FAST TIME-CORRELATION MEASUREMENTS IN NUCLEAR SAFEGUARDS

Transcription

1 POLITECNICO DI MILANO Dipartimento di Ingegneria Nucleare Dottorato di Ricerca in Scienza e Tecnologia negli Impianti Nucleari XIII o ciclo FAST TIME-CORRELATION MEASUREMENTS IN NUCLEAR SAFEGUARDS Misure di correlazione temporale veloce in salvaguardia nucleare Tutore : Chiar.mo Prof. Marzio MARSEGUERRA Co-tutore : Ing. Enrico PADOVANI Tesi di Dottorato di Ricerca di: Ing. Sara A. POZZI Anno Accademico

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3 To speak is to fall into tautologies. This useless and wordy epistle itself already exists in one of the thirty volumes of the thirty shelves in one of the uncountable hexagons and so does its refutation. The Library of Babel, J.L. Borges

4 Table of Contents List of Figures...iv List of Tables...ix Chapter 1: Scope of Nondestructive Assay Techniques Active Nondestructive Assay Measurement Configuration Scope and Organization of this Thesis... 3 Chapter 2: Overview of the Measurement Systems Timing with the Time to Amplitude Converter System Overview Detection System and Electronics The Nuclear Materials Identification System System Overview The 252 Cf Instrumented Source Detection and Data Acquisition System Definition of Covariance and Bicovariance Functions Time of Flight Measurements with the TAC and NMIS Chapter 3: Response in Plastic Scintillators and its Monte Carlo Simulation Response Function for Neutrons and Gamma Rays Neutron Detection Efficiency by a Time of Flight Method Neutron and Gamma Ray Energy Thresholds in Plastic Scintillating Detectors Detector Neutron Counting Efficiency Experimental Setup and Results: Neutron Response Experimental Setup and Results: Gamma Ray Response Comparison of Neutron and Gamma Ray Response Conclusions i

5 TABLE OF CONTENTS 3.4 Comparison of NMIS Time of Flight and MCNP-DSP Simulation Chapter 4: Measurements for Uranium Oxide Samples Measurement Configuration for Uranium Oxide Standards Experimental Results and Discussion Conclusions Chapter 5: The Effect of Neutron and Gamma Ray Cross Talk between Plastic Scintillating Detectors Introduction Measurement Setup Measurement Results and Analysis Source Detectors Bicovariance Functions for Varying Features from the Bicovariance Analysis of the 252 Cf f-n-n Triplet Effects of Neutron and Gamma Cross Talk on Covariance Functions Effect of the Lead Shields on Detector Cross Talk Conclusions Chapter 6: A Solution of the Inverse Problem Based on the Use of Artificial Neural Networks Cf-Source-Driven Simulations Selection of Features for the Sample Identification Algorithm Application of Neural Networks to Nuclear Materials Identification Systems Comparison of Results Summary and Conclusions Chapter 7: Conclusions...77 ii

6 TABLE OF CONTENTS Appendix A: Comparison of 252 Cf and the Associated Particle Sealed Tube Neutron Generator as Interrogation Sources for Uranium Metal Castings...79 Appendix B: The Effect of Voltage and Discriminator Level on Efficiency...85 References...90 Acknowledgments...95 iii

7 List of Figures Figure Typical configuration for source-driven correlation measurements. Figure Schematic diagram of experimental setup. Figure Two fast plastic scintillating detectors: crystal, photomultiplier tube and base are visible. Figure The electronics components of the system. Figure Schematic representation of the pulses arriving at the start and stop inputs of the TAC. Figure Typical NMIS measurement configuration: source and detectors are deployed around the container to be analysed. Figure Cf source ionization chamber and preamplifier. Figure Schematic representation of sequence of counts in 252 Cf source ionization chamber and two detectors. Figure Schematic drawing of the experimental setup. Figure Time of flight spectrum acquired with NMIS (red) and with the experimental apparatus that uses a TAC for timing (blue). Figure Three factors that distort the rectangular recoil proton energy spectrum. iv

8 LIST OF FIGURES Figure Neutron detection efficiency obtained from NMIS time of flight. The solid line has been drawn to guide the eye. Figure Detector efficiency for neutrons for three different CFD levels: 25, 45 and 75 mv. Lines show fits of experimental data points to Equation (3.1). Figure Neutron energy threshold as a function of CFD level (V CFD ): experimental points fitted with E th =0.017 V CFD Figure Detector response to gamma rays shown for various gamma sources. Figure Derivative of detector gamma response: experimental data for 137 Cs and 133 Ba. Maximum value is shown with a circle, half height of this maximum is shown with a square and selected Compton edge value is shown with a triangle. Figure Response data for gamma rays and neutrons as a function of the incident particle energy. Figure Neutron to gamma ray energy ratio as a function of CFD level (mv). Figure Schematic diagram of experimental setup. Figure Time of flight simulations performed with the MCNP DSP code using two different pulse generation times: 1 and 5 ns. Figure Neutron pulses from the detector anode captured with a fast digital oscilloscope. Figure Time of flight for source and detector (solid line) and MCNP DSP simulation of experiment (crosses). Figure Three storage containers for uranium oxide. Starting from the left, models 500 I, 1000 I, and 2000 I. Figure The experimental setup. The 252 Cf source is located in contact with the top detector (labeled A), at the center of its face. v

9 LIST OF FIGURES Figure Measurement result with three samples of enrichment wt% 235 U and mass 125, 500, and 1751 g. Figure Measurement result with three samples of enrichment wt% 235 U and mass 56, 556, and 1667 g. Figure Gamma peak area for uranium oxide samples of varying mass (g) and enrichment 35 wt% 235 U. Exponential fit to experimental data is shown with a solid line. Figure Schematic drawing of measurement setup: top view. Figure Source detectors bicovariance for = 5 cm. Figure Source detectors bicovariance for = 0 cm: top view. Figure Source detectors bicovariance for = 10 cm: top view. Figure Source detectors bicovariance for = 20 cm: top view. Figure Volumes of the ridges f-γ-γ, f-γ-n, f-n-n, and f-n-γ n as a function of the distance between the detectors,. Lines have been drawn to guide the eye. Figure Distribution of source-correlated detection events in detector 1, given a detection in detector 2 within the time range (90 ns). Distances between detectors: = 0, 5, and 25 cm. Figure Ratio of scattered neutron energy to incident neutron energy as a function of the scattering angle in the laboratory system, θ L. Figure Source detectors bicovariance for = 0 cm. Boundary lines given by Equation (5.2) correspond to scattering between detectors at the threshold angle, θ th. vi

10 LIST OF FIGURES Figure Source detectors bicovariance for = 5 cm. Boundary lines given by Equation (5.2) correspond to scattering between detectors at the threshold angle, θ th. Figure Detector 1 detector 2 covariance for different distances between detectors: = 0, 10, and 25 cm. Figure Comparison of features from bicovariance for detectors with and without lead. Figure Source detectors cross-correlation functions for uranium cylinders of different enrichments and fixed mass (20 kg). Figure Source detectors cross-correlation function (R 12 ) for uranium cylinders of varying masses and fixed enrichment (36 % wt 235 U). Figure Source detectors cross-correlation functions for uranium spheres of different enrichments and fixed mass (20 kg). Figure Source detectors cross-correlation function (R 12 ) for uranium spheres of varying masses and fixed enrichment (36 %wt 235 U). Figure Cylindrical samples: F 1 as a function of sample mass (kg) for the four different enrichments. Figure Spherical samples: F 1 as a function of sample mass (kg) for the four different enrichments. Figure Cylindrical samples: F 2 as a function of sample mass (kg) for the four different enrichments. Figure Spherical samples: F 2 as a function of sample mass (kg) for the four different enrichments. Figure Cylindrical samples: F 3 as a function of sample mass (kg) for the four different enrichments. vii

11 LIST OF FIGURES Figure Spherical samples: F 3 as a function of sample mass (kg) for the four different enrichments. Figure Cylindrical samples: F 4 as a function of sample mass (kg) for the four different enrichments. Figure Spherical samples: F 4 as a function of sample mass (kg) for the four different enrichments. Figure ANN structure for the prediction of sample mass and enrichment. Figure ANN and GA approach: selection of network parameters. Figure Neural network prediction of mass and enrichment on the basis of features F 1, F 2, F 3, and F 4 : training set of 19 cases relative to cylinder simulations. The true values are shown with the circles and the values predicted by the network with stars. Figure Neutral network prediction of mass and enrichment on the basis of features F 1, F 2, F 3, and F 4 : training set of 19 cases relative to sphere simulations. The true values are shown with the circles and the values predicted by the network with stars. Figure Neural network prediction of mass and enrichment on the basis of features F 1, F 2, F 3, and F 4 : test set of 11 cases relative to cylinder simulations. The true values are shown with the circles and the values predicted by the network with stars. Figure Neural network prediction of mass and enrichment on the basis of the features F 1, F 2, F 3, and F 4 : test set of 11 cases relative to sphere simulations. The true values are shown with the circles and the values predicted by the network with stars. viii

12 List of Tables Table Data for gamma sources and detector response. Table Characteristics of uranium oxide samples. Table Coefficients of Equation 6.5 for mass and enrichment prediction in both spherical and cylindrical samples. Table Error results for the cylindrical samples. Table Error results for the spherical samples. Table Results for uranium cylinders: ANN, GP, and regression predictions. Training cases are shown in gray, test cases in white. Table Results for uranium spheres: ANN, GP, and regression predictions. Training cases are shown in gray, test cases in white. ix

13 Chapter 1 Scope of Nondestructive Assay Techniques Active nondestructive assay (ANDA) is part of the relatively new measurement science of nondestructive assay (NDA). NDA developed in the late sixties as an alternative method to determine the properties of special nuclear materials, typically uranium and plutonium. At that time large efforts were made to develop methods to complement the more traditional chemical and physical analysis of nuclear materials. The advantages of NDA were soon clear when it became necessary to analyze samples enclosed in special, non-accessible containers. The fissile materials originate from spent fuel reprocessing plants or from the dismantlement of nuclear weapons. NDA systems make use of the penetrating characteristics of nuclear radiation to determine the attributes of the sample without the need of removing it from its container. Applications of this method include nuclear materials control and accountability, reactor physics measurements, nuclear criticality safety, and non-intrusive monitoring of enrichment processes. NDA is based on the spontaneous or stimulated emission of neutrons and gamma rays by the nuclear materials of interest. Isotopes of the fissile elements undergo radioactive alpha and beta decay, emitting a number of associated gamma rays. The evennumbered isotopes undergo spontaneous fission, emitting neutrons and gamma rays. In the odd-numbered isotopes, fission can be induced by the use of an external source of neutrons (ANDA). A wide variety of detectors and detection schemes have been developed to observe the spontaneous or stimulated characteristic radiations emitted by fissile samples. The principles applied in the NDA techniques can be divided in the following categories 1 : (1) gross counting of all radiation emitted, (2) net counting of radiation of a certain energy band, or (3) coincidence or correlation counting. In this thesis I will address the 1

14 SCOPE OF NONDESTRUCTIVE ASSAY TECHNIQUES third category and in particular will investigate the time-correlation measurement of fast neutrons and gamma rays in active mode. 1.1 Active Nondestructive Assay Measurement Configuration A typical configuration for active measurements is shown in Figure 1.1. Neutrons and gamma rays from an interrogation source interact with the material to be analyzed and are detected with appropriate radiation detectors placed on the opposite side of the sample. These detectors are sensitive to fast neutrons and gamma rays emitted from the source, as well as those emitted by the fissile sample. Before reaching the detectors, radiation from the source interacts with the sample according to various processes. Gamma rays interact most probably by Compton scattering. Elastic and inelastic scattering, absorption, and fission are the most likely interaction processes for neutrons. Inelastic scattering and absorption are followed by the emission of de-excitation gamma rays, often in a cascade, whereas fission produces two to three neutrons and seven to eight gamma rays, on average. ANDA is based on the fact that fission emits multiple particles essentially at the same instant, suggesting the use of coincidence counting as a valid method for the detection of fission events. Furthermore, the time at which induced fission occurs is related to the time of neutron emission from the interrogating source. This suggested the ingenious use of a timed source of neutrons by inserting 252 Cf inside a small ionization chamber [Mihalczo, 1970]. The Nuclear Materials Identification System (NMIS), an apparatus for the measurement of time- and frequency- dependent correlation functions between the pulses registered in the detectors, has been developed in the past few years at Oak Ridge National Laboratory [Mihalczo et al., 1997]. An overview of this system is provided in Section For a comprehensive overview of ANDA systems see T. Gozani, Active Nondestructive Assay of Nuclear Materials Principles and Applications, NUREG/CR

