by azaree t. lintereur
TRANSCRIPT
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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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© 2013 Azaree T. Lintereur
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For Angel, who taught me the impossible can be achieved
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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,
answered questions and suggested ideas, and even though I can’t name everyone
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. Edward
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 this process;
thank 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 competed 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 always be the first veterinarian I call …no matter where I live. I must also
thank my family, in 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, so I would like to
acknowledge that this project was supported by the United States Department of
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Energy NNSA, Office of Nonproliferation and Verification Research and Development
(NA-22). I am also grateful to the Next Generation Safeguards Initiative, Office 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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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 Alternatives .............................................................................................. 26
Objectives of this Work ........................................................................................... 30
2 MULTIPLICITY COUNTERS .................................................................................. 31
Principles of Operation............................................................................................ 31 Multiplicity Counter Designs .................................................................................... 43
3 COUNTER MODEL AND SIMULATIONS ............................................................... 51
MCNPX Simulation Methodology ............................................................................ 52 ENMC Template ..................................................................................................... 55
Boron-10 Based Detector Simulations .................................................................... 61 10B-Lined Plate Configuration ................................................................................. 71 6LiF/ZnS Based Detector Simulations ..................................................................... 72 Model Validation ..................................................................................................... 73 Performance Comparison ....................................................................................... 79
4 BENCH-TOP SYSTEM DESIGN ............................................................................ 83
6LiF/ZnS Physics..................................................................................................... 83 Light Transmission .................................................................................................. 85 Configuration .......................................................................................................... 89
Data Acquisition ...................................................................................................... 92 Pulse Shape Discrimination .................................................................................... 94
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5 MEASUREMENT RESULTS .................................................................................. 97
Neutron Measurements .......................................................................................... 98 Gamma Ray Measurements ................................................................................. 106
Trace Variations .................................................................................................... 116 Model Validation ................................................................................................... 121
6 THEORETICAL CONSIDERATIONS: GAMMA RAY EFFECTS .......................... 126
Neutron Moments ................................................................................................. 127 Gamma Ray Moments .......................................................................................... 130
Joint Distributions ................................................................................................. 134 Final Formulas ...................................................................................................... 136
Assay Affect .......................................................................................................... 138
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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LIST OF TABLES
Table page 1-1 Neutron capture properties for select materials. ................................................. 26
2-1 Spontaneous fission and (α,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 10B atoms in a system designed with BF3 filled proportional counters as 3He atoms present in the ENMC. .............................................................................. 64
3-2 Tube diameter variations and the required number to achieve the same number of 10B atoms as 3He atoms in the ENMC, assuming a lining thickness of 2.5 µm. ........................................................................................................... 67
5-1 Test unit measurement configuration summary.. ................................................ 97
5-2 Results from the 252Cf 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 252Cf source centered on the detector. .................................................................................. 103
5-4 Measurement summary for a single PMT coupled directly to the detector with the three different WLSP thicknesses tested. ................................................... 105
5-5 PMMA and WLSP (0.7-cm thick) measurement results with a 2.7 µCi 60Co gamma ray source. ........................................................................................... 107
5-6 Measurement summary with the 0.7-cm thick 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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LIST OF FIGURES
Figure page 1-1 Helium-3 neutron reaction cross section. ........................................................... 23
2-1 Neutron multiplicity distribution for the spontaneous fission of 252Cf and 240Pu... 32
2-2 Neutron multiplicity distribution for the spontaneous fission of 240Pu and the induced fission of 239Pu. ..................................................................................... 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 the 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 effective 240Pu (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 6LiF/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 3He alternative configurations. .................................................................................................... 56
3-3 Example simulated spectrum from a 3He filled proportional counter and a 10B-lined proportional counter. .................................................................................. 59
3-4 Die-away time fit for the baseline 3He system. ................................................... 61
3-5 The original ENMC footprint, with 121 2.54-cm diameter 3He tubes, compared to the final BF3 system footprint, with 155 5.08-cm diameter BF3 tubes. .................................................................................................................. 64
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3-6 The range of alpha particles in several possible compositions of the lining for 10B-lined proportional counters, and the range of the 7Li 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 10B-lined proportional counter configurations. .................................................................................................... 69
3-9 Surface contour of the FOM space mapped with the simulated 10B-lined proportional counter configurations. ................................................................... 70
3-10 The original ENMC footprint, with 121 2.54-cm diameter 3He tubes compared to the final 10B-lined system footprint, with 4725 0.40-cm diameter 10B-lined tubes. .................................................................................................................. 71
3-11 The original ENMC footprint, with 121 2.54-cm diameter 3He tubes compared to the final 6LiF/ZnS system footprint, with 20 6LiF/ZnS screens. ....................... 73
3-12 Model and measurement configuration for the 10B-lined proportional counter model validation. ................................................................................................. 74
3-13 The neutron capture efficiency and counting efficiency as a function of 10B lining thickness. .................................................................................................. 76
3-14 Measured pulse-height spectrum obtained with a 252Cf source located 25 cm from a 10B-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 10B-lined proportional counters. ............... 80
3-17 Final FOM comparison for the 3He alternative multiplicity counter configurations shown with the ENMC and the PCMC. ........................................ 82
4-1 Magnified (50x) view of a section of a 6LiF/ZnS sheet. ....................................... 84
4-2 The WLSP and PMMA sheets used for the bench-top test system. ................... 86
4-3 Emission Spectrum for the 6LiF/ZnS screens and the absorption and emission spectra for the WLSP. ......................................................................... 87
4-4 Refracted light between two media. .................................................................... 89
4-5 6LiF/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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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 60Co gamma ray traces and the 252Cf 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 252Cf source. .............................. 100
5-4 Charge ratio histogram of the traces collected with a 252Cf 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 252Cf source positioned in the center of the detector constructed with the 0.7-cm thick WLSP. ............. 104
5-6 PMMA response with a single PMT to a gamma ray flux of 5.9x107 γ/s and 8.5x106 γ/s. ....................................................................................................... 109
5-7 WLSP response with a single PMT to a gamma ray flux of 5.9x107 γ/s and 8.5x106 γ/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 5.9x107 γ/s with a single PMT and with two PMTs in coincidence. .......................................................................... 110
5-10 WLSP response to a gamma ray flux of 5.9x107 γ/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 252Cf 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 252Cf 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 252Cf source and an incident gamma ray flux. ............................ 115
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5-14 Example of the two neutron trace types collected with all of the systems measured.......................................................................................................... 117
5-15 Emission spectrum of the 6LiF/ZnS sheets from the time of excitation to 3.0 ms. .................................................................................................................... 118
5-16 Emission spectra from the 6LiF/ZnS without the polyester interface and from the polyester coated 6LiF/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 252Cf and 137Cs 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 240Pu sample with different values of M and α if the gamma ray distributions are not accounted for in the calculations for F, M and α. .................................. 139
6-5 Detail of the likely region of gamma ray efficiency of interest from Figure 6-4 for the 6LiF/ZnS based bench-top system......................................................... 141
B-1 The change in the calculated mass if M is held constant (M=1) and alpha (α) and the gamma ray efficiency (εγ) are varied. ................................................... 161
B-2 The change in the calculated mass if alpha (α) is held constant (α=0) and the Multiplication (M) and the gamma ray efficiency (εγ) are allowed to vary. ......... 162
C-1 Shift register diagram. ...................................................................................... 163
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LIST OF ABBREVIATIONS
ANMC Alternative Neutron Multiplicity Counter
BF3 Boron Triflouride
252Cf Californium-252
137Cs Cesium-137
60Co Cobalt-60
DA Destructive analysis
τ Die-away time
eV Electron volt
ENMC Epithermal Neutron Multiplicity Counter
FOM Figure-of-merit
3He Helium-3
HEU Highly enriched uranium
IAEA International Atomic Energy Agency
6LiF/ZnS Lithium-6 fluoride zinc sulfide
LANL Los Alamos National Laboratory
LEU Low enriched uranium
MOX Mixed oxide fuel
ε Neutron detection efficiency
NMC Neutron multiplicity counter
NDA Nondestructive analysis
PMT Photomultiplier tubes
Pu Plutonium
PFPF Plutonium Fuel and Production Facility
PMMA Polymethly Methacrylate
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PGF Probability generating function
PH Pulse height (F8) tally
PSD Pulse shape discrimination
PCMC Pyrochemical Neutron Multiplicity Counter
U Uranium
VCF Validation correction factor
WLSP Wave-length shifting plastic
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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 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 3He has 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
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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.
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CHAPTER 1 INTRODUCTION
Radiation detection is the measurement of the quanta emitted by a radionuclide or
radiation producing sources. 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 quantification. The fundamentals of
radiation detection apply to all of these applications; this work will focus on radiation
detection for sample 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 ionize
an atom, although it can deposit energy in matter in the form of heat. Ionizing radiation,
for energies of interest to nuclear radiation, can be placed into two general categories,
as defined by the International Commission on Radiation Units and Measurements
(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 not 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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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 titration techniques [5]. Non-
destructive analysis methods do not affect the sample. Nondestructive gamma ray
measurements are often used to identify the presence of a gamma ray source, or verify
the isotopic composition of a sample. Gamma rays can be shielded with materials that
have a high density and a large atomic number (such as lead). Samples can also “self-
shield,” which limits the region of the sample that can be effectively assayed through
gamma ray measurements to the outer layer of the sample.
Neutron 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 detection 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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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
detected). 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. (α,n) reactions on low Z materials (α) 4. neutron detection efficiency 5. variation in spatial detection efficiency (sZ) 6. variation in detection efficiency with energy (sE) 7. system die-away time – time from neutron emission to detection (τ) 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 measurements 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 coincidence 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 allow 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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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 counting statistics.
Nondestructive 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 and forms that are
assayed, which requires 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 plants, 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 characterized. Low 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
“active” systems). Fuel assembly assays at fuel fabrication plants are performed to
verify the fuel isotopics. Irradiated fuel measurements are performed to assay the
assemblies in spent fuel storage facilities [7]. An example of a measurement system
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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Savannah River Site (Georgia, USA). This counter measures the 235U 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
Member 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 independent, and so prior knowledge of the
sample cannot be assumed. Resultantly, the IAEA uses a variety of coincidence and
multiplicity 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 fundamental operation of all the counters relies upon basic
neutron detection principles.
Neutron Detection Basics
Free neutrons are generated via fission (spontaneous or induced) and nuclear
reactions (photoneutron, (α,n) reactions, and accelerated charged particle
reactions[(e.g. deuteron-deuteron]). Neutron interactions occur primarily 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, their electromagnetic interactions with the
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orbital electrons of an atom are negligible (the spin of a neutron means that there is an
internal non-zero charge distribution, which will cause an extremely small
electromagnetic force with electrons). Therefore, neutron detection relies on the
detection of the charged particles produced 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
recoil nuclei (produced by neutron scatter). The secondary radiation produced by
neutron interactions is ionizing, and will produce charge that can be detected, allowing
for the (indirect) detection of the neutrons. It should be noted that the charge produced
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 that 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
captured. The neutron will impart some of its energy to the nucleus off which it scatters,
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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.
