UNIVERSITY OF CINCINNATI

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1 UNIVERSITY OF CINCINNATI Date: I,, hereby submit this work as part of the requirements for the degree of: in: It is entitled: This work and its defense approved by: Chair:

2 On-Line Interrogation of Pebble Bed Reactor Fuel Using Passive Gamma-Ray Spectrometry A dissertation submitted to the Division of Research and Advanced Studies of the University of Cincinnati in partial fulfillment of the requirements for the degree of Doctorate of Philosophy By Jianwei Chen B.S., Harbin Engineering University, 1996 Nuclear and Radiological Engineering Program Mechanical, Industrial, and Nuclear Engineering Department College of Engineering University of Cincinnati Advisor: Dr. Ayman I. Hawari 2004

3 Abstract The Pebble Bed Reactor (PBR) is a helium-cooled, graphite-moderated high temperature nuclear power reactor. In addition to its inherently safe design, a unique feature of this reactor is its multipass fuel cycle in which graphite fuel pebbles (of varying enrichment) are randomly loaded and continuously circulated through the core until they reach their prescribed end-of-life burnup limit (~ 80, ,000 MWD/MTU). Unlike the situation with conventional light water reactors (LWRs), depending solely on computational methods to perform in-core fuel management will be highly inaccurate. As a result, an on-line measurement approach becomes the only accurate method to assess whether a particular pebble has reached its end-of-life burnup limit. In this work, an investigation was performed to assess the feasibility of passive gamma-ray spectrometry assay as an approach for on-line interrogation of PBR fuel for the simultaneous determination of burnup and enrichment on a pebble-by-pebble basis. Due to the unavailability of irradiated or fresh pebbles, Monte Carlo simulations were used to study the gamma-ray spectra of the PBR fuel at various levels of burnup. A pebble depletion calculation was performed using the ORIGEN code, which yielded the gamma-ray source term that was introduced into the input of an MCNP simulation. The MCNP simulation assumed the use of a high-purity coaxial germanium detector. Due to the lack of one-group high temperature reactor cross sections for ORIGEN, a heterogeneous MCNP model was developed to describe a typical PBR core. Subsequently, the code MONTEBURNS was used to couple the MCNP model and ORIGEN. This approach allowed the development of the burnup-dependent, one-group i

4 spectral-averaged PBR cross sections to be used in the ORIGEN pebble depletion calculation. Based on the above studies, a relative approach for performing the measurements was established. The approach is based on using the relative activities of Np-239/I-132 in combination with the relative activities of Cs-134/Co-60 (Co-60 is introduced as a dopant) to yield the burnup and enrichment for each pebble. Furthermore, a direct consequence of the relative approach is the ability to apply a self-calibration scheme using the multiple gamma lines of Ba-La-140 to establish the relative efficiency curve of the HPGe detector. An assessment of the expected uncertainty components in this approach showed that a maximum uncertainty of less than 5% should be feasible. To confirm the above findings, gamma-ray scans were performed on irradiated PULSTAR reactor fuel assemblies at North Carolina Sate University. The measurements used a 40% efficient n-type coaxial HPGe detector connected to an ORTEC DSPEC plus digital Gamma-Ray Spectrometer, and a data acquisition computer. The obtained results showed consistency with the predictions of the simulations including the observation of the I-132, Cs-134, Np-239 uncontaminated gamma lines. In addition, the Ba-La-140 lines were clearly observed confirming the ability to perform relative calibration of the spectrometer. ii

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6 Acknowledgements First of all, I would like to express my greatest gratitude to my advisor, Dr. Ayman I. Hawari, for guiding me through this work. He not only gave me the most valuable academic advice, but also precious suggestion and support when I was in difficult times during my five years graduate student life. His strong motivation and enthusiasm in academic research also impressed and encouraged me a lot, not only in the past five years, but also in the future of my career life. I will always appreciate the mentorship and opportunity that he provided throughout my graduate student career, which was crucial to my development as a Nuclear Engineer. Also, I would like to thank Dr. Bingjing Su, for his support and important advice to my research. I am also grateful for the tutorage and moral support of my other committee members, Dr. John Christenson and Dr. Henry Spitz. I really appreciate the opportunity that the University of Cincinnati Nuclear and Radiological Engineering Graduate Program provided for me to start my professional career in the Nuclear Engineering field. Special thanks to the staff of the North Carolina State University PULSTAR Nuclear Reactor Program, Andrew T. Cook, Scoot Lassell, Kerry Kincaid, and Larry Broussard. With their help, my experimental work became much easier and more pleasant. iii

7 I would like also to thank my colleague, Zhongxiang Zhao, for his discussion during this research. Finally, I would like to dedicate this work to my parents, Liangbi Chen and Xiahua Li. They have provided me endless love and support during all my life, which is the most precious treasure I will cherish forever. iv

8 Table of Contents List of Tables... vii List of Figures...viii... 1 Introduction The Pebble Bed Reactor Burnup Measurement Conventional Burnup Measurement Methods PBR Online Burnup Monitoring System Design Composition of Irradiated PBR Fuel Depletion Calculations Isotopic Calculations Using ORIGEN ORIGEN Cross Section Library Spectral-Averaged Cross Sections Monte Carlo Simulations of the PBR Monte Carlo N-Particle (MCNP) Transport Code Core Model for the PBR Burnup Dependent Cross Sections MONTEBURNS: Monte Carlo Fuel Depletion Simulations ORIGEN/MONTEBURNS/MCNP Simulation Pebble Depletion Calculations Passive Gamma-Ray Assay of PBR Fuel Gamma-ray Spectra Simulation Gamma-ray Source Term Construction Full Width Half Maximum vs. Energy Simulated Gamma-ray Spectra Burnup Measurement Using Absolute Indicators Absolute Activity Burnup Indicator Selection Criteria Power History Variation Search Minimum Detectable Activity Check Using Cs-137 as a Burnup Indicator Spectral interference analysis of Cs v

9 Peak Area Determination for Singlets Error Analysis for Using Cs-137 Full Energy Peak as Burnup Indicator Burnup Measurement Using Relative Indicators On-line Relative Efficiency Self-calibration Cs-134/Co-60 as a Burnup Indicator Built-in Relative Burnup Indicators Using Np-239/I-132 and Cs-134/Co-60 for the Simultaneous Determination of Burnup and Enrichment Experimental Considerations and Verification Introduction to PULSTAR Reactor at NCSU Gamma-Ray Verification Measurements Count Rate Effects and Distortions Probability Distribution Functions (PDFs) for Monte Carlo Simulations Random Summing Simulation Results Conclusions Bibliography Appendices Appendix A: ORIGEN/MONTEBURNS/MCNP Simulations How to run MONTEBURNS on Linux PBR MCNP5 Input File Monteburns Input File Appendix B: Data Process Scripts and Routines ORIGEN Data Process Script MCNP Data Processing Script MCNP Input Maker Appendix C Data Analysis Routines Absolute and Relative Burnup Indicator Search Routines Interference Check Routine Singlet Peak Area Determination Routine: SUM Appendix D: Variance Reduction in Pile-Up Simulations Appendix E: Random Summing Monte Carlo Program vi

10 List of Tables Table 2.1. Moderator Nuclear Properties at 300 K [21] Table 2.2. The double heterogeneous Cell Model Specifications Table 2.3. Comparison of one-group spectral averaged cross-sections Table 2.4. Burnup Dependent Cross Sections for PBR Table 2.5. Single Pebble Depletion Calculations. The numbers are calculated using Eq. 2.4 and assuming an average power of 265 MW-thermal Table 3.1. Gamma Emitters that Passed the Power History Variation Criterion Table 3.2. MDA Check Gamma Emitters at 5,000 MWD/MTU Table 3.3. Cs-137 Gamma Peak Interference Table 3.4. Cs kev net peak area interference bias Table 3.5. Error Components for Cs-137 Full Energy Peak Table 3.6. Relevant data for the nuclides used in relative efficiency calibration Table 3.7. Error Components for 134 Cs/ 60 Co Ratio Table 3.8. Potential activity ratio pairs for burnup measurement Table 3.9. Error Components for Np-239/I-132 Ratio Table Use of the Np-239/I-132 and Cs-134/Co-60 to determine burnup and enrichment Table 4.1. PULSTAR Reactor Technical Data Table 4.2. Pulse Pile-up Effect on Cs-137 Absolute Activity (1 µs) Table 4.3. Pulse Pile-up Effect on 134 Cs/ 60 Co Activity Ratio (1 µs) Table 4.4. Pulse Pile-up Effect on 239 Np/ 132 I Activity Ratio (1 µs) Table 4.5. Pulse Pile-up Effect on Cs-137 Absolute Activity (2 µs) Table 4.6. Pulse Pile-up Effect on 134 Cs/ 60 Co Activity Ratio (2 µs) Table 4.7. Pulse Pile-up Effect on 239 Np/ 132 I Activity Ratio (2 µs) vii

