials can effectively shield neutrons) and therefore can be used to obtain a more uniform measure of the entire sample with NDA techniques [5] While both gamma ray and neutron measurements play an important role in radiation detection applications (and are often used in conjunction) this work will focus on neutron det ection systems. The neutron detector used for a measurement depends on the sample of interest, and the information required. There are three basic forms of neutron detectors : those that count singles (the total neutron detection rate), those that count singles and

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19 doubles ( the rate at which two time correlated neutrons are detected), and those that count singles, doubles and triples (the rate at which three time correlated neutrons are dete cted ). Detectors that provide total neutron counts are suitable for identifying the presence of a source. However, additional information about the source cannot be inferred with only a total neutron counter unless certain source parameters are taken as known. If there is more than one unknown source parameter then additional information will have to be obtained through measurements to fully characterize a sample The factors that will influence the observed neutron fluence rate as noted by Ensslin et al. [6] are: 1. the spontaneous fission rate (F) 2. self multiplication (induced fission) factor (M) 3. 4. neutron detection efficiency 5. variation in spatial detection efficiency (s Z ) 6. variation in detection efficiency with energy (s E ) 7. system die away time 8. sample self shielding The source variables (1, 2, and 3) may be unknown the detector parameters (4, 5, 6 and 7 ) are typically assumed to be known through measurement s or modeling and the sample self shielding (8) can be disregarded for most neutron measurements. If there are two unknown source parameters then two variables must be measured; if there are three unknown source parameters then three variables have to be measured. Neutron c oincidence counters are used to determine up to two assay unknowns and neutron multiplicity counters are used to determine up to three assay unknowns The measurement of higher multiplicities would al low additional unknown parameters to be determined, but with the systems currently available the measurements are not practical. The efficiency for coincidence events scales as the detector efficiency

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20 squared, for triples events the efficiency scales as the detector efficiency cubed, and so forth for the higher multiplicities. A detector with a neutron detection efficiency of 50% would have a quadruple event efficiency of only 6.25%, which would lead to unacceptably long count times to produce adequate c ounting statistics. N ondestructive assay of neutron emitting samples can be required to monitor throughput at a fuel fabrication facility, quantify contents of waste drums, or verify the contents of holding containers. Sample assays with coincidence and multiplicity counters can be performed to quantify the mass of fissile material (plutonium or uranium) present in a sample [6] There are a variety of samples an d forms that are assayed, which require s the use of different counters as discussed by Doyle [5] The Plutonium Fuel and Production Facility (PFPF) in Japan (a mixed oxide [typically plutonium and uranium] or MOX fuel fabrication plant) accepts plutonium from several reprocessing plan ts and has over 20 coincidence counters installed to meet its material control and accounting requirements. Neutron multiplicity counters are used in facilities to assay impure Pu metals, oxides, waste, residues, and other samples that may not be well ch aracterized. L ow enriched uranium (LEU) oxide and pellets can be assayed with counters that have a built in neutron source to induce fissions in the samples (known as Fuel assembly assays at fuel fabrication plants are performed to ver ify the fuel isotopic s Irradiated fuel measurements are performed to assay the assemblies in spent fuel storage facilities [7] An example of a measurement syste m used to assay irradiated breeder reactor fuels is the underwater breeder counter used in Kazakhstan. Highly enriched uranium ( HEU ) spent fuels are assayed with active neutron coincidence counters, such as the Research Reactor Fuel Counter used at the

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21 Sa vannah River Site (Georgia, USA) This counter measures the 235 U in fuel that is returned to the United States (as part of the program to reclaim the spent fuel from the Atoms for Peace program) [5] In addition to facility measurements neutron coincidence and multiplicity counters are also used by the International Atomic Energy Agency (IAEA) for verification measurements of Pu and U samples [8] The IAEA is responsible for assuring that M ember States meet their accountancy obligations (that safeguarded material has been declared and is not being diverted). Therefore the IAEA is concerned with verification of nuclear material quantities. The verification measurements often require the use of high accuracy NDA techniques to confirm the declared quantity of nuclear material in a sample. The IAEA measurements must be in dependent, and so prior knowledge of the sample cannot be assumed. Resultantly the IAEA uses a variety of coincidence and mu ltiplicity counters to obtain as much information as possible regarding the surveyed source material [8] The counters used for these measurements are specialized for specific applications ; however, the funda mental operation of all the counters relies upon basic neutron detection principles. Neutron Detection Basics Free n eutrons are generated via fission (spontaneous or induced) and nuclear reactions (photoneutron, ( ,n) reactions, and acceler ated charged particle reactions[ (e.g. deuteron deuteron ] ) Neutron interactions occur primaril y with the nuclei of materials; the neutron can be captured by, or can scatter off, the nucleus. The probability of one of the reactions occurring is described by the reaction cross section [9] Because neutrons do not carry a charge the ir electromagnetic interactions with the

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22 orbital electrons of an atom are negligible (the spin of a neutron means that there is a n internal non ze ro charge distribution, which will cause an extremely small electromagnetic force with electrons). Therefore, neutron detection relies on the detection of the charged particles pro duced by nuclear absorption or elastic scattering reactions [10] Neutron interactions produce secondary radiation, either in the form of heavy charged particles or gamma rays (created by neutron capture or nuclear excitation ) or re coil nuclei (produced by neutron scatter). The secondary radiation produced by neutron interaction s is ionizing, and will produce charge that c an be detected allowing for the (indirect) detection of the neutrons. It should be noted that the charge produ ced by the secondary radiation can only be detected with an appropriately designed detector. For example, if the neutron is captured in material from which the charge cannot escape a detection event will not occur. The optimal material for a neutron detector must possess a high neutron cross section [4] The neutron interaction t hat occurs depends upon the neutron energy and the nucleus with which it interacts. For thermal neutrons the neutron capture cross section (reaction probability) tends to dominate, and is proportional to 1/E (where E is the kinetic energy of the neutron) as shown in Figure 1 1 Some materials have regions of strong interaction probability known as resonance regions, but these regions are typically superimposed over a 1/E trend [9] Resonance regions arise when a nucleus has discrete excited states that can enhance or suppress neutron interactions High energy neutrons are more likely to be scattered by a nucleus than to be captur ed. The neutron will impart some of its energy to the nucleus off which it scatters,

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23 until eventually it becomes thermalized ( on average 27 scatters off of a hydrogen atom are required to thermalize a 1 MeV neutron [10] ) and can be absorbed. The neutron capture cross section for thermal neutrons is orders of magnitude higher than the scattering cross section. Due to the high thermal neutron capture cross section, most neutron detectors rely on capture reactions and utilize moderation to thermalize the incident fast neutrons. Figure 1 1 Helium 3 neutron reaction cross section note the 1/E trend M aterials that have a large neutron cross section may have non negligible gamma ray interaction cross sections. A g amma ray interaction can lead to ionization in the detector which will produce a signal that may be detected in the s ame manner as a signal produced in response to a neutron interaction Therefore, if the gamma ray interaction cross section is not negligible the gamma ray s must be discriminat ed from the response generated by a neutron detector (to prevent gamma rays fr om being

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24 misidentified as neutrons) The materials sought for neutron detectio n are those that have a large Q value, or kinetic energy generated by the neutron capture reaction in the center of mass frame compared to the energy deposited by gamma rays If the Q value is large compared to the maximum energy deposited by gamma ray interactions the signal generated by neutrons can be distinguished from the one generated by gamma rays. The ideal neutron detector has a large neutron reaction cross section a nd a large Q value, or generates a distinguishable signal between neutrons and gamma rays. Helium 3 Shortage Helium 3 is a popular neutron detection media for a variety of applications due to its large neutron capture cross section (5330 b) lar ge Q value, gamma ray insensitivity and proportional gas amplification characteristics The 3 He neutron capture reaction has a cross section of 5330 b and produces a proton and a triton ( ) with a Q value of 0.764 MeV [4] An additional attribute of 3 He for radiation detection purposes is that it is an inert gas, which makes it safe to handle and non corrosive [4] Helium 3 is used in its gaseous state as a fill gas in proportional counters. The signal generated in 3 He gas is due to the ionization of th e gas in response to the motion of the neutron capture reaction products ( a proton and a triton) under an applied electric potential. Helium 3 is produced as a product of the beta particle decay of tritium, which was produced for nuclear weapons. The cu rrent 3 He supply is thus obtained from the decay of the tritium supply (which has a half life of 12.3 years). The decrease of the weapons stock pile has reduced the amount of available tritium, and consequently the supply of 3 He available for neutron dete ction applications The demand for 3 He has increased

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25 significantly since 2001, driven primarily by the deployment of radiation portal monitors for national security and use in neutron scattering science applications [11] There are potential alternative sources of 3 He production but none of them are currently utilized. The CANada Deuterium Uranium ( C ANDU) reactors produce tritium, but it is not harvested for 3 He recovery at this time D ue to the 12.3 year half life of tritium there is a delay between the start of tritium harvest and the production of 3 He ; therefore there will not be a near term supply from this source even if it becomes available There is a lso the potential to obtain 3 He from natural helium, but it is present in very low concentrations (~0.0001%) and it has not been demonstrated that it will be cost effective for it to be collect ed [11] The remaining 3 He is being rationed making it prohibitively expensive for the majority of detection uses. Thus, alternative thermal neutron detection t echnologies are necessary Helium 3 alternatives have already been identified for some applications (such as radiation portal monitors), but there are applications for which a viable solution has not yet been developed. Coincidence and multiplicity counters are two systems curren tly designed with 3 He filled proportional counters for which alternative configuration s are being researched The specialized nature of the measurements performed with coincidence and multiplicity counters require high performance from the neutron detecto rs used in the systems. The samples assayed with coincidence and multiplicity counters emit both neutrons and gamma rays, so to ensure high precision assays are obtained in a reasonable amount of time the detectors have to be both efficient at detecting neutrons and either insensitive to gamma rays or capable of gamma ray discrimination.

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2 6 The goal of this work is to identify a 3 He free multiplicity counter configuration that has equivalent capability to the highest performing multiplicity counter currently used. The multiplicity counter configuration was selected for the replacement study because an alternative detector capable of fulfilling the multiplicity counter requirements would also be capable of meeting the performance requirements of a coincidence counter. There is also a separate research effort currently exploring alternatives for coincidence counter applications [12] Helium 3 Alternatives The c ommercially available near term alternatives to 3 He for thermal neutron detection are detectors developed with 10 B and 6 Li. Both of t hese materials have large cross sections for thermal neutron capture and high Q values as shown in Table 1 1 with the 3 He values included as a reference point The Q value is divided between the reaction products according to the ratio of their masses. There are t wo reaction possibilities for neutron capture by 10 B, one where the 7 Li nucleus goes directly to the ground state (6% of the reactions), and one where the 7 Li nucleus is produced in its first excited state (94% of the reactions). The Q value for both rea ctions is shown in Table 1 1 Table 1 1 Neutron capture properties for select materials [4] Atom Neutron Capture Cross Section (b) Reaction Q Value (MeV) 3 He 5330 0.764 10 B 3840 2.792 2.310 6 Li 940 4.780 Boron 10 is available in both gaseous and solid form. Elemental boron (typically enriched to 96% 10 B) is chemically stable in air, and therefore can be used as a coating

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27 eit her for proportional counters or solid s tate detectors Boron tri fluoride is a g aseous form of 10 B that can be used as a fill gas in proportional counters. Boron tr i fluoride is not as well behaved a proportional gas as 3 He, and be gi ns to lose its proportional characteristics as the counter pressure increases, which results in higher applied voltages being required to drift the ions to the anode [4] Therefore, BF 3 is not available in tubes with fill pressure s as high as 3 He tubes ( 3 He fill pressures can be as large as 10 atmospheres while BF 3 fill pressures are typically less than 2 a tmospheres ) Detectors developed with a 10 B conversion layer have separate neutron capture and signal generating materials [13] The neutron is captured in the 10 B and then the reaction products must escape the lining to generate a signal in another medium. The signal generating material can either be a semiconductor [14] or a gas. In both options, the ions generated by the interactions of the neutron capture reaction product s are drifted under the influence of an electric field to generate a signal. The range of the 10 B neutron capture reaction products (alpha particle and 7 Li ion ) depends on the type and density of the coating. For a typical 10 B density of 2.34 g/cm 3 the range of the reaction products is 3. 5 m and 1 .8 m for the alpha particle and the 7 Li ion respectively ( as calculated using SRIM 20 1 3 [15] ) Due to the relatively short range of the reaction products the coating thickness is t ypically no more than a couple microns thick. Boron 10 loaded s ci ntillators (either liquid or plastic) are also available. Boron 10 loaded plastics have a higher sensitivity to gamma rays than BF 3 filled proportional counters or 10 B lined proportional counters. The signal produced by gamma rays can be distinguished from the signal produced by neutrons in liquid scintillators loaded with 10 B ; however, liquid scintillators are not a viable 3 He alternative for certain applications as

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28 liquids cannot be taken into all nuclear facilities due to criticality concerns and the flammability of most liquid scintillators Lithium 6 is not traditionally used as a coating in its elemental form as it is chemically unstable in air Howeve r, 6 Li is stable once bound in a matrix, so i t is often used in scintillators. Lithium 6 can be part of the scintillator (as with CLYC [16] ), bound directly into a scintillator [17] (as with 6 Li loaded glass fibers [18] ) or bound with another element and then used in a homogenous mixture with a scintillator ( such as 6 LiF/ZnS ) [19] The scintillators produce light in response to the neutron capture reaction products (alpha particle and triton) escaping the 6 Li and entering the scintillation material. The neutron captu re reaction products from 6 Li have more energy than the 10 B reaction products (due to the larger Q value of the reaction) a lower mass and charge, and thus a longer range (the alpha particle has a range of approximately 22 m in 6 Li and the triton a range of approximately 117 m [ as calculated using SRIM 2013 [15] ] ). A lthough the neutron capture cross section for 6 Li is approximately 25% that of 10 B the difference can be offset by the increased amount of 6 Li that can be used while still producing a signal. The limiting reaction product for 6 Li is the alpha particle which has a range of 22 m in 6 Li, compared to the limiting reaction product in 10 B, the 7 Li ion, which has a range of 1.8 m 10 B. There are some additional options for neutron detection besides 10 B and 6 Li Gadolinium has an extremely high neutron capture cross section (255 000 b for thermal neutrons ) ; however, it is sensitive to gamma rays and also produces a gamma ray with neutron capture [4] Additionally, t here are no currently commercially available gadolinium based detector s capable of meeting the detection criteria of material

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29 quantification applications. Lithium sheets are another option for increasing the detector response [20] However, as 6 Li is chemically unstable in air the manufacturing of the devices is challenging and they are not currently commercially available Thermal neutron detectors are not the only 3 He alternative option ; there are also fast neutron detectors that could be potential replacements for some applications Fast neutron detectors rely on neutrons scattering off of the target nuclei. The recoiled nucleus will ionize atoms along its path length, creating a detec table signal. Hydrogen has the highest neutron scatter cross section, which produces a recoiled proton (hydrogen nucleus) [4] One of the most common hydrogen bas ed fast neutron detectors is a proton recoil scintillator. Liquid scintillators are amongst the most popular scintillators for fast neutron detection; however, liquids are not always a realistic option for all measurement applications as liquids cannot be introduced into all facilities (due to the safety issues mentioned above ) Liquid scintillators are also sensitive to gamma rays and rely on pulse shape discrimination ( PSD ) to distinguish between the signals produced in response to neutrons and those pr oduced in response to gamma rays. Plastic scintillators offer an alternative to liquid scintillators for fast neutron detection [21] but plastics with adequate P SD are currently limited by the size that can be produced This project is focused on currently commercially available neutron detectors for near term 3 He replacement in multiplicity counter configurations Due to the project applications thermal neutron detectors were the emphasis of the replacement effort. Therefore, the alternatives considered for this work were BF 3 filled proportional counters, 10 B lined proportional counters and 6 LiF/ZnS scintillating screens.

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30 Objectives of this Work The objective of this work was to support the project in determining an appropriate 3 He alternative for use in neutron multiplicity counter configurations. The work included modeling and simulations to identify optimal design templates and the devel opment of a bench top test unit. Measurements were made with the test unit to demonstrate the capability of the system and validate the model predictions. The multiplicity equations were examined to explore the effect of using a 3 He alternative detector on the calculated assay results.