Materials that have a large neutron cross section may have non-negligible gamma
ray interaction cross-sections. A gamma ray interaction can lead to ionization in the
detector, which will produce a signal that may be detected in the same manner as a
signal produced in response to a neutron interaction. Therefore, if the gamma ray
interaction cross section is not negligible, the gamma rays must be discriminated from
the response generated by a neutron detector (to prevent gamma rays from being
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misidentified as neutrons). The materials sought for neutron detection 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 and
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), large Q-value, gamma ray insensitivity
and proportional gas amplification characteristics. The 3He 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 3He 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 3He gas is due to the ionization of the 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 current 3He 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
3He available for neutron detection applications. The demand for 3He has increased
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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 3He production, but none of them are currently utilized.
The CANada Deuterium Uranium (CANDU) reactors produce tritium, but it is not
harvested for 3He recovery at this time. Due to the 12.3 year half-life of tritium, there is
a delay between the start of tritium harvest and the production of 3He; therefore there
will not be a near-term supply from this source even if it becomes available. There is
also the potential to obtain 3He 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 collected [11].
The remaining 3He is being rationed, making it prohibitively expensive for the
majority of detection uses. Thus, alternative thermal neutron detection technologies 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
currently designed with 3He filled proportional counters for which alternative
configurations are being researched. The specialized nature of the measurements
performed with coincidence and multiplicity counters require high performance from the
neutron detectors 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.
26
The goal of this work is to identify a 3He-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 commercially available near-term alternatives to 3He for thermal neutron
detection are detectors developed with 10B and 6Li. Both of these materials have large
cross sections for thermal neutron capture, and high Q-values, as shown in Table 1-1,
with the 3He values included as a reference point. The Q-value is divided between the
reaction products according to the ratio of their masses. There are two reaction
possibilities for neutron capture by 10B, one where the 7Li nucleus goes directly to the
ground state (6% of the reactions), and one where the 7Li nucleus is produced in its first
excited state (94% of the reactions). The Q-value for both reactions 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)
3He 5330
0.764
10B 3840
2.792 2.310
6Li 940
4.780
Boron-10 is available in both gaseous and solid form. Elemental boron (typically
enriched to 96% 10B) is chemically stable in air, and therefore can be used as a coating
27
either for proportional counters or solid state detectors. Boron tri-fluoride is a gaseous
form of 10B that can be used as a fill gas in proportional counters. Boron tri-fluoride is
not as well-behaved a proportional gas as 3He, and begins 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, BF3 is not available
in tubes with fill pressures as high as 3He tubes (3He fill pressures can be as large as 10
atmospheres, while BF3 fill pressures are typically less than 2 atmospheres). Detectors
developed with a 10B conversion layer have separate neutron capture and signal
generating materials [13]. The neutron is captured in the 10B, 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 products are drifted
under the influence of an electric field to generate a signal. The range of the 10B
neutron capture reaction products (alpha particle and 7Li ion) depends on the type and
density of the coating. For a typical 10B density of 2.34 g/cm3, the range of the reaction
products is 3.5 µm and 1.8 µm for the alpha particle and the 7Li ion, respectively (as
calculated using SRIM-2013 [15]). Due to the relatively short range of the reaction
products, the coating thickness is typically no more than a couple microns thick. Boron-
10 loaded scintillators (either liquid or plastic) are also available. Boron-10 loaded
plastics have a higher sensitivity to gamma rays than BF3 filled proportional counters or
10B-lined proportional counters. The signal produced by gamma rays can be
distinguished from the signal produced by neutrons in liquid scintillators loaded with 10B;
however, liquid scintillators are not a viable 3He alternative for certain applications as
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. However, 6Li is stable once bound in a matrix, so it 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 6Li loaded glass fibers [18]) or bound with another
element and then used in a homogenous mixture with a scintillator (such as 6LiF/ZnS)
[19]. The scintillators produce light in response to the neutron capture reaction products
(alpha particle and triton) escaping the 6Li and entering the scintillation material. The
neutron capture reaction products from 6Li have more energy than the 10B 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 µm in 6Li and the
triton a range of approximately 117 µm [as calculated using SRIM-2013 [15]]). Although
the neutron capture cross section for 6Li is approximately 25% that of 10B, the difference
can be offset by the increased amount of 6Li that can be used while still producing a
signal. The limiting reaction product for 6Li is the alpha particle which has a range of 22
µm in 6Li, compared to the limiting reaction product in 10B, the 7Li ion, which has a range
of 1.8 µm 10B.
There are some additional options for neutron detection besides 10B and 6Li.
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, there are no currently commercially available
gadolinium based detectors capable of meeting the detection criteria of material
29
quantification applications. Lithium sheets are another option for increasing the detector
response [20]. However, as 6Li 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 3He 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 detectable signal. Hydrogen
has the highest neutron scatter cross section, which produces a recoiled proton
(hydrogen nucleus) [4]. One of the most common hydrogen based 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 produced in response to gamma rays.
Plastic scintillators offer an alternative to liquid scintillators for fast neutron detection
[21], but plastics with adequate PSD are currently limited by the size that can be
produced.
This project is focused on currently commercially available neutron detectors for
near term 3He 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 BF3 filled proportional
counters, 10B-lined proportional counters and 6LiF/ZnS scintillating screens.
30
Objectives of this Work
The objective of this work was to support the project in determining an appropriate
3He alternative for use in neutron multiplicity counter configurations. The work included
modeling and simulations to identify optimal design templates, and the development 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 3He alternative detector on the
calculated assay results.
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 multiplicity counters require longer counting times than coincidence
counters to achieve the necessary 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 multiplicity
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 isotope 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 (α,n) reactions, or for assays performed in
environments with significant background present [22]. Neutrons can also induce
fissions within the sample (multiplication), instead of escaping, which increases the total
neutron production rate above what would be expected for a given mass of a fissile
32
isotope. All of these potential neutron sources must be accounted for when
characterizing a sample based upon its neutron emissions. The effect of detecting
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 252Cf and 240Pu (the data for the figure was obtained from Verbecke [1][24] for 252Cf and Bodeman [25] for 240Pu).
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 also 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 distribution available for detection is corrected for the detector
parameters, as was demonstrated by Bohnel [23]). The moments of the emitted
33
neutron distribution can be expressed in terms of the sample parameters (such as the
fission rate, sample self-multiplication, and the (α,n) reaction rate). Therefore, if the
isotopic composition of the sample is known (typically determined with gamma ray
spectroscopy), the mass of the isotope of interest can be extracted from the measured
moments.
Figure 2-2. Neutron multiplicity distribution for the spontaneous fission of 240Pu and the induced fission of 239Pu (the data for the figure was obtained from Boldeman [25]).
Multiplicity counters record the neutron multiplicity distribution (from which the
factorial moments are calculated) using shift register logic. Multiplicity shift registers
organize the pulse train into time correlated groupings of 0, 1, 2, 3, … counts in a
specified duration, or gate [26]. The 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 distribution that is measured. Two counting gates are opened
34
when the shift register is triggered by a neutron event. The second counting gate opens
long after the first gate closes (approximately 4 ms later) when the correlated neutrons
from the original fission 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 represent 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 distribution of real, correlated events is represented by
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 expressed as [27]:
1
0
)()()()0(
1)(
n
i
inbirnfb
nr
Equation 2-1
The general form for the factorial moments of a probability distribution P(ν) is given
by:
)()!(
!max
Pkk
k
Equation 2-2
The factorial moments of the correlated distribution can be used to calculate the
total neutron count rate, or the “singles”, the rate of detection of two time-correlated
neutrons, or the “doubles”, and the rate of detection of three time-correlated neutrons,
or the “triples” [6]. The singles are equal to the trigger rate (W) at the gate of the
multiplicity shift register, where W is given by Sεν1 (the source rate, S, multiplied by the
detector efficiency, ε, and the first factorial moment of the source distribution ν1). The
doubles are equal to the trigger rate multiplied by the average number of correlated
neutrons, n , which is equivalent to the first factorial 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:
36
1)()!0(
!max
0
0
nrn
nr
n
nnrn
nr
n
)()!1(
!max
1
1
2
)1()(
)!2(
!max
2
2
nnnr
n
nr
n
The singles (U), doubles (D), and triples (T) can then be written with these three
factorial moments:
0WrU
1WrD
2RrT
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, r0, r1, and r2 must be expressed in terms of the
moments of f(n) and b(n). The moments from the measured distributions can be
substituted into the equations for U, D and T by deconvolving r(n) from b(n):
WU
Equation 2-4
)( 11 bfWD
Equation 2-5
2
))(2( 11122 bfbbfWT
Equation 2-6
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.
The 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 (α,n)
reactions) is:
1)()(S
Sq
S
FP sf
Equation 2-7
Where F = the fission rate Sα = the rate of (α,n) reactions qsf(ν) = the probability of ν spontaneous fission neutrons being emitted δ1,ν = 1 if ν=1, else = 0
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
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 developed 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]:
)1(11 sfMS
F
Equation 2-8
)]1(1
1[ 12
1
2
2
2
sfi
i
sf
MM
S
F
Equation 2-9
)]1(1
13])1(3[
1
1{ 1
2
2
2
1
3122
1
3
3
3
sfi
i
isfsfi
i
sf
MMM
S
F
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 (α,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 Figure 2-4.
39
Figure 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.
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:
max
)1()()(n
nn
nPnC
Equation 2- 11
where
n
is the binomial coefficient, and is given by
)!(!
!
nn
.
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
41
correlated detected neutron distribution can be expressed as [6] (derivation shown in
Appendix A):
N
jn
jn
t
j
t dtppj
ntfn
nCjr
1 0
1)1(1
)()(
)(
Equation 2-12
where 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 factorial 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:
10 r
Equation 2-13
)1(2 1
2
2
1
GPD
eer
Equation 2-14
2
1
3
3
2 )]1([3
GPD
eer
Equation 2-15
where 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 1.27τ to minimize the relative error
in the coincidence rate [31].
42
The singles, doubles and triples can now be written in terms of the factorial
moments of the detected distribution as follows.
1SU
Equation 2-16
)1(2
2
2
GPD
eeS
D
Equation 2-17
23
3
)]1([6
GPD
eeS
T
Equation 2-18
The expressions for ν1, ν2, and ν3 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 (α,n)
neutrons, α). With these equations the 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 M, F and α to produce the following
expressions [6]:
032 McMbMa
Equation 2-19
where
)(
)1(6
2332
2
12
isfisft
isf
Rf
Ta
)(
]3)1([2
2332
2213
isfisfd
isfisf
Rf
Db
1)(
6
2332
22
isfisfd
isf
Rf
Dc
Equation 2-20
43
The fission rate can be determined using the calculated value for M with the
following equation:
2
2
1
2
1
)1(2
sf
i
i
d
M
RMM
f
D
F
Equation 2-21
And then α is given by:
11
MF
R
s
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 developed to assay samples where
the (α,n) rate was not known and a third parameter had to be measured. The first
multiplicity counters were developed by adding additional detectors to existing
coincidence counters to increase the system efficiency (to improve the statistics on the
triples, which are proportional to ε3). Later, an additional decoding circuit was added to
the standard coincidence electronics to measure the multiplicity distributions. Simple
dead time corrections were also implemented; however, these corrections were
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 performance
requirements for a high detection efficiency and low die-away time. Moderation is
required to thermalize neutrons entering the detector, to increase the efficiency of the
system. However, the time it takes for the neutrons to lose energy through scattering in
the moderator 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 3He detectors
were used to 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 electronics were required to process the higher multiplicities [34]. Faster
electronics began to be incorporated into the multiplicity counter circuits and the
improved 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.