15 SCOPE OF NONDESTRUCTIVE ASSAY TECHNIQUES Source 1 2? 3 4 Detectors Figure 1.1. Typical configuration for source-driven correlation measurements. In time-correlation measurements performed with NMIS, it is common to use two or more adjacent detectors to acquire source detector and detector detector correlation functions. These and other signatures have been shown to be sensitive to the amount of fissile mass in the sample to be analyzed. The time-correlated counts in the detectors are closely related to the amount of fissile material inside the sample to be analyzed. Information on the sample s enrichment can be evinced from the cross-correlation measurements because the fission probability of a given fissile mass increases with enrichment. The sample s total mass, another attribute of interest, is related to the attenuation by the sample of the source radiation. In particular, mass is related to gamma ray attenuation features as will be shown in Chapter 4. Because the neutrons emitted by the source are fast, and the detectors sensitive to fast neutrons, the time scale for the correlation measurements is of the order a few tens of nanoseconds. The advantage of measuring fast neutrons over the more traditional use of thermal neutrons is that the fission chains originated by each interrogating neutron are distinct from each other. Indeed, the times involved with thermal neutrons are of the order of a few microseconds, causing the fission chains to interweave. The main disadvantage of measurements involving fast neutrons is that they make use of sophisticated electronics systems. The interaction of the source radiation with the sample depends on the geometry of the measurement configuration and on the composition and mass of the sample. The complexity of the problem suggests the use of Monte Carlo simulations as a valid tool for analysis. 1.2 Scope and Organization of this Thesis The scope of this thesis is to investigate a number of aspects of the safeguards measurements that make use of correlation counting of fast neutrons and gamma rays. 3

16 SCOPE OF NONDESTRUCTIVE ASSAY TECHNIQUES The thesis is organized as follows: Chapter 2 provides an overview of two measurement systems based on the measurement of time-dependent correlations between pulses in detectors. To design and analyze safeguards measurements of the type in consideration, it is very important to simulate correctly the experimental apparatus using Monte Carlo techniques. Chapter 3 contains a discussion on the simulations of the measurement configuration. A calibration of the plastic scintillating detectors is presented having the aim of determining experimental parameters to be used in the simulations. Chapter 4 describes the measurements performed on uranium oxide standards at JRC Ispra and the sensitivity of features extracted from the cross-correlation functions to the total mass of the sample. On the basis of experimental results performed on uranium oxide powder the effect of cross talk between detectors was analyzed. Cross talk consists in the same particle registering a pulse in two neighboring detectors. A set of measurements that make use of higher order statistics was designed and performed to identify the type and degree of cross talk in the standard measurement configuration used with NMIS. The results of these measurements are discussed in Chapter 5. Finally, in Chapter 6 an approach is presented based on the use of artificial neural networks to relate features extracted from the correlation functions to the quantities of interest: mass and enrichment of uranium samples. 4

17 Chapter 2 Overview of the Measurement Systems This chapter describes the characteristics of two measurement systems. The first is composed of commercially available modules and is used for fast neutron and photon time-correlation measurements at the Department of Nuclear Engineering of the Polytechnic of Milan. The second is the Nuclear Materials Identification System (NMIS) developed by the Instrumentation and Controls Division of the Oak Ridge National Laboratory [Mihalczo et al., 1996]. In both systems detection is achieved using plastic scintillating detectors that are sensitive to fast neutrons and gamma rays. The chapter is organized as follows: the next section provides a description of the detection and electronics components of the first measurement system. Section 2.2 describes NMIS. In Section 2.3 a set of measurements comparing the two systems is reported and a brief summary is included. 2.1 Timing with the Time to Amplitude Converter This section describes a measurement system composed entirely of commercially available modules. Correlation timing is achieved using a time to amplitude converter (TAC) System Overview The measurement system is composed of an interrogation source, radiation detectors, detector electronics, and a computer for data acquisition and display. A block diagram of the configuration is shown in Figure

18 OVERVIEW OF THE MEASUREMENT SYSTEMS NEUTRON AND GAMMA RAY SOURCE. NIM Bin N OTE : 1. HV, CFD, Delay, TAC and MCA are installed in NIM Bin on the cart. 2. Neutron source and detectors placed appropriately near item to be measured. DET 1 BC420 PMT PMT BASE ANODE HV CFD IN OUT TAC Start Stop MCA COMPUTER OUT IN OUT DET 2 BC420 PMT PMT BASE ANODE HV CFD DELAY IN IN OUT OUT Monitor Keyboard DET = Detector BC420 = Plastic Scintillator PMT = Photo Multiplier Tube HV = High Voltage CFD = Constant Fraction Discriminator TAC = Time to Amplitude Converter MCA= Multi Channel Analyzer Figure 2.1. Schematic diagram of experimental setup. (Adapted from Mattingly et al., 1998) Detection System and Electronics The detectors and the associated electronics are composed of commercially available modules. The two detectors used are plastic scintillators sensitive to fast neutrons and gamma rays. The crystal, Bicron BC 420, has dimensions 3 by 3 by 3 inches. Two high voltage power supplies power the photomultiplier tube (PMT) bases allowing for independent power adjustment of the two detectors. The detector signal has a rise time of a few ns, allowing very fast timing. A photograph of the two detectors is shown in Figure

19 OVERVIEW OF THE MEASUREMENT SYSTEMS Figure 2.2. Two fast plastic scintillating detectors: crystal, photomultiplier tube and base are visible. Figure 2.3. The electronics components of the system. The signal from the anode of the PMT base is sent to a constant fraction discriminator (CFD), which eliminates pulses having amplitude lower than an adjustable threshold and produces an output pulse that has a constant amplitude and adjustable width. The available CFD model has four independent channels, of which only two are used, one for each detector. The electronics components are shown in Figure 2.3. The first CFD output signal is sent to the start input of a TAC. The second CFD output is delayed by a fixed amount and sent to the stop of the TAC. The purpose of the TAC is that of finding the time interval between pulses to its start and stop inputs and generating an analog output pulse whose amplitude is proportional to the measured time. To minimize the dead time of this module, the start and stop signals are chosen so that the greater rate is at the stop. 7

20 OVERVIEW OF THE MEASUREMENT SYSTEMS The TAC uses an analog technique to convert small time intervals to pulse amplitudes. Two input signals give the start and stop instants to be measured, which are shown schematically in Figure 2.4. The arrival of the leading edge of the start signal opens the start switch, and the converter capacitor begins to charge. The charging continues until the leading edge of a stop signal opens the stop switch or if the TAC time (τ max ) elapses without the arrival of any stop pulse. Any start impulse arriving before the first stop is ignored (in Figure 2.4 start signals labeled 2 and 4), likewise any subsequent stop signal is ignored (stop signal labeled 2) Start signals Stop signals Figure 2.4. Schematic representation of the pulses arriving at the start and stop inputs of the TAC. The voltage developed on the capacitor is proportional to the time interval between the start and stop pulses. After a few microseconds, the TAC is ready to accept the next pair of events. This time will be referred to as the TAC recovery time (t rec ). The result is a train of rectangular output pulses having a width of a few microseconds and an amplitude that is proportional to the time interval between the start and the stop events. The distribution of these pulses is collected in a multichannel analyzer and a time spectrum, with a given time range, is acquired 1. These electronic components are located and powered within a nuclear instrument module bin as shown in Figure 2.3. An assortment of cables and connectors are used to connect the detectors to the processing electronics and data acquisition components. 1 On the basis of experience we can state that the measurement provided by the TAC is equivalent (proportional) to the cross-covariance function of the signals given by the two detectors. The assumptions are that the count rates at the detectors are small compared to the inverse of the delay range, and that the multiplicity (neutron and gamma) of the fission process is reduced to one start and one stop pulse (at most) at the detectors. These two assumptions are always verified in our measurements because the source intensity is not so high, and the detection efficiency is limited by a geometry effect. See also Sections 2.3 and

21 OVERVIEW OF THE MEASUREMENT SYSTEMS Data acquisition is achieved by a commercially available multichannel analyzer, which receives and processes the TAC output. The data from the multichannel buffer is then displayed on a personal computer. The system is compact and has good portability characteristics. 9

22 OVERVIEW OF THE MEASUREMENT SYSTEMS 2.2 The Nuclear Materials Identification System This section provides a brief discussion of the components of the Nuclear Materials Identification System (NMIS). The description begins with an overview of the configuration of NMIS and then provides a brief description of each component System Overview The main difference between NMIS and the measurement system described in Section 2.1 is that NMIS uses an instrumented 252 Cf source 2 [Mihalczo, 1970]. Spontaneous fission events in the source can thus be timed, with efficiency greater than 90%. A photograph of a typical NMIS configuration is shown in Figure 2.5 in which the source and detectors are deployed around the container of a fissile sample. The source is placed on one side of the container and the detectors are located on the opposite side of the container. The source and detector signals are sent to electronic modules for processing and then the signals are sent to the data processing components for data acquisition. Figure 2.5. Typical NMIS measurement configuration: source and detectors are deployed around the container to be analyzed. (Source: Mattingly et al., 1998) 2 The use of the associated particle sealed tube neutron generator as an alternative interrogation source is discussed in Appendix A. 10

23 OVERVIEW OF THE MEASUREMENT SYSTEMS The 252 Cf Instrumented Source A photograph of the source ionization chamber and its preamplifier is shown in Figure 2.6. It consists of a thin layer of 252 Cf plated inside a small parallel-plate ionization chamber, whose plates are 1 mm apart. At each fission, two fission fragments are emitted in opposite directions. The ionization chamber produces an electrical pulse each time a source fission occurs. A preamplifier is used to increase the amplitude of the pulse from the source ionization chamber. The rise time of the pulse is approximately 5 ns [Chiles et al., 1993]. The pulse is then input to a commercially available constant fraction discriminator (CFD), which eliminates pulses having amplitude below a given threshold and produces an output pulse that has constant amplitude and adjustable width. In this way, pulses from 252 Cf alfa-decay can be discarded and spontaneous fission pulses collected. The output of the CFD is input to a delay module, which is used to control the arrival time of pulses from the source to the data processor. The CFD and the delay module are contained within a commercially available nuclear instrument module (NIM) bin that supplies power to these components. An assortment of commercially available cables and connectors are used to connect the source to the electronic components and the data acquisition components. Figure Cf source ionization chamber and preamplifier. (Source: Mattingly et al., 1998) 11

24 OVERVIEW OF THE MEASUREMENT SYSTEMS Detection and Data Acquisition System The detectors are commercially available plastic scintillating detectors. The plastic scintillator is Bicron BC 420 coupled to a fast photomultiplier tube. Similarly to what occurs in the measurement system described in Section 2.1, the NMIS detector pulses are sent to a CFD to eliminate unwanted pulses. Data is acquired from the source and detector channels by a custom-made electronic board. Collection is attained with a 1 ns time resolution. 2.3 Definition of Covariance and Bicovariance Functions Let us consider the sequence of counts in the 252 Cf instrumented source and in two detectors. A schematic representation is given in Figure 2.7. The distribution of twoway coincidence between pairs of sequences over the time delay between counts is given by where τ xy = ty tx. xy x () t and () t R xy ( τ ) = E[ x( t ) y( t )] x y xy x R is known as the covariance between the two sequences of events y. The product of the means, x y, yields the rate of accidental coincidence between the two channels. The covariance is thus the distribution of real two-way coincidences. y 252 Cf 1 ns t x x Detector 1 y t y Detector 2 z t z τ xy τ xz Figure 2.7. Schematic representation of sequence of counts in 252 Cf source ionization chamber and two detectors. 12

25 OVERVIEW OF THE MEASUREMENT SYSTEMS The extension of the covariance function to three sequences of events yields the bicovariance function, or three-way coincidence among three sequences of events: R xyz ( τ, τ ) = E[ x( t ) y( t ) z( t )] x R ( τ τ ) y R ( τ ) z R ( τ ) x y z xy xz x y z yz xz xy xz xz xy xy This distribution is a function of two delays, τ xy = ty tx and τ xz = t z t x. The representation of the bicovariance is thus a three-dimensional surface. We will examine bicovariance functions in detail in Chapter Time of Flight Measurement with the TAC and NMIS A time of flight measurement was performed using the TAC and NMIS (two measurement systems described in Sections 2.1 and 2.2, respectively) with the aim of comparing them. The measurement configuration for the two measurements is given in Figure 2.8 and consists of the instrumented 252 Cf source placed at a distance of 100 cm from one plastic scintillator. The source detector covariance function (also known as time of flight) was collected separately using the two measurement systems. Instrumented source 252 Cf Detector 100 cm Figure 2.8. Schematic drawing of the experimental setup. The result of the two measurements is shown in Figure 2.9. The signature consists of two modes. The first is given by the gamma rays that travel at the speed of light and arrive at the detector after 3.3 ns from the originating 252 Cf fission. After about 10 ns the neutrons arrive on the detector with a distribution that depends on their time of flight and is given by the spectrum of 252 Cf. As it can be seen there is very good agreement between the results given by the two measurement systems. In our application, the count rates of the detectors (

26 OVERVIEW OF THE MEASUREMENT SYSTEMS counts/sec) are small compared to the inverse of the delay range (< 100 ns). In these conditions the TAC, which provides the time interval between successive pulses, can be assumed to give the equivalent of the covariance function of the signals from the two detectors TAC NMIS Source-correlated detector counts per Cf fission Delay (ns) Figure 2.9. Time of flight spectrum acquired with NMIS (red) and with the experimental apparatus that uses a TAC for timing (blue). 14