11 List of Figures Fig A schematic of a Pebble Bed Reactor [5]... 2 Fig A schematic of a PBR Fuel Pebble [5]... 3 Fig Configurations of the doubley-heterogeneous PBR Model Fig Spatial Effect on Neutron Spectrum Fig Temperature Effect on Neutron Spectrum Fig The effect of the thermal neutron spectrum on the spectral averaged crosssections Fig MONTEBURNS coupling of MCNP and ORIGEN Fig The burnup dependent neutron spectra as calculated by MCNP using core compositions that correspond to the shown burnup levels Fig A schematic of the gamma-ray burnup measurement detector Fig The FWHM fit to SYNTH data as used in MCNP Fig Simulated Gamma-ray Spectra for PBR fuel at various burnup levels Fig Continued Fig Burnup vs. Cs-137 activity correlation Fig The Cs kev peak with interference: (a) 20,000 MWD/MTU, Fig Cs kev peak without interference: (a) 20,000 MWD/MTU, Fig Evaluation of net peak areas using the SUM methodology Fig The Absolute Efficiency Curve of the Gamma-ray Spectrometer. The pebble was assumed to be 100 cm from the detector. The burnup is assumed to be 20,000 MWD/MTU Fig The Relative Efficiency Curve of the Gamma-ray Spectrometer. The pebble was assumed to be 100 cm from the detector Fig Burnup vs. 134 Cs/ 60 Co activity ratio correlation Fig Co kev Peak (a) and Cs kev Peak (b) in Fuel Pebble Spectra at Different Burnup Steps Fig Np kev Peak (a) and I kev Peak (b) in Fuel Pebble Spectra at Different Burnup Steps Fig Np-239 activity verification viii

12 Fig I-132 activity verification Fig The activity vs. burnup correlation for Np-239 and I Fig The Np-239/I-132 activity ratio. Although the activity of the individual isotopes is highly sensitive to power history variations the ratio is resistant to such variations Fig Enrichment and Burnup Correlations with Np-239/I-132 and Cs- 134/Co-60 Ratios Fig The PULSTAR reactor bay area Figure 4.2. A view of the PULSTAR reactor pool at 1 MW power Fig A schematic of the experimental setup Fig A Schematic of the fuel scanning system Fig Actual fuel scanning system during operation Fig 4.6. The Cs-137 peak in the irradiated spent fuel spectrum. Also visible are the interfering peaks of Nb-97, I-132, and Ce143 (marker points to the Cs-137 peak). 84 Fig Np-239, I-132, and Cs-134 gamma peaks as observed in the irradiated spent fuel spectrum Fig La-140 Peaks as observed in the irradiated spent fuel spectrum Fig Summing effect using 1 µs pulse width at 10 5 cps throughput rate Fig Summing effect using 2 µs pulse width at 10 5 cps throughput rate ix

13 1 Introduction 1.1 The Pebble Bed Reactor The Pebble Bed Reactor (PBR) is a helium-cooled, graphite-moderated high temperature reactor. This technology was successfully developed and demonstrated in the 1960s through the 1980s in Germany with the building of the AVR research reactor and the Thorium High-Temperature (power) Reactor (THTR). The current design of the modular PBR is a follow-on based on the fundamental research and development results gained on the previous two German plants [1]. Present designs describe a modular PBR that consists of a vertical steel pressure vessel, 6 m in diameter and 20 m high (Fig. 1.1) The pressure vessel is lined with a layer of graphite bricks. This graphite layer serves as an outer reflector for the neutrons generated by the nuclear reaction and a passive heat transfer medium. The graphite brick lining is drilled with vertical holes to house the control elements. The control elements include the control rods and the reverse shutdown units, which consist of absorber spheres. In addition, the graphite reflector encloses the core, which is 3.7 m in diameter and 9.0 m in height. When fully loaded, the core would contain 360,000 fuel pebbles. Helium flows through the pebble bed and removes the heat generated by the nuclear reaction from the core. The helium enters the reactor at a temperature of about 500 C and at a pressure of about 8.4 MPa and moves downward between the hot fuel spheres. It picks up the heat from the fuel sphere, which has been generated by the nuclear reaction, then leaves the reactor at a temperature of about 900 C. The standard thermal power 1

14 output is designed to be 265 MWt [2, 3], and recently new designs rated at 400 MWt have been presented [4]. Fig A schematic of a Pebble Bed Reactor [5]. 2

15 As shown in Fig.1.2, the fuel elements for the PBR are spherical pebbles that are composed of an outer graphite shell (~0.5 cm thick) surrounding an inner fuel zone (~2.5 cm radius). The fuel zone has a graphite matrix in which 10,000 15,000 silicon carbide (SiC) coated TRISO fuel microspheres (0.9 mm diameter) are embedded. The SiC coating assures that no fission products are released from the microsphere even at elevated temperatures. Depending on the details of the core design, each fuel pebble contains 7 9 g of Uranium enriched to anywhere from 4% 10% in U-235 particle Carbon layers UO 2 Kernel pebble 0.9 mm 6 cm Fig A schematic of a PBR Fuel Pebble [5]. 3

16 Compared to conventional light water reactors (LWRs), the PBR has a number of advantageous features. First, it has a higher thermal efficiency due to its higher coolant outlet temperature. Second, the SiC coating layer of fuel particles has a very good radionuclide retention capability up to a temperature of approximately 1600 C. Third, it has large passive heat removal capability due to the slender core and low power density. The size of the PBR core is such that it has a high surface area to volume ratio, which means that even without the active heat removal system, the heat it loses through its surface is more than the heat produced by the decay of fission products in the core. The reactor, therefore, never reaches a temperature at which significant degradation of the fuel can occur. In addition, thermal expansion of the graphite reduces moderation, so that the moderator density coefficient of reactivity is negative, although small. The reactivity feedback is dominated by the fuel Doppler coefficient, which is always negative in a thermal reactor. Overall, it has a strong negative temperature coefficient of reactivity. The helium, used as the reactor coolant and working fluid in the turbine, is chemically inert, non-combustible and transparent to neutrons. In addition to the inherent safety features mentioned above, another unique feature of the PBR is its online refueling scheme. The reactor is continuously refueled with fresh or reusable fuel pebbles from the top of the reactor, while used fuel pebbles are removed from the bottom. For each discharged fuel pebble, its burnup is measured by an on-line burnup monitoring system to determine if it reaches the prescribed end-of-life burnup limit (~ 80, ,000 MWD/MTU). If not, it will be reloaded back to the core. Otherwise, it is discarded to the spent fuel facility. Due to this on-line refueling scheme, a very small amount of excess reactivity is required while the reactor is 4

17 operating. This makes it possible for the reactor to shut itself down within a short period of time, even if there were a failure of the active shutdown systems. Also, because of this feature and the negative moderator density coefficient of graphite, optimal moderation could be achieved for this type of reactor at equilibrium [6]. Both the safety and economy of the reactor are improved by the selection of optimal moderation. In the interest of safety, LWRs must always operate on the under-moderated side of the curve of K eff versus fuel-to-moderator ratio. For a graphite-moderated reactor with stationary fuel, this kind of optimal moderation is only possible instantaneously since the composition of the fuel at each point is constantly changing. Only in a reactor with moving fuel, like the PBR, can the state of optimal moderation be preserved independently of time. Finally, an on-line refueling scheme makes the PBR able to operate uninterrupted for six years before scheduled maintenance, which is much longer than currently operating nuclear power plants (1 2 years). The long reactor core life time is economically preferable in nuclear power plant design. As stated above, the most important feature of the PBR is its on-line refueling operation. Therefore, unlike the situation with a conventional LWR, depending solely on computational methods to perform in-core fuel management will be highly inaccurate. As a result, the online refueling operation depends heavily on an online burnup monitoring system that can determine the burnup of each fuel pebble exiting the reactor core quickly and accurately. This system is the key component to guarantee that the reactor is operating economically without breaching prescribed fuel safety limits. On- 5

18 line burnup measurement of the fuel is the subject of this thesis. The following section surveys the various approaches to perform this task. 1.2 Burnup Measurement Burnup is defined as the integrated energy generated per unit mass of initially loaded fuel, and it is typically reported in units of megawatt days per metric ton of uranium (MWD/MTU). Consequently, it is directly related to the fission reactions occurring in a given fuel element Conventional Burnup Measurement Methods Most contemporary nuclear power plant reactor cores consist of stationary fuel assemblies. During each scheduled refueling outage (every 1 2 years), fuel assemblies are reshuffled. depleted fuel assemblies are pulled out and substituted with fresh fuel assemblies. Reactor in-core fuel management calculations are performed to decide the location of each fuel assembly with known loading enrichment. Typically, for these types of reactors, the neutron flux spatial distribution can be calculated using 3- dimentional simulators that utilize 2-group neutron diffusion theory methods. And with all of the stationary fuel assemblies residing in the core during the core life time, the power history of each fuel assembly is known. Therefore, the burnup of these types of nuclear reactor fuel can be accurately estimated computationally. Under these circumstances, fuel assay measurements are performed off-line (i.e., after the reactor has been shut down) only for the purpose of validating and benchmarking the computational methods and results [7, 8]. 6

19 Ideally, burnup can be assessed by measuring the amount of fissile material left in the fuel when the initial enrichment of the fuel assembly is known. This can be done by using active neutron interrogation methods to determine the amount of fissile materials in the fuel. However, to override the passive neutron signal from the irradiated fuel, these types of measurement techniques demand a highly active neutron source, such as Cf-252, or an accelerator, which usually introduces auxiliary systems such as heavy shielding, thus making the whole system cumbersome. Due to this reason, the use of active neutron systems in burnup measurements of power reactor fuel is limited. Nevertheless, passive nondestructive methods are incapable of yielding information on the amount of fissile materials in the irradiated fuel directly. This is mainly due to the existence of very strong sources of radiation in irradiated fuel that will overwhelm the direct signature of the fissile material. Therefore, passive burnup measurements are performed indirectly using the spontaneous emission of gamma-ray and/or neutron radiation by the fission products and heavy actinides that result upon irradiation of the fuel. Passive neutron counting can be used for burnup measurement. In this case, neutrons will be generated either due to the spontaneous fission of heavy actinides, or from (α, n) reactions that take place within the fuel. However, in most cases, the (α, n) component is negligible compared to the contribution of spontaneous fission. Moreover, the spontaneous fission component is dominated by the contribution from Cm-244 (~18.1 7