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31 CHAPTER 2 MULTIPLICITY COUNTERS The number of neutrons produced by spontaneous fission events is random. Different isotopes will have different neutron emission probability distributions, which are also known as multiplicity distributions. Multiplicity counters are specialized neutron detection systems that are used to measure the first three factorial moments of the detected neutron distribution. Multiplicity counters are capable of assaying samples with one two or three unknown parameters. Coincidence counters are typically preferred to multiplicity counters when the sample being assayed has only two unknown parameters as m ultiplicity counters require longer counting times than coincidence counters to achieve the nec essary statistics on the triplet count rates (rate at which three time correlated neutrons are detected which is proportional to the efficiency cubed ) Multiplicity counters also require more complex electronics than coincidence counters, and are more expensive. However, under certain conditions m ultiplicity counters are the detection systems that must be used to obtain an accurate sample assay Principles of Operation An assay is typically performed to quantify the amount of a fissile i sotope present in a sample The total neutron count rate cannot be directly correlated to the fissile isotope mass for samples that contain impurities (such as oxygen) that can result in neutrons being generated through ( ,n) reactions or for assays perf ormed in environments with significant background present [22] Neutrons can also induce fissions within the sample (multiplication) instead of escaping, which in creases the total neutron production rate above what would be expected for a given mass of a fissile

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32 isotope. All of these potential neutron sources must be accounted for when characterizing a sample based upon its neutron emissions. The effect of detect ing neutrons from sources other than the isotope of interest can be mitigated by taking advantage of the unique neutron multiplicity distributions generated by isotopes that decay via spontaneous fission ( Figure 2 1 ) Figure 2 1 Neutron multiplicity distribution for the spontaneous fission of 252 Cf and 240 Pu ( the data for the figure was obtained from Verbecke [1][24] for 252 Cf and Bodeman [25] for 240 Pu ). Induced and spontaneous multiplicity distributions are also distinguishable ( Figure 2 2 ) which allows the spontaneous fission rate to be extracted from measured data even when the sample a lso contains isotopes that undergo induced fission. The moments of the distributions that are measured with a multiplicity counter can be related to the moments of the neutron distribution that escapes the sample and is available for detection ( if the dis tribution available for detection is corrected for the detector parameters, as was demonstrated by Bohnel [23] ). The moments of the emitted

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33 neutron distribution ca n be expressed in terms of the sample parameters (such as the fission rate, sample self multiplication, and the ( ,n) reaction rate). Therefore, if the isotopic composition of the sample is known (typically determined with gamma ray spectroscopy) the mas s of the isotope of interest can be extracted from the measured moments. Figure 2 2 Neutron multiplicity distribution for the spontaneous fission of 240 Pu and the induced fission of 239 Pu (the data fo r the figure was obtained from Boldeman [25] ). Multiplicity counters record the neutron multiplicity distribution (from which the factorial moments are calculated) using shift regi ster logic. Multiplicity shift registers specified duration, or gate [26] T he measured multiplicity distributions are comprised of real and accidental neutron correlations. The distribution that can be related to the unknown sample parameters is the distribution of real correlated events, which has to be extracted from the distr ibution that is measured. Two counting gates are opened

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34 when the shift register is triggered by a neutron event. The second counting gate opens long after the fir st gate closes (approximately 4 ms later) when the correlated neutrons from the original fis sion burst are no longer present in the counter. Therefore, the correlated pulses measured in the second gate are used to determine the rate of accidental correlations, as shown in Figure 2 3 The first gate is typically referred to as the foreground, or reals and accidentals (R+A), gate and the second gate as the background, or accidentals (A), gate. Figure 2 3 Neutron distribution for a counter with a single exponential die away time. The Reals + Accidentals gate corresponds to the foreground and the Accidentals gate to the background. The red bars represent correlated neutrons from the initial fission event, the green bars repres ent the accidental correlations from fissions that are not associated with the initial fission, and the blue bars represent the uncorrelated background neutrons (adapted from Figure 6.11 from Ensslin et al. [28] ). The distribution in the R+A gate, f(n), is a convolution of the real and accidental correlations; the distribution in the A gate, b(n,) is based solely on the accidental correlations. If the probability d istribution of real, correlated events is represented by

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35 r(n) then the probability of obtaining no counts in the R+A gate (after it is triggered) is given by f(0) = r(0)b(0) The probability of there being one count in the R+A gate is given by f(1) = r(1)b(0) + r(0)b(1) the probability of two counts is f(2) = r(2)b(0) + r(1)b(1) + r(0)b(2) the probability of three counts is f(3) = r(3)b(0) + r(2)b(1) + r(1)b(2) + r(0)b(3) and so forth. The normalized distribution of correlated counts can be expres sed as [27] : Equation 2 1 The general form for the factorial moments of a probability distribution P( ) is giv en by: Equation 2 2 The factorial moments of the correlated distribution can be used to calculate the correlated neutrons, correlated neutrons, multiplicity shift register, where W is given by S 1 (the source rate, S, multiplied by the detector efficiency, and the first factorial moment of the source distribution 1 ). The doubles are equal to the trigger rate multiplied by the average number of correlated neutrons, which is equivalent to the first factoria l moment of r(n) The triples are equal to the trigger rate multiplied by the number of time correlated neutron pairs, which is equivalent to the second factorial moment of r(n) The first three factorial moments of r(n) can be calculated with Equation 2 2 :

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36 The singles ( U ), doubles ( D) and triples ( T ) can then be written with these three factorial moments: Equation 2 3 Recall that the distribution that is measured in the R+A gate is actually a convolution of the correlated and uncorrelated distributions. Therefore, to calculate U, D and T from the measured distributions r 0 r 1 and r 2 must be expressed in terms of the moments of f(n) and b(n ). The moments from the measured distributions can be substitute d into the equations for U, D and T by d econvolving r(n) from b(n) : Equation 2 4 Equation 2 5 Equation 2 6

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37 These three equations can be used to calculate U, D and T from the measured distributions, but to determine the unknown assay parameters the equations must be related to the neutron distribution emitted from the sample. Th e moments of the measured neutron multiplicity distribution can be related to the moments of the neutron distribution emitted by the sample if the emitted distribution is corrected for certain detector parameters. To express the moments of the detected distribution in terms of the sample parameters, the moments of the emitted neutron distribution must first be defined. The moments of the distribution of neutrons that escape a sample and are available for detection can be derived from the probability distribution of neutrons generated by a source event, as was demonstrated by Bohnel [23] The general expression for the probability distribution of source neutrons (with the inclusion of ( ,n) reactions) is: Equation 2 7 Where F = the fission rate S = the rate of ( ,n) reactions q sf ( ) = the probability of spontaneous fission neutron s being emitted 1, The expressions for the factorial moments of a neutron emission distribution have been derived by two different methods: from probability generating functions (PGF) [23] and with the use of event tree analysis [29] Event tree analysis does not produce a closed form solution; additional terms are included until their effect is negligible. A closed form solution for the factorial moments can be derived with a PGF. The

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38 equations used throughout this work were derived with the use of PGFs (which are discussed further in Appendix A), although identical equations could be devel oped using event tree analysis. The first, second and third factorial moments of the distribution of neutrons that escapes the sample and is available for detection are shown below (the derivation is provided in Appendix A) [30] : Equation 2 8 Equation 2 9 Equation 2 10 The physical meaning of the terms in Equation 2 8 through Equation 2 10 can be understood by considering the source events that could produce one, two, or three correlated neutrons, as are illustrated in the following figures. The figures were generated following the method demonstrated by Oberer [27] with ( ,n) events included The origin of the two terms in Equation 2 8 which describe the origin of single neutrons available for detection are illustrated in Figur e 2 4

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39 Figur e 2 4 The two neutron source events that correspond to the two terms in Equation 2 8 The lines are multiplying branches and the open circles represent neutrons available for detection. The origins of the three terms in Equation 2 9 that correspond to the production of two correlated neutrons are illustrated in Figure 2 5 Figure 2 5 The possible combinations of neutron source events that would result in double detections that correspond to the three terms in Equation 2 9 The lines are multiplying branches and the open circles represent neutrons available for detection. The six possibilities for producing three correlated neutrons available for detection (given in Equation 2 10 ) are shown in Figure 2 6

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40 Figure 2 6 The possible combinations of neutron source events that would produce the triple detection combinations that correspond to the six terms in Equation 2 12 The lines are multiplying branches and the open circles represent neutrons available for detection The detected distribution can be expressed in terms of the emitted neutron distribution corrected for the detector efficiency : Equation 2 11 where is the binomial coefficient and is given by The detected distribution must also be corrected for the fraction that arrives during the gate to produce the distribution that is actually counted by the shift register. The

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41 correlated detected neutron distribution can be expressed as [6] (derivation shown in Appendix A): Equation 2 12 w here the integral expression represents the probability of the shift register being triggered by a neutron, n, and j of the remaining n 1 neutrons being counted in the gate The factorial moments of r(j) are the correlated factorial moments which are related to the measured distributions. These f actorial moments can now be written in terms of the source parameters. As was shown earlier, in Equation 2 3 the measured singles rate is equal to the zeroth correlated moment times the total trigger rate, the doubles are equal to the first moment times the trigger rate, and so forth. The method to derive the factorial moments of Equation 2 12 is shown in Appendix A. The first three are given below: Equation 2 13 Equation 2 14 Equation 2 15 w here PD is the pre delay, or the time between the trigger and the opening of the gate that is set to prevent any electronic dead time from affecting the size of the gate, and G is the gate length. The gate length is typically set to 1.27 to minimize the rela tive error in the coincidence rate [31]

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42 The singles, doubles and triples can now be written in terms of the factorial moments of the detected distribution as fol lows. Equation 2 16 Equation 2 17 Equation 2 18 The expressions for 1, 2 and 3 from Equation 2 8 to Equation 2 10 can be substituted into Equation 2 16 to Equation 2 18 to produce equations in terms of the source parameters (the fission rate, F, the multiplication, M, and the ration of ( ,n) neutrons, With these equations t he sample parameters can be expressed in terms of the multiplicity counter output, without the need for prior sample information. The equations for U, D, and T can be solved for expressions [6] : Equation 2 19 w here Equation 2 20

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43 The fission rate can be determined using the calculated value for M with the following equation: Equation 2 21 And then is given by: Equation 2 22 Shift registers solve the equation for M by iteration using the Newtonian method with a first guess of 1 for the value of M [32] The relationship between the source emission distributions and the measured distributions make multiplicity counters a powerful tool for extracting the sample parameters in situations where impurities may be present, or there are background neutrons that can affect the assay. Multiplicity Counter Designs Multiplicity counters have evolved over time to meet specific performance requirements. Multiplicity counters were originally dev eloped to assay samples where to be measured. The first multiplicity counters were developed by adding additional detectors to existing coincidence counters to increase the system efficiency (to impro ve the statistics on the 3 ) Later, an additional decoding circuit was added to the standard coincidence electronics to measure the multiplicity distributions. Simple dead time corrections were also implemented; howeve r, these corrections were

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44 assumed to be uniform, which introduced a bias with the count rate. To overcome this, a correction based on the multiplicity probabilities was included and demonstrated to improve assay results [33] The design of multiplicity counters is complicated by competing performance parameters ( the detection efficiency and the die away time ) and stringent perf ormance requirements for a high detection efficiency and low die away time Moderation is required to thermalize neutrons entering the detector, to increas e the efficiency of the system. However, the time it takes for the neutrons to lose energy through scattering in the mod erator increases the die away time. The dual mode multiplicity counter was developed to work in two different configurations to provide additional insight into multiplicity counter operations. Optional cadmium sleeves around the 3 He detectors were used t o decrease the die away time; however, the efficiency was also reduced in this configuration due to neutrons being absorbed in the cadmium without being detected. Without the cadmium sleeves the efficiency was improved from 17% to 53%, but different elec tronics were required to process the higher multiplicities [34] Faster electronics began to be incorporated into the multiplicity counter circuits and the improv ed results demonstrated the importance of correctly designed read out systems. The drastic improvement in the results achieved with the multiplicity assay compared to the results from a traditional coincidence assay can be seen in Figure 2 7 Note that the impure oxides demonstrate more bias with conventional coincidence assay than the pure oxides. The difference is largely a result of the correction factor that is applied to account for the unknown parameters being less accurate when impurities are present in the sample.

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45 Figure 2 7 Comparison of the results from a conventional assay and a multiplicity assay for samples with different amounts of effective 240 Pu 1 ( adapted from Figure 7.3 Ensslin et al. [6] ). Multiplicity counters suitable for specialized measurements were constructed for specific applications, such as the Pyrochemical Neutron Multiplicity Counter ( PNMC ) which was designed specifically for in plant detection measurements. Monte Ca rlo simulations performed by La n gn er, et al. [35] and measurements made with the dual mode multiplicity counter, were used to select the final d esign for the PNMC. Based on the results from the studies of the various configurations the PNMC was constructed with four rings of 3 He detection tubes and an all polyethylene moderator. The measured 1 Effective 240 Pu ( 240 Pu eff ) is the mass of 240 Pu that would give the same response as that obtained from all of the even plutonium isotopes in the sample. The effective 240 Pu is calculated by 240 Pueff = 2.52 238 Pu + 240 Pu + 1.68 242 Pu, which can be solved to determine the mass of 240 Pu present in the sample.

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46 results were demonstrated to match the predicted capabilities within 4% for efficiency and die away time [34] Aluminum was used in the body of the detection syst em prior to this design and resulted in a decreased die away time when compared to a polyethylene body. However, the aluminum body also caused the die away time to be non exponential, which nullified any improvements gained from a shorter die away time. T he PNMC study demonstrated that systems must be carefully optimized for the measurements being made, and that slight changes to the configuration can have significant impacts. The highest performing multiplicity counter that has been developed i s the Epithermal Neutron Multiplicity Counter (ENMC) ( Figure 2 8 ) The ENMC contains 121 10 atm 3 He filled proportional counters. The neutron detection efficiency o f the ENMC is 65%, and the die away time is 21 sec [3 6] The counter was design ed to have a high efficiency and a short die away time, and both were achieved in a compact footprint. The sample chamber is lined with cadmium, iron and lead. The cadmium prevents thermal neutrons from returning to the sample chamber and inducing additional fissions the iron is a scattering media, and the lead is to reduce the gamma ray fluence incident upon the 3 He tubes. Graphite end plugs on the sample chamber improve the vertical uniformity of the neutron detection efficiency, and were selected based on simulat ions with several different media [36] The entire counter was carefully designed; h owever, the performance was primarily realized due to the large amount of 3 He p resent in the system (over 18 moles of 3 He are in the ENMC [13] ). The availability of 3 He decreased after the design of this counter, and building additional ENMC s has

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47 become prohibitively expensive. Therefore, high performance multiplicity counter configurations without 3 He that can replace the ENMC need to be identified. Figure 2 8 The ENMC shown with a sample being inserted into the chamber (photo courtesy of Dr. Daniela Henzlova) Helium 3 alternative neutron detectors for multiplicity counters are being researched by several groups. Helium 3 alternatives based on 10 B lined proportional counter technology have been considered by Proportional Technologies incorporated and Los Alamos National Laboratory. Proportional Technologies has examined the in house manufactured 10 B coated straw detectors for use in multiplicity counters [37] and Los Alamos National Laboratory has conducted a series of measurements to quantify the performance of t hree different 10 B based detectors [38] In addition to thermal neutron 3 He alternatives some fast neutron detection techniques for use in multiplicity counters have also been explored, such as the design

PAGE 48

48 developed by researchers at the University of Mich igan [39] Liquid scintillators can be designed to detect fast neutrons, and p ulse shape discrimination (PSD) techniques can be employed to distinguish between pulses generated by gamma rays and neutr ons. Liquid scintillators are fast, so there is a low accidental rate; however, like most fast neutron detectors they pro duce lower neutron detection efficiency than conventional thermal neutron detectors. A prototype counter based on 6 LiF/ZnS sheets was developed by Los Alamos National Laboratory [40] The light generated by the scintillation of ZnS was transmitted to photomultiplier tubes ( PMTs ) via wavelength shifting fibers. The fibers were bundled outside of the region with the 6 LiF/ZnS and tapered to the PMTs, which resulted in a relatively large configuration ( Figure 2 9 ) [41] The counter was designed with minimal moderation, which resulted in an extremely low die away time (< 5 s), however, the design relied upon pulse shape analysis to discriminate between pulses generated by neutrons and pulses generated by gamma rays. Therefore, the neutron detection efficiency was dependent upon the threshold applied for the gamma ray dis crimination. The counter was tested with a high count rate sample (2.1 million neutrons/second) and at the threshold required to produce a 1.6% gamma ray neutron identification the neutron detection efficiency was 23% [41] The efficiency was limited by the light collection efficiency of the fibers. While fibers are less gamma ray sensitive than large sheets of wavelength shifting plastic the light collection ef ficiency will limit the neutron detection efficiency. Customized electronics were developed to improve the PSD [40] but the length of the neutron pulses (several s) ultimately limited t he performance of the system.

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49 Figure 2 9 Prototype LANL developed 6 LiF/ZnS well counter (photo courtesy of Dr. Martyn Swinhoe) A similar system to the 6 LiF/ZnS counter designed by LANL was developed jointly by the University of Leeds and the University of London [42] This counter was designed for detection of heavy ions at low count rate appli cations, so the pulse length was not a concern. Unlike the prototype developed by LANL this system contained polyethylene moderator between the layers, and utilized wavelength shifting plastic sheets in place of the fibers. The polyethylene increased th e die away time of the design, but also boosted the efficiency. The neutron signal was distinguished from the gamma ray signal based on pulse shape discrimination. The electronics employed provided accurate neutron identification, but were never tested a t a high count rate such as would be required in traditional multiplicity counter applications

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50 There is a wide range of potential neutron count rates that multiplicity counters have to process. In addition to neutrons the samples will also emit gamm a rays. Some representative neutron count rates are shown in Table 2 1 and the gamma ray emissions for the same isotopes are shown in Table 2 2 These tables illustrate that not only will any 3 He alternative counter need to be capable of handling high neutron count rates, but will also require high gamma ray rejection capabiliti es. Table 2 1 Spontaneous fission and ( ,n) yields for u ranium and p lutonium isotopes [1][6] Isotope Spontaneous Fission Half Life (yr) Spontaneous Fission Yield (n/s g) Alpha Decay Half Life (yr) Alpha Yield ( /s g) ( ,n) Yield in Oxide (n/s g) ( ,n) Yield in Flouride (n/s g) 235 U 3.5x10 17 2.99x10 4 7.04x10 8 7.9x10 4 7.1x10 4 0.08 236 U 1.95x10 16 5.49x10 3 2.34x10 7 2.3x10 6 2.4x10 2 2.9 238 U 8.2x10 15 1.36x10 2 4.47x10 9 1.2x10 4 8.3x10 5 0.028 238 Pu 4.77x10 10 2.59x10 3 87.74 6.4x10 11 1.34x10 4 2.2x10 6 239 Pu 5.48x10 15 2.18x10 2 2.41x10 4 2.3x10 9 3.81x10 1 5.6x10 3 240 Pu 1.16x10 11 1.02x10 3 6.56x10 3 8.4x10 9 1.41x10 2 2.1x10 4 Table 2 2 Gamma ray yields for uranium and plutonium isotopes [5] [43] Isotope Total Half Life (yr) Gamma Ray Yield ( /s g) 235 U 7.04x10 8 5.55x10 10 236 U 2.34 x10 7 9.1x10 5 238 U 4.47 x10 9 7.18x10 6 238 Pu 87.74 3.02x10 8 239 Pu 2.41x10 4 8.58x10 5 240 Pu 6.56x10 3 4.43x10 6 The multitudes of counter configu rations that have been developed demonstrate the specialized nature of these systems. S everal performance parameters must be considered during the design to produce a system with the necessary capabilities within the physical constraints (i.e. footprint, height, weight, sample chamber size) associated with the measurements that will be made A change in one parameter can affect others, so a systematic study of capabilities is necessary for any new counter configuration.