27 Chapter 3 Response in Plastic Scintillating Detectors and its Monte Carlo Simulation In order to design and analyze safeguards experiments of the type described in Chapter 2, it is necessary to be able to accurately simulate the experimental configuration using a Monte Carlo code. To this end, it is important to understand the mechanisms of interaction of neutrons and gamma rays with the detector materials, and the physics of pulse formation inside the detector. The following section describes the response function of plastic scintillating detectors and the factors that affect it. Section 3.2 describes the measurement of neutron efficiency by a time of flight method and Section 3.3 presents a method for the neutron and gamma ray calibration of the detector. Finally, in Section 3.4 a comparison of a time of flight experiment performed with NMIS and the MCNP-DSP simulation of that experiment is presented. 3.1 Response Function for Neutrons and Gamma Rays Plastic scintillators are composed mainly of hydrogen and carbon. In a scattering interaction with hydrogen, the neutron loses a fraction of its energy with equal probability between zero and the full neutron energy. On average the recoil proton has energy equal to one-half the incoming neutron energy. Scattering from carbon is not likely to contribute directly to a detector count for two reasons. The first is that elastic scattering on carbon results in a maximum energy transfer of only 28% of the incoming neutron energy. The second is that scintillation efficiency decreases considerably for particles with high specific energy loss. For example, the light output of a proton is 40 times that of a carbon nucleus for an energy 15

28 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION deposition of 2 MeV [Verbinski et al., 1968]. It was also shown [Drosg, 1972] that for a 2 MeV neutron threshold the carbon contribution becomes important at neutron energies of about 12 MeV; the energies of interest in our application are considerably lower. However, scattering from carbon affects the detector response function indirectly because a neutron might proceed to interact with hydrogen before escaping from the scintillator. The incident neutron can thus lose between 0 and 28 percent of its initial energy to the first collision on carbon, and deliver a maximum energy between 100 and 72 percent of the original energy in a subsequent scattering on hydrogen [Knoll, 1989]. A simplified detection model for plastic scintillators can thus be developed by considering scattering on hydrogen the predominant mechanism of energy deposition by neutrons. The response function for incident neutron energy E n can be approximated by a rectangular distribution ranging from zero to E n. A number of factors combine to distort this simple distribution and will be discussed in the following paragraphs. Multiple scattering from hydrogen occurring within the scintillation decay time will cause the light from each interaction to be added together and will generate a single pulse. This will affect the response function at higher energy deposited at the expense of the lower energies. Interactions that occur close to the surface of the scintillator lead to the escape of the recoil protons from the surface itself. This circumstance is called edge effect and causes the energy recorded by the detector to be lower than the energy deposited by the neutron. The light output of the scintillator is nonlinear with energy deposition by neutrons. This behavior further distorts the expected rectangular response function. For many organic scintillators the light output is proportional to E 3/2 [Knoll, 1989]. Protons and electrons generate photons in the scintillating material. Another aspect to be considered is the absorption of the scintillation photons on their way to the photocathode through the scintillator material [De Leo et al., 1974]. This causes the detector response to be dependent on the location inside the scintillator at which the collision takes place. Finally, detector resolution affects the recoil proton energy spectrum. Detector response depends on the non-uniform light collection of the detector and other sources of noise. 16

29 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION The effect of three of these factors on the rectangular detector response is shown in Figure 3.1. Figure 3.1. Three factors that distort the rectangular recoil proton energy spectrum (source: Knoll, 1989). The light output of organic scintillating detectors is always higher for electrons per unit energy than for heavy charged particles [Knoll, 1989]. The low Z value of the elements present in plastic results in a very low photoelectric cross section. Compton scattering is the predominant mechanism of gamma ray interaction; a gamma ray spectrum taken with an organic scintillator will therefore show no photo-peak. To perform an efficiency calibration with gamma rays, some point on the Compton edge must be selected and associated with the maximum energy of a Compton recoil electron. I have adopted this procedure when developing a method to correlate the neutron and gamma ray energy thresholds to the discriminator bias level (see Section 3.3). Recently, Reeder and colleagues [1999] have shown that neutron and gamma pulses recorded by fast plastic scintillators cannot be distinguished on the basis of their shape. 17

30 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION Even though it is expected for neutron pulses to exhibit a more structured pulse due to multiple scatterings, gamma pulses were found to have a similar shape. In the following chapters we will see how neutron and gamma ray contributions to time-dependent signatures can be distinguished on the basis of their time of flight. 3.2 Neutron Detection Efficiency by a Time of Fight Method For correlation measurements to be meaningful, and to assure repeatability of the measurements, the detectors used must be operating at a determinate efficiency level. In this section I will describe a method that is standard in NMIS operation to measure neutron detection efficiency by a time of flight approach. The measurement is performed using NMIS by placing the instrumented 252 Cf source at a fixed distance of 100 cm from one plastic scintillator and acquiring the source detector cross-correlation function (also known as time of flight). Neutron detection efficiency is defined, for incident neutron energy E n, as the ratio of the number of neutrons detected C(E n ), to the number of neutrons impinging on the face of the detector N(E n ) ( En ) ( E ) C ε ( E n ) =. N n N(E n ) is defined as N E + de n n ( E ) S g χ( E ) de = ν, n En where S is the detected fission rate of the 252 Cf source ν is the average number of neutrons emitted per 252 Cf fission g is a geometry factor and χ(e) is the neutron fission spectrum of 252 Cf 18

31 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION The number of detections C(E n ) can be derived from the time of flight measurement by 1 d using the relationship between time and energy E n = m, where m is the mass of 2 t the neutron and d is the distance between the source and the detector. The energy of the incident neutron is assigned on the basis of its detection time t. If multiple scatterings occur, the time spent inside the detector is added to the neutron s time of flight. This results in the neutron energy being underestimated. Detector efficiency for a measurement performed with NMIS is shown in Figure 3.2. In NMIS operation, the maximum efficiency is set to approximately 60%. This is accomplished by varying the voltage at the detector s photomultiplier tube and repeating the time of flight measurement until the desired efficiency level has been reached Efficiency (%) Energy of the Incident Neutron Figure 3.2. Neutron detection efficiency obtained from NMIS time of flight. The solid line has been drawn to guide the eye. 1 A rule of thumb for the NMIS plastic scintillators is that a 5 V increase corresponds to a 1% increase in detector efficiency. 19

32 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION Many analytical expressions for the detection efficiency have been derived [Hausser et al., 1983; Fowler et al., 1980; Drogs, 1972]. Although it is desirable in such expressions to use physically meaningful parameters such as the hydrogen scattering cross-section, the density of hydrogen in the scintillator, the spectrum of the incident neutrons, and the discriminator bias, these parameters alone cannot account for all of the factors affecting the response function. Other authors have developed Monte Carlo codes to simulate the detection process [Gul, 1980]. These codes take into account the reaction processes of the neutron with the scintillating material and the light output of those reactions. 3.3 Neutron and Gamma Ray Energy Thresholds in Plastic Scintillating Detectors In this section I present an experimental approach to determine the neutron and gamma ray thresholds in the fast plastic scintillators used in our experiments. Neutron threshold energy is determined using a time of flight technique, whereas gamma ray threshold is inferred by locating the Compton edge on the gamma spectrum for various reference sources. These energy thresholds are then related to the constant fraction discriminator (CFD) levels used in these experiments. As we have seen in Chapter 2, in fast correlation measurements performed with the Nuclear Materials Identification System (NMIS), the output of the plastic scintillating detector is input to a constant fraction discriminator (CFD) which produces a fast NIM signal when a detector pulse exceeds the CFD level. This discriminator level can be set from 20 mv to 1000 mv. In the MCNP-DSP [Valentine, 1997] simulation of the experiment, the neutron and gamma ray thresholds are independently selected in terms of energy deposited in a detector rather than in terms of the detector output signal. It is therefore important to correlate the CFD level to the theoretical gamma and neutron energy thresholds. As we have seen in Section 3.1, the amplitude of the output signal from a detector depends not only on the energy deposited in the detector by a radiation but also on the mechanism of energy deposition. For a given amount of energy deposited, gamma rays 20

33 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION are more efficient than neutrons in producing light. This results in larger pulse amplitudes for gamma rays than for neutrons, given the energy deposited Detector Neutron Counting Efficiency The neutron counting efficiency of the detector versus CFD level was used to calibrate the detector response per neutron energy deposited [Knoll, 1989]. The detection efficiency approaches zero at the neutron energy corresponding to the threshold voltage. At this energy, only neutrons that transfer their entire energy to the recoil proton are detected. Therefore, at this energy the recoil proton energy is equal to the neutron energy. This zero crossing energy was determined by fitting the experimental data to the following empirical efficiency curve: k E = th ε ( E n ) 1 (3.1) En En where E th is the neutron threshold energy. 21

34 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION Experimental Setup and Results: Neutron Response The measurements were performed with the Nuclear Materials Identification System (NMIS) at Oak Ridge National Laboratory. A description of this system can be found in Section 2.2. The detector used in the calibration measurements was a commercially available plastic scintillator sensitive to fast neutrons and gamma rays. The crystal, Bicron BC 420, had dimensions of 3 by 3 by 4 inches. The high voltage setting for the photo-multiplier tube (PMT) of the detector was selected and kept constant throughout the experiment 2. Time of flight measurements were performed with varying CFD levels. The instrumented 252 Cf source was placed at a distance of 1 m from the detector. Efficiency data was acquired for CFD levels varying from 25 to 75 mv. Three of these efficiency curves are shown in Figure mv mv Efficiency (%) mv Energy (MeV) Figure 3.3. Detector efficiency for neutrons for three different CFD levels: 25, 45 and 75 mv. Lines show fits of experimental data points to Equation (3.1). 2 The effect of voltage and CFD level on neutron detection efficiency is discussed in detail in Appendix B. 22

35 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION The threshold energy E th was selected using the zero cross-over point of the theoretical fit given in Equation (3.1). Figure 3.4 shows E th as a function of the CFD level. A linear fit to the experimental values is also shown E th Neutron Energy Threshold (MeV) CFD Discriminator Level (mv) V CFD Figure 3.4. Neutron energy threshold as a function of CFD level (V CFD ): experimental points fitted with E th =0.017 V CFD

36 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION Experimental Setup and Results: Gamma Ray Response Detector response to gamma rays was determined by counting and accumulating the output of the CFD over a 10 second period. The counter records integrated counts in the Compton plateau above the gamma threshold. In order to correlate the gamma threshold to the CFD level, the measurement was repeated for different gamma sources and with varying CFD levels [Craun and Smith, 1970]. The results are shown in Figure 3.5 for various gamma sources: 137 Cs, 22 Na, 60 Co, 54 Mn, and 133 Ba. The location of the Compton edge was determined by taking the derivative of the integrated counts Cs Counts Na Ba-133 Co-60 Mn CFD Discriminator Level (mv) Figure 3.5. Detector response to gamma rays shown for various gamma sources. Previous studies [Dietze and Klein, 1982] have shown that the position of the Compton edge depends on detector resolution. On the basis of these studies we selected the energy corresponding to the midpoint between the Compton peak and half its height as the location of the Compton edge. 24

37 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION The derivative of the detector response is shown in Figure 3.6 for 137 Cs and 133 Ba, with the position of the Compton edge. The gamma energies of the sources are well known (Table 3.1) and can be used to find a relationship between gamma ray energy (MeV) and CFD threshold (mv) Cs-137 Ba-133 Counts/mV Discriminator Level (mv) Figure 3.6. Derivative of detector gamma response: experimental data for 137 Cs and 133 Ba. Maximum value is shown with a circle, half height of this maximum is shown with a square and selected Compton edge value is shown with a triangle. 25

38 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION Table 3.1. Data for gamma sources and detector response Isotope Gamma Energy Intensity Compton Edge Discriminator Level Corresponding to Compton Edge (MeV) % (MeV) (mv) Ba Cs Mn Co Na Comparison of Neutron and Gamma Ray Response The detector response for neutrons and gamma rays can be compared. Figure 3.7 shows the scintillator response as a function of the energy of the incident particle. Linear regressions showed the photon data to be linear with r 2 of 0.991, and r 2 of for the neutron data. Figure 3.8 shows the ratio of neutron-to-gamma ray energy. This ratio varies from 3.2 to 4.6, in good agreement with results found in literature [Craun and Smith, 1970]. 26

39 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION 10 2 CFD Discriminator Level (mv) PHOTON NEUTRON Energy (MeV) Figure 3.7. Response data for gamma rays and neutrons as a function of the incident particle energy Neutron to Gamma Ray Energy Ratio CFD Discriminator Level (mv) Figure 3.8. Neutron to gamma ray energy ratio as a function of CFD level (mv). 27