20 years half-life). Burnup measurement using passive neutron counting can be done by establishing a correlation between the total number of neutrons emitted by the fuel and its calculated burnup utilizing some kind of mathematical fit [9-12]. One commonly used expression representing the relationship between neutron rate and burnup is the following empirical power function [13]: β neutron rate = α(burnup), (1.1) where the value of β is usually between 3.0 and 4.0. Another type of radiation information from LWR fuel that can be related to burnup indirectly is electromagnetic Cerenkov radiation. Cerenkov radiation is emitted whenever a charged particle passes through a medium with a velocity exceeding the phase velocity of light in that medium. When the charged particle moves through the water, it tends to "polarize" (or orient) the water molecules in a direction adjacent to its path, thus distorting the local electric charge distribution. After the charged particle has passed, the molecules realign themselves in their original, random charge distribution. A pulse of electromagnetic radiation in the form of blue light is emitted as a result of this reorientation. When the speed of a charged particle is less than the speed of light, the pulses tend to cancel themselves by destructive interference; however, when the speed of the charged particle is greater than the speed of light (in water) the pulses are amplified through constructive interference. In this case, a brilliant soft blue glow can be seen from the fuel assembly. Irradiated fuel assemblies are an abundant source of beta particles, gamma rays, and neutrons. All three types of radiations can produce Cerenkov light, 8

21 either directly or indirectly. Since the absolute Cerenkov light level and its decay with time are related to burnup, the Cerenkov light intensity can be used as a burnup indicator [14]. For the passive gamma-ray spectrometry method, three types of information can be utilized to determine the fuel burnup. The buildup of specific fission products can be used to measure burnup quantitatively. For a fission product to be used as a burnup indicator, some criteria have to be considered. These criteria include equal fission yield from major uranium and plutonium fissile materials; small neutron capture cross section; long half-life compared to fuel irradiation time; and an intense and relatively high energy gamma ray. Cs-137 is the most widely accepted indicator for LWR fuel burnup measurement since it adequately satisfies all of these conditions [13, 15, 16]. Also, the total gamma-ray activity of the irradiated fuel is approximately proportional to burnup after a certain period of cooling time (> 1year). For shorter cooling times, the total gamma-ray activity is dominated by the short-lived radionuclides, activities of which depend mostly on the reactor operating history. Finally, the ratios of some fission product isotopes can serve as burnup indicators. The two most commonly used isotopic ratios are Cs-134/Cs-137 [15] and Eu-154/Cs-137. A simplified explanation is that Cs-134 and Eu-154 are produced from neutron captures on other directly produced fission products; thus, their activities are approximately proportional to the square of the integrated neutron flux. By dividing their activities by the Cs-137 activity, which is directly proportional to the integrated neutron flux, the ratio 9

22 is then roughly proportional to burnup [13]. The activity ratio method has an advantage over absolute activities in that only relative detector efficiencies must be known. A relative efficiency calibration can be performed using multiple gamma rays from Cs-134 and Eu-154 by utilizing only the original gamma-ray spectra PBR Online Burnup Monitoring System Design As discussed in the previous section, a number of approaches have been developed for burnup determination for conventional reactor fuel. However, due to the unique online refueling feature of the PBR, some approaches may no longer work for this scenario. In fact, some approaches may introduce even more uncertainties than occur with conventional reactors. On the other hand, some approaches may still work, but with different isotopes (i.e., indicators). In the case of the PBR, a fuel pebble continuously circulates in the reactor core, therefore, there is no knowledge of its power history when it exits from the bottom of the core. Thus, conventionally used computational methods are not accurate or dependable for PBR burnup determination. As a result, on-line measurement becomes the only accurate method to assess whether a particular pebble has reached its end-of-life burnup limit. Based on the above, several methods exist for burnup determination. However, the requirement of performing this determination on-line limits these options. In particular, both the use of total gamma-ray counting and Cerenkov radiation intensity 10

23 detection are susceptible to large inaccuracies due to the inherent dependence of these indicators on power history. Furthermore, passive neutron measurements may serve as a potential burnup assay approach. However, this approach may be complicated by signalto-noise issues. Therefore, the work of this thesis is focused on passive gamma-ray spectrometry assay using a high resolution system based on a HPGe detector. This type of detector is essential due to the fact that the PBR fuel will arrive at the detector within 48 hours after discharge from the core [17]. Consequently, highly complex gamma-ray spectra will represent the signal from which a power history independent burnup indicator should be selected. This dissertation discusses in detail the selection of the burnup indicator for online assay of PBR fuel. In addition, the work also addresses the issue of performing this task for fuel of varying initial enrichment. The work includes performing computational simulations to study the feasibility of passive gamma assay as the method of choice, and conducting verification measurements to confirm the systematics of the predicted results. 11

24 2 Composition of Irradiated PBR Fuel As stated in Chapter 1, fuel burnup monitoring can be performed by measuring the characteristic ionizing radiation (i.e., neutrons and/or gammas) of certain radionuclides (burnup indicators), which have an unambiguous correlation with burnup. To investigate the existence of such indicators, the fuel isotopic inventory at different burnup steps needs to be determined. Since there is no readily available PBR fuel pebble (irradiated or un-irradiated) to be investigated, computational simulation can be used to study virtually the irradiation of the fuel and to design the gamma-ray assay system. The starting point of this virtual study is the setup and implementation of a PBR model that allows estimation of the neutron spectrum within the core. The calculated spectrum can then be used to calculate the spectral-averaged one-group cross sections that are used in depletion calculations. The MCNP/MONTEBURNS/ORIGEN reactor simulation code system is the main tool used to perform this investigation. MCNP (Monte Carlo N- Particle transport code) is a 3-dimensional Monte Carlo transport code that can be used to model the PBR core. ORIGEN (Oak Ridge Isotope GENeration and depletion code) is a well-known code used to perform fuel depletion calculations. MONTEBURNS is a utility code that connects MCNP to ORIGEN, which performs depletion calculations based on the sophisticated MCNP model. The details of this analysis are given below. 2.1 Depletion Calculations In this work, the main objectives of the depletion calculations are to provide as much detail as possible on the composition of the irradiated PBR fuel and to quantify its 12

25 radioactive properties (i.e., the emitted radiation, and the isotopic activities). For the purposes of the current analysis, the focus will be on the ionizing radiation signatures that are emitted by the various isotopes contained in the irradiated fuel. Traditionally, a wide variety of computer codes are available for calculating the nuclide composition of nuclear reactor fuels. However, the calculations are usually performed within the context of the requirements of reactor physics studies such as in-core fuel management and fuel cycle analysis simulations. In addition, many of the codes that are used in the analysis are complex and require the use of multi-group neutron spectra and cross sections to estimate the composition of the nuclear fuel as a function of both space and time. Nevertheless, these codes are incomplete in that they track a limited number of nuclides that are known to be significant in the cases of interest (e.g., tracking 235 U, 239 Pu, and 135 Xe for core design work). For the purposes of this work, these reactor physics codes are inappropriate since they are cumbersome to use, and more importantly, they do not provide sufficient detail concerning the isotopic composition of the irradiated PBR fuel pebbles. Consequently, the ORIGEN code (version 2.2) was chosen to perform this analysis [18]. ORIGEN is a zero-dimension isotope generation and depletion code that is developed and maintained by Oak Ridge National Laboratory for calculating the buildup, decay, and processing of radioactive materials. Its main advantage is that a total of 1,300 unique nuclides are included in the ORIGEN data bases, which is extremely useful for the purposes of this work [18]. 13

26 2.1.1 Isotopic Calculations Using ORIGEN ORIGEN solves the Bateman equation for the concentration N i of isotope i in a material subject to neutron irradiation. In this case the Bateman equation can be written as dn dt i = j= i tr tr [ λ + ϕ(e, t) σ (E)dE] N + [ λ + ϕ(e, t) σ (E)dE] d ji ji i j= i d ji ji N j, (2.1) where λ d is the decay constant, ϕ(e, t) is the energy dependent neutron flux, σ tr ij is the cross section for transmutation from isotope j to i. In the above, the sum is to taken over all nuclides j present in the material. Since the particle flux is dependent on the composition of the material, the full time-dependent Bateman equation is solved for the correct prediction of the burnup in a reactor. Under certain conditions (e.g., small fluence, small transmutation cross sections, etc.) it is sufficient to assume a constant flux during a time interval t. Introducing the spectrum averaged transmutation cross section for the time interval tr 1 tr σ ij ϕ(e) σ ij (E)dE, (2.2) ϕ where ϕ = ϕ( E) de The Bateman equations are reduced to dn dt i j= i d tr d tr [ λ ji + σ ji ϕ] N i + [ λ ji + σ ji ϕ] N j =. (2.3) j= i The above equations can be written in vector form as dν dt = ΛΝ, (2.4) 14