45
Figure 2-7. Comparison of the results from a conventional assay and a multiplicity assay for samples with different amounts of effective 240Pu1 (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 Carlo
simulations performed by Langner, et al. [35], and measurements made with the dual
mode multiplicity counter, were used to select the final design for the PNMC. Based on
the results from the studies of the various configurations, the PNMC was constructed
with four rings of 3He detection tubes and an all polyethylene moderator. The measured
1 Effective 240Pu (240Pueff) is the mass of 240Pu that would give the same response as that obtained from all of the even plutonium isotopes in the sample. The effective 240Pu is calculated by 240Pueff = 2.52238Pu + 240Pu + 1.68242Pu, which can be solved to determine the mass of 240Pu present in the sample.
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 system 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.
The 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 is the
Epithermal Neutron Multiplicity Counter (ENMC) (Figure 2-8). The ENMC contains 121
10-atm 3He filled proportional counters. The neutron detection efficiency of the ENMC
is 65%, and the die-away time is 21 µsec [36]. The counter was designed 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 3He tubes. Graphite end plugs on the sample chamber
improve the vertical uniformity of the neutron detection efficiency, and were selected
based on simulations with several different media [36]. The entire counter was carefully
designed; however, the performance was primarily realized due to the large amount of
3He present in the system (over 18 moles of 3He are in the ENMC [13]). The availability
of 3He decreased after the design of this counter, and building additional ENMCs has
47
become prohibitively expensive. Therefore, high performance multiplicity counter
configurations without 3He 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 10B-lined proportional
counter technology have been considered by Proportional Technologies incorporated
and Los Alamos National Laboratory. Proportional Technologies has examined the in-
house manufactured 10B-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 three different 10B based detectors [38].
In addition to thermal neutron 3He alternatives some fast neutron detection
techniques for use in multiplicity counters have also been explored, such as the design
48
developed by researchers at the University of Michigan [39]. Liquid scintillators can be
designed to detect fast neutrons, and pulse shape discrimination (PSD) techniques can
be employed to distinguish between pulses generated by gamma rays and neutrons.
Liquid scintillators are fast, so there is a low accidental rate; however, like most fast
neutron detectors they produce lower neutron detection efficiency than conventional
thermal neutron detectors.
A prototype counter based on 6LiF/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 6LiF/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 µs), 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 discrimination.
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 efficiency will limit the neutron
detection efficiency. Customized electronics were developed to improve the PSD [40],
but the length of the neutron pulses (several µs) ultimately limited the performance of
the system.
49
Figure 2-9. Prototype LANL developed 6LiF/ZnS well counter (photo courtesy of Dr. Martyn Swinhoe).
A similar system to the 6LiF/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 applications, 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 the 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 at a high count rate,
such as would be required in traditional multiplicity counter applications.
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 gamma 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 3He alternative counter need to be capable of handling high neutron count
rates, but will also require high gamma ray rejection capabilities.
Table 2-1. Spontaneous fission and (α,n) yields for uranium and plutonium isotopes[1][6].
Isotope Spontaneous Fission Half-
Life (yr)
Spontaneous Fission Yield
(n/s-g)
Alpha Decay
Half-Life (yr)
Alpha Yield
(α/s-g)
(α,n) Yield in Oxide (n/s-g)
(α,n) Yield in Flouride (n/s-g)
235U 3.5x1017 2.99x10-4 7.04x108 7.9x104 7.1x10-4 0.08 236U 1.95x1016 5.49x10-3 2.34x107 2.3x106 2.4x10-2 2.9 238U 8.2x1015 1.36x10-2 4.47x109 1.2x104 8.3x10-5 0.028
238Pu 4.77x1010 2.59x103 87.74 6.4x1011 1.34x104 2.2x106
239Pu 5.48x1015 2.18x10-2 2.41x104 2.3x109 3.81x101 5.6x103
240Pu 1.16x1011 1.02x103 6.56x103 8.4x109 1.41x102 2.1x104
Table 2-2. Gamma ray yields for uranium and plutonium isotopes [5] [43].
Isotope Total Half-Life (yr) Gamma Ray Yield (γ/s-g) 235U 7.04x108 5.55x1010 236U 2.34x107 9.1x105 238U 4.47x109 7.18x106
238Pu 87.74 3.02x108
239Pu 2.41x104 8.58x105
240Pu 6.56x103 4.43x106
The multitudes of counter configurations that have been developed demonstrate
the specialized nature of these systems. Several 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.
51
CHAPTER 3 COUNTER MODEL AND SIMULATIONS
Radiation detection systems can be complex, and small design changes can
significantly affect their performance. Building different systems to test various
configurations typically is not a practical way to investigate multiple designs; models 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 simulation
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 the same questions, but
through different approaches. 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 particles 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
becoming progressively smaller; this method approaches the integro-differential
transport equation. Monte Carlo does not rely upon integrating the particles through
space or time; instead, the Monte Carlo method simulates the spatial transport of
individual particles between specific types of events. Because there are no spatial
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 (for 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) (ε2/τ) [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, as the
transport and tallying of heavy charged particles was required for some of the
simulations.
The simulations performed for the optimization of the 3He alternative multiplicity
counter configuration were comprised of two categories: one where the neutron capture
material and the signal generation material were the same (e.g., 3He filled proportional
counters), and one where the neutron capture material and the signal generating
material were different (10B-lined proportional counters) (Figure 3-1). There are several
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 determined 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, generated 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 the signal is generated in a separate media from where the neutron was captured (b).
Signal generation in neutron detectors that have a separate neutron capture
material and signal generating material is a two-step process. The neutron has to be
captured and 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 counting
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 7Li ion, was implemented in MCNPX v.2.6.0 [47]. The ability to require
correlation of the reaction products, with the correct two-branch Q-values for neutron
capture reactions in 10B, was added in MCNPX v.2.7b [46]. Prior to MCNPX v.2.7b, a
correction factor was applied to the simulated neutron capture 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 by 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 deposited 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
simulation). 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 count 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,
55
regardless of energy, create enough ionization to produce a detectable signal. 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 higher, 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
measurements are required to establish the relationship between the simulated
response and the measured response.
ENMC Template
The MCNPX 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 (excluding 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 µs. The ENMC template was reconstructed in MCNPX prior to any
modifications being performed for the 3He 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 µs, 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 adapted for alterations with the 3He alternative
56
technologies through the development of the Alternative Neutron Multiplicity Counter
(ANMC) template [13].
Figure 3-2. ENMC MCNPX model used as the template for the 3He 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 and ring by ring analysis 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 limit) and for
the configurations with detectors that were not based on a circular geometry (i.e., the
6LiF/ZnS simulations, which were not performed as part of this work).
57
Alternative configurations were simulated using detectors based on 10B and 6Li.
Two 10B based thermal neutron detectors, BF3 filled proportional counters and 10B-lined
proportional counters, were simulated using the ANMC template. A separate set of
simulations was performed to determine if plates lined with 10B and orientated at an
angle to the surface normal would increase the neutron detection efficiency. The 6Li
based detector simulated with the ANMC template was 6LiF/ZnS(Ag) sheets; however,
those models were developed separately from this research effort [44].
The BF3 efficiency tallies were performed with a F4 neutron capture tally and
verified with a neutron current tally (net neutrons entering the BF3 fill gas). The signal
produced by 10B-lined tubes is dependent upon one of the reaction products from the
neutron capture in the 10B 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
detector, the neutron detection efficiency (signal generating efficiency) was determined
by tallying the correlated reaction products escaping the 10B lining and entering the
signal generating fill gas. The 10B-lined tallies were verified by tallying the energy
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 10B-lining will enter the proportional 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
58
zero. This is a fundamentally different spectral shape compared to proportional
counters where the neutron is captured in the same material that generates the signal
(such as those filled with 3He or BF3). 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 3He filled proportional counter and a 10B-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 the required gamma ray rejection. The low-energy-threshold will not
significantly affect the efficiency of the 3He or BF3 proportional counters due to the large
separation between the signal produced in response to a neutron capture and that
produced by a gamma ray. However, the low-energy-threshold will have an impact on
the neutron detection efficiency of the 10B-lined proportional counters due to the energy
distribution of the reaction products entering the proportional gas. The standard low-
energy-threshold is approximately 100 keV, which will produce an effect around 10% on
the 10B-lined proportional counter detection efficiency [44]. This effect was not included
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.
59
(a)
(b)
Figure 3-3. Example simulated spectrum from a 3He filled proportional counter (a) and a 10B-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 3He spectrum corresponds to the Q-value for a neutron capture in 3He, 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 10B lining to the total energy deposited in the proportional gas are shown in the 10B-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 10B-lined proportional counters, the signal generated by the 6LiF/ZnS
sheets is a two-step process that is the result of the neutron capture reaction products
60
escaping the neutron capture material (6LiF) and entering the signal generating material
(ZnS). However, tracking the reaction products from the 6LiF into the ZnS is not
informative as the microscopic scale of the particles compromises the accuracy of the
simulations. Additionally, the final measured efficiency with the 6LiF/ZnS system is also
highly dependent upon the light collection efficiency, which cannot be simulated by
MCNPX v.2.6.0. Therefore, the neutron detection efficiency of the 6LiF/ZnS sheets was
simulated (separate from this research effort [44]) by the use of neutron capture tallies
in the 6Li 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 generated 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 fitting the results to
an exponential, such as is shown for the base-line 3He 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 simulation 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%.
61
Figure 3-4. Die-away time fit for the baseline 3He system.
Boron-10 Based Detector Simulations
The probability of a thermal neutron being captured by a 10B atom is lower than the
probability of a thermal neutron being captured by a 3He atom. Therefore, to have the
same number of neutron captures in a system built with 10B based neutron detectors as
would be seen in a system built with 3He based neutron detectors more 10B atoms than
3He atoms are required. The number of 10B atoms required to obtain an equivalent
number of neutron captures to 3He can be determined by multiplying the total number of
3He atoms present by the ratio of the neutron capture cross-sections. For a complete
system, the relationship between atoms of detection media and neutron detection
efficiency is not linear due to neutron scattering (as the system gets larger to
62
accommodate the increased amount of 10B, the neutrons will be more likely to lost in the
moderator).
The amount of 10B in all of the 10B based systems 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 too 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 10B instead of 3He as the neutron detection
medium were conducted with BF3 filled proportional counters. The initial BF3
simulations were performed by replacing the 121 2.54-cm-diameter 10-atm 3He tubes in
the ENMC with 1-atm BF3 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 three options to increase the number of 10B 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 10B atoms in the system without increasing the footprint, but the
tube pressure was limited to 2 atm, for availability purposes. BF3 is considered a
hazardous gas, due to its corrosive nature; BF3 also loses its proportional
characteristics at high pressures and requires a high operating voltage. The corrosive
nature of BF3 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
63
the tube volume, had to be increased. However, 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 BF3 tube
configuration is not determined solely by the number of 10B 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 (1.09x1025 atoms of 3He) are shown in Table 3-1
(although the lower neutron capture cross section of 10B 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. Likewise, a configuration with 1-atm tubes was
determined to be impractical for an actual physical configuration. The best option for
the BF3 filled proportional counters was identified 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 positioned 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 enough 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 not be moved by two people.
64
Table 3-1. Tube diameter and pressure combinations to achieve the same number of 10B atoms in a system designed with BF3 filled proportional counters as 3He atoms present in the ENMC.