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51 CHAPTER 3 COUNTER MODEL AN D SIMULATIONS Radiation detection systems can be complex, and small design changes can significantly affect the ir performance. Building different systems to test various configurations typically is not a practical way to investigate multiple designs; mode ls of detectors present an alternative method of performance characterization Simulations can be a valuable asset for detector development as different designs can be modeled much more efficiently than they could physically be built. However, the simula tion methodology must be validated with experimental data. A system model allows performance mapping with different changes, and should ultimately lead to the system with the highest performance within the design constraints There are various means of performing simulations to predict the response of a neutron detector. The basic simulation methods for radiation detection problems are either Monte Carlo or deterministic. The two methods seek to answer t he same questions, but through d ifferent approach es. For predicting the average behavior of radiation quanta deterministic methods solve the transport equation. Alternatively, Monte Carlo methods simulate individual particles and record their average behavior, which is then used to predict how the par ticles in the system will act Most deterministic methods rely on the discrete ordinates method, which divides a space into small units through which particles traverse in a differential amount of time. In the limit of the spatial regions becomin g progre ssively smaller ; this method approaches the integro differential transport equation. Monte Carlo does no t rely upon integrating the particles through space or time; instead, the Monte Carlo method simulates the spatial transport of individual particles be tween specific types of events. Because there are no s patial

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52 regions Monte Carlo methods are extremely useful for solving problems involving complex physical systems. Monte Carlo simulations use a random number selection to statistically sample each type of event during a particles life time. The probability distributions are sampled randomly, according to material cross section files, which are built into the code. The events happen sequentially, so an interaction and the new direction of travel (f or a scatter event) are sampled with at least two different random numbers. If additional particles are created through interactions of the original particles they are stored for later analysis [45] All of the simulations performed as part of this research effort were conducted with the Monte Carlo method. The performance for the simulated systems was evaluated based on the standard figure of merit ( FOM ) ( 2 / ) [44] MCNPX Simulation Methodology A standard Monte Carlo package used for radiation transport is the Los Alamos National Laboratory developed Monte Carlo N Particle transport code, MCNP [45] MCNP is capable of photon, neutron, and electron transport. MCNPX was developed to accommodate the transport of heavy charged particles (such as alpha particles and tritons) MCNPX v.2.7.0 [46] was used for all of the simulations in this work a s the transport and tallying of heavy charged particles was required for some of the simulations. The simulations performed for the optimization of the 3 He alternative multiplicity counter configuration were comprised of two categories : one where the neu tron capture material and the signal generation material were the same (e.g. 3 He filled proportional counters), and one where the neutron capture material and the signal generating material were different ( 10 B lined proportional counters) ( Figure 3 1 ) There are several

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53 options available for recording the particles generated in MCNPX simulations (normally referred to as a tally) to produce efficiency calculations However, not all tally methodologies are appropriate for the two types of simulations performed in this work. If the material that captures neutrons and the material that generates the signal are the same the neutron detection efficiency can be determine d in one step, by tallying the number of neutron captures. The F4 reaction tally, with a multiplier card that specifies capture reactions, can be used to simulate the number of neutron captures in the media of interest. A net neutron current tally, gener ated with the F1 tally (which is a basic surface counting tally, meaning the number of particles crossing a surface are tallied) and the use of cosine bins to track the direction of travel of the neutrons, was used to verify the F4 tally results. (a) (b) Figure 3 1 Illustration of the two scenarios simulated in this work: one where the neutron capture medial and the signal generating media are the same (a) and one where th e signal is generated in a separate media from where the neutron was captured (b). Signal generation in n eutron detectors that have a separate neutron capture material and signal generating material is a two step process. The neutron has to be captured an d the reaction products then have to escape the capture material and enter the signal generating material. Therefore, the neutron captures tallied with a F4 tally will over predict the signal generating, or counting, efficiency. An accurate system counti ng

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54 efficiency simulation for these detectors requires the tracking of the correlated reaction products into the signal generating material Heavy ion tracking, which is necessary to track the 7 Li ion, was implemented in MCNPX v.2.6.0 [47] The ability to requir e correlation of the reaction products, with the correct two branch Q values for neutron capture reactions in 10 B, was added in MCNPX v 2. 7b [46] Prior to MCNPX v.2.7b, a correction factor was applied to the simulated neutron capt ure efficiency to estimate the neutron detection efficiency. The use of a correction factor can produce an accurate efficiency estimate; however, the lining thickness will affect the die away time as well as the efficiency. Thus, for system capability estimates a correction factor is not adequate. The energy deposited b y the reaction products in the signal generating media can be simulated with the use of F8 pulse height (PH) tallies. The F8 tally differs from other MCNPX tallies in that the particles are tallied at the end of their life in the simulation. The energy d eposited in a specified region of the detector geometry is determined by comparing the energy of the particle at its entry into the region with the energy of the particle when it leaves the area of interest (or passes below the energy threshold for the sim ulation). As a result the F8 tally cannot be used to simulate the energy deposition of particles that are created in the same volume of interest in which they end (that would result in a net energy deposition of zero based on the definition of the tally methodology). However, for simulations where the particles are created in a separate region from where the energy is deposited the F8 tally can be used to determine the detection efficiency. The results of the tally can be verified with a F1 tally to co unt the number of reaction products entering the region of interest The reaction product currents (the F1 tallies) assume that all of the products that enter the region of interest

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55 regardless of energy, create enough ionization to produce a detectable s ignal. The F1 tally will over predict the detection efficiency by 1 2% as long as the current tally and the pulse height ( PH ) tally do not differ by more than a couple percent, and the current prediction is hi gher, the current tally (a well established method) can be used as a confirmation of the PH tally predicted efficiency MCNPX cannot be used to simulate any potential loss of signal that occurs after the particle energy deposition, or capture, in the signal generating media. Validation mea surements are required to establish the relationship between the simulated response and the measured response. E NMC Template The MCNP X simulations were performed starting with a template that was designed at Los Alamos National Laboratory [36] based on the ENMC. The model for the ENMC was used to select the design of the physical ENMC configuration and therefore it includes all of the system components (excludin g the electronics), as shown in Figure 3 2 The tube spacing, selected based on an optimization study [36] was approximately 1 cm tube to tube The measured efficiency of the ENMC is 65% and the die away time 22 s. The ENMC template was reconstructed in MCNPX prior to any modifications being performed for the 3 He alternative technologies. The efficiency for the baseline ENMC template was simulated with F4 neutron capture tallies, and the die away time by simulating the number of captures in specified time intervals. The simulated efficiency was 65.6% and the die away time 23.2 s which corresponds to a percent difference between the measured and simulated results of 1% and 5%, respectively After the model was verified by comparisons to the measured ENMC values the ENMC template was a dapted for alterations with the 3 He alternative

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56 technologies through the development of the Alternative Neutron Multi plicity Counter (ANMC) template [13] Figure 3 2 ENMC MCNPX model used as the template for the 3 He alternative configurations. ANMC Template The same geometry as in the ENMC MCNP input was used for the initial ANMC template However, the tubes were simulated such that a single master tube was used as a template for the rest of the tubes in the system [13] This methodology simplified tube by tube a nd ring by ring analysi s and detector substitutions All of the design changes to accommodate the alternative detectors were made external to the layer of polyethylene between the aluminum shell of the chamber and the first ring of tubes. Additional modifications were implemented for the configurations which contained more detector units than cells allowed by MCNPX ( MCNPX contains a 1000 cell limi t) and for the configurations with detectors that were not based on a circular geometry ( i.e. the 6 LiF/ZnS simulations, which were not performed as part of this work )

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57 Alternative configurations were simulated using detectors based on 10 B and 6 Li. T wo 10 B based thermal neutron detectors, BF 3 filled proportional counters and 10 B lined proportional counters were simulated using the ANMC template A separate set of simulations was performed to determine if p lates lined with 10 B and orientated at an an gle to the surface normal would increase the neutron detection efficiency. The 6 Li based detector simulated with the ANMC template was 6 LiF/ZnS( A g) sheets ; however, those models were developed separately from this research effort [44] The BF 3 efficiency tallies were performed with a F4 neutron capture tally and verified with a neutron current tally (net neutrons entering the BF 3 fill gas). The signal produced by 10 B lined tubes is dependent upon one of the reaction products from the neutron capture in the 10 B escaping the tube lining and entering the fill gas. Because the neutron capture material and the signal generating material are not the same for this detec tor the neutron detection efficiency (signal generating efficiency) was determined by tallying the correlated reaction products escaping the 10 B lining and entering the signal generating fill gas. The 10 B lined tallies were verified by tallying the energ y deposited in the fill gas by the reaction products (PH tallies). Momentum conservation requires that the reaction products be emitted in opposite directions. Therefore, only one reaction product per neutron capture in the 10 B lining will enter the prop ortional gas and generate a signal. The detection of one of the reaction products per neutron capture produces a spectrum with two distinct regions, one from each of the reaction products. The products will lose energy in the lining prior to entering the proportional gas. The amount of energy the products lose depends on the reaction location. Therefore, the regions are broad distributions that range from the full particle energy to

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58 zero. This is a fundamentally different spectral shape compared to pro portional counters where the neutron is captured in the same material that generates the signal (such as those filled with 3 He or BF 3 ). When the reaction products are created in the same media that generates the signal both of the reaction products will contribute to the detected signal (even though the reaction products are emitted in opposite directions). The two spectral shapes are illustrated by an example simulated spectrum from a 3 He filled proportional counter and a 10 B lined proportional counter shown in Figure 3 3 No conclusions should be inferred from the difference in the count efficiencies, as this figure simply illustrates the differences in the spectral shapes obtained with different detectors. Any gamma ray contribution to the signal will be evident in the low energy region of the spectra. A low energy threshold can be applied to produce th e required gamma ray rejection. The low energy threshold will not significantly affect the efficiency of the 3 He or BF 3 proportional counters due to the large separation between the signal produced in response to a neutron capture and that produced by a g amma ray. However, the low energy threshold will have a n impact on the neutron detection efficiency of the 10 B lined proportional counters due to the energy distribution of the reaction products entering the proportional gas. The standard low energy thre shold is approximately 100 k eV, which will produce an effect around 10% on the 10 B lined proportional counter detection efficiency [44] This effect was not inclu ded for the full system simulations, but was considered for the model validation studies. The spectra shown for the model validation all show the position of the low energy threshold that was applied.

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59 (a) (b) Figure 3 3 Example simulated spectrum from a 3 He filled proportional counter (a) and a 10 B lined proportional counter (b). The location of a 100 keV low energy threshold is marked in both figures. Note that the location of the peak in the 3 He spectrum corresponds to the Q value for a neutron capture in 3 He, and the two plateaus below the peak are due to the wall effect, or the result of some of the reaction products escaping prior to depositing all of their energy. The contributions of the two reaction products produced by a neutron capture in the 10 B lining to the total energy deposited in the proportional gas are shown in the 10 B lined proportional counter spectrum. Note that the low intensity upper region for each reaction product is due to the higher kinetic energy of the reaction products in the ground state reaction (6% probable). As with the 10 B lined proportional counters, the signal generated by the 6 LiF/ZnS sheets is a two step process that is the result of the neutron capture r eaction products

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60 escaping the neutron capture material ( 6 LiF) and entering the signal generating material (ZnS). However, tracking the reaction products from the 6 LiF into the ZnS is not informative as the microscopic scale of the particles compromises th e accuracy of the simulations. Additionally the final measured efficiency with the 6 LiF/ZnS system is also highly dependent upon the light collection efficiency, which cannot be simulated by MCNPX v.2.6.0. Therefore, t he neutron detection efficiency of t he 6 LiF/ZnS sheets was simulated (separate from this research effort [44] ) by the use of neutron capture tallies in the 6 Li only. A validation correction factor ( VCF) was applied to the simulation results to account for the difference between the neutron capture efficiency and the signal generating efficiency. The VCF was determined by comparing simulated to measured efficiency values [48] Because the simulation did not consider signal generation there were no spectral shapes generate d for this technology. The die away time for all of the technologies simulated was calculated by determining the number of neutrons captured per time interval, and fittin g the results to an exponential such as is shown for the base line 3 He system in Figure 3 4 Note that error bars are not shown on any of the reported simulation results. The MCNPX code provides tests to give the user reasonable confidence that the simulation results have adequately sampled all of the phase space. For all of the s imulation results reported here the MCNPX tests were passed and a large enough number of particles were simulated to produce a statistical uncertainty of less than 1%.

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61 Figure 3 4 Die away time fit for the baseline 3 He syst em. Boron 10 Based Detector Simulations The probability of a thermal neutron being captured by a 10 B atom is lower than the probability of a thermal neutron being captured by a 3 He atom. Therefore, to have the same number of neutron captures in a system built with 10 B based neutron detectors as would be seen in a system built with 3 He based neutron detectors more 10 B atoms than 3 He atoms are required. The number of 10 B atoms req uired to obtain an equivalent number of neutron captures to 3 He can be determined by multiplying the total number of 3 He atoms present by the ratio of the neutron capture cross sections. For a complete system the relationship between atoms of detection m edia and neutron detection efficiency is not linear due to neutron scattering (as the system gets larger to

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62 accommodate the increased amount of 10 B the neutrons will be more likely to lost in the moderator). T he amount of 10 B in all of the 10 B based sys tem s was maximized as much as possible to offset the lower cross section. However, while the amount of neutron detection media must be maximized it is also necessary to restrict the overall size of the system to prevent the die away time from becoming to o large. An additional physical size constraint was that the chamber be accessible without the need for additional equipment and that the entire counter could be moved by two people The first sets of simulations with 10 B instead of 3 He as the neut ron detection medium were conducted with BF 3 filled proportional counters T he initial BF 3 simulations were perform ed by replacing the 121 2.54 cm diameter 10 atm 3 He tubes in the ENMC with 1 atm BF 3 tubes (and keeping the rest of the ENMC design the same) The system performance with these parameters ( discussed in the Performance Comparison section, below ) was less than the ENMC target, due to the decrease in the available neutron capture sites. The thre e options to increase the number of 10 B atoms in the system were to increase the number of tubes, increase the tube volume, or increase the tube pressure. It is evident that an increase in the tube pressure would increase the number of 10 B atoms in the sys tem without increasing the footprint, but t he tube pre ssure was limited to 2 atm, for availability purposes. BF 3 is considered a hazardous gas, due to its corrosive nature ; BF 3 also loses its proportional characteristics at high pressures and requires a h igh operating voltage The corrosive nature of BF 3 and the high operating voltage required limit the available tube pressure. Therefore, to increase the number of neutron capture sites the number of tubes, and

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63 the tube volume had to be increased. How ever, a system that is comprised of more tubes, of a larger diameter, than those in the original ENMC configuration, will result in a larger die away time due to an increased footprint ; thus, the optimal BF 3 tube configuration is not determined solely by t he number of 10 B atoms present The entire design has to be considered when searching for overall performance optimization. Several options to produce a system with the same number of neutron capture sites as are present in the ENMC (1.09x10 25 atoms of 3 He) are shown in Table 3 1 (although the lower neutron capture cross section of 10 B will still result in a system with a lower efficiency) The physical constraints of the system eliminate an increase in the tube diameter beyond 5.08 cm. L ikewise, a configuration with 1 atm tubes was determined to be impractical for an actual physical configuration. The best option for the BF 3 filled proportional counters was identi fied as the 5.08 cm diameter tubes filled to a pressure of 2 atm. The factor of two increase in the tube diameter from the initial configuration increased the tube volume by a factor of four. However, due to the larger tube size fewer tubes could be pos itioned in each of the rings. Accordingly two additional rings were added to the design to accommodate the required number of tubes System optimization of the moderator and the tube placement resulted in a configuration with 155 5.08 cm diameter tubes spaced as closely as possible (approximately 0.1 cm spacing between the tubes in each ring) in a total of 6 rings. A comparison of the efficiency of each ring of tubes illustrated that the efficiency gained with the addition of a seventh ring was not enou gh to overcome the increase in the die away time. As shown in Figure 3 5 the footprint of the final design was larger than that of the ENMC, but not so large that the system could no t be moved by two people.

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64 Table 3 1 Tube diameter and pressure combinations to achieve the same number of 10 B atoms in a system designed with BF 3 filled proportional counters as 3 He atoms present in the ENMC. Pressure (atm) Tube Diameter (cm) Atoms/Tube Number of Tubes 1 2.54 8.81x10 21 1239 1 5.08 3.52x10 22 310 1 7.62 7.92x10 22 137 2 2.54 1.76x10 22 619 2 5.08 7.05 x10 22 155 2 7.62 1.58x10 23 68 (a) (b) Figure 3 5 The original ENMC footprint, with 121 2.54 cm diameter 3 He tubes compared to the final BF 3 system footprint, with 155 5.08 cm diameter BF 3 tubes. The second set of simulations performed with 10 B as the neutron capture material utilized 10 B lined proportional counters. Boron 10 lined proportional counters do no t have the same safety issues associated with BF 3 filled proportional counters, as they can be filled with an inert proportional gas. However, the neutron capture material is limited to a thin lining on the tube surface, which can make achieving the required

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65 efficiency challenging. The lining thickness is limited by the range of the reaction products (which varies with tube lining compositions) ; if the reaction products are unable to escape the tube lining a signal w ill not be generated in the proportional gas. As shown in Figure 3 6 the 7 Li ion has a shorter range than the alpha particle, and is the particle that limits the lining thickness. There is an optimal thickness for each lining composition that will stop the maximum number of neutrons and still result in a signal being generated. The neutron detection efficiency will increase with l ining thickness until approximately 3 m where the efficiency will begin to decrease as a result of fewer reaction products escaping the lining The first set of simulations consisted of replacing the 2.54 cm diameter tubes in the ENMC template with 2.5 4 cm diameter tubes lined with 2.5 m of 10 B and filled with argon gas at a pressure of 1 atm The performance of the initial system was not adequate, so as with the BF 3 filled proportional counter configuration, an increase in the amount of 10 B in the system was required The number of 10 B atoms in a system designed with 10 B lined proportional tubes can be increased by increasing the total surface area of the tubes, or the lining thickness. The use of a thicker tube lining will increase th e number of neutrons captured, but due to the physics of the detectors, not necessarily the signal generated. The overall surface area of the tubes in the system can be increased by increasing the number of tubes (of the same diameter), or by replacing ev ery tube by several smaller ones. As shown in Figure 3 7 four tubes with a diameter of 0.8 cm each occupy the same area as a tube with a diameter of 2 cm, but the fo ur smaller tubes have a surface area 1.6 times greater than that of the larger tube.

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66 (a) (b) Figure 3 6 The range of alpha particles in several possible compositions of the lining for 10 B lined proportional counters (a), and the range of the 7 Li ions in the same linings (b). Note that two KE thresholds are shown in both of the figures, one for the reaction which produces a ground state 7 Li ion (6% probable) and one for the reaction which produces an excited state 7 Li ion (94%) probable. The range values for both figures were calculated with SRIM 2013.

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67 Figure 3 7 Four tubes with a diameter of 0.8 cm occupy the same area as one tube with a diameter of 2.0 cm, but the combined surface area of the small tubes is greater than that of the large tube. Table 3 2 Tube diameter variations and the required number to achieve the same number of 10 B atoms as 3 He atoms in the ENMC, ass uming a lining thickness of 2.5 m. Tube Diameter (cm) Atoms/Tube Number of Tubes 5.08 7.05x10 22 274 2.54 1. 99 x10 22 547 0.40 3.14 x10 2 1 3470 Several small diameter tube configuration simulations were performed to increase the total tube surface area (and consequently the amount of 10 B in the system) while maintaining a reasonable system size. However, as shown in Table 3 2 the number of small diameter tubes required to obtain the same number of neutron capture sites as present in the ENMC was greater than the MCNPX cell limit. Therefore, the ANMC template was reconfigured with a lattice structure that permitted simulation of the number of cells required. The lattice parameters were changed based on the simulation being performed to accommodate various tube diameters (down to a 4 mm diameter). One of the potential consequences of decreasing the tube diameter is that the wall effect will begin to have a pronounced influence on the results. The wall effect is seen

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68 when the reaction products escape the tube before depositing all of their energy. As the tube diameter decreases the potential for the reaction products to esc ape the proportional gas increases. This effect was monitored by simulating the pulse height spectrum of the energy deposited in the fill gas and monitoring the loss of efficiency with the decrease in tube diameter It was determined that for tube diame ters down to 4 mm with a fill gas pressure of 1 atm, the loss of efficiency due to the wall effect was negligible [49] The evolution of the performance of the simulated 10 B lined systems can be seen by mapping the simulated FOM. As with the BF 3 based configurations the number and size of the detectors, as well as the amount of moderator, was altered until the system with the highest FOM within the phys ical constraints placed on the design was identified. The design alteration limits placed on the configuration were to keep the inner chamber the same as that of the ENMC, restr ict the height to less than 1 m, and limit the foot print to less than 1 x 1 m 2 An example of the progression of the simulated 10 B lined FOM is shown in Error! Reference source not found. The contour lines epresent constant FOM values, wi th the target performance of the ENMC shown for reference. The first system simulated was a simple substitution of the 3 He tubes in the ENMC with 10 B lined tubes. The following simulations included alterations in the number of tubes, tube diameter, 10 B thickness, tube placement, and the amount of moderation. Not all of the alterations improved the simulated FOM; the FOM changes were used to guide the system adjustment s implemented in the simulations. The same information shown in Figure 3 8 can be viewed in a more qualitative representation on a 3D plot ( Figure 3 9 ). The surf ace in Figure 3 9 illustrates the FOM

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69 space covered with the simulations, the black circles correspond to the FOM values of the simulated designs. Several of the conf igurations were labeled ; note that the labels in Figure 3 9 correspond to those in Figure 3 8 for comparison purposes. H owever, for clarity, labels were not included for all of the markers. Figure 3 8 FOM space mapped out with the simulated 10 B lined proportional counter configurations. The gray lines represent constant FOM contours. The performance goal was to have the same FOM as the ENMC, marked with the red circle.