27 where d ji tr Λ ji λ + σ ji ϕ. Based on the above, the formal solution is given by Ν(t) = e Λ t Ν (0), (2.5) where the exponential of the matrix is defined through the Taylor expansion valid for small times t: Λ 1 e t Λt + Λ t + K 2 (2.6) The above solution is known as the exponential matrix method and forms the basis of the burnup simulation in ORIGEN ORIGEN Cross Section Library As described above, ORIGEN utilizes one-group averaged cross sections, which are provided by an external program specifically targeting the particular system it is simulating, to perform the fuel cycle burnup calculation. The one-group averaged cross section is calculated by the following equation: σ = 0 σ(e) Φ(E) de, (2.7) 0 Φ(E) de Where Ф(E) is the normalized neutron energy spectrum obtained from neutron transport simulations of a given reactor. The standard libraries of ORIGEN include the 1-group spectral averaged cross sections calculated for the fuel of pressurized water reactors (PWR), boiling water 15

28 reactors (BWR), liquid metal fast breeder reactors (LMFBR), and the Canada deuterium uranium (CANDU) reactors. However, in all of its publicly released versions no data library exists for high temperature gas reactors (HTGR), which include the PBR. In addition, extensive literature searches yielded very limited information on the 1-group averaged cross sections for an HTGR. Mainly, this is due to some data that was recently published by the South African company ESKOM, which gives the information for a limited set of nuclides (see the discussion in section ) [19]. Therefore, to perform the detailed analysis that is required for this work, an HTGR library was generated using a Monte Carlo core depletion model of a PBR supercell. 2.2 Spectral-Averaged Cross Sections In order to solve the burnup equations, spectral-averaged neutron interaction cross sections are required. However, due to changes in the isotope concentrations in the fuel assembly with burnup, the neutron spectrum, and thus the spectral-averaged cross sections, become burnup dependent. Therefore, when creating a cross-section library, the spectrum dependence due to burnup must be known. When compared to a conventional Pressurized Water Reactor, one major characteristic of a PBR is its use of graphite as the moderator, which introduces a different rationale for generating the cross-section library [19-21]. Table 2.1 lists characteristic nuclear parameters for these two types of moderators. 16

29 Table 2.1. Moderator Nuclear Properties at 300 K [21]. Thermal ( ev) Epithermal Quantity Water Graphite (Reactor Grade) Σ a (1/m) Σ s (1/m) Mean free path (m) Σ a (1/m) Σ s (1/m) Mean free path (m) Within the traditional PWR fuel assembly, the mean free path for both thermal and epithermal neutrons in water is less than 1 cm, which is approximately one order of magnitude less than the PWR fuel assembly dimension (21.45cm 21.45cm) [13]. This implies that most neutrons originating from one fuel assembly are thermalized locally inside the fuel assembly itself; thus for a PWR, the neutron spectrum within the fuel assembly is dominated by the burnup of the fuel assembly itself. However, for the PBR, the mean free path for thermal and epithermal neutrons is about 2.4 cm, which is close to 3 cm, the radius of the fuel assembly (fuel sphere). Hence, the neutrons are very likely to escape from the fuel sphere from which they originated, and they are likely to get thermalized and absorbed in a fuel sphere relatively far away from where they are produced. Thus, from a neutronic point of view, the PBR has a relatively smaller dimension than the PWR. When considering the burnup dependent neutron spectrum within a fuel sphere, this implies that it is mostly determined by the 17

30 burnup of the surrounding spheres; while the burnup of the fuel sphere itself plays only a secondary role in developing the spectrum Monte Carlo Simulations of the PBR For the evaluation of the cross-section dependence on burnup, a spherical reactor model was constructed consisting of a single fuel sphere in the center, surrounded by a 1- m fuel driver zone and a 1 m graphite reflector using MCNP5. In this model, the neutron energy spectrum at several locations was used to generate the burnup dependent 1-group cross-section libraries that are needed by ORIGEN to perform the depletion calculations Monte Carlo N-Particle (MCNP) Transport Code MCNP is a general-purpose transport code, developed by Los Alamos National Laboratory, that can be used for calculations involving neutron, photon, electron, or coupled neutron/photon/electron transport, including the capability to calculate eigenvalues for critical systems. The code treats an arbitrary three-dimensional configuration of materials in geometric cells bounded by first- and second-degree surfaces and fourthdegree elliptical tori [22]. Monte Carlo methods are very different from deterministic transport methods. Deterministic methods, the most common of which is the discrete ordinates method, solve the transport equation for the average particle behavior. By contrast, Monte Carlo methods do not solve an explicit equation, but rather obtain answers by simulating individual particles and recording (i.e., tallying) some aspects of their average behavior. 18

31 Using the central limit theorem, the average behavior of particles in the physical system is then inferred from the average behavior of the simulated particles. Not only are Monte Carlo and deterministic methods very different ways of solving a problem, but what constitutes a solution is different. Deterministic methods typically give fairly complete information (for example, flux) throughout the phase space of the problem. Monte Carlo supplies information only about specific tallies requested by the user. When compared to a very complicated system, using a deterministic method is sometimes very difficult, even impossible, to give an explicit solution; while the Monte Carlo method can devise a reasonable solution that is sufficient for practical purposes Core Model for the PBR A double-heterogeneous MCNP5 spherical model was constructed to simulate a PBR core [23]. As shown in Table 2.2, the first-level heterogeneity is implemented at the fuel microsphere lattice level. At this level, a TRISO fuel kernel model has a 530 µmdiameter UO 2 kernel surrounded by, first, one buffer layer of low-density carbon, then, two pyro-carbon layers with one layer of SiC in between. This lattice structure is then filled into a 5-cm diameter fuel zone surrounded by a 0.5 cm thick graphite shell, consisting of a single fuel sphere pebble. Approximately, 11,000 fuel microsphere kernels are contained in one single fuel pebble. The second level of heterogeneity is implemented at the reactor core lattice level. The basic unit of the core lattice consists of a body-center-cubic cell [20]. The single cell contains a complete fuel pebble in the center and eight one-eighth pebbles, one in each corner of the cell. The complete pebble in the center touches each of the sectors; hence, the edge of the cell is 2d/ 3 where d is 19

32 the diameter of a single pebble (6 cm). The double-heterogeneous geometric configurations of the PBR model are shown in Fig Table 2.2. The double heterogeneous Cell Model Specifications. Parameter Radius / Thickness (cm) Density (g/cm 3 ) Kernel Cell Fuel Kernel Radius Packing Ratio Carbon Buffer Layer (0.013) Inner Pyro-Carbon Layer SiC Layer Outer Pyro-Carbon Layer Cell Width BCC Cell Fueled Zone Radius Packing Ratio Pebble Graphite Shell (0.68) Cell Width The described model was used to calculate the neutron spectrum in a fresh core in the central fuel kernel in pebbles located at the core s origin, at half the distance to the surface, and at the surface. The calculated spectra are displayed in Fig. 2.2, which shows that the variation in these spectra due to the variation in location is limited. However, the effect of temperature is clearly visible in Fig Therefore, it is expected that cross section estimates that do not take this effect into account will be erroneous. The above model was used to calculate the one-group spectral averaged crosssection for several radionuclides that are of interest to this work. Two sets of one-group spectrum-averaged cross-section data were generated based on the two neutron spectra 20

33 (i.e., at 300 and 1200 K). In addition, the neutron spectrum from the MIT-INEEL work was used to produce another set of cross-section data as a reference [20]. These three sets of cross-section data are listed in Table 2.3 and compared to typical PWR, and CANDU cross-sections as found in ORIGEN libraries [18], and to data published by the South African Company ESKOM [19]. (a) TRISO Fuel Micro-Sphere (b) Single Fuel Pebble (c) Core Lattice (d) Sphere Core Model Fig Configurations of the doubley-heterogeneous PBR Model. 21

34 Normalized Neutron Flux center pebble intermediate pebble outer pebble Energy (MeV) Fig Spatial Effect on Neutron Spectrum. 14.0x10-6 Neutron Flux (Neutrons/cm 2 /source particle) 12.0x x x x x x10-6 Thermal Treatment at 1200 K Free Gas Model at 300 K Energy (MeV) Fig Temperature Effect on Neutron Spectrum. 22

35 Table 2.3. Comparison of one-group spectral averaged cross-sections. Nuclide ORIGEN ORIGEN MIT ESKOM This Work This Work This Work CANDU PWR INEEL (barn) 300 K 1200 K 1200 K (barn) (barn) (barn) Free gas Free gas With (barn) (barn) binding (barn) Cs-137 (n,γ) N/A Cs-133 (n,γ) N/A Cs-134 (n,γ) N/A Co-59 (n,γ) N/A Te-132((n,γ)* N/A La-140 (n,γ) N/A Np-239 (n,γ) N/A U-235 (n,γ) U-238 (n,γ) U-239(n, γ) N/A Pu-239 (n,γ) Pu-241 (n,γ) U-235 (n,f) U-238 (n,f) Pu-239 (n,f) Pu-241 (n, f) *Parent of I-132 As shown in Table 2.3, the cross-section data generated using free gas treatment (at 300 K) is similar to the MIT-INEEL work, while the cross-section data employed with thermal treatment at 1200 K is closer to the ESKOM data. The reasons for these differences can be understood using Fig Clearly, at the lower temperature the thermal portion of the neutron spectrum is shifted to lower energies, which in the case of Pu-239 and U-235 overlaps with the 1/v portion of the cross section curve. At higher temperatures, the spectrum is harder. In the case of the Pu-239(n,f) reaction, the average energy of thermal neutrons at 1200 K (~ ev) overlaps with a low-lying resonance located at around 0.3 ev. This results in a significant increase in the one-group cross 23