Pressure (atm) Tube Diameter (cm) Atoms/Tube Number of
Tubes
1 2.54 8.81x1021 1239 1 5.08 3.52x1022 310 1 7.62 7.92x1022 137 2 2.54 1.76x1022 619 2 5.08 7.05 x1022 155 2 7.62 1.58x1023 68
(a) (b)
Figure 3-5. The original ENMC footprint, with 121 2.54-cm diameter 3He tubes, compared to the final BF3 system footprint, with 155 5.08-cm diameter BF3 tubes.
The second set of simulations performed with 10B as the neutron capture material
utilized 10B-lined proportional counters. Boron-10-lined proportional counters do not
have the same safety issues associated with BF3 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
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 will not be generated in the proportional gas. As
shown in Figure 3-6, the 7Li 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 lining thickness
until approximately 3 µm, 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 2.54-cm diameter tubes lined with 2.5-µm of 10B and filled with
argon gas at a pressure of 1 atm. The performance of the initial system was not
adequate, so, as with the BF3 filled proportional counter configuration, an increase in
the amount of 10B in the system was required.
The number of 10B atoms in a system designed with 10B-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 the 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 every 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 four smaller tubes have a surface
area 1.6 times greater than that of the larger tube.
66
(a)
(b)
Figure 3-6. The range of alpha particles in several possible compositions of the lining for
10B-lined proportional counters (a), and the range of the 7Li 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 7Li ion (6% probable) and one for the reaction which produces an excited state 7Li ion (94%) probable. The range values for both figures were calculated with SRIM-2013.
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 10B atoms as 3He atoms in the ENMC, assuming a lining thickness of 2.5 µm.
Tube Diameter (cm) Atoms/Tube Number of
Tubes
5.08 7.05x1022 274 2.54 1.99x1022 547 0.40 3.14x1021 3470
Several small-diameter tube configuration simulations were performed to increase
the total tube surface area (and consequently the amount of 10B 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
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 escape 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 diameters 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 10B-lined systems can be seen
by mapping the simulated FOM. As with the BF3 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 physical 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, restrict the height to less than 1 m, and
limit the foot-print to less than 1 x 1 m2. An example of the progression of the simulated
10B-lined FOM is shown in Error! Reference source not found.. The contour lines
epresent constant FOM values, with the target performance of the ENMC shown for
reference. The first system simulated was a simple substitution of the 3He tubes in the
ENMC with 10B-lined tubes. The following simulations included alterations in the
number of tubes, tube diameter, 10B 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 adjustments 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 surface in Figure 3-9 illustrates the FOM
69
space covered with the simulations, the black circles correspond to the FOM values of
the simulated designs. Several of the configurations were labeled; note that the labels
in Figure 3-9 correspond to those in Figure 3-8 for comparison purposes. However, for
clarity, labels were not included for all of the markers.
Figure 3-8. FOM space mapped out with the simulated 10B-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.
70
Figure 3-9. Surface contour of the FOM space mapped with the simulated 10B-lined proportional 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, which 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 increased with system
size. The amount of polyethylene between the tubes was optimized 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.
71
Likewise, less moderation decreased the die-away time, but also decreased the neutron
detection efficiency, resulting in a lower FOM than what was achieved with the
configuration shown below.
Figure 3-10. The original ENMC footprint, with 121 2.54-cm diameter 3He tubes compared to the final 10B-lined system footprint, with 4725 0.40-cm diameter 10B-lined tubes.
10B-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 10B could be increased by using configurations other tubes. The
plates attempted to maximize the path length that the neutrons could travel in the 10B 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 required
[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
72
system. The simulations for multiplicity counter applications included moderation
around the plates to increase the detection efficiency. Several different 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 with plate
orientation suggested that the moderation process of the neutrons mitigated any
advantage of the radial directionality of the plates.
6LiF/ZnS Based Detector Simulations
A 6LiF/ZnS scintillating sheet template was initially developed using rings of
6LiF/ZnS and plastic light guide layers that encircled the sample chamber. In this
design, the light guide also functioned as the neutron moderator, which decreased the
amount of polyethylene surrounding the detector media. The 6LiF/ZnS sheets were
simulated in a 1:2 ratio of 6LiF 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 6LiF/ZnS screens developed for the LANL prototype neutron capture
counter [44].
The signal generated 6LiF/ZnS sheets is due to the 6Li neutron capture reaction
products that escape the 6LiF 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 initial configuration consisted of 20
sheets of 0.05-cm thick 6LiF/ZnS layered with minimal plastic for the light guides.
However, optimization studies, as reported by Ely et al. [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
73
configuration consisted of 20 sheets of 0.05-cm thick 6LiF/ZnS layered with 0.7-cm thick
plastic light guide sheets, as shown in Figure 3-11. Due to the thin 6LiF/ZnS sheets 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 3He tubes compared to the final 6LiF/ZnS system footprint, with 20 6LiF/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 6LiF/ZnS
simulations. The simulated efficiency (generated with a F4 neutron capture tally) with a
single 5.08-cm diameter BF3 tube at a pressure of 1.18-atm was within 1% of the
measured results (1% over prediction of efficiency) [48]. The BF3 tube measurements
were performed outside with the tube located in polyethylene housing, which mitigated
the effect of neutron scatters. The 10B-lined tube measurements were performed
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 10B-lined
tube (manufactured by GE-Reuter Stokes, Twinsburg, OH) 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 than the 10B-lined tube), as shown in Figure 3-12. The room
effect had a greater influence on the measurements with a source-to-detector distance
over 50 cm; therefore the validation measurements and simulations presented here
were performed with a source to detector distance of 25 cm.
Figure 3-12. Model (left) and measurement (right) configuration for the 10B-lined proportional counter model validation (photo courtesy of Dr. Richard Kouzes).
The 10B-lined tube 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 10B
concentrations; 96% enriched 10B, B4C, and BN (96% to 50% 10B). The 10B 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 10B
concentration will affect the rate at which neutrons are captured). The change in the
75
simulated efficiency was not linearly related to the 10B concentration, due to the
differences in density of the compositions (10B has a density of 2.34 g/cm3, B4C has a
density of 2.52 g/cm3, and BN has a density of 3.45 g/cm3). 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 tallies of the reaction products entering the fill gas. The best
efficiency agreement between the simulated and measured results was obtained with a
0.75 µm thick 10B lining, which produced a 2.2% difference compared to the measured
efficiency (an over-prediction of efficiency). However, as 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 comparing
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 10B-lined
proportional counters. The pulse height spectra of the reaction 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 spectrum from a 10B-lined tube
demonstrates the two separate plateaus (one due to the alpha particle and due to the
7Li ion), as expected of a system where one of the two reaction products generated 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
76
demonstrate the same two-step response as the measured results. However, the
simulated results show different relative 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 10B lining thickness.
The additional information obtained with the pulse height spectra generated
suggests that although the 0.75 µm 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 B4C spectra have similar shapes to the measured results at
77
a thickness greater than 1.0 µm and less than 2.5 µm, 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 252Cf source located 25 cm from a 10B-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.
78
(a)
(b)
(c)
Figure 3-15. Simulated pulse height spectra for three different lining thickness (0.75 µm, 1.5 µm and 2.5 µm) for a 96% enriched 10B lining (a), a B4C 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 6LiF/ZnS based detector manufactured by Innovative
American Technologies (IAT) (Coconut Creek, FL) was used to establish an initial VCF.
Efficiency measurements were performed outdoors with four detector paddles located in
polyethylene housing, which were then simulated for comparison. Each paddle was
comprised of layers of 6LiFZnS and light guide fibers. The VCF obtained by comparing
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
0 0.5 1 1.5 20
0.5
1
1.5x 10
-5
Energy (MeV)
Eff
icie
ncy p
er
(10 k
eV
) B
in
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.
Performance 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 developed
with 121 2.54-cm diameter 1-atm BF3 filled proportional counters was 12. The six-ring,
155 5.08-cm diameter 2-atm tube BF3 system produced a detection efficiency of 57%,
and a die-away time of 44 µs, corresponding to a FOM of 74.
The initial 10B-lined tube system with 121 2.54-cm diameter tubes with a lining
thickness of 2.5 µm had a FOM of 8. The final system consisted of 4725 4-mm
diameter tubes. The initial simulations considered the optimal performance, so the
lining was simulated to produce 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 maximized; however, in multi-tube systems the efficiency of the
system must be maximized. A “thick” (2.5 µm) and “thin” (1.0 µm) lining were simulated
in a system with varying numbers of tubes (the amount of polyethylene moderator
between the tubes was held constant, 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
80
efficiency as compared to the thinner lining. However, as the number of tubes in the
system increased, the thinner lining produced better results because although fewer
neutrons were stopped per tube, a greater percentage of the reaction products per
neutron capture were detected (Figure 3-16).
Figure 3-16. The effect of the tube lining thickness on the FOM of a system simulated with various numbers of 4.0-mm diameter 10B-lined proportional counters.
With the large number of tubes simulated, the 1-µm 10B-lining was found to
produce the best FOM. The system with optimized moderation produced a final
simulated system efficiency of 39% and die-away time of 37 µs. These 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.
81
The FOM for the first 6LiF/ZnS configuration was 4. The final configuration
consisted of 20 sheets of 0.05-cm thick 6LiF/ZnS layered with 0.7-cm thick plastic light
guide. The efficiency of the system was found to be 38%, and the die-away time was 8
µs. The low die-away time achieved with this configuration is due to the minimal
moderation used. The FOM with the optimized 6LiF/ZnS system was found to be 238,
which is higher 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 performance is achieved with the
6LiF/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.
82
Figure 3-17. Final FOM comparison for the 3He alternative multiplicity counter configurations shown with the ENMC and the PCMC.
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 6LiF/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. The 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 6LiF/ZnS
sandwiched between light guides. The original VCF applied to the MCNPX simulations
was based on measurements 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 light 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 6LiF/ZnS sheets and the transmission properties of
the light guides.
6LiF/ZnS Physics
Silver activated zinc sulfide is a bright scintillator, generating ~160,000 photons
per captured thermal neutron in 6LiF [19]. However, ZnS is not transparent to its own
light, and so thin sheets are required to allow light to escape, maximizing the signal that
is available for transmission by the light guides. The 6LiF/ZnS sheets selected for the
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-µm
thick layer comprised of a 1:2 ratio of 6LiF:ZnS particles suspended in an organic
binder. The individual particles of 6LiF and ZnS were less than 10 µm in diameter
(Figure 4-1). The 6LiF/ZnS compound was sandwiched between two polyester sheets
(each 250-µm thick) by the manufacturer for support.
Figure 4-1. Magnified (50x) view of a section of a 6LiF/ZnS sheet (constructed by Eljen Technology) showing the individual 6LiF and ZnS pieces suspended in the binder (photo curtesy of Dr. Mary Bliss).
Zinc sulfide will respond to gamma rays as well as the heavy charged particles
created by the neutron capture in 6Li. 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
85
photons, compared to ~160,00 photons generated by thermal neutron capture [19]. The
pulse shapes produced by gamma rays and neutrons in 6LiF/ZnS are also different.
The heavy charged particles from the neutron capture deposit their energy 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 equilibrium. The same states
decay regardless of whether the excitation was caused by a neutron or a gamma ray.
Therefore, the emission wavelength of the luminescence generated from gamma rays
and neutrons is identical; however, the time it takes for the neutron-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 allows for the
pulses to be categorized and gamma rays to be discriminated.