40 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION Conclusions In this section I presented a method to correlate CFD level and energy deposition by neutrons and photons in a fast plastic scintillating detector. Neutron response data was determined using NMIS to acquire time of flight signatures for varying CFD levels. A number of reference gamma sources was used to determine the gamma ray response of the detector. The results are in good agreement with those found in literature, as well as those adopted in the past few years of NMIS operation. The relationship between neutron and gamma ray energy thresholds and CFD level will be used in finding an agreement between the measured and simulated time of flights and is the subject of the following section. 3.4 Comparison of NMIS Time of Flight and MCNP DSP Simulations MCNP DSP [Valentine, 1997] is an analog code developed from the Monte Carlo code MCNP 4A [Briesmeister, 1993] to simulate the interaction of neutrons and gamma rays with the materials present in the measurement configuration. The code calculates signatures in the time and frequency domain such as auto- and cross-correlation functions and multiplicity from the simulated sequence of counts in the detectors. The versatility of standard MCNP is inherent in the modified version of the code: the user can assign freely the geometry and composition of the measurement considered. The code allows several detector types, based on fission, scattering, and capture reactions. The detectors of interest in our application are scintillators sensitive to fast neutrons and photons and detection is based on scattering reactions. The detection process inside the scintillators is simulated by adding up the energy depositions for a given particle within a certain time denominated pulse generation time. The energy deposited is then compared with a given energy threshold that is specified separately for neutrons and gamma rays by the user. An agreement between the Monte Carlo simulations of cross-correlation functions and the measurement of those functions is essential to design and to analyze safeguards 28

41 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION experiments. Let us consider the simplest measurement that can be performed with NMIS: the 252 Cf instrumented source is placed at a distance of 100 cm from one plastic scintillator, as shown in Figure 3.9. The source detector cross-correlation function between the source and the detector is acquired. Instrumented source 252 Cf Detector 100 cm Figure 3.9. Schematic diagram of experimental setup. The simulation of this experiment using the Monte Carlo code MCNP DSP requires as inputs the neutron and gamma ray energy thresholds for the detection process, as well as the pulse generation time. All energy depositions occurring within this time are added together and compared to the threshold value. The results of simulations for pulse generation times of 1 and 5 ns are shown in Figure As it can be seen, a longer pulse generation time allows the low energy neutrons to contribute a pulse by multiple scattering. This results in the neutron distribution having a longer tail. Conversely, the gamma peak is unaffected by the variations in pulse generation time, because gamma rays travel at the speed of light. To select the correct pulse generation time for the simulation of the detection events inside the scintillator, we examined the detector pulse shape for neutrons experimentally. 29

42 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION pulse generation time = 5 ns pulse generation time = 1 ns Coincident counts per Cf fission per ns Delay (ns) Figure Time of flight simulations performed with the MCNP-DSP code using two different pulse generation times: 1 and 5 ns. A time of flight method was used to distinguish between neutron and gamma ray pulses from the detector. The 252 Cf instrumented source was placed at a distance of one meter from the detector and the signal from the source was delayed by a fixed amount (equal to the time it takes for a 1 MeV neutron to reach the detector). The delayed signal from the source and the signal from the detector were sent to an and gate. In this way we were able to distinguish the neutron pulses and capture a few of them with a fast digital oscilloscope (1 GHz bandwidth). Three of these pulses are shown in Figure

43 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION 0 0 Pulse amplitude (V) Pulse amplitude (V) Time (ns) Time (ns) Pulse Amplitude (V) Time (ns) Figure Neutron pulses from the detector anode captured with a fast digital oscilloscope. The structure in the neutron pulses is given by subsequent scattering events. As it can be seen, the pulse amplitude is essentially given by the first interaction of the neutron with the detector material; Subsequent scatterings appear in the pulse shape as wiggles below the maximum pulse amplitude and a pile-up effect is not likely to occur [see also Reeder et al., 1999; Stromswold et al., 1998]. As a result of this observation a short pulse generation time appears to be the best choice in the MCNP DSP simulation of the experiment. The neutron and gamma ray energy thresholds were selected using the experimental calibration discussed in Section 3.3. The pulse generation time was set at 1 ns. Figure 3.12 shows the comparison between the measured time of flight and the simulation of the measurement. In the measurement the CFD level was set at 40 mv, corresponding, by the calibration discussed in Section 3.3, to a neutron energy threshold of 1.16 MeV and a gamma ray energy threshold of 0.27 MeV. The pulse generation time was set at 1 ns on the basis of the discussion of the preceding paragraph. 31

44 RESPONSE IN PLASTIC SCINTILLATORS AND ITS MONTE CARLO SIMULATION As it can be seen in Figure 3.12, there is good agreement between the simulated and measured time of flight. Notice that in the simulation the gamma peak appears as a narrow peak at time equal to the time of flight of the gamma rays. In the measurement the gamma peak has a finite width of about 5 ns. This time gives an indication of the resolution of the entire NMIS system, consisting of the detector and the associated electronics. There is a slight disagreement in the tail of the neutron portion of the time of flight. This disagreement is given by the presence of the carbon atoms inside the detector materials. As we have seen in Section 3.1, neutron scattering on carbon is less efficient in terms of light production inside the detector. This effect is not taken into account in the code, in which energy depositions on protons and on carbon nuclei are given the same weight in terms of light production MCNP-DSP simulation NMIS measurement Coincident counts per Cf fission per ns Delay (ns) Figure Time of flight for source and detector (solid line) and MCNP DSP simulation of experiment (crosses). 32

45 Chapter 4 Measurements for Uranium Oxide Samples This chapter describes a set of measurements performed using the 252 Cf technique for the characterization of uranium oxide standards at the Performance Laboratory of the Joint Research Center, Ispra. The measurements had the aim of determining the total mass of the fissile samples. 4.1 Measurement Configuration for Uranium Oxide Standards The samples analyzed are 24 uranium oxide powder standards of varying mass and enrichment. The characteristics of the samples are given in Table 4.1. Mass values vary from 55 to 1750 g and enrichment values are 19.9, 35.0, 60.0, and 92.4 %wt 235 U. Table 4.1. Characteristics of Uranium Oxide Samples Sample Identification U-235 wt% Enrichment Total U Weight (g) Container Model U I U I U I U I U I U I U I U I U I U I U I U I U I U I U I U I 33

46 MEASUREMENTS FOR URANIUM OXIDE SAMPLES U I U I U I U I U I U I U I U I U I The uranium oxide powder is enclosed in cylindrical, steel containers. Three models are available: 500 I, 1000 I, and 2000 I. All containers have diameter equal to 9.5 cm, whereas their height is equal to 8.4, 14.4 and 29.4 cm, respectively. A photograph of the three containers is shown in Figure 4.1. Figure 4.1. Three storage containers for uranium oxide. Starting from the left, models 500 I, 1000 I, and 2000 I. The measurement system requires the use of an interrogation source, radiation detectors, detector electronics, and a computer for data acquisition and display. The system is described in detail in Section 2.1. The measurement setup was determined by performing a large number of Monte Carlo simulations using the MCNP-DSP code. A photograph of the final configuration is shown in Figure 4.2. The 252 Cf interrogating source is placed at the center of the face of Detector A. At each spontaneous fission of 252 Cf, a start pulse is given in Detector A. Then, neutrons and gamma rays from the source interact with the sample and are detected by a second detector placed underneath the sample (Detector B in Figure 4.2). 34

47 MEASUREMENTS FOR URANIUM OXIDE SAMPLES The distance between detectors is kept constant for all measurements. The measurement configuration allows the radiation from the source to traverse the material of the sample. A Uranium oxide sample B Figure 4.2. The experimental setup. The 252 Cf source is located in contact with the top detector (labeled A), at the center of its face. The signal from the anode of each PMT base is sent to a constant fraction discriminator (CFD), which eliminates unwanted pulses and produces an output pulse that has a constant amplitude and adjustable width. The CFD output signal is sent to the start of a time-to-amplitude converter (TAC). The second CFD output is delayed by a fixed amount and sent to the stop of the TAC. The TAC output is an analog pulse whose amplitude is proportional to the time interval between the two pulses. The data acquisition component is constituted by a commercially available multi-channel buffer, which receives and processes the TAC output. The true coincidence rate as a function of the delay between counts is given by the acquired signature minus the product of the rates at the two detectors, which constitutes the chance coincidence rate. 35

48 MEASUREMENTS FOR URANIUM OXIDE SAMPLES 4.2 Experimental Results and Discussion The following figures show the number of counts in Detector B correlated to counts in Detector A for different uranium oxide samples as a function of the delay between counts. Figure 4.3 shows the result for three masses and enrichment equal to 19.9 wt% 235 U. Figure 4.4 shows the result for enrichment equal to 92.4 wt% 235 U. Similar results were found with the samples of enrichment 35 and 60 wt%. 36

49 MEASUREMENTS FOR URANIUM OXIDE SAMPLES 10 0 Counts in det 1 correlated with counts in det 2 per Cf-252 fission g 500 g 1751 g Delay (ns) Figure 4.3. Measurement result with three samples of enrichment wt% 235 U and mass 125, 500, and 1751 g Counts in det 1 correlated with counts in det 2 per Cf-252 fission g 556 g 1667 g Delay (ns) Figure 4.4. Measurement result with three samples of enrichment wt% 235 U and mass 56, 556, and 1667 g. 37

50 MEASUREMENTS FOR URANIUM OXIDE SAMPLES The acquired signatures consist of two modes. The first is given by the gamma ray contribution: Gamma rays travel at the speed of light and reach Detector B after about 1 ns from the originating 252 Cf fission. The directly transmitted neutrons arrive on Detector B after about 10 ns. Then, the scattered neutrons and the neutrons from fission induced inside the sample arrive on the detector. The neutron distribution presents a larger spread because neutrons travel at different speeds (given by the energy spectrum of 252 Cf). Previous measurements and calculational studies [Mattingly et al., 1998] have shown the sensitivity of the neutron part of the distribution to the sample s enrichment. In the present measurements such sensitivity was not observed, perhaps because of the limited mass of the samples. From the observation of the measurement results shown in Figures 4.3 and 4.4 it is clear that the attenuation of the source radiation increases with increasing sample mass. On the basis of previous work [Mattingly et al., 1998; Pozzi and Segovia, 2000; Uckan et al., 1999] which showed the gamma ray contribution to the correlation curve to be related to the total mass of the sample, we selected the area of the gamma peak as the feature to be related to the total uranium oxide mass. The gamma peak area is shown in Figure 4.5 as a function of sample mass for the samples with 35 wt% 235 U enrichment. As it can be seen there is a variation of a factor of about 7 in the selected feature for variations in the sample mass from 140 to 1700 g, approximately. Similar sensitivity was observed for the sets of samples having different enrichment. 38

51 MEASUREMENTS FOR URANIUM OXIDE SAMPLES Area of gamma peak Mass (g) Figure 4.5. Gamma peak area for uranium oxide samples of varying mass (g) and enrichment 35 wt% 235 U. Exponential fit to experimental data is shown with a solid line 4.3 Conclusions In this chapter I have reported the results of measurements performed for the characterization of uranium oxide powder of varying mass and enrichment. The aim of the measurements was to find the total mass of the samples analyzed. The results reported in Section 4.2 show that the area of the gamma peak is a good indicator of the total mass of the samples. In particular, I have reported a variation of a factor of approximately 7 in the area of the gamma peak for variations in the sample mass of a factor of approximately 12. The analysis of an additional experimental configuration, in which the two plastic scintillators were placed close to each other revealed a pronounced gamma peak, presumably due to the gamma rays from nuclear de-excitation of the daughters of uranium-238. To investigate the possibility of a single gamma ray giving a pulse in adjacent detectors, a set of measurements was designed, and is the subject of the following chapter. 39

52 Chapter 5 The Effect of Neutron and Gamma Ray Cross Talk between Plastic Scintillating Detectors Cross talk occurs when a particle that is detected in a detector is subsequently detected in a neighboring detector. In this chapter a method is proposed to determine the type and degree of neutron and gamma ray cross talk between fast plastic scintillating detectors that are placed in proximity of one another. To this end, a set of measurements was performed using the Nuclear Materials Inspection System (NMIS) to acquire the time-dependent bicovariance functions [Mattingly, 1998] of the pulses in the detectors. The acquired signatures were then analyzed to infer the degree and type of neutron and gamma ray scattering between the detectors. Recently, a few works on the effect of cross talk on correlation counting experiments have been reported [Desesquelles et al., 1991; Wang et al., 1997]. Cross talk rejection methods have been suggested based on neutron proton kinematics and time of flight considerations [Ghetti et al., 1999]. 5.1 Introduction In fast time-correlation measurements it is common to use two or more adjacent detectors to acquire source detector and detector detector time-dependent correlation functions. These and other signatures have been shown to be sensitive to the amount of fissile mass in the sample to be analyzed. In such applications correlated counts are due to fission events induced in the fissile material, whereby neutrons and gamma rays are emitted simultaneously and correlated in time with the neutron that induced fission. The time-correlated counts in the detectors are thus closely related to the amount of fissile material inside the sample to be analyzed. 40