36 section as shown in Table 2.3. In the case of the U-235(n,f) reaction, the hardening of the spectrum shifts it to lower values along the 1/v region of the cross section curve, which results in a decrease in the one-group cross section. For completion purposes, Table 2.3 also shows the cross sections calculated while accounting for moderator binding effects at 1200 K (i.e., using S(α,β) treatment for graphite at 1200 K). It can be seen that the effect of binding on the cross sections of interest to this work is not large. Furthermore, temperature effects were taken into account by using the NJOY code system [24] to produce Doppler broadened cross sections for the nuclides of interest at 1200 K. Fig The effect of the thermal neutron spectrum on the spectral averaged crosssections. 24

37 Based on the above, the MCNP model that includes S(α,β) thermal treatment at 1200 K is used in the coupled MCNP/ORIGEN calculations (using MONTEBURNS) to develop burnup dependent cross-section libraries Burnup Dependent Cross Sections The effect of geometry and moderator temperature on the PBR neutron spectrum has been investigated in the previous two sections. The method of using the ORIGEN/MONTEBURNS/ MCNP code system to investigate the effect of fuel isotopic compositions on PBR neutron spectrum and, hence, develop PBR specific, burnup dependent cross-section data, is discussed in the following section MONTEBURNS: Monte Carlo Fuel Depletion Simulations MONTEBURNS is a fully automated tool that is designed to link MCNP and ORIGEN to perform a Monte Carlo burnup calculation. The primary way in which MCNP and ORIGEN interact with each other through MONTEBURNS is that MCNP calculates one-group microscopic cross sections and fluxes that are used by ORIGEN in depletion calculations. In addition, other neutronic information such as criticality and neutron economy information are also produced. After performing a burnup calculation using ORIGEN, MONTEBURNS extracts the information about isotopic composition of materials from the bulky ORIGEN output file, and passes them back to MCNP to update the material compositions automatically in the MCNP input file for the next burnup step. 25

38 As shown in Fig. 2.5, to increase the accuracy of the burnup calculation, a predictor step is performed in which ORIGEN is run halfway through the predefined burnup step. One-group average cross sections and fluxes are then calculated using the isotopic compositions at the midpoint of the burnup step using MCNP. Assuming the isotopics of the system at the midpoint of the burnup step are a reasonable approximation of the isotopics of the whole burnup step, ORIGEN is re-executed with the new generated one-group cross sections and fluxes at the midpoint for the entire burnup step. MCNP input file MONTEBURNS Initial material compositions ORIGEN Material compositions (halfway through step) MCNP Predictor step Cross sections and fluxes (halfway through step) ORIGEN MCNP Material compositions at end of step Fig MONTEBURNS coupling of MCNP and ORIGEN. 26

39 Precautions should be taken to satisfy the aforementioned assumption, i.e., the burnup intervals should not be too long. However, although substituting few long burnup intervals with many shorter burnup intervals can increase accuracy, this benefit comes at a cost of additional execution time. To balance the tradeoff between accuracy and execution time, it is common to recalculate the neutron flux spectrum using 5,000 MWD/MTU burnup steps [25, 26] ORIGEN/MONTEBURNS/MCNP Simulation For the ORIGEN/MONTEBURNS/MCNP coupled simulation, the power density is assumed to be 5.25 MW/m 3 (22 MW for the total power of the sphere core), which is similar to the power density of the ESKOM model (~5.22 MW/m 3 ) [21]. The core is depleted up to 80,000 MWD/MTU in 40 outer burnup steps in MONTEBURNS; for each step the burnup increases 2,500 MWD/MTU, which is more conservative than the 5,000 MWD/MTU criteria for the burnup step stated in Section For each outer burnup step, MONTEBURNS calculates the neutron flux Φ in the system using the following equation [27]: Φ = Φ 6 υ * P *10 W / MW ( J / MeV ) * k * n 13 eff * Q ave, (2.8) where Ф n is MCNP neutron flux tally in the fuel kernel (neutrons/cm 2 /source neutron), ν is the average number of neutrons produced per fission provided by MCNP, k eff is the effective multiplication factor obtained by MCNP, P is the power defined by the user for the system (in MW), and Q ave is the average recoverable energy per fission. 27

40 Subsequently, MONTEBURNS prepares the ORIGEN input file by dividing the outer burnup step into 40 smaller irradiation steps (inner burnup steps); in each step, the fuel is irradiated by the neutron flux calculated from Equation (2.3). By dividing the outer burnup step into even smaller segments, the ORIGEN calculation results are more accurate because the differences between the various computational techniques applied by ORIGEN are minimized. In this case, for those short-lived nuclides which have longlived parents (half-lives of less than 10% of the irradiation interval), a Gauss-Seidel successive substitution algorithm is employed by ORIGEN to solve the asymptotic solutions for the differential equations instead of using a matrix exponential method [18, 27]. Additionally, the physics and composition of fuel in the system may change significantly in a long irradiation time interval. Using a smaller time step for irradiation can ensure that parameters assumed to be constant (e.g., actinide cross sections and fission product yields) over the irradiation interval do so in a given burnup step. All of the nuclides available (a total of 258 nuclides for MCNP5, including 9 nuclides which we created) in the MCNP library are traced throughout the simulation. The spectrum-averaged cross sections and compositions of these nuclides are passed back and forth through ORIGEN and MCNP for each burnup step. The cross sections for nuclides of interest at given burnup steps are listed in Table 2.4. All the cross sections are prepared at 1200 K and account for binding effect of the graphite moderator and Doppler broadening for each nuclide. 28

41 Table 2.4. Burnup Dependent Cross Sections for PBR. Nuclide 0 GWD/MTU (b) 50 GWD/MTU (b) 100 GWD/MTU (b) Cs-137(n,γ) Cs-133(n,γ) Cs-134(n,γ) Co-59(n,γ) Te-132(n,γ) La-140(n,γ) Np-239(n,γ) U-235(n,γ) U-238(n,γ) U-239(n,γ) Pu-239(n,γ) Pu-241(n,γ) U-235(n,f) U-238(n,f) Pu-239(n,f) Pu-241(n,f) In the above table, the observed burnup dependence of the cross sections is explained by examining Fig In this case, MCNP simulations that were performed using the model given in Fig. 2.1 show that the thermal neutron flux decreases up to a burnup level of 50,000 MWD/MTU and subsequently increases as the core is depleted. This clearly correlates with the variation in the spectral averaged cross section as the core burnup increases. It should be noted that the maximum variation in the spectral-averaged cross section due to this effect is approximately 10 12%. 29

42 16.0x10-6 Neutron Flux (Neutrons / cm 2 /source paricle) 14.0x x x x x x x10-6 Fresh Core (0 MWD/MTU) Mid-Burnt Core (50,000 MWD/MTU) Highly Burnt Core (100,000 MWD/MTU) Energy (MeV) Fig The burnup dependent neutron spectra as calculated by MCNP using core compositions that correspond to the shown burnup levels. 2.3 Pebble Depletion Calculations Once reliable ORIGEN cross sections are available, depletion calculations can be performed of the pebbles going through the PBR core. These depletion calculations will provide estimates of the isotopic compositions of a given pebble, which can be subsequently used to study the emitted radiation from each pebble. Quantification of the radiation emission allows for the design of pebble assay and interrogation methods and systems, which is the subject of this dissertation. 30

43 For the multi-pass pebble bed reactor, the spherical fuel pebbles are continuously circulated through the reactor core until they reach the proposed burnup limit (~100,000 MWD/MTU). To simulate the fuel pebble irradiation process, it is crucial to understand how a pebble flows in the core once it is loaded at the top of the core. Past studies that were published showed that a pebble inserted at the top of the core at a particular location is most likely to move in a vertical direction with minimum radial movement [5, 21, 28]. It also shows that pebbles loaded at the center of the core travel at a greater speed than those loaded at peripheral regions of the core. Depending on the location of its insertion at the top of the core, the pebble could experience variations in the neutron energy spectrum and flux as it travels from top to bottom. The main sources of these variations are the spatial position of the pebble within the core, and the status of the surrounding pebbles (e.g., fresh, medium, or highly burned). Therefore, the appropriate ORIGEN depletion simulations for calculating pebble isotopics will differ from simulations that are usually performed to study the general behavior of the cores of traditional reactors. In the pebble depletion case, the simulation should be executed assuming constant flux conditions throughout the depletion process. Using this option, ORIGEN is prevented from adjusting the neutron flux as the pebble fissile content is depleted. This is in contradiction to the usual constant power assumption that is applied in core depletion calculations. Based on the above, an envelope of runs was defined to test the sensitivity of the various indicators to the irradiation conditions. Table 2.5 below gives the flux values that 31