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 gamma rays, unlike the
PMMA (although the WLSP contains a dopant that produces significant gamma ray
suppression compared to “normal” gamma ray sensitive plastic, such as PVT). Both the
WLSP and the PMMA will transmit light based on the laws of ray tracing optics;
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
86
manufacturer). Therefore, 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).
87
(a)
(b)
Figure 4-3. Emission Spectrum for the 6LiF/ZnS screens (from Eljen Technology EJ-426) (a) and the absorption and emission spectra for the WLSP (Eljen Technology EJ-280) (b) from the manufacturers specifications.
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
with Snell’s Law2) for the WLSP is 39.3o 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 (41.8o relative to the normal). Therefore, 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 88.8o 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 gamma 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 and 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 be used in the complete bench-top system to more accurately reflect the
performance of the complete bench-top system.
2 Snell’s law relates the angle of incidence and the angle of reflection for light passing from one media
into another as:
1
2
2
1
)sin(
)sin(
where η = the refractive index of each media.
89
Figure 4-4. Refracted light between two media when the incident angle is less than the critical angle and η1>η2 (a), reflected ray for an incident angle equal to the critical angle and η1>η2 (b) and total internal reflection when the incident angle is greater than the critical angle and η1>η2 (c).
Configuration
The highest performing simulated configuration consisted of 20 sheets of 6LiF/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].
The 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 five
sheets of 6LiF/ZnS layered with six sheets of plastic light guide. The configuration was
90
designed for testing the different light guides and determining the corresponding VCF
prior to a full bench-top system build.
Figure 4-5. 6LiF/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 be 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 support 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 achieved with 0.70-cm thick light guides based on the neutron
capture, but measurements were also made with 0.50-cm and 0.90-cm thick sheets.
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 detector 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 system wrapped in closed cell neoprene inside of a light tight box. Light
leaks were eliminated prior to any measurements, and the system was allowed a
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 and green wavelengths. The measurements with
the test unit were made with negatively biased H1161 PMTs (manufactured by
Hamamatsu). The PMTs were gain matched for the dual PMT measurements. The
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 µs (with a 1- µs offset to establish a baseline) to collect the
entire digitized neutron pulse. The neutron pulse tails extended beyond the 4 µs
window but the remaining signal was too low to trigger a new pulse and the additional
charge wasn’t necessary for PSD. The digitization 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
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. Although the filter settings were not relevant for
the trace analysis they can affect 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 quarter 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 measurements 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 buffer, 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 were 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 will 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.
94
Pulse Shape Discrimination
The digitized traces were analyzed to distinguish between the signals produced in
response to gamma rays and the signals produced in response to neutrons. All of the
data analysis for this work was performed with MATLAB® (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 into histograms to
determine the neutron 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 (252Cf) source and
a gamma ray (60Co) source measured simultaneously. The neutron source was
centered above the detector and the gamma ray source was located 10-cm from the
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 approximately equal neutron and gamma ray
regions in the PSD histogram.
Figure 4-9. Histogram illustrating the charge ratio region from the 60Co gamma ray traces and the 252Cf neutron traces.
A large separation region and clear 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 Gaussians is
calculated by [54] (Figure 4-10):
raygammaneutron
SFOM
_
Equation 4- 1
96
where S is the distance between the center of the neutron region and the gamma ray
region, and δ 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 3σ separation between the Gaussians) [21].
The two window PSD technique is relatively easy to implement, and can be
performed quickly, but can be inadequate 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 alternatives 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.
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 rejection 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 measurement 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 252Cf; two different 252Cf sources
were used, one with a source strength of 20 ± 3 µCi on December 15, 2003 (source A)
and one with a source strength of 21.9 ± 1.3 µCi on October 1, 2009 (source B). The
gamma ray measurements were performed with 60Co and 137Cs sources. The 60Co
98
source had a strength of 9.4 ± 1.4 µCi on June 1, 2003, and the 137Cs source was 10 ±
1.5 mCi on October 1, 1996.
The top of the detector (the top piece of light guide) was 3.8 cm from the top of the
detector holder when the 0.5-cm thick light guides were used. The source 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
shown 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 – 300 for the entire trace and
channel 15 – 300 for the tail of the trace, corresponding to 0 – 600 ns and 30 – 600 ns
respectively (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 pulses. 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 30 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.
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 measurements for the same
configuration built with the 0.7–cm thick WLSP; the histograms obtained from the two
systems with the 252Cf 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 252Cf source was negligible even without shielding, as is evident in the minimal
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 252Cf 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
measurement 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
absolute neutron detection efficiency estimates, which were calculated for each of the
different configurations (the source strength on the dates of the measurements with the
PMMA and the 0.7-cm thick WLSP was 8.0x103 ± 1.2x103 n/s). The statistical errors
associated with the measurements are shown in all of the tables, but error bars are not
included on any of the figures for clarity (and for most of the histogram regions of
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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 light
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
with 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, the PMMA
configuration had higher absolute neutron detection efficiency when the source was
positioned closer 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 252Cf 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) 1.00 ± 0.04 5.30 ± 0.09 N/A PMMA 252Cf (1) 161.2 ± 0.5 22.7 ± 0.2 0.020 ± 0.003 PMMA 252Cf (2) 126.6 ± 0.5 22.6 ± 0.2 0.016 ± 0.002 PMMA 252Cf (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 252Cf (1) 268.5 ± 0.6 33.0 ± 0.2 0.033 ± 0.005 WLSP 252Cf (2) 321.6 ± 0.6 36.2 ± 0.2 0.040 ± 0.006 WLSP 252Cf (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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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).
The 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 intensity
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. The
PMMA configuration suffered from a greater reduction in the recorded neutron count
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
6LiF/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 indicate that a coincident
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measurement technique may be a method for suppressing 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 252Cf source in the center of the detector (position 2) constructed with 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 252Cf 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 252Cf (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 252Cf (2) 270.8 ± 2.3 23.6 ± 0.7 0.034 ± 0.005
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Figure 5-5. Charge ratio histogram of the traces collected with a 252Cf 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 thinner sheets still demonstrate lower neutron detection efficiency than the
thicker 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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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 source 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 8.0x103 ± 1.2x103 n/s and on the dates of
the measurements with the 0.9-cm thick WLSP the source strength was 5.5x103 ±
8.3x102 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 detection 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 252Cf 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 dominated 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 252Cf 259.6 ± 0.5 30.8 ± 0.2 0.032 ± 0.005 WLSP 0.7 cm 252Cf 321.6 ± 0.6 36.2 ± 0.2 0.040 ± 0.006 WLSP 0.9 cm 252Cf 332.0 ± 1.1 39.2 ± 0.37 0.045 ± 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 improved 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 simulations with the
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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 the 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 overall size of the system.
The neutron detection efficiency with the use of light guides was improved by 38% for a
single PMT, and 17% for the coincident PMT measurements. The coincident PMT
signal improvement estimate is conservative. The detector configuration was modified
to accommodate the additional length 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 configuration 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 60Co and 137Cs sources.
High intensity gamma ray measurements were made using the 137Cs source alone and
in conjunction with a 252Cf 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 6LiF, therefore the pulses are
more likely to be attenuated before being detected by the PMTs. Because of this, the
measurements with the 60Co source demonstrated a stronger change in the recorded
count rate with source position than the neutron source measurements. Due to the
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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 60Co 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 identified 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 detection efficiency
(as discussed below).
Table 5-5. PMMA and WLSP (0.7-cm thick) measurement results with a 2.7 µCi 60Co 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 60Co (1) 1.80 ± 0.04 14.5 ± 1.0
PMMA 60Co (2) 1.20 ± 0.04 7.4 ± 0.9
PMMA 60Co (3) 1.10 ± 0.03 6.4 ± 0.8
PMMA C (BG) 0.30 ± 0.02 0.20 ± 0.01 PMMA C 60Co (3) 0.30 ± 0.02 0.20 ± 0.01
WLSP (BG) 2.10 ± 0.05 6.50 ± 0.08 WLSP 60Co (1) 3.10 ± 0.06 25.6 ± 0.2 WLSP 60Co (2) 2.50 ± 0.05 17.7 ± 0.1 WLSP 60Co (3) 2.40 ± 0.05 16.3 ± 0.1
Coincidence (BG) 2.10 ± 0.05 6.50 ± 0.08 WLSP C 60Co (3) 2.10 ± 0.05 6.00 ± 0.08
High gamma ray count rate measurements were made with a 6.9 mCi ± 1.03 mCi
(on the day of the measurements) 137Cs 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 pile up effects (with both the PMMA and WLSP
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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. The percentage of emitted gamma 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 detector surface for the two positions
(on the top of the light tight box and at a height of 34.3 cm) were 5.9x107 γ/s and
8.5x106 γ/s, respectively. It should be noted that a better performance prediction could
be obtained with a more uniform gamma ray exposure. 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 misidentifications 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) that 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 technique for distinguishing neutron pulses from gamma ray
pulses under high count rate conditions. However, as was seen with the 60Co
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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Figure 5-6. PMMA (0.7-cm thick) response with a single PMT to a gamma ray flux of 5.9x107 γ/s (blue) and 8.5x106 γ/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 5.9x107 γ/s (blue) and 8.5x106 γ/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.
110
Figure 5-8. Trace examples showing the system response to a high gamma ray rate.
Figure 5-9. PMMA (0.7-cm thick) response to a gamma ray flux of 5.9x107 γ/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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Figure 5-10. WLSP (0.7-cm thick) response to a gamma ray flux of 5.9x107 γ/s with a single PMT (blue) and with two PMTs in coincidence (red).
In addition to the137Cs only measurements, data was collected with the detector
configurations simultaneously exposed to the 137Cs source and a 252Cf source. These
measurements were used to determine the PSD capabilities of the detector in the
presence of both gamma rays and neutrons. The 252Cf source used for these
measurements was source B (9.4 ± 0.6 µCi on the dates the measurements were
performed). A distinct gamma ray and neutron region are visible with the PMMA light
guide configurations for measurements made with an incident gamma ray flux of
5.9x107 γ/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 flux of 8.5x106 γ/s is 2.08; while this level of PSD is
adequate for most applications the stringent accuracy requirements for multiplicity
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counting require not only an adequate PSD FOM but also consideration of any potential
misidentified gamma rays. As can be seen in Table 5-6, there is a 5% higher neutron
count rate with a gamma ray flux of 8.5x106 γ/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 5.9x107 γ/s. The neutron
detection rate with two PMTs in coincidence and an incident gamma ray flux of 5.9x107
γ/s and 8.5x106 γ/s is 2% and 9% lower, respectively, than without the 137Cs source
present. These changes in the neutron count rate are higher than what would be
acceptable for assays requiring 1% measurement accuracy. Assay measurements 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 252Cf source (4.0x104 n/s) and an incident gamma ray flux of 5.9x107 γ/s (blue) and 8.5x106 γ/s (red).
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Figure 5-12. Charge ratio histograms with the 0.7-cm thick PMMA and two PMTs in coincidence in response to a 252Cf source (4.0x104 n/s) and an incident gamma ray flux of 5.9x107 γ/s (blue) and 8.5x106 γ/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 5.9x107 γ/s and
the 252Cf 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 8.5x106 γ/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 neutron 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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signal suppressed by the coincident signal requirement, was due to the increase in the
dead-time of the system produced 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 be 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 for 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
threshold 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 misidentification rate on the assay precision is considered in Chapter 6.