53 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS In this context, it is desirable to minimize the amount of false coincidences given by neutron and gamma ray cross talk. These events give time-correlated pulses in the detectors that are not directly related to fission events, thus concealing the required signal. Cross talk identification is of interest in many other applications in which detectors are placed close to each other and correlation measurements are performed. Such applications include the study of heavy-ion induced reactions and spectroscopy [Kuznetsov et al., 1994; Wang et al., 1997] and interferometric experiments [Desesquelles et al., 1991; Ghetti et al., 1999; Pluta et al., 1998]. The organization of the chapter is as follows: Section 5.2 is a description of the measurement setup, whereas Section 5.3 gives measurement results and analysis. In Section 5.4 comments are made on the effect of cross talk on covariance functions. In Section 5.5 the effect of lead shields placed on the detectors is examined. Finally, in Section 5.6 conclusions are drawn and a brief summary is given Measurement Setup Active measurements were performed with NMIS in which the 252 Cf instrumented source was placed at a distance of one meter from the two detectors, as shown in Figure 5.1. The 252 Cf source provides a timed source of neutrons and gamma rays. Each spontaneous fission event emits, on average, four neutrons and seven to eight gamma rays. The detectors are Bicron - BC 420 fast plastic scintillators. The crystal dimensions are 3.75 by 3.75 by 4 inches. The sides of the detectors are shielded with 1/4 inch of lead. The distance d between the source and each detector was held constant at 100 cm. Six measurements were performed, with distance between detectors equal to 0, 5, 10, 15, 20, and 25 cm. By increasing the distance between the detectors the solid angle between them decreases [Gotoh and Yagi, 1971]. Therefore more cross talk should occur for smaller and less for larger. Conversely, true coincidences from the multiple particles emitted by 252 Cf are independent of the distance between the detectors because the solid angle subtended by the detectors to the source does not change. There is however some anisotropy among the fission products [Vandenbosch and Huizenga, 1973]. For example, the angle between fission neutrons is more likely to be 180 and 0 and less likely to be 90. This circumstance should not affect our measurements 41

54 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS because the distance d between the source and the detectors is considerably larger than the distance between the detectors. Lead shield d Det. 1 Cf 252 d Det. 2 Figure 5.1 Schematic drawing of measurement setup: top view Measurement Results and Analysis The source detector 1 detector 2 bicovariance consists of pairs of counts in the two detectors correlated with a 252 Cf fission. This signature is shown in Figure 5.2 for = 5 cm. The time at which a pulse occurs in detector 1 after a source fission is τ 1, and τ 2 is the time at which it occurs in detector 2 after a source fission. The following are the possible triplets of events that contribute to the bicovariance: 1. f-γ-n and f-n-γ 2a. f-n-n and f-n -n 2b. f-n 1 -n 2 3. f-n-γ n and f-γ n -n 4. f-γ-γ where f is a 252 Cf fission, γ is a gamma detection, and n is a neutron detection. The order represents a 252 Cf fission, detection in detector 1 and detection in detector 2. The pair n 1 -n 2 indicates two different neutrons, while the pair n-n indicates the same neutron before and after scattering. 42

55 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS The features in Figures 5.2 and 5.3 are numbered according to the possible triplets of events given above. In feature 1, a gamma pulse in one detector is followed by a neutron pulse from the same fission in the second detector. For example, a gamma ray reaches detector 1 at τ 1 equal to 3.3 ns, whereas a neutron reaches detector 2 at τ 2 greater than τ 1, and varying according to the spectrum of the neutrons emitted by 252 Cf. This occurrence gives the ridge along axis τ 2. The opposite is also possible, giving a second, symmetric ridge along axis τ 1. In features 2a and 2b, two neutron pulses in the two detectors form the triplet. This instance can be given by two different neutrons n 1 -n 2 generated by the same 252 Cf fission event as in 2b or by the scattering of one neutron from one detector to the other n-n as in 2a. These two different cases give rise to two components: the first gives a small, broad distribution oriented in the center of the τ 1, τ 2 plane (2b), whereas the second gives two distinct, symmetric ridges (2a). A neutron generating a gamma ray in one detector n-γ n that gives a pulse in the other detector produces feature 3. The secondary gamma rays can be generated by a (n, n γ) reaction or a (n, γ) reaction. The result is a ridge along the τ 1= τ 2 line, because the gamma ray reaches the second detector almost instantaneously. Finally, fission-gamma-gamma triplets f-γ-γ, labeled 4, can be originated by two distinct gamma rays or by a single gamma ray scattering from one detector to the other. Either process results in the same τ 1 -τ 2 pair. The two process therefore cannot be resolved as in the n-n cases between feature 2a and 2b of the bicovariance. 43

56 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS 2a 2b τ 2 4 τ 1 Figure 5.2 Source detectors bicovariance for = 5 cm. 44

57 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS Source Detectors Bicovariance Functions for Varying. Figures 5.3 through 5.5 show the top view of the source detectors bicovariance functions for = 0, 10, and 20 cm respectively. Inspection of these figures shows that some of the ridges depend on the detector-detector distance whereas others do not. The fission-gamma-neutron ridges, f-γ-n, (labeled 1) are not affected by changes in. This is because there are no (γ, n) processes present. The fission-neutron-neutron ridges, f-n-n (labeled 2a) move and decrease as increases. On the other hand, the f- n 1 -n 2 feature is only mildly dependent on. The f-γ n -n ridge (labeled 3) and the fission gamma-gamma ridges, f-γ-γ (labeled 4) do not change position although their volume changes, as will be shown in the Section b 3 τ 2 2a 1 4 τ 1 Figure 5.3 Source detectors bicovariance for = 0 cm: top view. 45

58 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS Figure 5.4 Source detectors bicovariance for = 10 cm: top view. Figure 5.5 Source detectors bicovariance for = 20 cm: top view. 46

59 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS Features from the Bicovariance Figure 5.6 shows the volumes of the ridges given by the f-γ-γ, f-γ-n, f-n-n, and f-n-γ n triplets as a function of the distance between the detectors,. As it can be seen, only f-γ-n triplets are independent of the distance between detectors, indicating that scattering does not affect this particular signature. On the other hand f-γ-γ, f-n-n, and f-n-γ n triplets are strongly affected by scattering. The volume of the ridge given by these triplets increases approximately by a factor of two for the f-γ-γ triplet and a factor 14 for the f-n-n, and f-n-γ n triplets f-γ-γ f-γ-n f-n-n f-n-γ n Volume of ridges from bicovariance function Distance between detectors (cm) Figure 5.6 Volumes of the ridges f-γ-γ, f-γ-n, f-n-n, and f-n-γ n as a function of the distance between the detectors,. Lines have been drawn to guide the eye. Integration of the source detectors bicovariance function along one of the τ axes yields a signature that is related to the source detector covariance function. More precisely, it represents the number of counts in one detector correlated to a source fission, given that a pulse has occurred in the second detector within the time range considered (90 ns, in 47

60 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS our case). This integration of the bicovariance functions collected in Section gives the signatures shown in Figure 5.7 for distance between detectors equal to 0, 5, and 25 cm. The top curve represents the configuration with the greatest amount of cross talk: the detectors are adjacent. By increasing the distance between the detectors, cross talk probability decreases. Correspondingly, the source-correlated detections decrease. As it can be seen in Figure 5.7 the effect is considerable. Figure 5.7. Distribution of source-correlated detection events in detector 1, given a detection in detector 2 within the time range (90 ns). Distances between detectors: = 0, 5, and 25 cm 48

61 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS Analysis of the 252 Cf f-n-n Triplet The f-n-n scattering process can be modeled based on a single hydrogen scattering assumption. From this model the outer boundary of the f-n-n ridges can be predicted. Let τ 1 and τ 2 be the times after a 252 Cf source fission at which a detection occurs in detector 1 and detector 2, respectively. In the following discussion is based on the following assumptions: 1. scattering occurs on H only, and 2. only one scattering event occurs before the neutron escapes the detectors. Let E 1 be the neutron energy before detection in detector 1. The energy after the first collision is E E 2 2 = 1 cos θ (5.1) L where θ L is the scattering angle in the laboratory system. A plot of the ratio of the energy of the scattered neutron to that of the incident neutron is given in Figure 5.8. Neutron scattering on hydrogen is forwardly directed in the laboratory system E 2 / E θ L Figure 5.8 Ratio of scattered neutron energy to incident neutron energy as a function of the scattering angle in the laboratory system,θ L. 49

62 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS The relationship between energies allows us to write a relationship between τ 1 and τ 2 d = τ 2 τ 1 1 (5.2) d1 cosθ L where d 1 and d 2 are the distances from the source to the first collision and from the first to the second collision respectively. As we have seen in Chapter 3, for a count to be recorded in the detectors the neutron must deposit an energy exceeding the threshold value set at the constant fraction discriminator (CFD). This minimum energy corresponds to a maximum scattering angle θ th given by 1 E θ cos th th = (5.3) E1 A neutron scattered at an angle greater than θ th cannot register a pulse in the second detector because it has insufficient energy. In our experiment, the CFD level was set at 40 mv, corresponding to a neutron energy threshold of 1.16 MeV. Using Equation (5.3) with E 1 = 2 MeV, for example, gives θ th scattering once in the first detector at angles less than θ th = For larger values of, neutrons cannot hit the second detector. Substituting θ th into Equation (5.2) allows us to determine the relationship between detection times that is shown with solid black lines in Figures 5.9 and These lines are the outer boundary of the fission-neutron-neutron cross talk ridges, and correspond to the longest delay between counts in the two detectors for a single scattering on hydrogen. 50

63 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS Figure 5.9. Source detectors bicovariance for = 0 cm. Boundary lines given by Equation (5.2) correspond to scattering between detectors at the threshold angle, θ th. Figure Source detectors bicovariance for = 5 cm. Boundary lines given by Equation (5.2) correspond to scattering between detectors at the threshold angle, θ th. 51

64 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS 5.4 Effects of Neutron and Gamma Cross Talk on Covariance Functions Source detector and the detector detector covariances are among the signatures acquired with NMIS. These signatures have been shown to be sensitive to sample enrichment. The effect of cross talk on these signatures can be divided into two categories. The first is given by particles that are unrelated to the source fission (for example gamma rays coming from the deexcitation of the nuclei of the sample or background radiation). The second is due to particles that are time-correlated to the source. The use of higher order statistics [Mattingly et al., 2000] to correlate detector pulses to the initiating source fission can eliminate the effect of the first type of scattering 1, but not the effect of the second. Detector detector covariances were acquired with NMIS for varying distances between detectors, in the measurement configuration described in Section 5.2. Figure 5.11 shows the detector detector covariances for different values of. The combined effect of γ-γ and n-γ n scattering between detectors is evident in the gamma peak. The n-n scattering gives two symmetric peaks. In common operation, = 0 cm and this effect appears as shoulders to the gamma peak. As expected, γ-n and n-γ pairs are not affected by scattering. 1 In particular, a method was proposed [Mattingly et al., 2000] based on the measurement of sourcecorrelated detector pairs (source detectors bicovariance functions) for the reduction of background processes that produce mutually correlated particles. Such processes include spontaneous fission or multiple gamma emissions from nuclear deexcitation. 52

65 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS Evidence of (γ γ ) and (n γ n) scattering Evidence of (n n ) scattering (γ n) pairs Figure Detector 1 detector 2 covariance for different distances between detectors: = 0, 10, and 25 cm. 5.5 Effect of the Lead Shields on Detector Cross Talk The experiment described in Section 5.2 was repeated with the lead shields removed from the detectors, for distance between detectors equal to zero. Figure 5.12 shows the volumes of the ridges defined in Section 5.3 for this experiment in comparison with the same configuration using the lead shields. As it can be seen, the volume of the ridges resulting from a measurement performed using lead shields on the detectors are considerably smaller than the volume of the ridges from the measurement without the shields. In particular, f-γ-γ triplets increase by a factor six when the lead shields are removed. These triplets are composed of both true gamma-gamma coincidences and gamma-gamma scattering events (cross talk). Because the probability of true coincidences does not change in the two measurements, the increase is attributed to 53

66 NEUTRON AND GAMMA RAY CROSS TALK BETWEEN PLASTIC SCINTILLATORS gamma-gamma cross talk. Similarly, f-n-γ n increases by 93%, f-γ-n by 40% and f-n-n by 74%. 1,20E+05 1,00E+05 8,00E+04 6,00E+04 4,00E+04 Serie1 Pb Serie2 bare 2,00E+04 0,00E+00 (f, 1γ, γ ) (f, 2n, γ n ) (f, γ, 3n) (f, n, 4n ) Figure Comparison of features from bicovariance for detectors with and without lead. 5.6 Conclusions In this chapter measurements performed with NMIS have been used to quantify the interaction between fast plastic scintillating detectors used in time-correlation measurements. By maintaining a constant distance between source and detectors, and varying the distance between detectors, it turns out that both neutron and gamma ray cross talk contribute significantly to the observed signatures. Furthermore, gamma rays that are generated by neutron interactions in one detector can proceed to give correlated pulses in the second detector. These effects are considerable and must be taken into account in determining the rate of true coincidences in measurements that make use of detectors placed close to each other. The methodology proposed in this chapter is applicable to other situations in which detectors are stacked and correlation measurements are performed. Such applications include nuclear interferometry, in-beam studies of heavy-ion induced reactions, and spectroscopy. 54