44 were used in ORIGEN for the pebble depletion calculations. The neutron flux values were evaluated using the relation [18] ( P) Φ =, (2.9) f f X i σ R i i i where P is the power defined by the user for the system (in MW), X f i is the amount of fissile nuclides i in fuel (g atom), σ f i is the microscopic fission cross section for nuclide i, and R i is the average recoverable energy per fission. Notice that Table 2.5 shows the results for the case of the pebble passing through an environment composed of fresh, medium or highly burnt pebbles, which may create minor spectral variations. Alternatively, the passage of a pebble near the center or the periphery of the core will highly influence the power (flux) that the pebble experiences. The values used for the power (flux) are based on an average thermal power of 265 MW-thermal and on the spatial distributions as published in the literature for a realistic PBR core [29, 30]. Table 2.5. Single Pebble Depletion Calculations. The numbers are calculated using Eq. 2.4 and assuming an average power of 265 MW-thermal. Neutron Flux Fresh Pebble Medium Burnt Highly Burnt Irradiation Interval Low (n cm -2 s -1 ) days Power= MW Medium(n cm -2 s -1 ) days Power= 265 MW High (n cm -2 s -1 ) Power= 530 MW days Pebble depletion calculations were performed using the flux values shown in Table 2.5. The produced isotopic information was examined to find the burnup indicators that showed the least variation in their activity versus burnup correlation as the flux is varied. The results of this analysis are presented in Chapter 3. 32

45 3 Passive Gamma-Ray Assay of PBR Fuel In Chapter 2, the ability to calculate reliably the isotopic composition of irradiated pebbles as a function of burnup was developed. As a result, this allowed for the quantification of the radiation emitted by the pebble. In particular, this work focuses on the characteristic gamma-rays emitted by the fission products and actinides that are produced upon the irradiation of a fuel pebble. The above information is essential for performing the studies described in this dissertation. This is due to the fact that neither fresh nor irradiated pebbles were available for performing experimental studies. Therefore, computational simulations become the primary tools for assessing the various methods of assaying and interrogating the fuel pebbles. The gamma-ray spectrum measured from the nuclear fuel is expected to be very complicated due to the hundreds of radioactive isotopes being produced during the irradiation of the fuel. Consequently, High Purity Germanium (HPGe) detectors, which are known for their high (energy) resolution, are expected to be most suited for performing passive gamma assay measurements on the PBR fuel as it circulates in and out of the core. In this work, a burnup monitoring system based on a coaxial n-type HPGe detector is proposed. Computational simulations based on the ORIGEN isotopic information and using the MCNP and SYNTH [31] codes were employed to visualize the gamma-ray spectra measured from the fuel pebble at different burnup steps. 33

46 3.1 Gamma-ray Spectra Simulation The realistic simulation of the gamma-ray spectrum as measured by an HPGe detector requires accurate accounting of the emission source spectrum, faithful representation of the source-detector geometry and material properties (including interaction cross sections) to ensure correct radiation transport calculations, and accurate representation of the charge carrier production and collection in the detector. The information produced by the ORIGEN depletion calculation is insufficient to simulate a gamma-ray spectrum that is emitted by an irradiated pebble. This is due to the fact that ORIGEN provides only the isotopic composition and the gamma source term in coarse 18-group photon energy bins, which does not permit performing accurate gammaray spectrometry analysis. Therefore, a finer source representation needs to be constructed using the ORIGEN isotopic information. On the other hand, MCNP is highly capable of accurately modeling the source-detector geometry and the radiation interaction in the pebble and the detector using extensive photon and electron interaction cross section libraries. Fig. 3.1 shows a schematic of the basic MCNP model that is used to perform virtual gamma-ray spectrometry on the irradiated pebbles. MCNP performs a coupled photon-electron transport calculation using photons that are emitted within the pebble and utilizes the F8 tally to calculate the pulse height spectrum within the active volume of a detector [22]. It was assumed that the pebble is located at 100 cm above the detector s end-cap and along the centerline. The detector was modeled using the nominal 34

47 manufacturer s parameters for a 100% efficient n-type coaxial HPGe [32]. The fueled zone in each pebble was modeled as a homogeneous mixture of graphite and UO 2, thus, the gamma-ray emitting nuclides are assumed to be distributed uniformly within the fueled zone. Based on this model, the gamma-ray spectra were simulated for different burnup steps. MPBR Fuel Pebble Graphite Layer Fuel Zone 100 cm 100% Coaxial HPGe Detector Fig A schematic of the gamma-ray burnup measurement detector. However, MCNP s current capabilities do not include the ability to simulate the process of charge carrier generation and collection, which is directly responsible for the statistical contribution to the finite HPGe detector resolution. Therefore, the response function as calculated by MCNP includes full energy gamma energy peaks that do not exhibit the characteristic Gaussian peak shape. 35

48 Consequently, to simulate a realistic gamma-ray spectrum, the limitations of the current codes in accurately producing an accurate photon source term and simulating a finite detector response function had to be addressed. The details of this investigation are given below Gamma-ray Source Term Construction From the ORIGEN depletion calculation, 344 radionuclides of non-zero activity are produced, most of which are gamma emitters. For each gamma line emitted from a given radionuclide, its intensity can be calculated as follows: I A i Γi, j = (3.1) where A i is the activity of i-th radionuclide, and Γ i,j is the branching ratio of j-th gamma line emitted by i-th radionuclide. To establish the gamma-ray source term using these radionuclides, the SYNTH software and its databases were utilized. SYNTH is a synthetic gamma-ray spectrometry software developed by Pacific Northwest National Laboratory, which uses empirical relationships to construct detector response functions. It contains three rather comprehensive databases of radionuclide nuclear properties (half-life, gamma line energy, and branching ratio) in Microsoft Access format: synth_es.mdb, TORI.mdb, and PC_nudat.mdb. To utilize these databases, a database table in Microsoft Access format is constructed from ORIGEN output radionuclide activities. When a combination query is performed on these databases, it shows that using TORI.mdb (Table of Radioactive Isotopes) will generate the most gamma lines from the 344 radionuclides calculated by 36

49 the ORIGEN depletion simulation. Thus, the TORI.mdb database is used for the gamma source term construction. This database includes 3,472 radionuclides emitting 74,722 gamma lines. Using this database, a total of 11,840 gamma lines are picked up for the 344 non-zero activity radionuclides produced within the fuel pebble. To construct the source term in the MCNP model, the source input energy bin is refined to be 0.5 kev/bin, extending from 0 MeV to 10 MeV. The intensity probability distribution for each bin is calculated as N Ai Γi, Ek i= 1 P E = k E N (3.2) A Γ max Ek = E0 i= 1 i i, Ek where E k is the k-th energy bin, N is the total number of radionuclides contributing to the gamma source, in this case 344, A i is the activity of i-th radionuclide, and Γ i, Ek is the branching ratio for the i-th radionuclide emitting a gamma-ray at energy E k. To input this source probability distribution into an MCNP model automatically, a program called input_maker was written in C++ to perform this task (see Appendix 7.2.3) Full Width Half Maximum vs. Energy As mentioned above, the detector response function can be simulated by performing a photon-electron transport calculation using the F8 pulse height tally in MCNP. The pulse height tally provides the energy distribution of pulses created in a cell 37

50 that models a physical detector (active volume in HPGe detector). However, this tally does not account for the statistical variation in the number of charge carriers (electronhole pairs in HPGe detectors) produced by the interactions of gamma rays in the detector. Therefore, the full energy peak in the spectrum of a monoenergetic source appears as a single spike falling into one energy bin, which is impossible for a real detector system. For a realistic detector system, there are a number of potential sources of fluctuation in the response of a given detector that result in imperfect energy resolution. These include any drift of the operating characteristics of the detector during the time period of measurement, sources of random noise (parallel and series noise) within the detector and instrumentation system, and more importantly, the statistical noise due to the discrete nature of the measured signal itself. When combined together, all of these effects can be represented by a parameter known as the Full Width at Half Maximum (FWHM), to describe the detector system resolution performance. The total FWHM is the quadrature sum of the FWHM values for each individual component [33]: 2 overall ( FWHM ) ( FWHM ) + ( FWHM ) + ( FWHM ) +... (3.3) = statistical noise drift To simulate this effect in MCNP, the Gaussian Energy Broadening (GEB) treatment is used. In this case, the FWHM behavior of a detector system can be included in the MCNP model using the relationship [22]: FWHM + 2 = a + b E ce, (3.4) where E is energy in MeV; and a, b, and c are constants provided by the user. 38

51 Usually, Eq. (3.4) is fit to the experimental data of a real detector system. Since no experimental data is available for the modeled system, the SYNTH code and its data base of detector response functions, for a similar detector, is used to obtain this relationship. In this step of the analysis, a series of monoenergetic sources ranging from 100 kev to 5 MeV are placed 100 cm away from a 100% HPGe detector. For each monoenergetic source, the FWHM of the full energy peak is obtained. The obtained data was fit using Eq. (3.4) to obtain the value of the a, b and c constants. The result is shown in Fig The constants obtained from the fit are a = , b = , and c = Thus, for the simulated detector system, the full energy peaks are broadened using the following relationship: FWHM = E E (3.5) FWHM (MeV) Energy (MeV) Fig The FWHM fit to SYNTH data as used in MCNP. 39

52 3.1.3 Simulated Gamma-ray Spectra Using the results presented above, gamma-ray spectra at different burnup steps, namely, 20,000 MWD/MTU, 50,000 MWD/MTU, and 80,000 MWD/MTU, are produced for the simulated system shown in Fig Figure 3.5 shows the produced gamma-ray spectra. The spectra were produced by performing MCNP runs using 2 x 10 9 initial photons. To assure acceptable statistical results each spectrum was divided into 4 energy regions and each region was run separately. Subsequently, the total spectrum was produced as the weighted combination of the individual regional spectra. Once the spectra are available detailed gamma-ray spectroscopy analysis becomes feasible. The evaluation of issues such as peak interference, minimum detectability check, and error analysis is performed. This analysis, combined with the searches performed on the ORIGEN radionuclides activity output (see section 3.2), guide us to find the indicators that can be used for fuel burnup measurement using gamma-ray spectrometry methodology Counts / source particle ,000 MWD/MTU Energy (kev) Fig Simulated Gamma-ray Spectra for PBR fuel at various burnup levels. 40