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Figure 5-13. Charge ratio histograms with the 0.7-cm thick WLSP and a single PMT in response to a 252Cf source (4.0x104 n/s) and an incident gamma ray flux of 8.5x106 with a single PMT (blue) and with two PMTs in coincidence (red).
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Table 5-6. Measurement summary with the 0.7-cm thick PMMA and 0.7-cm thick WLSP. Coincident measurements are marked with a “C”, the “H” in parenthesis indicates an incident gamma ray rate of 5.9x107 γ/s and the “L” in parenthesis indicates an incident gamma ray rate of 8.5x106 γ/s. In all cases the source was centered above the detector. 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 ± 0.08 N/A WLSP (BG) 2.8 ± 0.06 13.5 ± 0.15 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 137Cs (H) 653.3 ± 7.1 2786.5 ± 14.6 1.1x10-5 ± 1.2x10-7
PMMA 137Cs (L) 31.4 ± 0.7 352.5 ± 2.5 3.7x10-6 ± 8.8x10-8
WLSP 137Cs (H) 10721.0 ± 53.0 1459.0 ± 19.6 1.8x10-4 ± 9.0x10-7
WLSP 137Cs (L) 404.0 ± 4.9 2323.0 ± 11.7 4.8x10-5 ± 5.8x10-7
PMMA C 137Cs (H) 0.5 ± 0.09 1.2 ± 0.14 8.4x10-9 ± 1.5x10-9
WLSP C 137Cs (H) 584.1 ± 7.9 548.6 ± 7.7 9.8x10-6 ± 1.3x10-7
Gamma Ray and Neutron
Configuration *εabs, **εabs,γ/εabs
PMMA 252Cf, 137Cs (H) 1403.7 ± 11.3 2797.2 ± 15.9 **2.26 ± 0.02 PMMA 252Cf, 137Cs (L) 652.0 ± 4.0 396.5 ± 3.1 **1.05 ± 0.01 WLSP 252Cf, 137Cs (L) 1732.0 ± 12.1 2176.2 ± 13.6 **1.09 ± 0.01
PMMA C 252Cf, 137Cs (H) 210.3 ± 2.1 55.7 ± 1.1 **0.91 ± 0.01 PMMA C 252Cf, 137Cs (L) 224.7 ± 2.1 42.9 ± 0.9 **0.98 ± 0.01 WLSP C 252Cf, 137Cs (L) 1152.5 ± 8.0 65.0 ± 1.9 **0.95 ± 0.01
PMMA 252Cf 622.2 ± 3.6 73.2 ±1.2 *1.5x10-2 ± 1.2x10-4
PMMA C 252Cf 230.2 ± 2.2 38.5 ± 0.9 *5.7x10-3 ± 6.1x10-5
WLSP 252Cf 1592.4 ± 7.6 79.7 ± 1.7 *4.0x10-2 ± 2.7x10-4
WLSP C 252Cf 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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when compared to background measurements); however, they do not appear to be
complete traces. The quantized 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 performed3 to eliminate variations in the light emission of the
ZnS over the trace collection period on the shape of the traces recorded. A 6LiF/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
sponsored by the Department of Energy’s Office of Biological and Environmental Research located at Pacific Northwest National Laboratory.
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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 6LiF/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 6LiF/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 output on the side with the polyester compared to the side
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without 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 emission spectra between the sample side with
polyester and the sample side without polyester, as a function of the excitation
wavelength, indicates 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 6LiF/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. Therefore, 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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(a)
(b)
(c)
Figure 5-16. Emission spectra from the 6LiF/ZnS without the polyester interface (left) and from the polyester coated 6LiF/ZnS (right) for three different excitation wavelengths: 380 nm (a) 342 nm (b) and 300 nm (c).
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Model Validation
One of the primary functions of the bench-top test unit was to determine the
validation correction factor (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
simulations). 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 compared to the
measured results. The measured neutron detection efficiencies for several
configurations were compared to the simulated neutron detection efficiencies, producing
the VCFs shown 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 neutron captures in the
6LiF 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 6LiF/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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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 different bench-top test units measured. All of the VCFs presented are for measurements and simulations with the 252Cf source centered on the light-tight box, the coincident measurements are noted by “Coin.”. The error reported is dominated by the source uncertainty.
Measurement Configuration VCF
IAT Reference System 0.57 ± 0.04 PMMA 0.7 cm 0.42 ± 0.06
PMMA Coin. 0.7 cm 0.12 ± 0.02 WLSP 0.5 cm 0.98 ± 0.15
WLSP Coin. 0.5 cm 0.78 ± 0.12 WLSP 0.7 cm 1.07 ± 0.16
WLSP Coin. 0.7 cm 0.90 ± 0.14 WLSP 0.9 cm 1.07 ± 0.17
WLSP Coin. 0.9 cm 0.92 ± 0.14
The validation correction factors greater than one indicate that either the chemistry
of the 6LiF/ZnS sheets doesn’t contain enough 6Li, or gamma rays are being
misidentified as neutrons in the measured results. As was discussed in Chapter 3, the
composition of the 6LiF/ZnS sheets was simulated based on the vendor supplied
6LiF/ZnS ratio (1:2), 6Li atom density, and previously reported binder compositions.
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However, the 6LiF/ZnS sheets used to construct the bench-top test unit consisted of a
custom proprietary blend. Inaccuracies in the modeled 6LiF/ZnS composition, and the
binder quantity, would clearly impact the simulated results. Future measurements will
be performed to obtain a more accurate estimate of the atom densities in the 6LiF/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 6LiF/ZnS sheets
manufactured by Eljen Technology. The same results (within statistics) were obtained
with a lead shielded 252Cf 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 6LiF/ZnS based multiplicity
counter will be better than predicted.
Post processing 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).
124
Figure 5-18. Gamma ray rejection and VCF for different pulse height thresholds applied to the 252Cf and 137Cs coincidence measurements 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 the 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, the gamma ray rejection capability,
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.
126
CHAPTER 6 THEORETICAL CONSIDERATIONS: GAMMA RAY EFFECTS
Neutrons and gamma rays can both be emitted by isotopes that decay via fission.
The 3He neutron detectors used in traditional multiplicity counters are sensitive only to
neutrons except at high gamma ray doses. The lack of gamma ray sensitivity allows the
unknown sample parameters to be extracted based on the neutron multiplicity
moments, as was shown in Chapter 2. However, not all of the 3He alternative detectors
considered for use in multiplicity counters are capable of the same level of gamma ray
rejection that can be achieved with 3He. As was seen in Chapter 5, the 6LiF/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 the equations used to
extract the sample parameters such that they account for potential gamma ray
contributions. The change in the calculated assay variables (F, M and α are considered
here, although the unknown parameters could be any three of the assay variables) for
different gamma ray sensitivities is one of the factors to consider when selecting a pulse
height threshold.
The gamma ray sensitivity is likely to be low in the detectors selected for use in
neutron multiplicity counters, but the 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
127
contribution from gamma rays in 3He alternative-based counters. The 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 (fk and bk) 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 assayed. For the purposes
of these equations, all of the moments are expressed in terms of the source event rate,
with the inclusion of (α,n) reactions.
The singles, doubles, and triples for a detector that is only sensitive to neutrons
were given in Chapter 2 as [6]:
)1(1 SfnMFU
Equation 6- 1
))1(1
1(
212
1
2
22
sfi
i
Sfn
d MM
FfD
Equation 6- 2
)]1(1
13))1(3(
1
1[
61
2
2
2
1
3122
1
3
33
sfi
i
isfisf
i
Sfn
t MMM
FfT
Equation 6- 3
where νsfk = the factorial moments of the neutrons generated by spontaneous fission event νik = the factorial moments of the neutrons generated by an induced fission event F = the spontaneous fission event rate
128
α = the ratio of (α,n) to spontaneous fission neutrons =
M = the sample multiplication (which accounts for additional neutrons in the
sample due to induced fission) = 11
1
ii
i
p
p
εn = neutron detection efficiency
Note that in these equations the substitutions for the factorial moments of the emitted
probability distribution have been made, and fd and ft 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
distribution, νk):
11 nCU
Equation 6- 4
2
2
2 nCD
Equation 6- 5
3
3
3 nCT
Equation 6- 6
where C1, C2, and C3 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 (µk),
as follows:
129
)( 111 nCU
Equation 6- 7
)( 2
2
2
2
2 nCD
Equation 6- 8
)( 3
3
3
3
3 nCT
Equation 6- 9
The above equations include neutron and gamma ray contributions; however, 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 jn,γ. The joint moment of the distribution
of neutron and gamma ray quanta that could produce a detection of two neutrons and
one gamma ray is represented by jn,n,γ; similarly the joint moment for one neutron and
two gamma rays is represented by jn,γ,γ. Then the final equations for D and T will have
the form of:
)( ,2
2
2
2
2 nnn jCD
Equation 6- 10
)( ,,
2
,,
2
3
3
3
3
3 nnnnnn jjCT
Equation 6- 11
The gamma ray and joint moments have to be expressed in terms of source
parameters before their effect on the assay results can be determined.
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 Figure 2-4 for the neutrons. The
diagrams (Figure 6-1 to Figure 6-3) are based on the discussion in Oberer’s Thesis [27],
but here (α,n) reactions are also considered. It is assumed that the gamma 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 (α,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 potential 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 neglected 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 (α,n) reaction. This effect could be included as a gamma ray
emission associated with the neutron generated by the (α,n) reaction, but is not included
in this work. Another source of gamma rays that is not accounted for are those emitted
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 is 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:
νk = the factorial moments of the neutrons generated in a sample
νsfk = the factorial moments of the neutrons generated by spontaneous fission
events
νik = the factorial moments of the neutrons generated by induced fission
events
µsk = the factorial moments of the gamma ray source distribution
µsfk = the factorial moments of the gamma rays generated by spontaneous
fission events
µik = the factorial moments of the gamma rays generated by induced fission
events
S = F + Sα = the total source event rate
F = the spontaneous fission event rate
= the ratio of (α,n) to spontaneous fission neutrons =
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) = 11
1
ii
i
p
p
εn = neutron detection efficiency
εγ = 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]):
1
1)1(
1
11
11
i
iSf
Sfs
M
S
F
S
F
Equation 6- 12
132
The three terms (note that the (1 + α) factor produces two terms) in Equation 6- 12
correspond to the three potential sources of single gamma rays 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 factorial moment of the gamma ray probability distribution is:
)]1
1
1
12(
1
1)1(
1
1
1
12[
2
1
2
12
1
1
2
12
1
1
2
1
2
12
1
1
1122
i
ii
i
iii
i
sf
i
isf
sf
i
iSfSfS
MMMM
M
S
F
S
F
Equation 6- 13
The five source terms in Equation 6- 13 correspond to the five potential origins of
double gamma rays available for detection illustrated in Figure 6-2.
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:
))]1
1
1
12(
1
1
1
1(3
1
13(
1
1)1()
1
1
1
12
(1
13
1
1))
1
1
1
12
(1
1
1
1(3
1
13[
2
1
2
12
1
1
2
12
1
1
2
1
2
121
1
1123
1
1
2
1
2
12
1
1
2
1
2
2
1
12
3
1
3
13
2
1
2
12
1
1
2
1
2
1
1
2
1
2
121
1
11233
i
ii
i
iii
i
i
i
iii
i
iiii
i
sf
i
ii
i
ii
i
i
isf
i
isf
i
ii
i
ii
i
i
sf
i
isfSf
i
isfSfSfS
MMMM
MMMM
MMMM
MMM
S
F
S
F
Equation 6- 14
The eight source terms in Equation 6- 14 correspond to the eight potential sources
of triple gamma rays available for detection, illustrated in Figure 6-3.