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70 Figure 3 9 Surface contour of the FOM space mapped with the simulated 10 B lined proport ional counter configurations. Note the markers represent simulated values and the labels correspond to the marker numbers in Figure 3 8 The configuration with the best performance of the simulated systems consisted of 4725 tubes with 4 mm diameters. A ring by ring efficiency analysis illustrated that the system performance could be improved by increasing the number of tubes above the required 3470, w hich resulted in the final 4725 tube configuration. The addition of tubes beyond 4725 did not produce a sufficient increase in the neutron detection efficiency to counter the corresponding increase in the die away time which increase d with system size. The amount of polyethylene between the tubes was optimiz ed for both efficiency and die away time resulting in final configuration with a lattice pitch (tube center to tube center distance) of 0.35 cm which is shown in Figure 3 10 More moderation increased the efficiency, but also increased the die away time, resulting in a lower overall FOM

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71 Likewise, less moderation decreased the die away time, but also decreased the neutron detection efficiency, resulting in a lower FOM t han what was achieved with the configuration shown below. Figure 3 10 The original ENMC footprint, with 121 2.54 cm diameter 3 He tubes compared to the final 10 B lined system footprint, with 4725 0.40 cm diameter 10 B lined tubes. 10 B Lined Plate Configuration The large number of tubes simulated without satisfactory performance led to the exploration of other geometries. A plate configuration was simulated to determine if the efficiency per mole of 10 B could be increased by using configurations other tubes. Th e plates attempted to maximize the path length that the neutrons could travel in the 10 B to increase the likelihood of being captured. The plate approach has been shown to be successful for neutron scattering applications where large area detectors are re quired [50] The detectors used for scattering measurements do not include moderation so the neutrons will enter the detector parallel to the sheets of neutron capture media, increasing the probability that a capture will occur prior to the neutron exiting the

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72 system. The simulations for multiplicity counter applications included moderat ion around the plates to increase the detection efficiency. Several d ifferent plate orientations were simulated to determine if the efficiency would change with plate angle to the normal (relative to the source) However, the lack of significant change w ith plate orientation suggested that the moderation process of the neutrons mitigated any advantage of the radial directionality of the plates 6 LiF/ZnS Based Detector Simulations A 6 LiF/ZnS scintillating sheet template was initially developed using ri ngs of 6 LiF/ZnS and plastic light guide layers that encircled the sample chamber. In this desig n the light guide also functioned as the ne utron moderator, which decreased the amount of polyethylene surrounding the detector media. The 6 LiF/ZnS sheets wer e simulated in a 1:2 ratio of 6 LiF to ZnS, as reported by the vendor, and held together with an organic binder. The composition of the organic binder is vendor proprietary, so for these simulations the binder composition was assumed to be the same as that used by Bicron in the 6 LiF/ZnS screens developed for the LANL prototype neutron capture counter [44] The signal generated 6 LiF/ZnS sheets is due to the 6 Li neutron capture reaction products that escape the 6 LiF and enter the ZnS, causing the ZnS to scintillate. The ZnS scintillation light that is transmitted via the plastic light guides to a photomultiplier tube ( PMT ) produces the detected signal. The in itial configuration consisted of 20 sheets of 0.05 cm thick 6 LiF/ZnS layered with minimal plastic for the light guides. However, optimization studies as reported by Ely et a l. [44] demonstrated that improved neutron detection efficiency could be achieved by increasing the amount of plastic (and therefore the neutron moderation) between the screens. The final

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73 configuration consisted of 20 sheets of 0.05 cm thick 6 L iF/ZnS layered with 0.7 cm thick plastic light guide sheets, as shown in Figure 3 11 Due to the thin 6 LiF/ZnS s heet s and the minimal moderation in the final system the original footprint of the ENMC was maintained with this configuration. The light transmission was not simulated, so the configuration optimization was based on the neutron capture efficiency and the die away time. Figure 3 11 The original ENMC footprint, with 121 2.54 cm diameter 3 He tubes compared to the final 6 LiF/ZnS system footprint, with 20 6 LiF/ZnS screens layered with 0.7 cm thick plastic light guides. Model Validation Simple detector geometries were measured and simulated to validate the simulation methodology, and establish the appropriate VCF for the 6 LiF/ZnS simulations The simulated efficiency (generated with a F4 neutron capture tally) with a single 5.08 cm diame ter BF 3 tub e at a pressure of 1.18 atm was within 1 % of the measured results (1% over prediction of efficiency) [48] The BF 3 tube measurements were performed outs ide with the tube located in polyethylene housing, which mitigated the effect of neutron scatters. The 10 B lined tube measurements were performed

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74 indoors due to climate constraints; the simulated results demonstrated sensitivity to the model of the room The entire room was modeled, and a 2.54 cm diameter 10 B lined tube (manufactured by GE Reuter Stokes, Twinsburg, O H ) was positioned in a 7.62 cm x 7.62 cm polyethylene block with a 2.54 cm diameter hole in the center that was 62 cm long (9.12 cm shorter t han the 10 B lined tube) as shown in Figure 3 12 The room effect had a greater influence on the measurements with a sour ce to detector distance over 50 cm; therefore the validation measurements and simulations presented here were performe d with a source to detector distance of 25 cm. Figure 3 12 Model (left) and measurement (right) configuration for the 10 B lined proportional counter model validation (photo courtesy of Dr. Richard Kouzes) The 10 B lined t ube simulations are highly dependent upon the details of the simulated lining. The organic binder of the lining is vendor proprietary; thus, simulations were performed with several lining compositions covering a range of possible 10 B concentrations ; 96% e nriched 10 B, B 4 C, and BN (96% to 50% 10 B) The 10 B lining thickness, composition and density affect not only the neutron capture efficiency and counting efficiency, but also the die away time of system simulations (as the 10 B concentration will affect the rate at which neutrons are captured). The change in the

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75 simulated efficiency was not linearly related to the 10 B concentration, due to the differences in density of the compositions ( 10 B has a density of 2.34 g/cm 3 B 4 C has a density of 2.52 g/cm 3 and B N has a density of 3.45 g/cm 3 ). Therefore, each composition had to be simulated separately. The efficiency of the signal generated was simulated with F8 energy deposition tallies for the reaction products in the fill gas, and verified with current tallie s of the reaction products entering the fill gas. The best efficiency agreement between the simulated and measured results was obtained with a 0.75 m thick 10 B lining which produced a 2. 2 % difference compared to the measured efficiency (an over prediction of efficiency) However, a s shown in Figure 3 13 several lining thicknesses will produce a similar efficiency (more neutrons are stopped with a thicker lining ; however, if the lining is thicker than the range of the reaction products fewer secondary particles will escape to generate a signal). The lining thickness will affect the die away time as well as the efficiency. Consequently simply co mparing measured to simulated efficiency is not necessarily a reliable indicator of the ability of a model to accurately predict the performance of a system developed with 10 B lined proportional counters. T he pulse height spectra of the rea ction products can be compared to the measured spectra when energy bins are applied to the F8 tallies The spectral shapes can be used to obtain additional insight into the appropriate lining thickness and composition The measured pulse height spectr um f rom a 10 B line d tube demonstrates the two separate plateaus (one due to the alpha particle and due to the 7 Li ion) as expected of a system where one of the two reaction products generate d is detected (due to the particles being emitted in opposite directions) as shown in Figure 3 14 The pulse height spectra for different lining thicknesses and compositions

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76 demonstrate the same two step response as the measured results. However, the simulated results show different rel ative contributions by the two reaction products for different lining compositions and thicknesses as can be seen in Figure 3 15 As the lining thickness increases the average energy deposited by the reaction products decreases, because the particles must travel further through the lining, which reduces the peak appearance noted with the thinner linings [51] Figure 3 13 The neutron capture efficiency and counting efficiency as a function of 10 B lining thickness. The additional information obtained with the pulse height spectra generated sug gests that although the 0.75 m lining may produce the closet efficiency to that measured the actual lining is likely thicker (note the absence of any peaks in the measured spectrum). The B 4 C spectra have similar shapes to the measured results at

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77 a thickness greater than 1.0 m and less than 2.5 m, suggesting a thicker lining with a slight organic contribution is probably closest to the actual tube lining. Figure 3 14 Measured pulse height spectrum obtained with a 252 Cf source located 25 cm from a 10 B lined proportional counter. The kinetic energy thresholds for the two reaction products (for both the ground state and excited state reaction) are marked with the pink dashed lines. The low energy threshold is marked with the red dashed line.

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78 (a) (b) (c) Figure 3 15 Simulated pulse height spectra for three different lining thickness (0.75 m, 1.5 m and 2.5 m) for a 96% enriched 10 B lining (a), a B 4 C lining (b) and a BN lining (c). The pink dashed lines represent the kinetic energy thresholds for the two reaction products (for both the ground state and excited state reaction) and the low energy threshold is marked with the red dashed line. A commercially available 6 LiF/ZnS based detector manufactured by Innovat ive American Technologies (IAT) (Coconut Creek, FL) was used to establish an initial VCF. Efficiency m easurements were performed outdoors with four detector paddle s located in polyethylene housing, which were then simulated for comparison. Each paddle was comprised of layers of 6 LiFZnS and light guide fibers. The VCF obtained by comparing

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79 the measured efficiency with this system to the simulated neutron captures was 0.57 (multiplicative factor ). The IAT VCF was applied to the simulations of the complete ANMC configuration; however, due to the difference in light guides between the IAT and ANMC design the correct VCF for the ANMC must be verified with the construction of a bench top system. Perfor mance Comparison The performance of the final optimized configurations for the three technologies simulated was compared based on the FOM. The target performance for all of the systems was the FOM of the ENMC, 189. The initial FOM for the counter develop ed with 121 2.54 cm diameter 1 atm BF 3 filled proportional counters was 12 The six ring 155 5.08 cm diameter 2 atm tube BF 3 system produced a detection efficiency of 57 % and a die away time of 44 s, corresponding to a FOM of 74 The initial 10 B lined tube system with 121 2.54 cm diameter tubes with a lining thickness of 2.5 m had a FOM of 8 The final system consisted of 47 25 4 mm diameter tubes. The initial simulations considered the optimal performance, so the lining was simulated to produ ce the maximum FOM, not the lowest percent difference with the measured results. It should be noted that as the number of tubes in the system changes so does the optimal lining thickness. In single tube systems the efficiency of the tube must be maximi zed; however, in multi tube systems the efficiency of the m) lining were simulated in a system with varying numbers of tubes (the amount of polyethylene moderator between the tubes was held con stant, thus the total system moderation increased with the number of tubes). For this particular configuration when the total number of tubes was below approximately 1,000 the thicker lining produced superior neutron detection

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80 efficiency as compared to the thinner lining. However, as the number of tubes in the system increased the thinner lining produce d better results because although fewer neutrons were stopped per tube, a greater percentage of the reaction product s per neutron capture were detected ( Figure 3 16 ) Figure 3 16 The effect of the t ube lining thickness on the FOM of a system simulated with various numbers of 4.0 mm diameter 10 B lined proportional counters. With th e large number of tubes simulated the 1 m 10 B lining was found to produce the best FOM. The system with optimized moderation produced a final simulate d system efficiency of 39 % and die away time of 37 s The se values correspond to a FOM of 40. The values for the FOM with a lining simulated to produce maximum performance were not near enough to the target values of the ENMC for this research effort to pursue additional simulations with other lining compositions.

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81 The FOM for the first 6 LiF/ZnS configuration was 4 The final configuration consisted of 20 sheets of 0.05 cm thick 6 LiF/ZnS layered with 0.7 cm thick plastic light guide. The efficiency of the system was found to be 3 8 % and the die away time was 8 s. The low die away time achieved with this configuration is due to the minimal moderation used. The FOM with the optimized 6 LiF/ZnS system was found to be 238, which is hig her than that of the ENMC ( due to the extremely small die away time ) It should be noted that the efficiencies reported are the neutron capture efficiencies corrected with the VCF obtained from the IAT system. The final performance will depend on the VCF calculated with a bench top system that utilizes light guide sheets as opposed to fibers The sheets will have a higher optical efficiency than the fibers and therefore a higher VCF. The final performance of all three systems is compared in Figure 3 17 on a constant FOM contour plot. It is evident that the best perfor mance is achieved with the 6 LiF/ZnS configuration. Included in the plot is the ENMC contour and the PCMC contour (for comparison purposes). The exact efficiency and die away time of the ENMC are noted with the red marker.

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82 Figure 3 17 Final FOM comparison for the 3 He alternative multiplicity counter configurations shown with the ENMC and the PCMC.

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83 CHAPTER 4 BENCH TOP SYSTEM DESIGN The simulation results were used to select a technology for a bench top system build. Based on the comparison of the final templates the 6 LiF/ZnS scintillating sheets were chosen as the neutron capture technology to be used in the bench top system A bench top test unit was configured to determine the best physical configuration for the complete bench top system T he predictions from the simulations did not account for the light collection attenuation from the ZnS through the light guide to the photomultiplier tubes, and thus measurements were made to identify the design that produced the highest collected signal. The bench top test unit was also constructed to determine the appropriate validation correction factor ( VCF ) for systems built with sheets of 6 LiF/ZnS sandwiched between light guides The original VCF applied to the MCNPX simulations was based on measurem ents using the IAT detector configuration, which utilizes fibers for the transmission of the scintillation light The sheets used for the light guides in the final MCNPX design have different ligh t transmission properties than fibers The appropriate VCF varies depending on the configuration, and must be established for each of system measured. The primary considerations in the construction of the bench top test unit were the physics of the 6 LiF/ZnS sheets and the transmission properties of the light gui des. 6 LiF/ZnS Physics Silver activated z inc sulfide is a bright scintillator, generating ~160,000 photons per captured thermal neutron in 6 LiF [19] However, ZnS is not transparent to its own light, and so th in sheets are required to allow light to escape maximizing the signal that is available for transmission by the light guides Th e 6 LiF/ZnS sheets selected for the

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84 test unit construction were manufactured by Eljen Technology Sweetwater, TX ( the sheets were a customized version of EJ 426HD2). The sheets consisted of a 500 m thick layer comprised of a 1:2 ratio of 6 LiF:ZnS particle s suspended in an organic binder. The individual particles of 6 LiF and ZnS were less than 10 m in diameter ( Figure 4 1 ). The 6 LiF/ZnS compound was sandwiched betwee n two polyester sheets (each 250 m thick) by the manufacturer for support. Figure 4 1 M agnified (50x) view of a section of a 6 LiF/ZnS sheet (constructed by Eljen Technology) showing the individual 6 LiF and ZnS pieces suspended in the binder (photo curtesy of Dr. Mary Bliss) Zinc s ulfide will respond to gamma rays as well as the heavy charge d particles created by the neutron capture in 6 Li. Gamma rays and neutrons do not produce the same number of photons in ZnS; one MeV of gamma ray energy will produce ~75,000 ZnS LiF

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85 photons, compared to ~160,00 photons generated by thermal neutron capture [19] The pulse shapes produced by gamma rays and neutrons in 6 LiF/ZnS are also different. The heavy charge d particles from the neutron capture deposit their ener gy over a short distance in the ZnS; thus a large amount of energy is transferred to a small region. The gamma rays release energetic electrons that, in turn, deposit small amounts of energy over a long trail, allowing the states to quickly return to equi librium. The same states decay regardless of whether the excitation was caused by a neutron or a gamma ray. T herefore, the emission wavelength of the luminescence generated from gamma rays and neutrons is identical ; however the time it takes for t he neu tron excited states to de excite is longer than the time required for the gamma ray excited states The difference in the shape of the light pulse generated from gamma rays and neutrons a llows for the pulses to be categoriz ed and gamma rays to be discrimi nated. Light Transmission The light emitted by the ZnS must be transmitted to the PMTs for a signal to be generated. Two different light guides were considered : wavelength shifting plastic (WLSP) (EJ 280 from Eljen Technology Sweetwater, TX ) and non scintillating polymethyl methacrylate (PMMA) (PMMA from Eljen Technology Sweetwater, TX ) both shown in Figure 4 2 The WLSP scintillates in response to gamm a rays, unlike the PMMA (although the WLSP contains a dopant that produces significant gamma ray Both the WLSP and the PMMA will transmit light based on the laws of ray tracing op tics; however, the location of origin of the light that is transmitted is different between the two materials The WLSP captures the light emitted by the ZnS and re emits it isotropically at a different (longer) wavelength with a quantum efficiency of 95% (as reported by the

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86 manufacturer). T herefore the light that is transmitted to the PMTs originates within the WLSP sheets. The ZnS emission spectrum and the absorption and emission spectra for the WLSP sheets used for the test unit are shown in Figure 4 3 (a) (b) Figure 4 2 The WLSP (a) and PMMA (b) sheets used for the bench top test system (photos taken by the author)

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87 (a) (b) Figure 4 3 Emission Spectrum for the 6 LiF/ZnS screens (from Eljen Technology EJ 426) (a) and the a bsorption and emission spectra for the WLSP ( El jen Technology EJ 280 ) (b) from the manufacturers specifications

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88 The light that is incident on the WLSP air interface with an angle greater than the critical angle will be transmitted (as shown in Figure 4 4 ); the critical angle (calculated 2 ) for the WLSP is 39.3 o relative to the normal The PMMA will only transmit the light that reflects off of the PMMA air interface at an angle greater than the critical angle ( 4 1.8 o relative to the normal ) T herefore, only the light that is incident on the PMMA at an angle greater than that which will result in a critical angle at the opposite interface will be transmitted For the 0.7 cm thick PMMA the incident angle must be greater than 88.8 o to generate a critical angle at the opposite interface, as light bends towards the normal in the material with a higher reflective index, as can be seen by tracing the ray in Figure 4 4 (a) backwards. The comparison of light transmission illustrates that the PMMA will have a lower optical efficiency than the WLSP; however, both light guides were tested so that not only the neutron detection efficiency, but also the g amma ray rejection capabilities of the two systems could be compared. The optical efficiency will clearly be higher for short sheets than long sheets (for both the WLSP and the PMMA) due to less light attenuation; however, physical constraints (number an d location of PMTs, for example) prevented short sheets from being used in this configuration as the active region in the final design had to have the same dimensions as the ENMC The sheets used in the test unit were the same length as those that will b e used in the complete bench top system to more accurately reflect the performance of the complete bench top system. 2 into another as: where = the refractive index of each media.