53 ,000 MWD/MTU Counts / source particle Energy (kev) ,000 MWD/MTU Counts / source particle Energy (kev) Fig Continued 41

54 3.2 Burnup Measurement Using Absolute Indicators As mentioned previously, fuel burnup is defined as the energy generated per unit mass of fuel and is typically reported in units of megawatt-days per metric tons of uranium (MWD/MTU). Consequently, it is directly related to fission reactions that take place in a given fuel element. Ideally, burnup can be assessed by measuring the amount of fissile material left in the fuel when the initial fuel enrichment is known. However, passive nondestructive methods are not capable of yielding that information directly. This is mainly due to the existence of very strong sources of radiation in irradiated fuel that will overwhelm the direct signatures of the fissile material. Therefore, passive burnup measurements are performed indirectly using the spontaneous emission of gamma and neutron radiation by fission products and heavy actinides that result upon irradiation of the fuel. To identify all of the possible burnup indicators, the radionuclides produced by ORIGEN were scrutinized based on the criteria developed below Absolute Activity Burnup Indicator Selection Criteria In this work, the ORIGEN simulations assumed a PBR power of 265 MWthermal and UO 2 fuel that is enriched anywhere from 6% to 10% in U-235. The fuel was assumed to go through several periods of irradiation and cooling that simulated the circulation of the pebbles in and out of the core during a pebble s irradiation cycle. As a result, 344 non-zero activity radionuclides were produced that can, potentially, be used in passive assay of the fuel. However, the choice of a burnup indicator can be facilitated by observing three criteria: 42

55 1) The ideal indicator should provide the required burnup information independent of the variations in the pebble s exposure history (i.e., power history) as it passes through the core since, for this type of reactor, a fuel pebble may have a different path every time it is circulated through the core. Two factors will contribute to this variation: 1) the total neutron flux level which the pebble is experiencing while it is passing different zones of the core; and 2) the average burnup of fuel pebbles surrounding it in these zones, which affects the neutron spectrum that irradiates the pebble and introduces variations in the one-group spectrumaveraged cross sections. Failure to fulfill this criterion will result in large uncertainties in the measurement of fuel burnup, which may lead to operating with unoptimized fuel cycles or to breaching the fuel operating safety limits, thus increasing the probability of fuel failure. 2) The indicator should have a monotonically increasing or decreasing relationship between activity and burnup in order to give a unique correlation that can be used to determine a certain burnup level. Also, the difference of activities between different burnup steps should be prominent (greater than the measurement uncertainty) in order to distinguish one burnup step from another. 3) The indicator should emit gamma rays that are detectable within the counting period of interest for on-line monitoring. In gamma-ray spectrometry, this criterion can be quantified using the minimum detectable activity (MDA) concept, as established by Currie [34, 35]. 43

56 Consequently, many of the radionuclides that are produced in the simulation may be excluded from use as burnup indicators. To apply these criteria to find potential burnup indicators, a search program called AbsIsoSearch is written in C++ to search the ORIGEN outputs (see Appendix 7.3.1) Power History Variation Search In this search, all 344 non-zero activity radionuclides produced by the ORIGEN depletion calculations are individually examined. For each radionuclide, the burnup steps are divided into eight steps from 10,000-80,000 MWD/MTU, and the calculations are performed using nine sets of activity vs. burnup data accounting for three different neutron energy spectra at three different total neutron flux levels. During the search process, the power history variation of a radionuclide is examined by looking at the differences among those nine activities corresponding to each burnup step, the criteria being applied here is that the maximum difference should be less than 15%. Also, the differences between a certain burnup step compared to its previous and next burnup steps are set to be greater than 5% to guarantee that the radionuclide s activity can be used to distinguish one burnup step from another. Any radionuclide that does not have a monotonically increasing or decreasing activity vs. burnup relationship is excluded from the output. A total of 31 radionuclides survived the search. These 31 radionuclides are then input to the TORI.mdb database to perform the search for gamma-emitting radionuclides. 44

57 Twenty-one gamma-emitters passed the power history variation search. These 21 radionuclides are listed in Table 3.1. with their half-lives and activities at typical burnup steps Minimum Detectable Activity Check For the 21 radionuclides to be used as burnup indicators, the gamma rays have to be detectable over the background of the gamma-ray spectrum of the fuel pebble. The Minimum Detectable Activity (MDA) of their major gamma lines is calculated based on the simulated gamma-ray spectrum in Section 3.1. Table 3.1. Gamma Emitters that Passed the Power History Variation Criterion. Radionuclide Half-life 20,000MWD/MTU (Ci/pebble) 50,000MWD/MTU (Ci/pebble) 80,000MWD/MTU (Ci/pebble) Ag sec Ag-108m yr Ba-137m sec Cd-113m 13.7 yr Cs yr Cu hr Eu yr Eu yr Ho-166m yr I yr Kr yr Kr yr Nb yr Sb-126m 19 min Sn-121m 55.0 yr Sn yr Tc yr Tc yr Te yr U d Zr yr The MDA can be calculated as follows [36]: 45

58 N D MDA =, (3.6) fεt where N D is the minimum value of net source counts given by n N D = 3.29 N B (1 + ) , (3.7) 2m N B is the background count, n is the peak channel number, m is the background channel number, ε is the absolute detection efficiency, f is the gamma-ray yield per disintegration, and T is the counting time, which is 30 seconds. The background count N B, in Equation (3.8), is obtained from the simulated spectrum. Based on this analysis, very few radionuclides remain that can be used as potential burnup indicators. Table 3.2. lists the MDA values for a single pass (5,000 MWD/MTU) burnup step for these radionuclides. Table 3.2. MDA Check Gamma Emitters at 5,000 MWD/MTU. Radionuclides Half-life (years) Activity (Ci/pebble) MDA (Ci/pebble) Energy (kev) Cs Eu Eu Kr However, as seen in Table 3.2., for most of the radionuclides the activity is barely greater than the MDA, except Cs-137, which has an activity of almost five orders 46

59 of magnitude greater than the MDA. Hence, the gamma peaks of Eu-154, Eu-155, and Kr-85 are very difficult to identify from the spectrum, while the 661 kev gamma peak emitted by Cs-137 is prominent. The feasibility of using Cs-137 as a burnup indicator is investigated further in the following section Using Cs-137 as a Burnup Indicator To further investigate the feasibility of using Cs-137 as a burnup indicator, an upper and lower bound for the variation in the Cs-137 activity within a pebble at different power levels and through different fuel zones are extracted from the ORIGEN output. The burnup vs. activity correlation for Cs-137 is plotted in Fig As it can be seen, the maxium variation is 10% at discharge, which shows good power history independence. Looking closely at the general expression for the buildup and decay of a fission product α as a function of irradiation time can provide more physical insight about this process, which can be described by the following equation: dn dt α = Yα N f σf φ+ λ iαn i + σ jαφn j (λ α + σαφ)nα, (3.8) i j (1) (2) (3) (4) where f indicates a fissile material, i indicates a decaying parent, j indicates a capture precursor, N is the concentration of a given specie, Y α is the independent fission yield of α, φ is the one group scalar flux, λ is the decay constant, and σ is the spectral- averaged cross-section for a particular reaction. Equation (3.8) represents the balance relation for the production of α by fission (term 1), decay of radionuclide i (term 2), and neutron 47

60 transmutation of nuclide j (term 3). The destruction of α (term 4) is due to its decay and transmutation by neutron absorption. By examining (1), it is clear that power history independence is enhanced if term 4 is considered negligible (i.e., α is long-lived and has a small absorption cross-section). Furthermore, if terms 2 and 3 are negligible, then α is considered a primary fission product with an activity that may be linearly correlated to fissile material consumption, i.e., burnup (This is especially true if fissile Pu production is considered as it is in the case of LWR calculations.) high_bound low_bound Burnup (MWD/MTU) Activity (Ci/pebble) Fig Burnup vs. Cs-137 activity correlation. Cs-137 has a rather long half-life (compared to the total in-core time of three years), and a very small neutron absorption cross section, which combine to make term 4 negligible. The major production of Cs-137 is from fission, which makes term 1 the most 48

61 dominant term in the right-hand side of Equation (3.10) and results in the behavior shown in Fig Although Cs-137 has good resistance to power history variation, which is a property for being a good burnup indicator, two major issues may prevent it from being a perfect one. These issues are: 1. Given the details of the pebble s gamma-ray spectra, a clean, interference-free gamma peak is very important for a gamma line to be useful because determining the peak area becomes a tricky problem when multiple gamma peaks are located close to each other. Under such circumstances, large error could be introduced due to the interference from neighboring peaks. 2. Cs-137 is a direct fission product. Its concentration (as a function of burnup) could be approximated by term 1 of Eq However, if pebbles of differing enrichment exist in the core, unique identification of the burnup of a pebble independent of its enrichment may will not be possible Spectral interference analysis of Cs-137 Cs-137 has only one major gamma peak (branching ratio 0.85) at kev. The typical FWHM value for HPGe detector at kev is approximately 1.22 kev. A rule of thumb to resolve two equal amplitude peaks is that they should be separated by at least more than one value of detector FWHM [33]. When investigating the kev neighboring region, strong gamma lines emitted by other radionuclides have been found. 49