67 Chapter 6 A Solution of the Inverse Problem Based on the Use of Artificial Neural Networks As we have seen in the preceding chapters, nuclear materials safeguard efforts necessitate the use of nondestructive methods to determine the attributes of fissile samples enclosed in special, non-accessible containers. Usually, a given set of statistics of the stochastic neutron photon coupled field, such as source detector, detector detector cross correlation functions, and multiplicities are measured over a range of known samples to develop calibration algorithms. In this manner, the attributes of unknown samples can be inferred by the use of the calibration results. The sample identification problem, in its most general setting, is then to determine the relationship between the observed features of the measurement and the sample attributes and to combine them for the construction of an optimal identification algorithm. The goal of this chapter is to develop an artificial intelligence (AI) approach to this problem whereby artificial neural networks (ANN) are used for sample identification purposes. To this end, the time-dependent MCNP DSP Monte Carlo code has been used to simulate the neutron photon interrogation of sets of uranium metal samples by a 252 Cf source. The resulting sets of source detector correlation functions, R 12 (τ) as a function of the time delay, τ, served as a data-base for the training of the AI algorithms. The organization of this chapter is as follows: Section 6.1 describes the Monte Carlo simulations of source detector cross correlation functions for a set of uranium metallic samples interrogated by the neutrons and photons from a 252 Cf source. From this database, a set of features is extracted in Section 6.2. The use of ANN to provide sample mass and enrichment values from the input sets of features is illustrated in Section 6.3. Section 6.4 presents the comparison of two artificial intelligence methods. Finally, in Section 6.5 conclusions are drawn. 55

68 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN Cf-Source-Driven Simulations 1 The uranium sample to be analyzed is placed between the source and two fast plastic scintillating detectors. The source is located at 25.4 cm from the center of the uranium metal sample at a height of 10 cm. The detectors, cm width and height and 5.08 cm thick, are placed one on top of the other at a distance of 25.4 cm from the center of the sample. Simulations were performed with cylindrical and spherical samples of seven different masses (8, 10, 12, 14, 16, 18, and 20 kg). The different masses were obtained by increasing the sample radius, both in the case of the cylinders (in which case the height was kept constant at 20 cm) and in that of the spheres. For each mass, four different enrichments were tested ranging from depleted to highly enriched (0.2, 36.0, 50.0, and wt% 235 U). Two additional simulations were run for both cylinders and spheres giving a total of 30 simulations for the cylindrical samples and 30 for the spherical ones. An additional simulation run with no sample between source and detectors will be referred to as the void simulation. The source detectors cross-correlation functions [R 12 (τ)] are generated by correlation of the source signal with the combined signal from the two detectors, and normalizing to the source count rate to remove the dependence on the source strength. In Figure 6.1 the cross-correlation R 12 (τ) as a function of the delay time between source fission and corresponding detection is shown for cylinders of varying enrichment and fixed mass (20 kg). The curve consists of two major components: a first peak due to directly transmitted gamma rays from the 252 Cf fission (the photon peak), and a second, broader peak given by directly transmitted and scattered neutrons from the source and secondary neutrons and gamma rays from fission induced inside the uranium sample. As it can be seen from the figure, the directly transmitted gamma rays are not very sensitive to the fissile mass because gamma ray attenuation is not related to fission. On 1 The simulations presented in this chapter were performed previously to the work described in Chapter 3. Thus, the energy thresholds for neutrons and gamma rays and the pulse generation time parameters used in the simulations were selected on the basis of experience and not optimized. This fact does not invalidate the methodology presented in this chapter. 56

69 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN the other hand, the second peak of the cross-correlation function depends strongly on enrichment. In the first part of the second peak the curves show similar behavior for time lags below 20 ns, because the directly transmitted neutrons and secondary photons are not strongly dependent on enrichment. Above time lags of about 20 ns, the peak broadens: neutrons generated by secondary fission inside the fissile material increase and the number of neutron generations increases. The total path covered by the neutrons before a detection event occurs also increases. In Figure 6.2 the cross-correlation function obtained with spherical samples is shown. The first peak is much higher than in the case of the cylinders. This can be explained in terms of the greater attenuation given by the geometry of the cylindrical samples whereas the spherical samples allow more gamma rays from the source to reach the detectors directly. Figures 6.3 and 6.4 show the source detectors cross-correlation function in the case of cylinders and spheres of varying mass and constant enrichment (36 wt% 235 U). In this case, both the gamma peak and the secondary peak height are inversely related to mass: as the sample mass increases, so does the attenuation of gamma rays and neutrons. A similar relationship was found with other values of enrichment. 57

70 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN wt% 50 wt% wt% 10-5 Source-correlated detector counts per source fission Delay ns Figure 6.1. Source detectors cross-correlation functions for uranium cylinders of different enrichments and fixed mass (20 kg) kg 14 kg 8 kg Source-correlated detector counts per source fission Delay ns Figure 6.2. Source detectors cross-correlation function (R 12 ) for uranium cylinders of varying masses and fixed enrichment (36 % wt 235 U). 58

71 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN Source-correlated detector counts per source fission wt% 50 wt% wt% Delay (ns) Fig Source detectors cross-correlation functions for uranium spheres of different enrichments and fixed mass (20 kg) Source-correlated detector counts per source fission kg 14 kg 8 kg Delay (ns) Figure 6.4. Source detectors cross-correlation function (R 12 ) for uranium spheres of varying masses and fixed enrichment (36 %wt 235 U). 59

72 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN 6.2 Selection of Features for the Sample Identification Algorithm The selection of features for the sample identification algorithm was performed on the basis of their relationship to sample attributes and of their ability to discriminate between close numerical values within each attribute group. The first feature (F 1 ) chosen is the integral of the cross-correlation function at time lags from 0 to 8 ns, normalized to the same integral of the void calculation. It essentially corresponds to the normalized area of the first peak of the cross-correlation function. F 8 R i= 0 = 1 8 R i= Void ( τ ) i ( τ ) i (6.1) A plot of F 1 as a function of the sample s total mass is given in Figures 6.5 and 6.7, for all values of enrichment. Figure 6.5 refers to cylinder simulations, whereas Figure 6.6 refers to sphere simulations. As expected, F 1 depends only on the sample mass. The second feature chosen is the integral of the cross-correlation function at time lags from 0 to100 ns, normalized to the same integral of the void simulation. F 100 R i= 0 = R i= Void ( τ ) i ( τ ) i (6.2) Inspection of Figures 6.7 and 6.8 shows that F 2 is sensitive to both the sample s total mass and enrichment. The moments of the cross correlation function were also examined: τ ( n) 100 R i= 0 = 100 R i= 0 12 n ( τ ) i τ i 12 ( τ ) i (6.3) 60

73 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN However, up to n=3, all the moments examined looked very much alike, with the n=1 moment giving the best resolution. Hence, the average delay time, τ, was selected as the feature F 3, shown in Figures 6.9 and 6.10 for cylindrical and spherical samples, respectively. This feature is essentially constant for the depleted samples, increases with sample enrichment and for high enrichments is very sensitive to sample mass. Because the asymmetry of the second peak is generated by the neutron induced fission in the sample, the skewness of the cross correlation function was selected as feature, F 4, defined by the relation below. µ 3 3 σ F = (6.4) 4 where σ 3 is the cube of the standard deviation and µ 3 is the third moment about the mean value of the distribution. As shown in Figures 6.11 and 6.12, F 4 is especially sensitive to the lower values enrichment of the samples. 61

74 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN F % 36.0% 50.0% 93.15% Mass (kg) Figure 6.5. Cylindrical samples: F 1 as a function of sample mass (kg) for the four different enrichments F % 36.0% 50.0% 93.15% Mass (kg) Figure 6.6. Spherical samples: F 1 as a function of sample mass (kg) for the four different enrichments. 62

75 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN % 36.0% 50.0% 93.15% F Total mass (kg) Figure 6.7. Cylindrical samples: F 2 as a function of sample mass (kg) for the four different enrichments % 36.0% 50.0% 93.15% F Total mass (kg) Figure 6.8. Spherical samples: F 2 as a function of sample mass (kg) for the four different enrichments. 63

76 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN wt% 36.0 wt% 50.0 wt% wt% 30.5 F Mass (kg) Figure 6.9. Cylindrical samples: F 3 as a function of sample mass (kg) for the four different enrichments wt% 36.0 wt% 50.0 wt% wt% F Mass (kg) Figure Spherical samples: F 3 as a function of sample mass (kg) for the four different enrichments. 64

77 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN F wt% 36.0 wt% 50.0 wt% wt% mass (kg) Figure Cylindrical samples: F 4 as a function of sample mass (kg) for the four different enrichments wt% 36.0 wt% 50.0 wt% wt% 1.6 F mass (kg) Figure Spherical samples: F 4 as a function of sample mass (kg) for the four different enrichments. 65

78 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN 6.3. Application of Neural Networks to Nuclear Materials Identification Systems Two three-layered artificial neural networks were trained to generate a mapping from input (F 1, F 2, F 3, and F 4 ) to output (sample s mass and enrichment). Artificial neural networks are information processing systems composed of simple processing elements (nodes) linked by weighted connections [Marseguerra et al., 1992; Rumelhard and McClelland, 1986; Uhrig, 1991]. In the simplest form, the multilayered feed-forward neural network consists of three layers of processing elements: the input, the hidden and the output layers. The signal is processed forward from the input to the output layer. Each node collects the output values, weighted by the connection weights, from all the nodes of the preceding layer, processes this information through a transfer function, and then delivers the result towards all the nodes of the successive layer. The values of the connection weights are determined through a training procedure. In this case we have adopted the well-known error back-propagation algorithm which follows from the general gradient descent method. It consists of an iterative gradient algorithm designed to minimize the mean square error between the network output and the true value. After a series of preliminary calculations the activation functions were chosen to be sigmoidal from the input to the hidden layer, and linear from the hidden layer to the output. The number hidden nodes was set to two. The values of learning rate and momentum for the training were optimized by a genetic algorithm as described in the following section. The network structure is shown in Figure

79 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN Input layer: features F 1 F 2 F 3 F 4 Bias Hidden layer: Sigmoidal activation function Bias Output layer: Linear activation function Sample mass or enrichment Figure ANN structure for the prediction of sample mass and enrichment. The genetic algorithm technique is based on the concepts of Darwinian evolution. There is an initial population of chromosomes strings of data each containing a certain number of genes, one for each quantity of interest. An objective function (fitness function) to be maximized is properly defined and each chromosome gives a different value of the objective function. An initial, random population is allowed to evolve mainly through mating, cross-over, and mutation, similarly to what happens in biological systems. Each individual in the population is then assigned a fitness value (the fitness function depending on the nature of the problem to be solved). The evolution of the population is governed in such a way as to maintain genetic diversity, so that several possible chromosomes are explored. At the same time, the successive generations gradually converge towards the fittest chromosome, which gives the highest value of the objective function. 67

80 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN In our application each chromosome codes the learning rate and momentum values of a neural network which is trained for a predetermined number of iterations (typically 1000 cycles). The fitness function is defined as the inverse of the training error. The individuals are sorted in order of decreasing fitness, and a new population is created according to the rules of mating, cross-over, mutation, etc. The procedure is repeated until a pre-established number of generations is reached. The values of learning rate and momentum which maximize the fitness function are then used in training the neural network for predicting the total mass and enrichment on the basis of the four features F 1 -F 4. The structure of the ANN-GA approach is shown in Figure Genetic Algorithm Population of chromosomes (bit - strings) Individuals sorted Decoding Network error Assignment of Fitness True Mass/Enrichment Network parameters: Learning rate Momentum Features F 1, F 2, F 3, F 4 Neural network Predicted Mass/Enrichment Figure ANN and GA approach: selection of network parameters. Having chosen the ANN structure shown in Figure 6.13, the output is given by the simple analytical formula below: 68

81 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN Output = 1+ e a i= bi F i + b e a 2 i= ci F i + c 5 + a 3 (6.5) where a i, (i=1,2,3), b j, c j, (j=1, 5) are coefficients which depend on the network s weights, given in Table 6.1, and the output is the sample mass and enrichment. Table 6.1: Coefficients of Equation 6.5 for mass and enrichment prediction in both spherical and cylindrical samples. Cylinder mass Cylinder enrichment a Sphere mass a a a a a b b b b b b 3.34 b b b b c c c c c c c c c c a Sphere a a enrichment a a a b b b b b b b b b b c c c c c c c c c c The sample mass and enrichment predictions obtained with the ANN GA approach are shown in Figures 6.15 through simulations, about two thirds of the data available, were selected for the ANN training. Figures 6.15 and 6.16 refer to cylinder simulations and sphere simulations, respectively, used during the network training. The ANN were tested with the remaining 11 cases: The results are shown in Figures

82 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN and Inspection of these results shows that the present type of neural network can predict enrichment and mass values for uranium metallic samples to a very good approximation both in the case of the training patterns and in the test cases. 70