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 Distributions
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 (α,n) reactions and to be
consistently expressed in terms of the source rate. The joint moment of interest for the
doubles rate is jn,γ, 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.
135
))1
1)(1(
1
1
1
1( 2
1
1111
1
2
1
111 i
i
iiisf
i
sf
i
isfSfn
MMM
MMMM
S
F
S
Fj
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 the distribution
that would make two neutrons and one gamma ray available for detection, jnnγ, and one
for the distribution that would make one neutron and two gamma rays available for
detection, jnγγ. Similar to the doubles expression, the origin of each of the terms of the
joint moments can be shown in a diagram (not included).
)))]1
1(
1
12
1
1(
1
1)
1
1((
1
1)1(
)1
1)
1
1(
1
12(
1
1)
1
1([
1
1211
1
2
2
1
122
1
1
2
3
2
1
21
2
21
1
1
2
2
2
1
1
1
1211
1
2
2
1
13
2
2
1
1
2
21
i
iiii
ii
iii
i
ii
i
iiii
i
sf
i
i
i
i
iiii
i
sf
i
isfi
i
sfsfSfnn
MMM
MMM
M
MMM
MM
M
MMM
MMM
M
MM
MM
S
FM
S
F
S
Fj
Equation 6- 16
136
))]1
1
1
12(
1
1
)1
1(
1
12(
1
1
))1
1(
1
1
1
1(2(
1
1)1(
))1
1(
1
12)
1
1
1
12(
1
1(
1
1))
1
1
(1
1
1
1(2[
2
1
2
12
1
1
2
12
1
1
1211
2
1
12
2
1
2
13
1
1211
1
1
1
12112
1
1
1
1211
2
1
1
2
1
2
12
1
1
2
12
1
2
2
1
2
13
1
12
11
1
1
1
12112
i
ii
i
iii
i
i
iiii
i
ii
i
ii
i
iiii
i
i
i
iiiii
i
sf
i
iiii
i
i
i
ii
i
iii
i
sf
i
isf
i
ii
ii
i
sf
i
isfSfsfSfn
MMMM
MMM
MMM
MMM
MMMM
M
MMM
MM
MMM
MM
MM
MM
S
FMM
S
FM
S
F
S
Fj
Equation 6- 17
Final Formulas
The 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:
))]1(1
1()1([
1
1111
i
iSfSfSfn
M
S
F
S
FMSU
Equation 6- 18
))]1
1)(1(
1
1
1
1(
))1
1
1
12(
1
1)1(
1
1
1
12())1(
1
1([
2
2
1
1111
1
2
1
111
2
1
2
12
1
1
2
12
1
1
2
1
2
12
1
1
112
2
12
1
2
22
i
i
iiisf
i
sf
i
isfSfn
i
ii
i
iii
i
sf
i
isf
sf
i
iSfSfsfi
i
Sfn
d
MMM
MMMM
S
F
S
F
MMMM
M
S
F
S
FMM
S
FSfD
Equation 6- 19
137
)))]]1
1
1
12(
1
1
)1
1(
1
12(
1
1))
1
1
(1
1
1
1(2(
1
1)1(
))1
1(
1
12)
1
1
1
12(
1
1(
1
1))
1
1
(1
1
1
1(2[
)))]1
1(
1
12
1
1(
1
1)
1
1((
1
1)1(
)1
1)
1
1(
1
12(
1
1)
1
1([
)))]1
1
1
12(
1
1
1
1(3
1
13(
1
1)1()
1
1
1
12
(1
13
1
1))
1
1
1
12
(1
1
1
1(3
1
13([
))]1(1
13))1(3(
1
1([[
6
2
1
2
12
1
1
2
12
1
1
1211
2
1
12
2
1
2
13
1
12
11
1
1
1
12112
1
1
1
1211
2
1
1
2
1
2
12
1
1
2
12
1
2
2
1
2
13
1
12
11
1
1
1
12112
2
1
1211
1
2
2
1
122
1
1
2
3
2
1
21
2
21
1
1
2
2
2
1
1
1
1211
1
2
2
1
13
2
2
1
1
2
21
2
2
1
2
12
1
1
2
12
1
1
2
1
2
121
1
1123
1
1
2
1
2
12
1
1
2
1
2
2
1
12
3
1
3
13
2
1
2
12
1
1
2
1
2
1
1
2
1
2
121
1
1123
3
1
2
2
2
1
3122
1
3
33
i
ii
i
iii
i
i
iiii
i
ii
i
ii
i
ii
ii
i
i
i
iiiii
i
sf
i
iiii
i
i
i
ii
i
iii
i
sf
i
isf
i
ii
ii
i
sf
i
isfSfsfSfn
i
iiii
ii
iii
i
ii
i
iiii
i
sf
i
i
i
i
iiii
i
sf
i
isfi
i
sfsfSfn
i
ii
i
iii
i
i
i
iii
i
iiii
i
sf
i
ii
i
ii
i
i
isf
i
isf
i
ii
i
ii
i
i
sf
i
isfSf
i
isfSfSf
sfi
i
isfisf
i
Sfn
t
MMMM
MMM
MMM
MM
MMM
MMM
MMM
MM
MMM
MM
MM
MM
S
FMM
S
FM
S
F
S
F
MMM
MMM
M
MMM
MM
M
MMM
MMM
M
MM
MM
S
FM
S
F
S
F
MMMM
MMMM
MMMM
MMM
S
F
S
F
MM
S
FM
SfT
Equation 6- 20
138
If εγ = 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 and 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 work, 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 εγ > 0 the formulas used to calculate M, F
and α (Equation 2-19, Equation 2-21 and Equation 2-22) will no longer be valid. The
effect on M, F and α, calculated assuming that εγ = 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 εγ > 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
values of M and α is shown in Figure 6-4, for a detector with the same parameters as
the simulated 6LiF/ZnS based multiplicity counter (a neutron detection efficiency of 43%
and a linear die-away time of 8 µs). The data for Figure 6-4 was generated by
calculating the singles, 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 assumes εγ = 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 α also change when εγ > 0, but those dependencies are not
shown here (for more detail see Appendix B).
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 significant, 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 240Pu sample with different values of M and α if the gamma ray distributions are not accounted for in the calculations for F, M and α. Note that the values for M and α in the legend are the starting values, but as the gamma efficiency changes the calculated values for M and α will also change.
The PSD criteria applied 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 an 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 the capability of concern for the bench-top model). However, this
improvement in gamma ray rejection is accompanied by a decrease in the neutron
140
detection efficiency. The gamma ray rejection performance goal for the bench-top test
unit was selected to be better than 10-6. Achieving the target gamma ray rejection will
depend on the data acquisition parameters, and the post processing thresholds. The
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 εγ 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 α > 0. This is due to the fact that for α > 0 there is a larger
contribution to the singles rates 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 simulations where α = 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.
141
Figure 6-5. Detail of the likely region of gamma ray efficiency of interest from Figure 6-4 for the 6LiF/ZnS based bench-top system.
The impact of correlated gamma rays 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 measurements 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
approximately 0.009% (as simulated for a sample with M = 1 and α = 0, the affect 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
significant 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
142
determine the gamma ray rejection capability were made with an incident gamma ray
flux of 5.9 x 107, 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
Table 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 the 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 α 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). However, solutions for M, F and α
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 the impact of εγ > 0 on a measurement, as less than 1-
s is required to compute an answer. The proposed technique should be applied to data
acquired with the 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
143
sample parameters. The PSD parameters could also be relaxed to study the effects of
the misidentified gamma rays on the assay predictions.
144
CHAPTER 7 SUMMARY AND FUTURE WORK
The shortage of 3He has driven an interest in identifying alternatives for neutron
detection applications. This research effort explored 3He free multiplicity counter
configurations. The work performed encompassed three separate areas: simulations,
measurements, and theoretical corrections. The simulations compared the
performance achieved with 10B-based detectors in a multiplicity counter configuration to
a traditional Epithermal Neutron Multiplicity Counter. The simulation methodology
applied for the 10B-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 performing 6LiF/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 10B-based detectors. However, the
simulated performance with the final 6LiF/ZnS model exceeded the Epithermal Neutron
Multiplicity Counter capability. Therefore, 6LiF/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 6LiF/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 of 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
145
plastic light guides layered with 6LiF/ZnS sheets, and photomultiplier tubes coupled to
each end of the detector with tapered light guides.
The gamma ray sensitivity of 6LiF/ZnS is higher than the gamma ray sensitivity of
3He. 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 and 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 have not previously been considered
because of the high level of gamma ray discrimination achievable with 3He. However,
as 3He replacements are explored, the validity of the assumption that the gamma ray
contributions to the measured distributions are negligible 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 system. 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 will 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 efficiencies. The mass should be
calculated both with and without accounting for the gamma ray moments to verify that
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 rays 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 electronics 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 shift register was developed (Appendix C) and tested
compared to traditional shift register outputs, using data collected with a 3He system.
The virtual shift register will have to be adapted for the 6LiF/ZnS bench-top system
outputs, but is expected to provide 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 6LiF/ZnS based system has the potential to be a
viable near-term alternative to 3He for use in neutron multiplicity counters.
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 probabilities 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 (where 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:
6543210
6
1
6
1
6
1
6
1
6
1
6
10)( uuuuuuuuf
The first term of the polynomial represents the probability of obtaining a 0 (note
that the polynomial could be extended beyond u6 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:
x
xuxZP
uZPuZPuZPuZPuZPuZPuf
)(
...)5()4()3()2()1()0()( 543210
Equation A-1
Consider again the PGF for a fair die, it is apparent that
)0()0( ZPf , and
116
11
6
11
6
11
6
11
6
11
6
110)1( xxxxxxxf
148
In general x
xZPf 1)()1(
Equation A-2
The first derivative of f(u) can be taken, and the result is:
5432
6543210
6
16
6
15
6
14
6
13
6
12
6
10
6
1
6
1
6
1
6
1
6
1
6
10)(
uuuuu
udu
du
du
du
du
du
du
du
du
du
du
du
du
duf
du
d
If the derivative is evaluated at u=1 then:
x
xZxPfdu
d)()1(
The expectation value of a function is given by:
x
xZPxfZfE )()())((
Equation A-3
So )()()1( ZExZxPfdu
d
x
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.