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89 Figure 4 4 Refracted light between two media when the incident angle is less than the critical angle and 1 2 (a), reflected ray for an incident angle equal to the critical angle and 1 2 (b) and total internal reflection when the incident angle is greater than the critical angle and 1 2 (c). Configuration The highest performing simulated configuration consisted of 20 sheets of 6 LiF/ZnS in a cylindrical configuration. Additional simulations were carried out to compare the optimal configuration with one that would be more practical to physically construct [44] T he initial bench top test unit was designed to be one quarter of one of the sections of the modified system, as shown in Figure 4 5 The bench top test unit was built with f ive sheets of 6 LiF/ZnS layered with six sheets of plastic light guide. Th e configuration was

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90 designed for testing the different light guides and determining the corresponding VCF pri or to a full bench top system build. Figure 4 5 6 LiF/ZnS system (a) and a modified concept for the construction of the initial systems (b) with the bench top test unit equivalent marked. The length of the sheets was selected to b e that of the simulated length, 71.12 cm (which also corresponds to the active area of the ENMC) to allow for the effect of the light attenuation down the sheets of plastic to be accounted for in the measurements The width of the test unit was 15.24 cm, which was selected based on the simulated slab configuration shown in Figure 4 5 and conversations with the vendor The assembled test unit (in a supp ort structure) is shown in Figure 4 6 The outside of the unit was wrapped with Teflon tape to minimize light loss (as can be seen in Figure 4 6 ) Several light guide thicknesses were tested to determine which produced the optimal measured performance. The full system simulations indicated that the best performance would be achi eved with 0.7 0 cm thick light guides based on the neutron capture but measurements were also made with 0.5 0 cm and 0.9 0 cm thick sheets

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91 The three light guide thicknesses were measured to establish the impact of the light guide thickness on the efficiency of the system due to changes in light collection. Figure 4 6 Bench top test unit assembled on a support structure with two PMTs and no tapered light guides (photo taken by the author) Measurements were made with a single PMT, and with one PMT on each end of the unit so a simultaneous trigger could be required for a signal to be recorded. The measurements were performed both with and without the use of tapered light guides between the d etector and the PMT(s) The base of the tapered light guides matched the dimensions of the ends of the configured unit (with the 0.7 cm thick plastic sheets ) and were tapered (based on a design selected by Eljen Technology for optimal efficiency) to match the 5.08 cm diameter PMTs. The tapered light guides added length and expense to the test unit, but increased the number of photons detected by the PMT as discussed in Chapter 5 These competing factors were considered during the measurements. The test unit with the tapered light guides attached is shown in Figure 4 7 Due to the visible light sensitive nature of the detectors the measurements were made with the s ystem wrapped in closed cell neoprene in side of a light tight box. Light leaks were eliminated prior to any measurements and the system was allowed a

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92 minimum of 24 hours settling time after an exposure to room light before measurements were performed Figure 4 7 Test unit with a tapered light guide attached (photo taken by the author) Data Acquisition The photomultiplier tubes used to collect the signals were selected for a fast response and high sensitivity to blue an d green wavelengths. The measurements with the test unit were made with negatively biased H 1161 PMTs (manufactured by Hamamatsu) The PMTs were gain matched for the dual PMT measurements. T he signals produced by the PMTs were digitized, to preserve the waveforms. The initial testing utilized a XIA (Hayward, CA) Pixie 500 for the digitization of the pulses [ 52] The trace length was set to 4 s (with a 1 s offset to establish a baseline) to collect the entire digitized neutron pulse The neutron pulse tails extended beyond the 4 s window but the remaining signal was too low to trigger a new pulse and the additional The dig itization rate of the Pixie 500 is 500 MHz, so each bin of the digitized trace was 2 ns in duration All of the traces collected were stored for post processing. The software used for the data collection was IGORPro

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93 V6.2 (WaveMetrics, Lake Oswego, OR) Because the traces were analyzed separately from the data collection the filter capabilities and analysis methods of the Pixie 500 (as applied by IGORPro) were not utilized A lthough the filter settings were not relevant for the trace analysis they can af fect the how the trigger is applied ; therefore the settings were selected to pass as many of the trigger pulses through the filter settings to the output ( produce the closest input and output rates ) as possible The Pixie 500 trigger corresponds to one q uarter of the digitized trace maximum amplitude (for example, if the trigger is set at 25 any pulse amplitude greater than 100 will pass the trigger) in ADC units [53] ; but if the filter rise time is considerably longer than the pulse rise time the trigger response will not be consistent. A low threshold (5 ADC units) was selected for all of the measuremen ts to maximize the recorded signal. A software threshold was set during the post processing to determine the effect of raising the threshold on both the gamma ray and neutron detection efficiency. The Pixie 500 stores the digitized traces in a bu ffer, and when the buffer is full it is written to the output file. The dead time incurred with the digitization process is due to the time required to write the traces. Several buffer options are available with the Pixie 500 All of the measurements w ere performed with a 16/16 (or continuous) buffer. The 16/16 buffer minimizes dead time by storing traces while the buffer is being written out. However, in the software version of IGORPro used for the data collection there are instances where buffers wi ll be written twice; this is a known problem but as of yet is unaddressed. Therefore the double buffer possibility was accounted for (by eliminating identical buffers) in the post processing of the traces.

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94 Pulse Shape Discrimination The digitized trace s were analyzed to distinguish between the signals produced in response to gamma ray s and the s ignals produced in response to neutron s All of the data analysis for this work was performed with M ATLAB (2011b, The MathWorks, Natick, MA) For the initial bench top configuration the PSD was performed with a standard two window technique. The PSD compared the area under the tail of the pulse to the area under the entire pulse ( Figure 4 8 ) The area in the two regions was calculated by integrating the trace over specified regions of interest Figure 4 8 Neutron (a) and gamma ray (b) digitized traces illustrating the regions of charge integration for the PSD methodology applied. The entire pulse was integrated from arrow 1 to arrow 3 and the tail of the pulse from arrow 2 to arrow 3. The integral ratios calculated from the traces were binned in to histograms to determine the ne utron and gamma ray count rates, as shown in Figure 4 9 Note that the data for Figure 4 9 and Figure 4 10 was collected with a neutron ( 252 Cf) source and a gamma ray ( 60 Co) source measured simultaneously. The neutron source was centered above the detector and the gamma ray source was located 10 cm from the

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95 PMT (or 25.56 cm closer to the PMT than the neutron source). The gamma ray source was positioned closer to the PMT to obtain a pproximately equal neutron and gamma ray regions in the PSD histogram. Figure 4 9 Histogram illustrating the charge ratio region from the 60 Co gamma ray traces and the 252 Cf neutron traces. A large separation region and cle ar distinction between the neutron and gamma ray portions of the histogram is imperative for gamma ray discrimination. A standard FOM for the separation between two regions that can be approximated by Gaussian s is calculated by [54] ( Figure 4 10 ) : Equation 4 1

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96 w here S is the distance between the center of the neutron region and the gamma ray region, and is the full width half maximum of each of the regions (as shown in Figure 4 10). The minimum FOM for adequate PSD is 1.27 (as can be calculated by requiring greater than 3 [21] The two window PSD technique is relatively easy to implement and can be performed quickly, but can be ina dequate for data trains with piled up pulses (i.e. distinguishing between a neutron and two piled up gamma rays can be challenging for the two window PSD method). Methods of PSD that rely upon filtering the data through various templates are possible alt ernatives to the two window PSD technique [55] However, those methods were not applied to this data. Figure 4 10 Parameters for a standard FOM calculation illustrating gamma ray and neutron separation.

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97 CHAPTER 5 MEASUREMENT RESULTS The neutron detection efficiency and gamma ray rejection capabilities were measured with the different test unit configurations. The configurations tested are summarized in Table 5 1 The first sets of measurements were performed to compare the neutron detection efficiency and the gamma ray rejec tion capability between the PMMA and WLSP (using the 0.7 cm thick light guides ). The next set of measurements compared the neutron detection efficiency between the 0.5, 0.7 and 0.9 cm thick WLSP sheets. Measurements were then performed with different PMT configurations, and with the tapered light guides. Table 5 1 Test unit measureme nt configuration summary. LG refers to measurements with the tapered light guide (as shown in Figure 4 7 ). Light Guide PMT Configuration PMMA 0.7 cm 1 PMT WLSP 0.5 cm 1 PMT WLSP 0.7 cm 1 PMT WLSP 0.9 cm 1 PMT PMMA 0.7 cm 2 PMTs WLSP 0.5 cm 2 PMTs WLSP 0.7 cm 2 PMTs WLSP 0.9 cm 2 PMTs WLSP 0.7 cm 1 PMT with LG WLSP 0.7 cm 2 PMTs with LG Several different sources were used for the measurements with the test unit The neutron source measurements were performed with 252 Cf ; t wo different 252 Cf sources were used, one with a source strength of 20 3 Ci on December 15, 200 3 (source A) and one with a source strength of 2 1.9 1.3 Ci on October 1, 2009 (source B). The gamma ray measurements were performed with 60 Co and 137 Cs sources. The 60 Co

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98 source had a strength of 9.4 1.4 Ci on June 1, 20 0 3 and the 137 Cs source was 10 1.5 mCi on October 1, 1996 The top of the detector (the top piece of lig ht guide) was 3 .8 cm from the top of the detector holder when the 0.5 cm thick light guides were used The sour ce was raised for the measurements with the thicker light guides to preserve the source to detector distance Neutron Measurements The first set of neutron measurements were made with the 0.7 cm thick PMMA. A single PMT was coupled directly to the end of the detector with a silicon rubber pad. Data were collected with the source located in three different positions (1, 2, and 3 as show n in Figure 5 1 ). The neutron and gamma ray count rates were calculated by integrating the neutron and gamma ray regions of the charge ratio histograms generated with the traces collected for each measurement (as discussed in Chapter 4). The integrated regions, for all the traces, were channel 0 3 00 for the entire trace and channel 15 3 00 for the tail of the trace, corresponding to 0 6 00 ns and 3 0 6 00 ns respe ctively (it should be noted that similar PSD results were obtained with regions extending to 400 ns). The length of the window for the tail pulse was selected based on the width of the gamma ray pulse s As can be seen in Figure 5 2 a comparison of a neutron and gamma ray pulse illustrates that the majority of the gamma ray signal occurs within the first 3 0 ns, therefore, any charge in the region beyond 30 ns will be the result of a neutron. Note that the peak heights have been aligned for this figure, not the trigger location, which accounts for the slight off set in the pulse rise times.

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99 Figure 5 1 Horizontal source positions for the bench top test unit measurements. Figure 5 2 Example gamma ray and neutron traces recoded with the Pixie 500 with peak heights aligned, zoomed in on the x axis to show detail The PMMA measurements were compared to the meas urements for the same configuration built with the 0.7 cm thick WLSP; the histograms obtained from the two systems with the 252 Cf centered on the detector (position 3) are shown in Figure 5 3 Measurements were made with and without lead shielding around the source to minimize the any gamma ray signal. It was found that the gamma ray contribution from the 252 Cf source was negligible even without shielding, as is evide nt in the minimal

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100 signal in the charge ratio histogram below approximately 0.4 (the region where the gamma ray contribution would have been apparent) in Figure 5 3 Figure 5 3 Charge ratio histogram of the traces collected with the 0.7 cm thick WLSP and the 0.7 cm thick PMMA in response to a 252 Cf source centered on the detector. The neutron and gamma ray count rates for the measurements were estimated by integrating over the gamma ray and neutron regions for the charge ratio histograms ( 0 to 0.5 for the gamma ray region and 0.5 to 1 for the neutron region ). A summary of the measu rement results (both the neutron and gamma ray count rates) with the 0.7 cm thick light guides is presented in Table 5 2 Also presented in Table 5 2 are the a bsolute neutron detection efficiency es timates which were calculated for each of the different configurations (the source strength on the dates of the measurements with th e PMMA and the 0.7 cm thick WLSP was 8.0x10 3 1.2x10 3 n/s ) The statistical error s associated with the measurements are shown in all of the tables, but error bars are not included on any o f the figures for clarity (and for most of the histogram regions o f

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101 interest the error associated with each bar is too small to be observed). Note that for the absolute neutron detection efficiency measurements the error was dominated by the source uncertainty The PMMA neutron detection efficiency demonstrated a higher dependence upon source location than the WLSP measurements The superior l ight transmission properties of the WLSP compared to the PMMA produce a system that is less dependent on source position The highest neutron detection efficiency measured w ith the WLSP was with the source in the center location, as the WLSP was able to benefit from the increased neutron interaction area Unlike the WLSP, t he PMMA configuration ha d higher absolute neutron detection efficiency when the source was positioned c loser to the PMT compared to when the source was centered over the detector. The greater neutron detection efficiency dependence on the source position of the PMMA system than the WLSP system is due to greater light attenuation with the PMMA light guides than with the WLSP light guides. Table 5 2 Results from the 252 Cf measurements with the 0.7 cm thick PMMA and WLSP with a single PMT coupled directly to the end of the detector. The source position is given in parenthesis for each of the measurements (corresponding to the source locations marked in Figure 5 1 ) Measurement Configuration Neutron Count Rate (cps) Gamma Ray Count Rate (cps) Absolute Neutron Detection Efficiency PMMA (BG) 1.0 0 0.04 5.3 0 0.09 N/A PMMA 252 Cf (1) 161.2 0.5 22.7 0.2 0.020 0.003 PMMA 252 Cf (2) 126.6 0.5 22.6 0.2 0.016 0.002 PMMA 252 Cf (3) 84.0 0.4 17.8 0.2 0.010 0.002 WLSP (BG) 2.60 0.05 13.5 0.1 N/A WLSP 252 Cf (1) 268.5 0.6 33.0 0.2 0.033 0.005 WLSP 252 Cf (2) 321.6 0.6 36.2 0.2 0.040 0.006 WLSP 252 Cf (3) 264.2 0.5 32.1 0.2 0.033 0.005 The second set of measurements was made with the same detector configurations (0.7 cm thick PMMA and WLSP) and two PMTs (one on each end, both coupled to the

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102 detector surface with a silicon rubber pad) Each PMT was connected to a separate input channel of the Pixie 500 (both set with the same trigger and energy filter settings) T he Pixie 500 was configured such that output traces were recorded only if both PMTs were triggered within 13.33 ns of each other (13.33 ns is the smallest window that can be set for coincidences between channels in the Pixie 500 the user specified coincidence window time is added to a preset (by Igor Pro) processing time of 66 ns) It should be noted that for these measurements coincidence refers to a temporal coincidence between two PMTs, not a temporal coincidence between two neutrons. The coincident measurements slightly decreased the neutron detection efficiency, but resulted in a greater suppression of the gamma ray response, as the lower intens ity gamma ray signal is less likely to be detected by both PMTs than the neutron signal The comparison between the single PMT and the coincident PMT measurements for the PMMA and WLSP detector configurations are shown in Figure 5 4 and Figure 5 5 T he PMMA configuration suffered from a greater reduction in the recorded neutron co unt rate when operated in coincidence mode than did the WLSP configuration. As discussed in Chapter 4 the WLSP has better light transmission than the PMMA, which is also evident in the higher source position dependence of the neutron detection efficiency observed with the PMMA configuration ( Table 5 2 ). Therefore, there is a lower probability of obtaining a signal at both PMTs from a single neutron capture in the 6 L iF/ZnS when the light guide is PMMA than when the light guide is WLSP. The neutron and gamma ray count rates for the coincident measurements for both systems are compared in Table 5 3 Note the suppression of the count rate in the gamma ray regions for the coincident configuration. The results in dicate that a coincident

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103 measurement technique may be a method for suppressi ng the gamma ray count rate from samples that produce a large number of gamma rays. Figure 5 4 Charge ratio histogram of the traces collected with a 252 Cf source in the center of the detector (position 2 ) constructed w ith the 0.7 cm thick PMMA and a single PMT (green) and with two PMTs in coincidence (red). Table 5 3 PMMA and WLSP coincident PMT measurement results with a 252 Cf source centered on the detector (position 2, as marked in Figure 5 1 ). The error reported is statistical. Measurement Configuration Neutron Count Rate (cps) Gamma Ray Count Rate (cps) Absolute Neutron Detection Efficiency PMMA (BG) 0.30 0.02 0.2 0.01 N/A PMMA 252 Cf (2) 36.2 0.3 7.0 0.2 0.0044 0.0006 WLSP (BG) 1.90 0.05 7.4 0.09 N/A WLSP 252 Cf (2) 270.8 2.3 23.6 0.7 0.034 0.005

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104 Figure 5 5 Charge ratio histogram of the traces collected with a 252 Cf source positioned in the center of the detector (position 2 ) constructed with the 0.7 cm thick WLSP and a single PMT ( blue ) and with two PMTs in coincidence (red). A series of comparison measurements was performed with the 0.5 cm 0.7 cm and 0.9 cm thick WLSP sheets The thinner sheets of WLSP have less volume in which the gamma rays can interact, improving the gamma ray rejection capabilities of the system, but the thinner sheets also lose more light decreasing the neutron detection efficiency The WLSP sheets do not suffer from the same rate of light loss as the PMMA sheets, but the th inner sheets still demonstrate lower neutron detection efficiency than the thick er sheets. It should also be noted that the thinner sheets provide less source moderation than the thicker sheets. The lower source moderation results in a lower simulated die away time; but to determine the optimal configuration the decrease in die away time must be balanced against the decrease in neutron detection efficiency. The comparison of the neutron and gamma ray count rates, and the absolute neutron detection efficiencies for the three different WLSP light guide thicknesses is shown in

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105 Table 5 4 The measurements with the 0.9 cm thick WLSP sheets were made at a later date than the measurements with the 0.5 cm and 0.7 cm thick WLSP sheets. Therefore the s ource activity at the time of the 0.9 cm measurements was lower than with the other two WLSP thicknesses (on the dates of the measurements with the 0.5 cm and 0.7 cm thick WLSP the source strength was 8.0x10 3 1.2x10 3 n/s and on the date s of the measureme nts with the 0.9 cm thick WLSP the source strength was 5.5x10 3 8.3x10 2 n/s) The lower source activity for the 0.9 cm WLSP measurements accounts for the similar count rates reported between the 0.7 cm and 0.9 cm WLSP sheets but the higher neutron detec tion efficiency with the 0.9 cm thick WLSP. Table 5 4 Measurement summary for a single PMT coupled directly to the detector with the three different WLSP thicknesses tested. The 252 Cf measurements were with the source centered over the detector (position 2 in Figure 5 1 ) The count rate error reported is statistical the error on the absolute neutron detection efficiency is domina ted by the source uncertainty Measurement Configuration Neutron Count Rate (cps) Gamma Ray Count Rate (cps) Absolute Neutron Detection Efficiency WLSP 0.5 cm BG 3.0 0.06 11.0 0.1 N/A WLSP 0.7 cm BG 2.6 0.05 13.5 0.1 N/A WLSP 0.9 cm BG 7.0 0.15 19.1 0.25 N/A WLSP 0.5 cm 252 Cf 259.6 0.5 30.8 0.2 0.03 2 0.005 WLSP 0.7 cm 252 Cf 321.6 0.6 36.2 0.2 0.04 0 0.006 WLSP 0.9 cm 252 Cf 332.0 1.1 39.2 0.37 0.0 4 5 0.007 The 0.9 cm thick WLSP light guide produced the highest efficiency of the three thickness measured. The measured efficiency with the 0.9 cm thick WLSP light guides was 15% higher than with the 0 .7 cm thick WLSP light guides. The increase in efficiency is due both to the additional neutron moderation and the i mproved light transmission. Therefore, the improvement in the neutron detection efficiency with the 0.9 cm thick WLSP light guides is not expected to increase uniformly as the number of sheets increases and polyethylene is included in the design. The sim ulations with the