83 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN enrichment % wt mass (kg) Figure Neural network prediction of mass and enrichment on the basis of features F 1, F 2, F 3, and F 4 : training set of 19 cases relative to cylinder simulations. The true values are shown with the circles and the values predicted by the network with stars enrichment % wt mass (kg) Figure Neural network prediction of mass and enrichment on the basis of features F 1, F 2, F 3, and F 4 : training set of 19 cases relative to sphere simulations. The true values are shown with the circles and the values predicted by the network with stars. 71

84 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN enrichment % wt mass (kg) Figure Neural network prediction of mass and enrichment on the basis of features F 1, F 2, F 3, and F 4 : test set of 11 cases relative to cylinder simulations. The true values are shown with the circles and the values predicted by the network with stars enrichment % wt mass (kg) Figure Neural network prediction of mass and enrichment on the basis of the features F 1, F 2, F 3, and F 4 : test set of 11 cases relative to sphere simulations. The true values are shown with the circles and the values predicted by the network with stars. 72

85 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN 6.4 Comparison of Results The inverse problem was also solved using genetic programming (GP) [Pozzi and Segovia, 2000], an artificial intelligence algorithm based on the concept of parse tree. A parse tree represents a mathematical expression that codes the transfer function between input and output values. Parse trees constitute the elements of a population that is allowed to evolve according to rules that resemble those of a genetic algorithm. After a predetermined number of generations, the fittest individual is selected, representing an explicit mathematical expression that solves the problem. Both ANN and GP predicted the mass and enrichment of the unknown samples with good approximation. In order to make a more meaningful comparison of the results we applied a standard regression to predict the mass and enrichment of the cylindrical and spherical samples. Tables 6.2 and 6.3 summarize the error for the three techniques for both training and test cases. The error measure used is: Error = i real i i predicted real i i Table 6.2: Error results for the cylindrical samples. Cylinder PREDICTED BY GP PREDICTED BY ANN PREDICTED BY Regression MASS ENRICH MASS ENRICH MASS ENRICH Training 0.71% 1.67% 0.22% 2.07% 3.05% 14.81% Test 1.34% 2.16% 0.81% 2.14% 2.69% 12.68% Extra 0.45% 8.18% 0.13% 9.05% 1.87% 10.52% Table 6.3: Error results for the spherical samples. Sphere PREDICTED BY GP PREDICTED BY ANN PREDICTED BY Regression MASS ENRICH MASS ENRICH MASS ENRICH Training 0.17% 2.95% 0.27% 2.20% 1.95% 21.37% Test 0.15% 2.38% 0.27% 4.59% 2.18% 14.71% Extra 0.38% 14.00% 0.72% 13.33% 1.08% 43.40% 73

86 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN The tables show that ANN and GP are comparable and more effective than a regression in solving the prediction problem. ANN and GP are capable of dealing with non-linear problems and this is demonstrated in the case of the enrichment for both configurations, cylinder and sphere, in which the linear solution, the regression, performs very poorly, indicating that the problem is strongly non-linear. We have found non-remarkable differences in the performance of the artificial intelligence techniques. The last two cases (bottom two rows in the following tables) of the test sets had enrichment values selected outside of the training set range. These can be used to test the overfitting of the models. The error in predicting these enrichment values range from 8% to 14%, indicating that some overfit has taken place. This can be explained by considering that there were only four values of enrichment in the training set, covering a wide range of enrichment, from depleted to highly enriched uranium. Better results can be obtained by adding more cases to the training set. Tables 6.4 and 6.5 show the prediction results and error for both GP and ANN compared to the linear regression for cylinders and spheres, respectively. 74

87 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN Table 6.4: Results for uranium cylinders: ANN, GP, and regression predictions. Training cases are shown in gray, test cases in white. REAL PREDICTED BY GP ERROR PREDICTED BY NN ERROR PREDICTED BY RegreERROR MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH 8,00 0,20 8,0-0,03 0,02 0,23 8,0-0,09 0,00 0,29 8,6 14,23 0,6 14,03 10,00 0,20 9,9 0,23 0,08 0,03 10,0 0,88 0,01 0,68 10,5 14,36 0,5 14,16 12,00 0,20 11,9 0,63 0,12 0,43 12,0 1,30 0,04 1,10 12,5 7,23 0,5 7,03 14,00 0,20 14,0 0,47 0,01 0,27 14,0-0,25 0,03 0,45 14,1-0,96 0,1 1,16 16,00 0,20 16,0 1,48 0,04 1,28 16,0-0,06 0,02 0,26 15,8-8,05 0,2 8,25 18,00 0,20 17,8 2,18 0,24 1,98 17,8 0,20 0,20 0,00 17,1-12,70 0,9 12,90 20,00 0,20 20,2-0,18 0,17 0,38 20,0 0,57 0,00 0,37 18,6-19,80 1,4 20,00 8,00 36,00 8,0 36,20 0,01 0,20 8,0 36,79 0,01 0,79 8,2 37,40 0,2 1,40 10,00 36,00 10,0 36,56 0,02 0,56 10,0 35,82 0,03 0,18 10,2 42,57 0,2 6,57 12,00 36,00 11,9 37,54 0,13 1,54 12,0 37,25 0,02 1,25 12,6 42,76 0,6 6,76 14,00 36,00 14,0 34,85 0,02 1,15 14,0 35,12 0,04 0,88 14,4 40,42 0,4 4,42 16,00 36,00 16,0 35,58 0,01 0,42 16,0 36,28 0,00 0,28 16,4 40,25 0,4 4,25 18,00 36,00 17,7 34,90 0,34 1,10 17,9 36,43 0,13 0,43 18,1 38,77 0,1 2,77 20,00 36,00 19,8 35,01 0,17 0,99 20,1 39,43 0,06 3,43 19,8 41,67 0,2 5,67 8,00 50,00 8,0 51,94 0,00 1,94 8,0 46,45 0,02 3,55 7,9 43,54 0,1 6,46 10,00 50,00 10,1 49,06 0,05 0,94 10,0 49,50 0,04 0,50 10,0 52,34 0,0 2,34 12,00 50,00 12,0 51,12 0,01 1,12 12,0 50,52 0,01 0,52 12,5 55,34 0,5 5,34 14,00 50,00 14,2 50,28 0,18 0,28 14,1 48,35 0,11 1,65 14,5 54,75 0,5 4,75 16,00 50,00 16,0 50,23 0,02 0,23 16,1 47,82 0,08 2,18 16,6 53,02 0,6 3,02 18,00 50,00 17,9 50,89 0,10 0,89 18,0 47,63 0,03 2,37 18,4 52,20 0,4 2,20 20,00 50,00 20,7 52,47 0,67 2,47 20,4 50,22 0,43 0,22 20,4 54,75 0,4 4,75 8,00 93,15 8,0 92,45 0,02 0,70 8,0 92,30 0,02 0,85 7,0 69,83 1,0 23,32 10,00 93,15 10,1 93,53 0,08 0,38 10,0 94,32 0,03 1,17 9,1 84,38 0,9 8,77 12,00 93,15 11,9 93,51 0,10 0,36 12,0 93,23 0,01 0,07 11,6 89,51 0,4 3,64 14,00 93,15 14,2 93,71 0,22 0,56 14,0 92,71 0,02 0,45 13,8 92,79 0,2 0,36 16,00 93,15 16,2 95,09 0,25 1,94 16,0 93,61 0,03 0,46 16,0 93,74 0,0 0,59 18,00 93,15 17,6 92,77 0,38 0,38 17,8 91,47 0,20 1,68 17,9 91,69 0,1 1,46 20,00 93,15 20,1 92,94 0,15 0,21 20,0 93,33 0,00 0,18 20,0 92,32 0,0 0,83 15,00 65,00 15,0 68,93 0,00 3,93 15,0 64,51 0,01 0,49 15,6 69,32 0,6 4,32 17,00 15,00 16,9 17,61 0,14 2,61 17,0 21,75 0,03 6,75 17,0 19,09 0,0 4,09 75

88 A SOLUTION OF THE INVERSE PROBLEM BASED ON THE USE OF ANN Table 6.5: Results for uranium spheres: ANN, GP, and regression predictions. Training cases are shown in gray, test cases in white. REAL PREDICTED BY GP ERROR PREDICTED BY NN ERROR PREDICTED BY Regre ERROR MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH MASS ENRICH 8,00 0,20 8,0 2,04 0,00 1,84 8,0 0,49 0,02 0,29 7,8 31,08 0,25 30,88 10,00 0,20 10,0-0,85 0,03 1,05 10,0-1,90 0,01 2,10 10,3 18,43 0,28 18,23 12,00 0,20 12,0-1,09 0,04 1,29 12,0-2,76 0,00 2,96 12,5 7,86 0,47 7,66 14,00 0,20 14,0 0,05 0,04 0,15 14,0-1,24 0,02 1,44 14,4-0,31 0,43 0,51 16,00 0,20 16,0 0,40 0,00 0,20 16,1-0,32 0,10 0,52 16,2-7,30 0,25 7,50 18,00 0,20 18,0-0,01 0,02 0,21 18,1 0,50 0,07 0,30 17,9-13,73 0,14 13,93 20,00 0,20 20,0-0,19 0,04 0,39 20,0-0,10 0,01 0,30 19,4-21,25 0,65 21,45 8,00 36,00 8,0 33,77 0,02 2,23 8,0 34,14 0,04 1,86 7,7 41,67 0,29 5,67 10,00 36,00 10,0 35,95 0,02 0,05 10,0 36,14 0,00 0,14 10,2 35,97 0,24 0,03 12,00 36,00 12,0 37,54 0,03 1,54 12,0 36,82 0,02 0,82 12,4 34,22 0,45 1,78 14,00 36,00 14,0 35,15 0,01 0,85 14,0 35,38 0,04 0,62 14,4 33,19 0,41 2,81 16,00 36,00 16,0 35,99 0,04 0,01 16,1 35,10 0,07 0,90 16,3 36,76 0,30 0,76 18,00 36,00 18,0 37,44 0,02 1,44 17,9 34,82 0,13 1,19 18,0 43,12 0,03 7,12 20,00 36,00 20,0 33,15 0,02 2,85 20,1 34,19 0,06 1,82 19,6 49,50 0,40 13,50 8,00 50,00 8,0 51,73 0,01 1,73 8,0 42,75 0,04 7,25 7,3 53,82 0,68 3,82 10,00 50,00 10,0 53,13 0,00 3,13 10,0 49,36 0,04 0,64 9,9 49,56 0,10 0,44 12,00 50,00 12,0 47,52 0,02 2, ,79 0,00 1, ,09 0,14 4,91 14,00 50,00 14,0 50,71 0,00 0,71 14,0 51,36 0,02 1,36 14,2 48,61 0,18 1,39 16,00 50,00 16,0 51,70 0,01 1, ,85 0,05 0, ,98 0,10 2,98 18,00 50,00 17,9 52,04 0,05 2, ,71 0,01 1, ,77 0,17 9,77 20,00 50,00 20,0 47,02 0,03 2,98 19,9 48,14 0,07 1,87 19,5 67,54 0,48 17,54 8,00 93,15 8,0 91,80 0,01 1, ,65 0,04 1, ,48 0,54 26,67 10,00 93,15 10,0 93,57 0,05 0, ,28 0,03 0, ,82 0,04 21,33 12,00 93,15 12,0 92,58 0,01 0,57 12,0 91,28 0,02 1,87 12,2 80,42 0,25 12,73 14,00 93,15 14,0 92,14 0,03 1, ,23 0,05 0, ,07 0,30 3,08 16,00 93,15 16,0 93,33 0,02 0, ,97 0,01 1, ,54 0,22 1,39 18,00 93,15 18,0 95,31 0,02 2,16 17,9 91,02 0,06 2,14 18,1 95,40 0,05 2,25 20,00 93,15 20,0 93,27 0,03 0, ,40 0,03 0, ,09 0,12 0,94 17,0 40,00 17,1 47,20 0,10 7,20 17,2 46,64 0,18 6,64 17,2 48,94 0,23 8,94 9,0 15,00 9,0 14,50 0,00 0,50 9,0 14,31 0,01 0,69 9,0 29,93 0,05 14, Summary and Conclusions Monte Carlo simulations of the source detector cross-correlation function for various sample shapes, mass, and enrichment values were performed to serve as a training set for artificial neural networks. The input presented to the algorithms was in the form of features extracted from the physical properties of the cross-correlation functions related to mass (beam attenuation) and to enrichment (fission induced pulse broadening). The ANN algorithm showed good capabilities and robustness for mass and enrichment predictions of uranium metal samples. These results serve as a proof of principle for the application of combined stochastic and artificial intelligence methods to safeguards procedures. 76