)()()1()1(2
2
ZVarxZPxxfdu
d
x
The general expression for a factorial moment is given by:
)()!(
!max
xPkx
xx
k
k
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 gi(u) for u with the
conditional probability P(x,i), which is the probability distribution of obtaining the value x
149
under the condition i. Then let Qi be the probability of obtaining the condition i, the PGF
for x (without condition i) is given by:
0
)()(i
ii ugQuf
Equation A-5
because
0 00 000
)(),(),()(i x
x
i
x
x
i
x
i
x
i
ii uxPuQixPQuixPugQ
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 distribution R(n) can be
defined as:
0
)()(n
nunRuH
Equation A-6
The expression for the probability distribution of neutrons generated by a source
event, including neutrons produced by (α,n) reactions is:
1)()(S
Sq
S
FP sf
Equation A-7
Where F = the fission rate, from which neutrons are emitted with a probability
distribution qsp(ν), Sα = the rate of (α,n) reactions, from which only one neutron can be
obtained, and S = the source rate = F + Sα. The required distribution is that for the
neutrons which escape the sample and are available for detection. Neutrons are
150
independent and indistinguishable, therefore the neutrons that escape per source event
(which generates n neutrons) are simply the percentage that escapes per neutron,
raised to the nth 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, pi. Given that pi 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-pi). When a neutron induces a fission it will
generate n neutrons with a probability piqi(n) where qi(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:
0
1 )()(n
nunruh
Equation A-8
If there is more than one neutron in the system then the PGF is hn(u), which is
equal to h1(u)n, because neutrons are assumed to be independent and
indistinguishable. If multiplication is included:
n
n
iini nrnqppnr ))(()()1()(0
,1
, then the PGF h1(u) is given by:
0
1
00
1 )()())(()()1()(n
n
n
ii
nn
n
iii uhnqpunrnqpupuh
Equation A-9
151
Where
0 0
11 )()()()(n n
n
ii
n
ii uhnqpuhnqp and
0
1 )()(n
n
i uhnq is the PGF for the
number of neutrons emitted by an induced fission event, fi(h1(u)), under the second
property 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(ν) (the probability of ν
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 νth power.
0
1
0 00
)]()[()()()()(
uhPunrPunRuH n
nn
n
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(ν) produces:
0
11 )]())[(()(
uhqS
F
S
SuH sf
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, fsf[h1(u)]. Then,
)]([)()( 11 uhfS
Fuh
S
SuH sf
The derivative of H(u) is:
du
udh
du
uhdf
S
F
du
udh
S
S
du
udH sf )()]([)()( 111
152
1
1 )]([sf
sf
du
uhdf (from the first property of PGFs given above)
And the derivative of h1(u) can be calculated from Equation A-9:
du
udhpp
du
uhdfp
du
upd
du
udhiii
i
i
i )()1(
)]([)1()( 111
Equation A-11
Then
ii
i
p
p
du
udh
1
1)(1
Equation A-12
which is the definition of M.
Now ν1 can be expressed as:
11
)(sfM
S
FM
S
S
du
udH
S, F and Sα are not all known parameters, so ν1 is expressed in terms of α, a
source parameter that can be calculated with multiplicity analysis, which is given by:
1sfF
S
Equation A-13
Then
)1(11 sfMS
F
Equation A-14
Note that the 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 )1(11 sfM .
The higher order derivatives of H(u) can be taken to obtain the second and third
factorial moments.
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 solution 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, corrected for efficiency, as given
in Ensslin et al. [6]:
max
)1()()(n
nn
nPnC
Equation A-15
where
n
is the binomial coefficient and is given by
)!(!
!
nn
.
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
interval (the “gate fraction”). The probability of obtaining a trigger (given n neutrons) is:
dttnf )(
Where f(t) is the detector response function given in Bohnel [22] for an event that
occurs at time t as tetf
1
)( .
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:
154
GPDt
PDt
t dssfp )(
Equation A-16
If you look over all time, the probability of obtaining a trigger and counting j
additional neutrons is:
0
1
, )1(1
)( dtppj
ntfnp jn
t
j
tjt
Equation A-17
So the total probability of counting j neutrons of the detected distribution in a gate
after a trigger is given by:
N
jn
jn
t
j
t dtppj
ntfn
Z
nCjr
1 0
1)1(1
)()(
)(
Equation A-18
Where Z represents a normalization constant. 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 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 on.
By definition, the first factorial moment of a probability distribution must equal one,
which can be used to determine Z. As given in Equation A-4 the factorial moments of a
probability distribution are given by:
155
)()!(
!max
xPkx
xx
kx
k
, so
max
0 1 0
1max
0
max
0
0 )1(1
)()(
)()()!0(
!
j
N
n
jn
t
j
t
jj
dtppj
ntfn
Z
nCjrjr
j
jr
The binomial theorem can be applied to the terms dependent on j which yields:
)1( tt pp =1
Then the integral of f(t) over the given limits is 1, so
1)(
1
0
N
n Z
nnCr
Therefore
N
n n
nnN
n nPnnnCZ
1
max
1
)1()()(
via proof by induction (shown
below) the limits of the summation can be changed as follows:
max
0 0
)1()(
n
nn
nPnZ then
max
0 0
)1()(
n
nn
nnPZ and
0
)1(n
nn
nn
Equation A-19
(Relationship A, shown below) then
1
max
0
max
0
)()(
imumimum
PPZ
Relationship A (proof):
...)1())!2(!2
!(2)1()
)!1(!1
!(10
)1()!(!
!)1(
2211
00
n
nn
n
nn
nnn
nn
Let ν=3, then
156
3366363
366)21(3)1())!0(!3
!3(3)1()
)!1(!2
!3(2)1()
)!2(!1
!3(1
33232
3322031221
Applying Relationship A and the binomial theorem allows the first factorial moment
to be derived as follows:
max
1 2 0
1max
1
max
1 2 0
1
1
max
max
1 2 0
1
1
max
1
max
1
1
)1(1
)()1()(
)1(1
)(
)1()(
)1(1
)()(
)()()!1(
!
j
N
n
jn
t
j
t
n
nn
j
N
n
jn
t
j
t
n
nn
j
N
n
jn
t
j
t
jj
dtppj
ntf
nnP
j
dtppj
ntfn
nP
j
dtppj
ntfn
nCjjjrjr
j
jr
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,
N
n
t
n
nn dtptfn
Pnnr2 0
max
1
1 )()1()()1(1
The integral of the terms dependent upon t can be moved 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:
001
1 )1()1()()(1
n
nnN
n
tn
nnPdtptfr
The second summation is the variance of a distribution, and equal to:
157
nn
nn
nn
n
nn
n
nn
nnnnn
n
nnnn
nnn
)1()!()!2(
)!2()1()1(
)!(!
!
)!2(
!
)1()!(!
!)1()1()1(
2
22
2
00
Now let k=ν-2 and l=n-2, then
lklk
l lkl
k
)1()!(!
!)1(
0
2
Which via the binomial theorem = ν(ν-1)ε2x1
So then,
2
01
1 )1()()(1
N
n
t Pdtptfr
Earlier n =2 was stated, so then
01
2
2
1 )( dtptfr t
This is the first moment of the measured distribution (note that similar steps can be
used to obtain r2). Solving the integrals yields the gate fractions, and then rk can be
used in the equations for the singles, doubles and triples to relate the measured
parameters to the source parameters.
)1(2 1
2
2
1
GPD
eer
Equation A-20
2
1
3
3
2 )]1([3
GPD
eer
Equation A-21
158
101 SrSU s
Equation A-22
111 rSRrD
Equation A-23
2!2
212 rSRrT
Equation A-24
Where S ≡ the source rate. The substitution for r1 and r2 can be made which
produces the following expressions:
)1(2
)1(2
2
2
2
2
1
GPDGPD
eeS
eeS
D
23
323
3
)]1([6
)]1([6
GPDGPD
eeF
eeF
T
Substitution for v1, v2, and v3 can be made to produce expressions in terms of F,
M, and α.
Proof by Induction for Change of Limits (Example)
For a given distribution defined as:
M
n
M
n
nf0
),(
Demonstrate that the limits can be changed as follows:
M
n
M
n
M
n
nfnf0 00
),(),(
Let
M
n
M
n
nfS0
),(
then for
M = 0: )0,0(),(0
0
0
fnfSn n
159
Now let
M
n
nfS0 0
' ),(
then for
M = 0: )0,0(),(0
0 0
' fnfSn
So for M = 0 S = S’.
Now let M = M + 1:
1
010
1
0
1
0
1
0
1
0
1
1
)1,(),1(),()1,(),(
)1,(),(),(
M
n
M
M
M
n
M
n
M
n
M
n
M
n
M
n
M
n
M
n
M
n
M
MnfMfnfMnfnf
MnfnfnfS
M
M
Mf1
),1( is not allowed, therefore
1
0
1 )1,(M
n
M MnfSS
1
0
1
00 0
1
0 0
1
0 0
'
1 )1,(')1,(),(),(),(M
n
M
n
M
n
M
n
M
n
M MnfSMnfnfnfnfS
So for M = M + 1 SM+1 = S’M+1.
Therefore the change of limits will not change the value of the summation.
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, α and F. The M and α variables were
individually held constant while the other variable and F were allowed to vary. The
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 MatLab® 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 α
constant on the difference between the 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 α. Therefore,
an inaccurate assumption for M has a larger impact on the calculated mass value.
Simulations with additional values for M and α could be performed to see how the
variation in the calculated mass is affected.
161
Figure B-1. The change in the calculated mass if M is held constant (M=1) and alpha (α) and the gamma ray efficiency (εγ) are varied.
162
Figure B-2. The change in the calculated mass if alpha (α) is held constant (α=0) and the Multiplication (M) and the gamma ray efficiency (εγ) are allowed to vary.
163
APPENDIX C VIRTUAL LIST MODE SHIFT REGISTER
Traditional shift registers group the perturbations in the pulse train that arrive at
the shift 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 the first
trigger that is long when compared to the die-away time (the delay time is typically
about 4 µs). 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 grouped 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 diagram.
Example calculations for the singles, doubles and triples from data obtained with
12 3He 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.
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(ν) R+A A
0 3895 4571
1 1745 1338
2 575 389 3 150 87
4 33 18
5 6 3 6 1 0.4 7 0 0 8 0 0 ν0 1 1 ν1 0.55 0.39 ν2 0.41 0.25
Singles=U= sum(A) 6406 Doubles=U*( ν1(R+A)-ν1(A)) 1051
Triples=U*( ν2(R+A)-ν2(A)-2*ν1(A)*(ν1(R+A)- ν1(A)))/2
105
The factorial moments were calculated with the formula:
)()!(
!max
Pkk
k
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 register (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 algorithm. The shift register was
constructed to be forward looking, each pulse activated a window to open after the
predelay and the number of pulses with time-stamps less than the trigger pulse time
plus the length of the window were grouped and the appropriate R+A multiplicity was
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 3He 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. The results, below, were found to be in good agreement 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 corresponding factorial moments and singles, doubles and triples.
P(ν) R+A A
0 3896 4685
1 1774 1202
2 574 341 3 143 77
4 30 15
5 5 3 6 1 0.3 7 0 0 8 0 0 ν0 1 1 ν1 0.55 0.39 ν2 0.41 0.25
Singles=U= sum(A) 6323 Doubles=U*( ν1(R+A)-ν1(A)) 1310
Triples=U*( ν2(R+A)-ν2(A)-2*ν1(A)*(ν1(R+A)- ν1(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
different gate locations (the list mode shift register is “forward looking”). There is also
dead-time present in the electronics used to produce the time-stamped pulses for use in
166
the list mode shift 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.
167
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BIOGRAPHICAL SKETCH
Azaree Lintereur received her bachelor’s degree in physics from the University of
Wisconsin Stevens Point and her master’s degree in medical physics from the
University of Florida. Azaree’s research for her master’s degree was in the exploration
of BiI3 for room-temperature gamma ray spectroscopy, culminating in the master’s
project “Theoretical Room Temperature Gamma-Ray Spectroscopy Ability of Bismuth
Tri-Iodide”. Azaree performed the research for her doctorate at Pacific Northwest
National Laboratory, where she has worked on projects involving the identification of
3He-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 Material Management.