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106 entire system predicted an 18% increase in the die away time with the thicker light guides. Thus, although the best performance for the bench top test unit was achieved with the 0.9 cm thick WLSP the 0.7 cm thick WLSP was selected for t he development of the complete bench top unit. The effect of the tapered light guides on the end of the detector (as shown in Figure 4 7 ) was measured with the 0.7 cm thick WLSP. The light guides added a total of 20 cm of length (10 cm each light guide), increasing the overa ll size of the system. T he neutron detection effici ency with the use of light guides was improved by 38 % for a single PMT and 17% for the coincident PMT measurements. The coi ncident PMT signal improvement estimate is conservative T he detector configuration was modified to accommodate the additional len gth of the dual light guides, and a correction was applied to the measurements based on comparison measurements between the two configurations, but the correction was conservatively calculated. Based on these measurements the complete bench top configura tion will be designed with the use of tapered light guides between the detector surface and the PMTs. Gamma Ray Measurements The gamma ray measurements were performed with 60 Co and 137 Cs sources. High intensity gamma ray measurements were made using t he 137 Cs source alone and in conjunction with a 252 Cf neutron source to determine the effect of the gamma ray signal on the neutron detection efficiency Gamma rays generate fewer photons in ZnS than the reaction products from a neutron capture in the 6 Li F therefore the pulses are more likely to be attenuated before being detected by the PMTs. Because of this, t he measurements with the 60 Co source demonstrated a stronger change in the recorded count rate with source position than the neutron source measu rements Due to the

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107 positional sensitivity of the gamma ray measurements requiring a coincident signal between a PMT at each end of the detector significantly attenuated the gamma ray response with both the PMMA and the WLSP light guides The 60 Co measurement results with the 0.7 cm thick PMMA and WLSP are tabulated in Table 5 5 The false neutron identification rate (rate of gamma rays identif ied as neutrons) can be reduced by increasing the threshold, or raising the location of the cut for the neutron region. However, both of those options for decreasing the false neutron identification rate come at the expense of decreasing the neutron detec tion efficiency (as discussed below). Table 5 5 PMMA and WLSP (0.7 cm thick) measurement results with a 2.7 Ci 60 Co gamma ray source. The source position is shown in parenthesis (corresponding to those marked in Figure 5 1 ) and the coincidence measurements are marked with a C. The error reported is statistical. Measurement Configuration Neutron Count Rate (cps) Gamma Ray Count Rate (cps) PMMA (BG) 1.00 0.04 5.30 0.09 PMMA 60 Co (1) 1.8 0 0.04 14.5 1.0 PMMA 60 Co (2) 1.2 0 0.04 7.4 0. 9 PMMA 60 Co (3) 1.1 0 0.03 6.4 0. 8 PMMA C (BG) 0.3 0 0.02 0.2 0 0.0 1 PMMA C 60 Co (3) 0.3 0 0.02 0.2 0 0.0 1 WLSP (BG) 2. 1 0 0.05 6.5 0 0. 08 WLSP 60 Co (1) 3.1 0 0. 0 6 25.6 0. 2 WLSP 60 Co (2) 2.5 0 0. 05 17.7 0. 1 WLSP 60 Co (3) 2.4 0 0. 0 5 16.3 0. 1 Coincidence (BG) 2.1 0 0.05 6.5 0 0.0 8 WLSP C 60 Co (3) 2.1 0 0.05 6. 0 0 0.0 8 High gamma ray count rate measurements were made with a 6.9 mCi 1.03 mCi (on the day of the measurements) 137 Cs source and the 0.7 cm thick PMMA and WLSP light guides to assess the effects of gamma ray pile up on the test unit. Single PMT measurements suffered from pi le up effects (with both the PMMA and WLSP

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108 configurations) at a lower gamma ray flux than the coincident PMT measurements. Two different vertical source positions were used to generate two different incident gamma ray rates. T he percentage of emitted gam ma rays incident upon the surface of the detector for each position was simulated with MCNPX and the simulated percentages were used to estimate the incident gamma ray rate on the detector surface The estimates for the incident gamma ray rates on the de tector surface for the two positions (on the top of the light tight box and at a height of 34.3 cm) were 5.9x10 7 /s and 8.5x10 6 /s respectively It should be noted that a better performance prediction could be obtained with a more uniform gamma ray exp osure. Testing limitations prevented the bench top test unit from being measured under a uniform gamma ray flux ; however, that is a measurement that will be made with the complete bench top unit. As can be seen in Figure 5 6 for the system with PMMA light guides and Figure 5 7 for the system with WLSP light guides there is a high rate of gamma ray mi s identifications when measurements are made with one PMT For the WLSP the gamma rays are piled up to a degree (as shown in Figure 5 7 ) th at the two window PSD technique identifies the majority of the traces as neutrons Example traces from the measurements with the WLSP and a single PMT are shown in Figure 5 8 ; it is evident that the large number of pulses in the trace will produce a tail charge greater than zero even if the triggering pulse was the result of a gamma ray interaction Therefore, the charge ratio histograms will not be an effective tech nique for distinguishing neutron pulses from gamma ray pulses under high count rate conditions However, as was seen with the 60 Co measurements, the gamma ray signal is largely suppressed for both the WLSP and the PMMA in coincidence mode ( Figure 5 9 and Figure 5 10 )

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109 Figure 5 6 PMM A (0.7 cm thick) response with a single PMT to a gamma ray flux of 5.9x10 7 /s (blue) and 8.5x10 6 /s (red) (note that the response from a neutron source would be expected between 0.5 and 1 Qtail/Qtotal) Figure 5 7 WLSP (0.7 cm thick) response with a single PMT to a gamma ray flux of 5.9x10 7 /s (blue) and 8.5x10 6 /s (red) (note that the response from a neutron source would be expected between 0.5 and 1 on the x axis ). Note the difference in the vertical scale between the PMMA and the WLSP.

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110 Figure 5 8 Trace examples showing the system response to a high gamma ray rate Figure 5 9 PMMA (0.7 cm thick) respo nse to a gamma ray flux of 5.9x10 7 /s with a single PMT (blue) and with two PMTs in coincidence (red) (note that the coincident response is too low to be seen on this scale).

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111 Figure 5 10 WLSP (0.7 cm thick) response to a gam ma ray flux of 5.9x10 7 /s with a single PMT (blue) and wit h two PMTs in coincidence (red) In addition to the 137 Cs only measurements data was collected with the detector configurations simultaneously exposed to the 137 Cs source and a 252 Cf source. These measurements were used to determine the PSD capabilities of the detector in the presence of both gamma rays and neutrons. The 252 Cf source used for these measurements was source B (9.4 0.6 Ci on the dates the measurements were performed). A distinct gamma ray and neutron r egion are visible with the PMMA light guide configurations for measurements made with an incident gamma ray flux of 5.9x10 7 /s and one PMT; however, there is clearly a large component of the gamma ray signal in the neutron region ( Figure 5 11 ). The PSD FOM for this configuration is 0.85 less than what is required for basic PSD (which is 1.27) The PSD FOM obtained with an incident gamma ray f lux of 8.5x10 6 /s is 2.08 ; while this level of PSD is adequate for most applications the stringent accuracy requirements for multiplicity

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112 counting require not only a n adequate PSD FOM but also consideration of any potential misidentified gamma rays. A s can be seen in Table 5 6 there is a 5 % higher neutron count rate with a gamma ray flux of 8.5x10 6 /s than what is measured with the same neutron source and no gamma ray source (besides background) and a 226% higher neutron count rate when the incident gamma ray flux is 5.9x10 7 /s The neutron detection rate with two PMTs in coincidence and an incident gamma ray flux of 5.9x10 7 /s and 8.5x10 6 /s is 2 % and 9% lowe r respectively, than without the 137 Cs source present. These changes in the neutron count rate are higher than what would be acceptable for assays requiring 1% measurement accuracy. Assay me asurements with the complete system will require that additional gamma ray suppression techniques be implemented. Figure 5 11 Charge ratio histograms with the 0.7 cm thick PMMA and a single PMT in response to a 252 Cf sour ce (4.0x10 4 n/s) and an incident gamma ray flux of 5.9x10 7 /s (blue) and 8.5x10 6 /s (red).

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113 Figure 5 12 Charge ratio histograms with the 0.7 cm thick PMMA and two PMT s in coincidence in response to a 252 Cf source (4.0x10 4 n/s) and an incident gamma ray flux of 5.9x10 7 /s (blue) and 8.5x10 6 /s (red). Note that the y axis has been scaled down compared to the other PMMA images to show histogram detail. Measurements with the WLSP and the incident gamma ray flux of 5.9x10 7 /s and the 252 Cf neutron source were not performed due to dead time issues with the detector. For this system the gamma ray and neutron measurements were limited to those with an incident gamma ray flux of 8.5x10 6 /s, as shown in Figure 5 13 The PSD FOM with the single PMT was 1.4 Note that the PSD FOM was not calculated for any of the coincident measurements as there was no clear gamma ray region. The measured neutron count rate was 9% higher with the gamma ray source present and a single PMT system than without the gamma ray source. The increase in the neutron count rate is due to gamma ray traces being identified as neutrons. For the coincident PMT measurements the neut ron count rate was 5% lower with the gamma ray source than without. The decrease in the neutron detection efficiency, even with the gamma ray

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114 signal suppressed by the coincident signal requirement, was due to the increase in the dead time of the system pr oduced by the time required to process the incoming signals for the required trigger pattern (a coincident pattern) As with the PMMA configuration the changes in the neutron detection efficiency in the presence of gamma rays are higher than what would b e acceptable for the high precision assay measurements required for material accountancy The performance of the two systems is compared in Table 5 6 It should be noted that the detector electronics suffered from large dead time rates (greater than 50%) for all of these experimental measurements. This is primarily due to the data acquisition process for these experiments, where the signal is digitized, and saved fo r post analysis. For a full scale system, the pulse processing would need to be performed in real time, and therefore the dead time would be much smaller (not saving each digitized pulse). The dead time could be reduced by increasing the trigger threshol d during data acquisition, but that would result in a decrease in the neutron detection efficiency. The required gamma ray discrimination rate must be determined based on the effect on assay precision, and the threshold set accordingly. The gamma ray mis identification rate on the assay precision is considered in Chapter 6.

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115 Figure 5 13 Charge ratio histograms with the 0.7 cm thick WLSP and a single PMT in response to a 252 Cf source (4.0x10 4 n/s) and an incident gamma ray flux of 8.5x10 6 with a single PMT (blue) and with two PMTs in coincidence (red)

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116 Table 5 6 Measurement summary with the 0.7 cm thick PMMA and 0.7 cm thick WLSP. incident gamma ray rate of 5.9x10 7 gamma ray rate of 8.5x10 6 /s. In all cases the source was centered above the dete ctor. The error reported is statistical. Measurement Configuration Neutron Count Rate (cps) Gamma Ray Count Rate (cps) Gamma Ray Discrimination PMMA (BG) 1.0 0.04 3.7 0.0 8 N/A WLSP (BG) 2. 8 0.0 6 13.5 0.1 5 N/A PMMA C (BG) 0.3 0.02 0. 2 0.02 N/A WLSP C (BG ) 2.0 0.06 5.8 0.1 N/A PMMA 137 Cs ( H ) 653.3 7.1 2786.5 14.6 1.1x10 5 1.2x10 7 PMMA 137 Cs ( L ) 31.4 0. 7 352.5 2. 5 3.7x10 6 8.8x10 8 WLSP 137 Cs ( H ) 10721.0 53.0 1459.0 19.6 1.8x10 4 9.0x10 7 WLSP 137 Cs ( L ) 404.0 4.9 2323.0 11.7 4.8x10 5 5.8x10 7 PMMA C 137 Cs ( H ) 0.5 0.09 1.2 0.1 4 8.4x10 9 1.5x10 9 WLSP C 137 Cs ( H ) 584.1 7.9 548.6 7.7 9.8x10 6 1.3x10 7 Gamma Ray and Neutron Configuration abs abs PMMA 252 Cf, 137 Cs ( H ) 1403.7 11.3 2797.2 15.9 **2.26 0.0 2 PMMA 252 Cf, 137 Cs ( L ) 652.0 4.0 396.5 3.1 **1.05 0.0 1 WLSP 252 Cf, 137 Cs ( L ) 1732.0 12.1 2176.2 13.6 **1.09 0.0 1 PMMA C 252 Cf, 137 Cs ( H ) 210.3 2.1 55.7 1.1 **0.91 0.01 PMMA C 252 Cf, 137 Cs ( L ) 224.7 2.1 42.9 0.9 **0.98 0.01 WLSP C 252 Cf, 137 Cs ( L ) 1152.5 8.0 65.0 1.9 **0.95 0.01 PMMA 252 Cf 622.2 3.6 73.2 1.2 *1.5x10 2 1.2x10 4 PMMA C 252 Cf 230.2 2.2 38.5 0.9 *5.7x10 3 6.1x10 5 WLSP 252 Cf 1592.4 7.6 79.7 1.7 *4.0x10 2 2.7x10 4 WLSP C 252 Cf 1217.0 8.3 51.7 1.7 *3.0x10 2 2.6x10 4 Trace Variations In addition to the pulses shown in Figure 5 2 a third class of traces was recorded (with all of the systems measured). These traces had a less definitive shape than the standard neutron pulses and exhibited less decrease in amplitude over the trace length as can be seen in Figure 5 14 (note the similarity to the traces with the piled up gamma rays shown in Figure 5 8 ) The traces were generated in response to the neutron source (they were evident in an intensity proportional to the source strength

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117 when compare d to background measurements) ; however they do n ot appear to be complete traces. The q uantized packets in the absence of a clear neutron envelope illustrated in Figure 5 14 minimize the ability of the dual window PSD technique to separate between the traces generated in response to a neutron and those generated in response to multiple gamma rays. Figure 5 14 Example of the two neutron trace types collected with all of the systems measured. The red trace contains less charge and does not have as well defined shape as the blue trace. Measurements were performed 3 to eliminate vari ations in the light emission of the ZnS over the trace collection period on the shape of the traces recorded A 6 LiF/ZnS sample was excited with a laser and the emission spectrum was measured as a function of time ( over a duration of 3 ms). Figure 5 15 demonstrates that the spectral 3 These measurements were performed by Dr. Wang using EMSL, a national scientific user facility Pacific Northwest National Laboratory.

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118 shape of the ZnS light emission does not change with time after excitation. The uniformity of the emission over time indicates that the PMT response will not be affected regardless of the section of pulse detected, and does not account for the difference in the shape of the recorded traces. Figure 5 15 Emission spectrum of the 6 LiF/ZnS sheets from the time of excitation to 3.0 ms in 0.27 ms steps. The potential effect of the polyester support sheets on the emission spectrum of the ZnS was investigated by measuring the emission spectrum with and without the polyester film present. The 6 LiF/ZnS sheets were excited with a laser at three different wavelengths, both with and without the polyester substrate present. The resulting emission spectra (observed from the same side as excited by the laser) demonstrated a decrease in intensity of the outpu t on the side with the polyester compared to the side

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119 with out the polyester (although the shape of the emission spectra was similar). The decrease was much more pronounced with the shorter excitation wavelengths The difference in the intensity of the em ission spectra between the sample side with polyester and the sample side without polyester, as a function of the excitation wavelength, indicat es the lower intensity of the polyester side emission is primarily due to the attenuation of the exciting laser, not the attenuation of the emission spectrum (as the emission spectrum does not change with the energy of the excitation laser) ( Figure 5 16 ). The emission spectrum of the 6 LiF/ZnS sheets (as reported by Eljen Technology Sweetwater, TX ), as was shown in Figure 4 3 illustrates that the maximum emission occurs at ~450 nm. Theref ore, as the most significant attenuation of the laser occurred when the wavelength was below 350 nm the light generated by the sheets will only be minimally affected by the polyester backing. The elimination of both time variance of the ZnS emission and the effect of the polyester substrate on the wavelengths of interest (the emission wavelengths) indicate that the pulses without the clear neutron structure are due to either the light collection properties of the system or the ZnS emission itself. A CsI scintillator was tested with the Pixie 500 system, and pulses without a distinct neutron envelope were not observed. Therefore, it is unlikely that the electronics are introducing artifacts into the signal.

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120 (a) (b) (c) Figure 5 16 Emission spectra from the 6 LiF/ZnS without the polyester interface (left) and from the polyester coated 6 LiF/ZnS (right) for three diff erent excitation wavelengths: 38 0 nm (a) 342 nm (b) and 3 0 0 nm (c).

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121 Model Validation One of the primary functions of the bench top test unit was to determine the validation correction f actor ( VCF ) for a system with sheets for light guides, not fibers (as was in the IAT system that was used for the initial VCF used in the full system simulatio ns) The VCF for the sheet configuration once determined with the test bench top unit could be applied to the full system simulations to obtain a more accurate performance estimate for each of the potential configurations To calculate the VCF a model of the bench top unit was constructed and the simulated results com pared to the measured results. The measu red neutron detection efficiencies for several configurations were compared to the simulated neutron detection efficiencies producing the VCFs sho wn in Table 5 7 The same simulation methodology as was utilized for the full system simulations was applied to the bench top unit simulations The number of neut ron captures in the 6 LiF was tallied (using a F4 capture tally), but the reaction products were not tracked nor was the light propagation followed down the light guides. The bench top model ( Figure 5 17 ) included the complete bench top system (six sheets of a plastic light guide, and five sheets 6 LiF/ZnS supported on polyester sheets ), the plastic support system, the light tight box and the table upon which the unit was positioned. The rest of the room components were far from the detector and the contributions to the simulated results considered negligible. Each of the three light guide thicknesses measured (0.5 cm, 0.7 cm and 0.9 cm) were simulated.

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122 Figure 5 17 Simulated bench top detector inside the light tight box (top views) and shown with components labeled in the cross section view (bottom). Table 5 7 Validation correction factors for the diffe rent bench top test units measured. All of the VCFs presented are for measurements and simulations with the 252 Cf source centered on the light tight box, the coincident measurements The error reported is dominated by the source unce rtainty. Measurement Configuration VCF IAT Reference System 0.57 0.04 PMMA 0.7 cm 0.42 0.06 PMMA C oin. 0.7 cm 0.1 2 0.02 WLSP 0.5 cm 0.9 8 0.15 WLSP C oin. 0.5 cm 0.78 0.12 WLSP 0.7 cm 1.0 7 0.16 WLSP C oin. 0.7 cm 0. 90 0.14 WLSP 0.9 cm 1. 07 0.17 WLSP C oin. 0.9 cm 0.9 2 0.14 The validation correction factors greater than one indicate that either the chemistry of the 6 LiF/ZnS sheets 6 Li, or gamma rays are being misidentified as neutrons in the measured results As was discussed in Chapter 3 the composition of the 6 LiF/ZnS sheets was simulated based on the vendor supplied 6 LiF/ZnS ratio (1:2) 6 Li atom density, and previously reported binder compositions.