89 Chapter 7 Conclusions In this work a number of aspects were investigated concerning safeguards measurements based on fast time-correlations between the neutron and gamma pulses registered by appropriate detectors. The measurement system under consideration uses 252 Cf as a timed source of neutrons and gamma rays for the interrogation of fissile samples. Plastic scintillators placed on the other side of the item to be analyzed detect fast neutrons and gamma rays originating from the source and from the item. Source detector and detector detector covariance functions are acquired. These and other signatures from the time and frequency domain were shown to be sensitive to the mass and enrichment of the fissile samples. This methodology is based on the fact that fission emits simultaneously multiple particles, and that this emission is correlated in time with the neutron that induced the fission. The novelty of this approach is that it employs fast neutrons so that the time scales are of the order of tens of nanoseconds. The applications of this method include reactor physics measurements, nuclear criticality safety, nondestructive analysis and monitoring of enrichment (or deenrichment) processes. To the end of designing and analyzing safeguards experiments it is important to be able to accurately simulate the entire measurement configuration, consisting of the interrogation source, the material to be analyzed, and the radiation detectors. The interaction of the neutrons and gamma rays with the fissile sample and the detectors is complex, suggesting the use of Monte Carlo simulations as a valid tool for analysis. Detector response was investigated to determine the parameters that are needed for the Monte Carlo simulation of the measurement configuration. To this end, a calibration of the plastic scintillators to neutrons and gamma rays was performed. A set of measurements was described for the characterization of uranium oxide standards. The source detector covariance function was acquired for samples of 77

90 different enrichment and mass. A feature from the covariance, the area of the gamma peak, was shown to be sensitive to the total uranium oxide mass. On the basis of experimental results performed on the uranium oxide samples, the effect of cross talk between detectors was analyzed. Cross talk occurs when the same particle registers a pulse in two neighboring detectors. A methodology based on the use of higher order statistics was presented: a set of measurements to acquire source detectors bicovariance functions was designed and performed to identify the type and degree of cross talk in the standard measurement configuration used with the Nuclear Materials Identification System. Evidence of neutron neutron and gamma gamma cross talk was found and independently evaluated. Furthermore, an effect was identified by which neutrons interacting in one detector generate a gamma ray by inelastic scattering, which then proceeds to register a pulse in a neighboring detector. The results of these measurements showed that cross talk effects in the plastic scintillators under consideration are significant. Future work will be aimed at cross talk rejection procedures in the configurations examined. The method proposed is applicable to other situations in which detectors are stacked and correlation measurements are performed. Finally, an approach was presented based on the use of artificial neural networks to successfully relate features from the correlation functions to the quantities of interest: mass and enrichment of uranium samples. A properly trained neural network enables real time sample identification, an important characteristic in safeguards operations. The training of the neural network was accomplished with Monte Carlo simulations of the measurements. The system described, composed of detectors and associated electronics and a properly trained ANN is a portable tool for the real time characterization of fissile materials. 78

91 Appendix A Comparison of 252 Cf and the Associated Particle Sealed Tube Neutron Generator as Interrogation Sources for Uranium Metal Castings A few preliminary simulations were performed to evaluate the associated-particle sealed tube neutron generator (APSTNG) for use as an interrogation source in the sourcedriven noise analysis method for the assay of nuclear materials. In the Nuclear Materials Identification System (NMIS) developed at the Oak Ridge National Laboratory, the cross-correlation function between the detector responses and the neutron source is one of the signatures acquired. Previous studies and measurements have demonstrated the sensitivity of this and other related signatures to fissile mass. A few of the practical advantages associated with the APSTNG timed source of neutrons are: it is directional, can be turned off, and emits only one neutron per deuterium tritium reaction. The main disadvantages being that it is larger than the 252 Cf spontaneous fission source and that it is much more costly. The purpose of the simulations reported here is to compare the sensitivity of the APSTNG source to a 252 Cf source for the assay of uranium metal castings. To this end, a large number of MCNP-DSP Monte Carlo simulations were performed to obtain source-detector covariance functions. The results compare the simulated signatures for two different types of sources: (1) 252 Cf source in an ionization chamber and (2) an associated particle DT neutron generator of 14.1 MeV neutrons. The commercially available associated particle 14.1 MeV neutron generator detects a cone of alpha particles from the DT reaction. Because the 14.1 MeV neutrons are emitted in opposite direction with respects to the alpha particle, a cone of neutrons is defined and can be aimed at the fissile material. 79

92 COMPARISON OF 252 Cf AND APSTNG AS INTERROGATION SOURCES This source has several advantages over 252 Cf, three of which are: (1) one neutron is emitted per source event so all pairs come from induced fissions, (2) all neutrons emitted have the same velocity so all transmitted neutrons arrive at the detectors at a known time with all fission neutrons arriving at the detector at later times, and (3) it is directional. MCNP-DPS simulations were performed for the standard uranium metal castings [Mattingly et al., 1998] for storage at the Oak Ridge Y-12 plant with the source on one side and four fast plastic scintillation detectors on the opposite side, as shown in Figure A.1. The detectors, cubes of side 7.62 cm, were placed one on top of the other in a 2 by 2 array. The distance between the source and the casting, x s and the distance between the detectors and the castings, x d in Figure A.1 were varied to study the effect of distance on sensitivity of the time dependent signatures to fissile mass. Uranium metal casting Detectors Source x s x d Figure A.1. Top view of the geometry used in the MCNP-DSP simulations. x s and x d are the source-to-casting and detector-to-casting distances, respectively. The source-detectors covariance functions [R 12 (τ)] are generated by correlating the source signal the emission of an alfa-particle within the useful cone with the combined signal from the four detectors, and normalizing to the number of neutrons emitted by the source. The resulting signature represents the number of counts in the detectors correlated with a source event, per source neutron. R 12 (τ) is calculated for different distances of the source and detectors from the outer diameter of the casting (distances labeled x s and x d in Figure 2.1 equal to 0, 20 and 35.5 cm) and two enrichments 93.2 and 0.2 wt% U-235. The following figures illustrate the separate neutron and photon contributions to the cross-correlation functions for the different geometric configurations. The figures show 80

93 COMPARISON OF 252 Cf AND APSTNG AS INTERROGATION SOURCES that time of flight effects distort the neutron signature when 252 Cf is used as an interrogation source so that at large distances the differences between the neutron distributions after 252 Cf fission decrease, making the distinction between enrichments more difficult. For the source and detectors in contact with the casting the results presented in Figures A.2 and A.3 show that it does not matter which source is used to distinguish highly enriched uranium from depleted uranium, for either neutron or the photon signatures. The result for x s = x d = 20 cm presented in Figures A.4 and A.5 show that for the neutron signatures for the 252 Cf source the ability to distinguish between highly enriched uranium and depleted is evident after about 30 ns and that for the photons occurs as early as 10 ns. For the APSTNG source the results are distinguishable after the transmitted 14.1 MeV neutrons reach the detectors. The ability to distinguish is least for the 252 Cf source at larger spacing: x s = 41.7 and x d = 35.5 cm. These results are shown in Figures A.6 and A.7. For this distance the APSTNG source is superior to 252 Cf for ability to distinguish between highly enriched uranium and depleted. Using the 252 Cf source the ability to distinguish between the two samples is evident at 60 ns whereas that for the APSTNG occurs much earlier, at approximately 18 ns. 81

94 COMPARISON OF 252 Cf AND APSTNG AS INTERROGATION SOURCES coincident counts per neutron Number of source events 60 e6 APSTNG deplete APSTNG 93 wt% Cf-252 deplete Cf wt% x s =0 cm x d =0 cm Delay (ns) Figure A.2. Source-detector covariance functions for uranium metal castings of different enrichments interrogated by 252 Cf and APSTNG source. Neutrons only. coincident counts per neutron Number of source events 60 e6 APSTNG deplete APSTNG 93 wt% Cf-252 deplete Cf wt% x s =0 cm x d =0 cm Delay (ns) Figure A.3. Source-detector covariance functions for uranium metal castings of different enrichments interrogated by 252 Cf and APSTNG source. Photons only. 82

95 COMPARISON OF 252 Cf AND APSTNG AS INTERROGATION SOURCES coincident counts per neutron Number of source events 120 e6 APSTNG deplete APSTNG 93 wt% Cf-252 deplete Cf wt% x s = 20 cm x d = 20 cm Delay (ns) Figure A.4. Source-detector covariance functions for uranium metal castings of different enrichments interrogated by 252 Cf and APSTNG source. Neutrons only coincident counts per neutron Number of source events 120 e6 APSTNG deplete APSTNG 93 wt% Cf-252 deplete Cf wt% x s =20 cm x d =20 cm Delay (ns) Figure A.5. Source-detector covariance functions for uranium metal castings of different enrichments interrogated by 252 Cf and APSTNG source. Photons only. 83

96 COMPARISON OF 252 Cf AND APSTNG AS INTERROGATION SOURCES 10-3 coincident counts per neutron Number of source events 300 e6 APSTNG deplete APSTNG 93 wt% Cf-252 deplete Cf wt% x s = 35.5 cm x d = 41.9 cm Delay (ns) Figure A.6. Source-detector covariance functions for uranium metal castings of different enrichments interrogated by 252 Cf and APSTNG source. Neutrons only coincident counts per neutron Number of source events 300 e6 APSTNG deplete APSTNG 93 wt% Cf-252 deplete Cf wt% x s = 35.5 cm x d = 41.9 cm Delay (ns) Figure A.7. Source-detector covariance functions for uranium metal castings of different enrichments interrogated by 252 Cf and APSTNG source. Photons only. 84

97 Appendix B The Effect of Voltage and Discriminator Level on Efficiency A set of measurements was performed with NMIS to study the effect of voltage and discriminator level on detection efficiency. Source-detector time of flight was acquired using a 4 by 4 by 4 inch detector. Voltage on the PMT tube was varied from 1460 to 1600 V and discriminator level was varied from 30 mv to 100 mv. Figure B.1 shows the time of flight for fixed voltage (1500 V) and varying CFD level. Figure B.2 shows the time of flight for fixed CFD level (40 mv) and varying voltage. Table B.1 gives the values of the neutron and photon peak areas of the covariance function, whereas Table B.2 gives the values of the maximum detection efficiency for neutrons and neutron energy threshold for varying voltage and CFD level. A graphical representation of this data is given in Figures B.3 and B Counts in detector correlated to source fission mv 60 mv 100 mv Time lag (ns) Figure B.1. Time of flight for source and detector for different CFD levels: 30, 60, and 100 mv. Voltage was kept constant at 1500 V. 85

98 THE EFFECT OF VOLTAGE AND DISCRIMINATOR LEVEL ON EFFICIENCY 10-2 Count in detector correlated to source fission V 1550 V 1600 V Time lag (ns) Figure B.2. Time of flight for source and detector for different voltages: 1500, 1550, and 1600 V. CFD level was kept constant at 40 mv. 87

99 THE EFFECT OF VOLTAGE AND DISCRIMINATOR LEVEL ON EFFICIENCY Table B.1.a: Neutron Peak Area PMT Voltage (V) CFD level Table B.1.b: Photon Peak Area PMT Voltage (V) CFD level x x Neutron Peak Area Photon Peak Area CFD level (mv) Voltage (V) CFD level (mv) Voltage (V) 1600 Figure B.3. Neutron peak area and photon peak area as a function of CFD level (mv) and voltage (V). 88

100 THE EFFECT OF VOLTAGE AND DISCRIMINATOR LEVEL ON EFFICIENCY Table B.2.a: Maximum Neutron Efficiency PMT Voltage (V) CFD level Table B.2.b: Neutron Energy Threshold PMT Voltage (V) CFD level Maximum Efficiency Neutron Threshold (MeV) CFD level (mv) Voltage (V) CFD level (mv) Voltage (V) Figure B.4. Maximum neutron efficiency and neutron energy threshold as a function of CFD level (mv) and voltage (V). 89

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106 Acknowledgments I wish to express my deepest gratitude to my advisor, Professor Marzio Marseguerra. He was a constant source of support, ideas, and excellent guidance. He is in good part responsible for my professional and personal growth. I also wish to thank my co-advisor, Enrico Padovani, for the useful discussions in the course of the years spent working together. My gratitude also goes to the students, staff, and technical personnel of the Department of Nuclear Engineering of the Polytechnic of Milan. In particular, I would like to thank Dr. Enrico Zio, Francesca Gasparini, Francesca Giacobbo, Mirko da Ros, and Stefania Ramoni for the good times spent together. Part of the research presented in this document was performed during two research periods at Oak Ridge National Laboratory. Working at the Instrumentation and Controls Division at ORNL has been an honor, and there are many people whose help I wish to acknowledge. Firstly, I thank Professor Rafael Perez and his sweet wife Concita for their warm welcome to the United States and for making me feel part of their beautiful family. Professor John Mihalczo was an inextinguishable source of ideas and tomatoes. Working with John was a rare privilege that I will miss greatly. I also wish to thank Dr. John Mattingly for his support and encouragement together with Dr. Timothy Valentine and Jim Mullens. A great part of this document was performed with the help of Lisa Chiang and Richard Oberer: thank you for the many interesting discussions and the time spent together both inside and outside the lab. My stay at the lab would not have been possible without the help and support of Dr. José March-Leuba to whom I express my deepest gratitude. Dr. Barbara Hoffheins and Dr. George Copeland are true friends: Thank you for it all. Finally, I wish to thank my family: It is by their example and support that I have made it to here. My utmost gratitude is due to my husband, Giorgio, for his love and support, and for his spirit of adventure during our stay overseas. I am truly proud of him. 95