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123 However, the 6 LiF/ZnS sheets used to construct the bench top test unit consisted of a custom proprietary blend. Inaccuracies in the modeled 6 LiF/ZnS composition, and the binder quantity, would clearly impact t he simulated results. Future measurements will be performed to obtain a more accurate estimate of the atom densities in the 6 LiF/ZnS sheets. The current VCFs for the bench top test unit suggest that the simulated results are under predicting the efficiency that can be achieved with the 6 LiF/ZnS sheets manufactured by Eljen Technology The same results (within statistics) were obtained with a lead shielded 252 Cf source which indicates that the discrepancy is not solely due to gamma rays being categorized as neutrons during post analysis PSD. However, the effect of gamma rays on the measured results is considered further in Chapter 6. The VCFs will be recalculated with the complete bench top system; the test unit VCFs indicate that the performance that can be achieved with a 6 LiF/ZnS based multiplicity counter will be better than predicted. Post p rocessing pulse height thresholds can be implemented to improve the gamma ray rejection capabilities of the system. However, the improvement in gamma ray rejection comes at the expense of the neutron detection capability. This can clearly be illustrated by comparing the calculated VCF with the gamma ray rejection capability of the bench top test unit for different post processing pulse height thresholds. A comparison is shown in Figure 5 18 for the 0.7 cm thick WLSP light guide configuration operated in coincidence mode (temporal coincidence between two PMTs)

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124 Figure 5 18 Gamma ray rejection and VCF for different pulse height threshold s applied to the 252 Cf and 137 Cs coincidence measurement s with the 0.7 cm thick WLSP light guides. The necessary gamma ray rejection for high precision assay measurements is considered in Chapter 6. The required gamma ray rejection will determine the appropriate VCF to apply to the full system simulations. Based on the measurement results of t he four systems constructed the highest neutron detection efficiency was achieved with the 0.9 cm thick WLSP. The system constructed with the PMMA produced the best gamma ray discrimination as PMMA does not scintillate in response to gamma rays, unlike WLSP. However, the lower neutron detection efficiency of this system eliminated it as the optimal option for the complete bench top system configuration. The final choice for the complete bench top system, considering the neutron detection efficiency, th e gamma ray rejection capability,

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125 and the simulated die away time, was the 0.7 cm thick WLSP sheets The simulations of the complete system demonstrated an increase in the die away time with the 0.9 cm thick WLSP light guides that would not be compensated for in the FOM by the increase in efficiency if it is not linear. Further, the improvement due to the increased moderation will be diminished with the addition of polyethylene in the final system design.

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126 CHAPTER 6 THEORETICAL CONSIDERATIONS: GAMMA RAY EFFECTS Neutrons and gamma rays can both be emitted by isotopes that decay via fission. The 3 He neutron detectors used in traditional multiplicity counters are sensitive only to neutrons except at high gamma ray doses The lack of gamma ray sensitivity a llows the unknown sample parameters to be extracted based on t he neutron multiplicity moments as was shown in Chapter 2 However, not all of the 3 He alternative detectors considered for use in multiplicity counters are capable of the same level of gamma ray rejection that can be achieved with 3 He. As was seen in Chapter 5 the 6 LiF/ZnS bench top test unit will produce a signal in response to gamma rays. The gamma ray signal can be minimized with a pulse height threshold during the PSD post processing A pulse height threshold will decrease the gamma ray sensitivity and the number of misidentified gamma rays but it will also decrease the neutron detection efficiency, which will affect the statistics on the recorded singles, doubles and triples and thus decrease the accuracy of the measurement. The effect of gamma ray detections on the singles, doubles and triples can be determined by modifying t he equations used to extract the sample parameters such that they account for potential gamma ray contribution s. The change in the calculated assay variables (F, M and are considered here, although the unknown parameters could be any three of the assay variables) f or different gamma ray sensitivities is one of the factors to consider when selecting a pulse heig ht threshold. The gamma ray sensitivity is likely to be low in the detectors selected for use in neutron multiplicity counters, but t he assay precision goal is to calculate the sample mass within 1% in less than 1000 s [5] which could be influenced by even a small

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127 contribution from gamma rays in 3 He alternative based counters T he equations necessary to consider contributions from the neutrons and the gamma rays are shown below Neutron Moments The formulas used to extract the sample parameters from the measured distributions were discussed in Chapter 2 and will be briefly revisited here. The measured foreground and background distributions (f k and b k ) can be related to the unknown sample parameters. The unknown sample parameters can be related to the emitted neutron multiplicity distribution, which when corrected for detector parameters can be used to extract information about the sample being assaye d. For the purposes of these equations all of the moments are expressed in terms of the source event rate, with the inclusion of ( ,n) reactions. The singles, doubles, and triples for a detector that is only sensitive to neutrons were given in Chapte r 2 as [6] : Equation 6 1 Equation 6 2 Equation 6 3 w here sfk = the factorial moment s of the neutrons generated by spontaneous fission event ik = the f actorial moment s of the neutrons generated by an induced fission event F = the spontaneous fission event rate

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128 M = the sample multiplication (which accounts for additional neutrons in the sample due to induced fission) = n = neutron detection efficiency Note that in these equations the substitutions for the factorial moments of the emitted probability distribution have been made, and f d and f t represent the double and triple gate fractions, respectively. However, if gamma rays are also detected (and trigger the shift register) these formulas must be modified to include the gamma ray contributions. The additions to the equations that must be made to account for the correlated gamma ray contributions can be seen by starting with the basic forms for the singles, doubles and triples. The structure of the singles, doubles and triples equations with only neutron detections considered are (in terms of the factorial moments of the emitted neutron probability distributio n, k ) : Equation 6 4 Equation 6 5 Equation 6 6 w here C 1 C 2 and C 3 are simply constants that encompass the source rate, gate fractions, and normalization factors. Each of the equations will have to be modified based on the gamma ray efficiency and the moments of the gamma ray distribution ( k ) as follows:

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129 Equation 6 7 Equation 6 8 Equation 6 9 The above equations include neut ron and gamma ray contributions; howev er, they only account for independent neutron and gamma ray detections. The possibility of detecting a double event that consists of one neutron and one gamma ray, and the possibility of detecting a triple event that consists of two neutrons and one gamma ray or one neutron and two gamma rays must also be considered The joint moment of the distribution of neutron and gamma ray quanta that could produce a detection of one neutron and one gamma ray is represented by j n, The joint moment of the dis tribution of neutron and gamma ray quanta that could produce a detection of two neutrons and one gamma ray is represented by j n,n, ; similarly the joint moment for one neutron and two gamma rays is represented by j n, The n the final equations for D and T will have the form of: Equation 6 10 Equation 6 11 The gamma ray and joint moments have to be expressed in terms of source parameters befor e their effect on the assay results can be determined.

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130 Gamma Ray Moments The factorial moments of the gamma ray distribution can be derived following the same methodology as was used to derive the neutron moments, and are given by Pazsit [56] The source of the terms in the equations can be better illustrated with the use of a diagram, as was shown in Figure 2 3 to Figur e 2 4 for the neutrons. The diagram s ( Figure 6 1 to Figure 6 3 ) are based on the discussion in Oberer [27] but here ( ,n) reactions are also considered. It is assumed that t he g amma rays themselves do not induce additional gamma rays (the gamma ray chains are non multiplying) ; however, gamma rays will be produced as a result of induced fissions along the neutron chain. Therefore, the neutron chains must be followed to account for all of the gamma rays. The gamma ray moments derived by Pazsit [56] are given in terms of source events. If the sample is not comprised of a pure metal (e.g. the sample is an oxide ) a source event could be either spontaneous fission or an ( ,n) reaction. Therefore, as with the neutron moments, the moments of the gamma ray emission probability distribution must be weighted to account for the different source events For the purposes of this work only gamma rays produced as a result of either spontaneous or induced fission are considered. There are other pote ntial sources of gamma rays that are not considered here. One of the potential sources of gamma rays are those released simultaneously with alpha emission, the probability associated with this emission for the isotopes of interest is quite low, and neglec ted in the following equations [57] Gamma rays could also be emitted by the target nucleus if it is left in an excited state after the ( ,n) reaction. This effe ct could be included as a gamma ray emission associated with the neutron generated by the ( ,n) reaction, but is not included in this work Another source of g amma rays that is not accounted for are those emitted

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131 as a result of inelastic neutron scatters [27] ; the equations are currently limited to source events, although scattering is an effect that could be considered. Gamma ray attenuation by the sample itself i s not addressed here but is an additional effect that could be added. The same general notation is used for the gamma ray and joint moments as was used for the moments of the neutron distribution: k = the factorial moment s of the neutrons generated in a sample sfk = the factorial moment s of the neutrons generated by spontaneous fission event s ik = the f actorial moment s of the neutrons generated by induced fission event s sk = the factorial moments of the gamma ray source distribution s f k = the factorial moments of the gamma rays generated by spontaneous fission events i k = the factorial moments of the gamma rays generated by induced fission events S = F + S = the total source event rate F = the spontaneous fission event rate pi = the probability that a neutron induces fission within the sample M = the sample multiplication (which accounts for additional neutrons in the sample due to induced fission) = n = neutron detection efficiency = gamma ray detection efficiency The equation for the first factorial moment of the gamma ray probability distribution for source events is given as (modified from Pazsit [56] ) : Equation 6 12

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132 T he three terms (note that the (1 + ) factor produces two terms) in Equation 6 12 correspond to the three potential sources of single gamma ray s available for detection as illustrated in Figure 6 1 Figure 6 1 Single gamma ray sources for the first factorial moment of the gamma ray probability distribution. The solid lines represent multiplying chains and the dashed lines represent non multiplying chains The gray circles represent induced fissions from which a gamma ray is available for detection ( which is represented with an open circle). The second fact orial moment of the gamma ray probability distribution is: Equation 6 13 The five source terms in Equation 6 13 correspond to the five potential origins of double gamma ray s available for detection illustrated in Figure 6 2

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133 Figure 6 2 Double gamma ray sources for the second factorial moment of the gamma ray probability distribution. The solid lines represent multiplying chains and the dashed lines represent non multiplying lines. The third factorial moment of the gamma ray probability distribution is: Equation 6 14 The eight source terms in Equation 6 14 correspond to the eight potential sources of tripl e gamma ray s available for detection illustrated in Figure 6 3

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134 Figure 6 3 Triple gamma ray sources for the third factorial moment of the gamma ray probability distribution. The solid lines represent multiplying chains and the dashed lines represent non multiplying lines. Joint Distribution s The joint distributions, or the moments for the probability distribution comprised of neutrons and gamma rays are also required to fully account for the potential gamma ray effect The joint moments were derived by Pazsit [30] and Oberer [27] The given joint moments were modified to include the effect of ( ,n) reactions and to be consistently expressed in terms of the source rate. The joint moment of interest for the doubles rate is j n, which represents the moment of the distribution of joint neutron and gamma ray quanta that would make a neutron and a gamma ray available for detection

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135 Equation 6 15 As with the neutron and gamma ray moments each of the terms in Equation 6 15 can be related back to a source event using a diagram. Due to the complexity of the images they are not included here. Two joint moments are required for the triples expression ; one for th e distribution that would make two neutron s and one gamma ray available for detection j nn and one for the distribution that would make one neutron and two gamma ray s available for detection j n Similar to the doubles expression, the origin of each of the terms of the joint moments can be shown in a diagram (not included). Equation 6 16

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1 36 Equation 6 17 Final Formula s T he neutron, gamma ray and joint moments can now be inserted into Equation 6 7 Equation 6 10 and Equation 6 11 to produce equations for the detected and counted singles, doubles and triples as follows: Equation 6 18 Equation 6 19

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137 Equation 6 20

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138 If = 0 in the above equations forms identical to Equation 6 15 to Equation 6 17 will be obtained It should be noted that the formulas for U, D an d T assume that the neutron and gamma ray die away times are the same. The die away time depends on the detector design, but it is unlikely to be the same for neutrons and gamma rays. The effect of different die away times could be considered in future w ork, the gamma ray die away time could be determined with MCNPX simulations of a gamma ray source in the sample chamber of the final design. If > 0 the formulas used to calculate M, F and ( Equation 2 19 Equation 2 21 and Equation 2 22 ) will no longer be valid. The effect on M, F and calculated assuming that = 0 (i.e., the equations assume there are no gamma rays present ), if the singles, doubles and triples include contributions from the correlated gamma ray moments is considered below Assay Affect A detector with > 0 cannot be used to accurately calculate the sample mass if the singles, doubles and triples are assumed to be generated only by neutron detections The effect of the gamma ray efficiency on the calculated mass for different Figure 6 4 for a detector with the same parameters as the simulated 6 LiF/ ZnS based multiplicity counter (a neutron detection efficiency of 43 % and a linear die away time of 8 s) The data for Figure 6 4 was generated by calculating the si ngles, doubles and triples from Equation 6 18 to Equation 6 20 for a range of gamma ray efficiencies and then calculating the mass using Equation 2 21 which assume s = 0. The known mass in Figure 6 4 was the mass used for the calculation of the singles, doubles and triples rates. It should be noted that the calculated values for M and also change when > 0 but those dependencies are not shown here (for more detail see Appendix B)

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139 Figure 6 4 demonstrates that the impact of correlated gamma rays being detected and counted as part of the correlated events cannot only be significan t, but will vary depending on the parameters of the sample being assayed. Figure 6 4 The effect of the gamma ray efficiency on the calculated mass for a 10 g 240 Pu sample with different values of M and if the gamma ray distributions are not accounted for in the calculations for F, M and Note that the values for M and in the legend are the starting values, but as the gamma efficiency changes the calculated values for M and will also change. The PSD criteria appli ed during post processing can be selected to minimize the effect of the gamma ray efficiency. Recall that for this detector system PSD is used to eliminate the gamma ray contribution to the signal. Therefore, gamma ray efficiency is less of a n issue than gamma rays that are misidentified as neutrons. As was shown in Figure 5 18 raising the pulse height threshold will improve the gamma ray rejection (which is th e capability of c oncern for the bench top model). H owever this improvement in gamma ray rejection is accompanied by a decrease in the neutron

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140 detection efficiency. The gamma ray rejection performance goal for the bench top test unit was selected to be b etter than 10 6 Achieving the target gamma ray rejection will depend on the data acquisition parameters, and the post processing thresholds T he initial measurements with gamma ray sources demonstrated that the performance goal could readily be achieved The effect of the correlated gamma ray moments on the calculated mass for the gamma ray rejection levels likely to be achieved with the bench top system was considered by letting equal the gamma ray misidentification factor and is shown in Figure 6 5 Note that in the gamma ray efficiency region shown in Figure 6 5 there is a smaller difference between the actual and calculated mass for a simulation with an > 0 This is due to the fact that for > 0 there is a larger contribution to the singles rate s from the neutron moments than the gamma ray moments ( at low gamma ray efficiencies) which produces a smaller discrepancy in the calculated mass value than with simulation s where = 0. As the gamma ray detection efficiency increases so does the gamma ray contribution to the signal, and the effect of M > 1 will become the more significant contribution to the difference in the actual and calculated mass.

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141 Figure 6 5 Detail of the likely region of gamma ray efficiency of i nterest from Figure 6 4 for the 6 LiF/ZnS based bench top system. The impact of correlated gamma ray s for an efficiency (or for this system a gamma ray misidentification factor ) below 0.2% is relatively low (less than 2% for the simulated scenarios); however, the assay precision goal is to generate a mass estimate within 1% of the actual value in a short measurement time. Initial measurement s with the test unit demonstrated that a gamma ray rejection below 10 5 could be achieved with the unit operated in coincidence mode and PSD applied. For a gamma ray rejection of 10 5 the effect of the gamma ray moments on the calculated mass would be ap proximately 0.009 % (as simulated for a sample with M = 1 and = 0 the a ffect of the source parameters on the results is further considered in Appendix B ) The pulse height threshold necessary to achieve the gamma ray rejection of 10 5 would not have a s ignificant impact on the VCF (and therefore the neutron detection efficiency) as was shown in Figure 5 18 However, the measurements with a gamma ray source used to

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142 d etermine the gamma ray rejection capability were made with an incident gamma ray flux of 5.9 x 10 7 which is similar to the gamma ray flux that would be generated in a 10 mg sample of Pu (depending on the source isotopic composition ) as approximated from T able 3A.2 in Doyle [5] It should be noted that the gamma ray flux estimate does not include any potential shielding in the counter design, or self shielding by th e source itself. The dead time in the electronics used in the measurements reported here to collect the traces needs to be minimized before higher count rate measurements are performed. Measurements will need to be performed to confirm a similar gamma ray rejection can be achieved with the full system and higher count rate sources. A closed form solution for M, F and when the gamma ray distributions are included in the equations for the singles, doubles and triples ( Equation 6 18 Equation 6 19 and Equation 6 20 ) would be non trivial to obtain, and would require solving an equation in the fifth power for the multiplication ( M ) Howe ver, solutions for M, F and can be generated for measured singles, doubles and triples by solving the equations iteratively using a least squares method to compare the measured U D and T to calculated values The least squares method (implemented using a MatLab script) is an efficient means of addressing th e impact of > 0 on a measurement, as less than 1 s is required to compute an an swer. The proposed technique should be applied to data acquired with t he complete bench top system using known sources to determine if an improvement in the accuracy of the calculated mass could be realized The electronic thresholds could be adjusted to produce different gamma ray efficiencies for testing the ability of the modified singles, doubles and triples equations to adequately calculate the

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143 sample parameters. The PSD parameters could also be relaxed to study the effects of the misidentified gamma rays on the assay predictions.

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144 CHAPTER 7 SUMMARY AND FUTURE W ORK The shortage of 3 He has driven an interest in identifying alternatives for neutron detection applications. This research effort explored 3 He free multiplicity counter configurations. The work performed encompassed three separate areas: simulations, m easurements, and theoretical corrections. The simulations compared the performance achieved with 10 B based detectors in a multiplicity counter configuration to a traditional Epithermal Neutron Multiplicity Counter. The simulation methodology applied for the 10 B lined proportional counters included tracking the correlated neutron capture reaction products, a new MCNPX feature. Measurements were performed to validate the simulation methodology. Parallel to this project, simulations to identify the best pe rforming 6 LiF/ZnS multiplicity counter design within the physical constraints were performed. The simulation results showed that the target performance could not be achieved in a practical configuration with the 10 B based detectors. However, the simulate d performance with the final 6 LiF/ZnS model exceeded the Epithermal Neutron Multiplicity Counter capability. Therefore, 6 LiF/ZnS sheets were selected as the technology for use in the construction of a prototype test unit. The test unit demonstrated that a thermal neutron detector could be developed with 6 LiF/ZnS sheets layered with a plastic light guide. The design used the light guides to both transmit light to photomultiplier tubes and thermalize the incident neutrons, which will minimize the amount o f additional moderator required. Two different light guide materials, and three different thicknesses, were tested with several photomultiplier tube configurations. The final configuration selected for the development of a complete bench top system was 0.7 cm thick wave length shifting

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145 plastic light guides layered with 6 LiF/ZnS sheets, and photomultiplier tubes coupled to each end of the detector with tapered light guides. The gamma ray sensitivity of 6 LiF/ZnS is higher than the gamma ray sensitivity of 3 He. Thus, the potential effect of gamma ray detections on the accuracy of a mass estimate was considered. The equations for the singles, doubles and triples were adapted to include the correlated gamma ray an d joint (to account for mixed gamma ray and neutron detections) moments. The variation in the predicted mass was simulated as a function of gamma ray efficiency. Potential options for minimizing error in the calculations were presented. These effects ha ve not previously been considered because of the high level of gamma ray discrimination achievable with 3 He. However, as 3 He replacements are explored, the validity of the assumption that the gamma ray contributions to the measured distributions are negli gible will have to be re evaluated. Based on the results of this research effort a complete bench top system will be built. Measurement results will be compared to simulated values to determine the appropriate validation correction factor for a full sy stem. Future work should consider modifications to the electronics to reduce the dead time produced by the current method of pulse digitization with a XIA Pixie 500 waveform digitizer. Further, more sophisticated methods of pulse shape discrimination wil l have to be implemented when pile up becomes an issue. Different threshold levels should be applied to the post processing analysis of data collected with the complete bench top system to compare the predicted mass values for different gamma ray efficien cies. The mass should be calculated both with and without accounting for the gamma ray moments to verify that

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146 the least squares solution is valid for improving assay accuracy in systems that respond to gamma rays, as well as neutrons. Additional future work should examine the effects of the assumptions in the equations for the gamma ray moments that were included in this research effort. The gamma rays from inelastic neutron scatters, gamma rays released by nuclei excited by alpha particles, and gamma r ays emitted with the alpha particles, should all be considered. Another modification that should be made to the equations is to account for the different die away times for the neutrons and gamma rays in a complete system. Traditional shift register ele ctronics cannot process the Pixie 500 pulses. Furthermore, gamma ray rejection based on post processing pulse shape discrimination means that a virtual shift register will have to be utilized for multiplicity measurements. A MatLab virtual list mode shi ft register was developed (Appendix C) and tested compared to traditional shift register outputs, using data collected with a 3 He system. The virtual shift register will have to be adapted for the 6 LiF/ZnS bench top system outputs, but is expected to prov ide an adequate method for obtaining multiplicity data. While there are still significant measurements to be made with this technology, the initial results demonstrate that a 6 LiF/ZnS based system has the potential to be a viable near term alternative to 3 He for use in neutron multiplicity counters.

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147 APPENDIX A DERIVATION OF EQUATIONS The derivations for the equations used in this work [23] [6] are shown below. Probability Generating Functions An example of a probability generating function ( PGF ) and how it can be used to obtain an expectation value, is considered here for the pro babilities associated with a fair die. The values (x) that can be obtained with a six sided die are: Z = 1, 2, 3, 4, 5, 6 where Z is the variable (the number on the die). Then the probability of generating any one of these variables is P(Z=x) = 1/6 (wh ere x is any one of the possible values). A PGF that is a polynomial with coefficients that are the probabilities of the different outcomes can be identified as: The first term of the polynomial represents the probability of obta ining a 0 (note that the polynomial could be extended beyond u 6 but all of the terms would be equal to 0). Note that the probabilities for any discrete distribution could be used for this example. So a general PGF is given by : Equ ation A 1 Consider again the PGF for a fair die, it is apparent that and

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148 In general Equation A 2 The first derivative of f(u) can be taken, and the result is: If the derivative is evaluated at u=1 then: The expectation value of a function is given by: Equation A 3 So Which is the definition of the first factorial moment of P(Z). The second derivative evaluated at u=1 is to the second factorial moment, or the variance, and so on. The general expression for a factorial moment is given by: Equation A 4 The second property of PGF required to develop an expression for the emitted neutron probability distribution is as follows. Consider the PGF g i (u) for u with the conditional probability P(x,i), which is the probability distribution of obtaining the value x

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149 under the condition i. Then let Q i be the probability of obtaining the condition i, the PGF for x (without condition i) is given by: Equation A 5 because Emitted Neutron Distribution Derivation The detected distribution can be derived from the emitted neutron probability distribution as follows. The number of neutrons that escape the sample must be determined before the detected distribution can be derived. Let R(n) be the probability that n neutrons leave the system for one source event; this expression is the probability that n neutrons are generated by a source event weighted to account for the number that escape and are available for detection. The PGF for the distr ibution R(n) can be defined as: Equation A 6 The expression for the probability distribution of neutr ons generated by a source event, including neutrons produced by ( ,n) reactions is : Equation A 7 Where F = the fission rate, from which neutrons are emitted with a probability distribution q sp ( ) S = the rate of ( ,n) reactions, from which only one neutron can be obtained, and S = the source rate = F + S The required distribution is that for the neutrons which escape the sample and are available for detection Neutrons are

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150 inde pendent and indistinguishable, therefore the neutrons that escape per source event (which generates n neutrons) are simply the percentage that escape s per neutron, raised to the n th power. The expression to describe the number of neutrons that escape the system for one starting neutron is given as follows The neutrons that are captured prior to escaping the sample (and are not available for detection) will induce fission, given by a probability, p i Given that p i is the probability a neutron induces a fission the probability that the neutron escapes (without inducing a fission), and can be detected is given by (1 p i ) Whe n a neutron induces a fission it will generate n neutrons with a probability p i q i (n) where q i (n) is the probability of obtaining n neutrons through induced fission. Let r(n) be the probability that n neutrons leave the system because of one source neutron then a PGF for the number of neutrons leaving the system based on a single source neutron can be defined as: Equation A 8 If there is more than one neutron in the system then the PGF is h n (u) which is equal to h 1 (u) n because neutrons are assumed to be independent and indistinguishable. If multiplication is included: then the PGF h 1 (u) is given by : Equation A 9

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151 Where and is the PGF f or the number of neutrons emitted by an induced fission event f i (h 1 (u)) under the second p roperty of PGFs given above The expression for the number of neutrons that escape the sample because of one starting neutron can now be used to obtain an expression for H(u) (the PGF for the probability distribution of neutrons that leave the system due to one source event). The probability of n neutrons leaving the source is given by P( ) (the p robability of neutrons being emitted by a source event) multiplied by the sum of all r(n) over n (the probability that n neutrons leave the system per source neutron) to the th power Equation A 10 The derivative of this point generating function is the first factorial moment of the neutron distribution that escapes the sample, which is what is required to determine the detected distribution. Substituting Equation A 7 for P( ) produces: The second component of the expression is the PGF for the number of neutrons that are available for detection due to a spontaneous fission event, f s f [h 1 (u)] Then, The derivative of H(u) is:

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152 (from the first property of PGFs given above ) And the derivative of h 1 (u) can be calculated from Equation A 9 : Equation A 11 Then Equation A 12 which is the definition of M. Now 1 can be expressed as: S, F and S are not all known parameters, so 1 is expressed in terms of a source parameter that can be calculated with multiplicity analysis which is given by: Equation A 13 Then Equation A 14 Note that th e first factorial moment used in Ensslin et al. [ 6] is given for the neutrons emitted per spontaneous fission, not per source event, so there is no source term normalization and The higher order derivatives of H(u) can be taken to obtain the second and third factorial moments.

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153 Detected Neutron Distribution Derivation The factorial moments of the emitted neutron distribution are not the same as the detected and counted factorial moments. The emitted distributions must be corrected for the detector efficiency and the gate fractions (the components of the emitted distributions that are present in the counting intervals). Unlike the derivation of the factorial moments of the emitted distribution, a closed form solut ion for the factorial moments of the detected distribution can be derived (in terms of the factorial moments of the emitted distribution) without the use of PGFs. The detected distribution can be expressed in terms of the emitted neutron distribution cor rected for efficiency, as given in Ensslin et al. [6] : Equation A 15 where is the binomial coefficient and is given by The total number of neutrons counted will depend not only on the detected distribution, but also on the number of detected neutrons that are within the counting Where f(t) is the detector response function given in Bohnel [22] for an event that occurs at time t as The probability that one of the remaining neutrons is captured in the window from the pre delay (PD) to the end of the gate (G) is given by:

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154 Equation A 16 If you look over all time, the probability of obtaining a trigger and counting j additional neutrons is: Equation A 17 So the total probability of counting j neutrons of the detected distribution in a gate after a trigger is given by: Equation A 18 Where Z represents a normalization constan t. The factorial moments of the distribution r(j) are the factorial moments of the correlated detected distribution that are measured and counted If the factorial moments of r(j) are related back to the sample parameters they can be used to determine the unknown sample information. This can be done by recognizing that the measu red singles rate is equal to the zeroth correlated moment times the total trigger rate, the doubles are equal to the first moment times the trigger rate, and so on. By definition, the first factorial moment of a probability distribution must equal one, w hich can be used to determine Z As given in Equation A 4 the factorial moments of a probability distribution are given by:

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155 so The binomial theorem can be applied to the terms dependent on j which yields: =1 Then the integral of f(t) over the given limits is 1, so Therefore via proof by induction ( shown below ) the limits of the summation can be changed as follows: then and Equation A 19 ( Relationship A, shown below) then Relationship A (proof): Let =3, then

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156 Applying Relationship A and the binomial theorem allows the first factorial moment to be derived as follows: Through a change of limits (shown valid with a proof by induction such as the example shown below ) the terms dependent upon j can be grouped, and Relationship A applied. Then, The integral of the terms dependent upon t can be move d outside of the summation, the summation limits can be changed (the change is shown valid with a proof by induction such as the example shown below ) and the terms within the summation grouped via dependence so that: The second summa tion is the variance of a distribution, and equal to:

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157 2 and l=n 2, then 2 x 1 So then, Earlier n =2 was stated, so then This is the first moment of the measured distribution (note that similar steps can be used to obtain r 2 ). Solving the integrals yields the gate fractions, and then r k can be used in the equations for the singles, doubles and triples to relate the measured parameters to the source parameters. Equation A 20 Equation A 21

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158 Equation A 22 Equation A 23 Equation A 24 Where S the source rate The substitution for r 1 and r 2 can be made which produces the following expressions : Substitution for v 1 v 2 and v 3 can be made to produce expressions in terms of F, M, and Proof by Induction for Change of Limits (Example) For a given distribution defined as: Demonstrate that the limits can be changed as follows: Let then for M = 0:

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159 Now let then for M = 0: Now let M = M + 1: is not allowed therefore So for M = M + 1 S M+1 M+1 Therefore the change of limits will not change the value of the summation.

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160 APPENDIX B SAMPLE PARAMETER EFFECT ON THE CALCULATED MASS The influence of the individual sample parameters on the predicted mass was examined through a set of simulations. The three sample parameters assumed to be unknown for these considerations were M, and F. The M and variables were individually held co nstant while the other variable and F were allowed to vary T he difference between the known sample mass and the calculated sample mass was calculated with each of the scenarios for different gamma ray efficiencies. The calculations were performed with M atLab using the equations from Chapter 6. The effect of not allowing M to vary on the difference between the actual sample mass and the simulated mass is shown in Figure B 1. Figure B 2 shows the effect of holding constant on the difference between th e actual and simulated mass. The figures demonstrate that a larger discrepancy is produced if M is not allowed to vary, which is consistent with the results shown in Chapter 6. The multiplication has a larger effect on the gamma ray contributions as the gamma ray efficiency increases than Therefore, an inaccurate assumption for M has a larger impact on the calculated mass value. Simulations with additional values for M and could be performed to see how the variation in the calculated mass is affect ed.

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161 Figure B 1 The change in the calculated mass if M is held constant (M=1) and alpha ( ) and the gamma ray efficiency ( ) are varied.

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162 Figure B 2 The change in the calculated mass if alpha ( ) is held constant ( =0) and the Multiplication (M) and the gamma ray efficiency ( ) are allowed to vary.

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163 APPENDIX C VIRTUAL LIST MODE SHIFT REGISTER Traditional shift registers group the perturbations in the pulse train that arrive at the shif t register into multiplicities. When each perturbation in the pulse train arrives at the trigger the number of signals in the counter gate are grouped and the appropriate multiplicity scaler increments by one. There is a second trigger at a time after th e first trigger that is long when compared to the die away time (the delay time is typically about 4 s ). When one of the perturbations in the pulse train arrives at the second trigger the number of pulses that are currently in the counter window are grou ped and the appropriate accidental scaler is incremented by one. The multiplicity distributions are then grouped to calculate the foreground and background factorial moments of the distribution. Figure C 1 Shift register d iagram. Example calculations for the singles, doubles and triples from data obtained with 12 3 He tubes arranged in 4 polyethylene blocks (3 tubes per block) and a JSR shift register operated in 2150 mode are shown in Table C 1

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164 Table C 1 Example distribution from a JSR shift register in multiplicity mode and the corresponding factorial moments and singles, doubles and triples P( ) R+A A 0 3895 457 1 1 1745 1338 2 575 38 9 3 150 8 7 4 3 3 1 8 5 6 3 6 1 0.4 7 0 0 8 0 0 0 1 1 1 0.55 0.39 2 0.41 0.25 Singles =U= sum(A) 6406 Doubles 1(R+A) 1(A) ) 1051 Triples =U 2 (R+A) 2(A) 2* 1(A) *( 1(R+A) 1(A) ))/2 105 The factorial moments were calculated with the formula: Note that the distributions were normalized for the factorial moment calculations. Digitized pulse trains that require the application of PSD techniques cannot be fed directly into a traditional shift register. A list mode shift register, which can be used to group the time stamped neutron pulses must be used. A list mode shift registe r (built in MatLab) was structured as follows to group individually time stamped pulses into multiplicity distributions. A predelay, gate window, and delay time were selected. The time stamps with each pulse were fed into the alg orithm. The shift regis ter was constructed to be forward looking, each pulse activated a window to open after the predelay and the number of p ulses with time stamps less than the trigger pulse time plus the length of the window were grouped and the appropriate R+A multiplicity w as

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165 incremented by one. Every time a gate opened a second gate was opened after the delay time and the number of pulses with time stamps within the second gate were grouped and the appropriate A multiplicity was incremented by one. An example distribution from data collected with the same 3 He system as was used to collect the data shown in Table C 1 is shown in Table C 2 for the distribution generated with the list mode shift register. The singles, doubles and triples calculated with this data are also shown. T he results, below, were found to be in good agr eement to the results calculated with a traditional shift register for the same detector. Table C 2 Probability distributions generated with a virtual shift register from the data collected in list mode and the correspondi ng factorial moments and singles, doubles and triples. P( ) R+A A 0 389 6 4 685 1 1774 1 202 2 5 74 3 41 3 1 43 7 7 4 3 0 1 5 5 5 3 6 1 0.3 7 0 0 8 0 0 0 1 1 1 0.55 0.39 2 0.41 0.25 Singles=U= sum(A) 6 323 1(R+A) 1(A) ) 1 310 2 (R+A) 2(A) 2* 1(A) *( 1(R+A) 1(A) ))/2 101 The difference in the singles, doubles and triples calculated with the distributions from the traditional shift register and the list mode shift register are due to the slightly dead time present in the electronics used to produce the time stamped pulses for use in

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166 the list mode shif t register that affects the distributions. The discrepancy was not of concern for this analysis, but could be minimized with the use of electronics with less dead time and by altering the gate locations in the virtual shift register.

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167 LIST OF REFERENCES [1] F.M. Khan, The Physics of Radiation Therapy Lippincott Williams & Wilkins, 2003. [2] J.T. Bushberg, J.A. Seibert, E. M. Leidholdt Jr. and J.M. Boone, The Essential Physics of Medical Imaging, 2 nd Edition, Lippincott Williams & Wilkins, 2002. [3] F. H. Attix, Introduction to Radiological Physics and Radiation Dosimetry, John Wiley & Sons, Inc., 1986. [4] G. F. Knoll, Radiation Detection and Measurement 3 rd Edition, John Wiley & Sons, Inc., 2000. [5] J. E. Doyle, Nuclear Safeguards, Security and Nonproliferation Elsevier, 2008. [6] N. Ensslin, W.C. Harker, M.S. Krick, D.G. Langner, M.M. Pickrell and J.E. Stewart, Application Guide to Neutron Multiplicity Counting, Los Alamos National Laboratory Report LA 13422 M (1998) [7] J.P. Lestone, M.E. Abhold, J. Halbig, H.O. Men love, P. Polk, P.M. Rinard, J. Sprinkle, P. Staples and R. Holbrooks, An Underwater Instrument for Breeder Reactor Spent Fuel Assemblies, Los Alamos National Laboratory Report LA UR 98 1588 (1998). [8] Safeguards Techniques and Equipment 2003 Edition, IAEA, 20 03. [9] R. D. Evans, The Atomic Nucleus, McGraw Hill, Inc., 1955 [10] J. E. Turner, Atoms, Radiation, and Radiation Protection 2 nd Edition John Wiley & Sons, Inc., 1995 [11] R. T. Kouzes, The 3 He Supply Problem, Pacific Northwest National Laboratory Report PNNL SA 18388 (2009). [12] E.R. Siciliano, J.L. Rogers, J.E. Schweppe, A.T. Lintereur and R.T. Kouzes, Uranium Neutron Coincidence Collar Model Utilizing 3 He, Pacific Northwest National Laboratory PNNL 21581 (2012). [13] J.H. Ely, E.R. Siciliano and M. T. Swinhoe, Alternatives to Helium 3 for Neutron Multiplicity Detectors, Proceedings of the 52 nd Annual Meeting of the Institute of Nuclear Materials Management, July 17 21 2011, Palm Springs, California, USA. Paper 603. [14] D.S. McGregor, S.M. Vernon, H.K. Gersch, S.M. Markham, S.J. Wojtczuk and D.K. Wehe, IEEE Trans. Nucl. Sci. 47 (2000) 1364. [15] J.F. Ziegler and J.P. Biersack, SRIM 2013 Code (IBM Company, 2013).

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172 BIOGRAPHICAL SKETCH Azaree Lintereur rec hysics from the University of Wisconsin Stevens Point and her m hysics from the University of Florida r her m in the exploration of BiI 3 for room temperature gamma ray spectroscopy, culminating in the m T h eo r e t i c al Room T em p e r atu r e G a mm a Ray S p e c t r o sc o py A b i li ty of B i s mu t h Tr i I o d i de performed the research for her doctorate at Pacifi c Northwest National Laboratory, where she has worked on projects involving the identification of 3 He alternative thermal neutron detectors. Azaree has presented her research at the IEEE Nuclear Science Symposium, SPIE Hard X Ray, Gamma Ray, and Neutron Detector Physics Conference the IEEE Symposium on Radiation Measurements and Applications, and the Annual Meeting of the Institute of Nuclear Materi al Management.