62 The radionuclides and their gamma peaks are listed in Table 3.3. Also, the detailed gamma-ray spectrum in that region is shown in Fig for different burnup steps. Table 3.3. Cs-137 Gamma Peak Interference. Radionuclide Energy (kev) Half-life (parent information) Ag-110m d Nb h (Zr-97, 16.8h) I h (Te132, 3.2d) Cs y Ce d Te-131m d I h (Te132, 3.2d) As seen in Table 3.3. and Fig. 3.5, the Cs kev peak can experience interference by the Nb-97, I-132, and Ce-143 peaks. To investigate the effect of this interference on the ccuracy of peak area determination, the simulated spectra are imported into ORTEC s GammaVision software to facilitate the gamma-ray spectroscopy analysis [37]. In GammaVision, the multiple-peak region can be unfolded using leastsquares fitting assuming a Gaussian peak shape as shown in Fig [37]. The analysis method applied in GammaVision treats the contribution of the individual peaks as a weighted sum of the Gaussian peak shapes. The weighting factors of each component are proportional to the area of that component s peak. The shape is calculated for the peak at the given energy (based either on a library value or as obtained from the spectral energy calibration), eventhough the change in shape with energy within the energy range of the multiplet is small. The contribution of a unit-height peak is calculated for each channel in the multiplet range and for each candidate energy. This matrix of peak amplitudes multiplied by the weighting factors and summed is equal to the net spectrum. The peak positions for all peaks are allowed to shift in the fitting process to obtain the reduced chi- 50

63 square. The fit is iterated until the reduced chi-square for the fit changes by less than 1% from the previous iteration up to a maximum of 10 iterations. (a) (b) (c) Fig The Cs kev peak with interference: (a) 20,000 MWD/MTU, (b) 50,000 MWD/MTU, (c) 80,000 MWD/MTU. The marker indicates the kev peak. 51

64 As it can be seem in Fig. 3.5, the Cs-137 peak is growing as burnup increases, while the surrounding peaks are decreasing; therefore, the Cs-137 peak has less interference effect at high burnup than during the first few cycles. However, to quantify this uncertainty, which was introduced by interference from the neighboring gamma peaks, three additional MCNP calculations were performed with these interference gamma peaks removed artificially from the neighboring region of the kev peak. Fig shows the Cs kev gamma peak without interference. The net peak areas of Cs kev without interference are determined using a routine called SUM, written in C language, implementing the channel summation method for peak area analysis [38, 39] (see Appendix 7.3.3). By comparing the net peak area of Cs-137 peak with and without interference, we can quantitatively define the uncertainty due to peak interference. The details of this peak area determination analysis is presented below Peak Area Determination for Singlets In general, peak area determination in gamma ray spectrometry is made by one of two methods. The first is based on summing the contents of user defined peak channels and introducing a correction for the background continuum on which the peak rides. The second is based on fitting an appropriate function (usually, either a pure Gaussian or a variation of a Gaussian) to an identified peak. For gamma ray spectra that contain well resolved peaks, with high signal to noise ratio, and a slowly varying background, studies have shown that summation methods produce peak areas with uncertainties approaching the theoretical limits predicted by counting statistics. Therefore, a summation algorithm called SUM is utilized to determine the Cs-137 peak with no interference. The SUM 52

65 method requires the user to define the left and right peak boundaries. It also requires the identification of left and right background channels from which a linear background is estimated under the peak. A schematic of the method is given in Fig (a) (b) (c) Fig Cs kev peak without interference: (a) 20,000 MWD/MTU, (b) 50,000 MWD/MTU, (c) 80,000 MWD/MTU. The marker indicates the kev peak. 53

66 Counts per Channel L R L Background Channel Number R Fig Evaluation of net peak areas using the SUM methodology. The net peak area is determined by the following expression: C net R = C i= L i B, (3.9) where C net is the the net peak area, C i is the counts of channel i, and B is the background area. The background area is determined by finding the area of the trapezoid in Fig and is given by L 1 R+ R R L B = + Ci C 2 L L L R R+ 1 i, (3.10) 54

67 where R is the right boundary of the peak, L is the left boundary of the peak, and is the number of background channels. Based on the above, the variance in the net peak area is given by R L 1 R = R 2 R L σ C C net i ( ) Ci Ci. (3.11) 2 2 i= L 2 L L L R R+ 1 A routine written in C language implements this algorithm to automate peak area calculations. The definition of the net peak area and background channels is maintained for different burnup step spectra for consistency throughout this analysis. The net peak areas of the Cs kev peak calculated from Fig. 3.5., using deconvolution fitting for the interfered multiplets, are compared to the net peak areas determined from Fig by applying SUM to the clean singlet. The difference between these two is introduced by interference. The statistical error in the peak areas throughout this analysis is approximately 0.1%. Table 3.4. Cs kev net peak area interference bias. Net Peak Area (Counts) No Interference (SUM) Interference (Gaussian Fitting) Interference Bias 20,000 MWD/MTU % 50,000 MWD/MTU % 80,000 MWD/MTU % As seen in Table 3.4., due to the interference from other radionuclides, using the full energy peak of Cs kev peak will introduce a large bias at the beginning of 55

68 the fuel cycle, and this interference effect will improve as burnup increases; however, the uncertainty due to this factor remain around 8.54% at discharge (80,000 MWD/MTU) Error Analysis for Using Cs-137 Full Energy Peak as Burnup Indicator Once the full energy peak area of its characteristic gamma peak is determined from the measured spectrum, the activity of one radionuclide can be calculated as C A =, (3.12) ΓεT where A is the activity, C is the net peak area counts, Γ is the branching ratio for the gamma line, T is the counting time, and ε is the full peak energy efficiency. To use Cs-137 as a burnup indicator, one has to determine the net peak area counts for the kev peak, then calculate the activity of OR from Equation (3.15). As the activity is derived, the burnup can be determined from the relationship presented in Fig During this process, several components introduce error to the final prediction of fuel burnup. The first component of uncertainty comes from the net peak area counts. This component, in turn, is composed of two components: 1) the error introduced from interference, which is discussed in Section ; and 2) the statistical error of the peak area. These two components can be added together in quadrature to obtain the total uncertainty of the net peak area. 56

69 The second error component is contributed by ε, the absolute efficiency obtained from absolute efficiency calibration. To obtain an absolutely calibrated efficiency curve with high accuracy for the prototype detection system is not easy. The monoenergetic standard used to calibrate the system has to be prepared as a uniformly distributed Cs-137 source mixed in UO 2 matrix with similar construction to a typical fuel pebble. In addition, variability between standard and pebble will be introduced due to the expected variation between different pebbles. Under the best circumstances, this uncertainty component is expected to be around 3% [33, 35, 36]. The third error component is the branching ratio. The relative error of this term is estimated to be 0.2% [40]. In addition to all of the above, error is introduced by power history variation of fuel pebbles in the core. The detailed error analysis for these components is listed in Table 3.5. Table 3.5. Error Components for Cs-137 Full Energy Peak. Uncertainty Components 20,000 MWD/MTU 50,000 MWD/MTU 80,000 MWD/MTU Spectral Interference ± 37.4% ± 26.6% ± 8.54% Counting Statistics ± 0.1% ± 0.1% ± 0.1% Absolute Efficiency Calibration ± 3% ± 3% ± 3% Branching Ratio ± 0.2% ± 0.2% ± 0.2% Power History* ± 1.46% ± 1.02% ± 0.86% Quadrature Sum ± 37.5% ± 26.8% ± 9.1% *Throughout this dissertation, the 1σ component is estimated assuming a uniform interval distribution of width ±10%. 57

70 While Cs-137 can be used as an absolute on-line indicator of burnup for PBR fuel, its use will not be possible if the core is loaded with pebbles of different enrichments. Therefore, an alternative technique based on using relative indicators has been investigated for the simultaneous determination of burnup and enrichment. This technique is discussed in the section below. 3.3 Burnup Measurement Using Relative Indicators The burnup of irradiated fuel can also be determined using the ratio of radionuclide activities. Traditionally, this type of relative measurements has been found to be more accurate than absolute measurements that were presented in the previous section. The isotopic ratios (R) can be determined from the activity ratios, which can be derived from the net peak areas (A), branching ratios (Γ), and the relative efficiency (ε) of the two gamma lines i and j. R = Ai A j Ciε jγ j = C ε Γ j i i (3.13) Notice from Equation (3.18), that in order to determine the activity ratio of two radionuclides, there is no need to know the absolute efficiency of each gamma line; only the relative efficiency ε j /ε i is required. This relative efficiency can be obtained from the fuel pebble gamma-ray spectrum on-line if there is a radionuclide that is produced by irradiation within a fuel pebble emitting a series of gamma lines with intensities strong enough and spanning an energy range that is wide enough to cover the energy range of interest. In this case, the activity ratio of two gamma lines is unity, since both gamma 58

71 lines are emitted from the same radionuclide; therefore, the relative efficiency can be determined as ε i ε j CiΓ j = C Γ j i (3.14) Since irradiation produces many radionuclides, which emit a series of gamma lines, it is highly possible to find one that is suitable for on-line relative efficiency calibration On-line Relative Efficiency Self-calibration To achieve the objective of performing the on-line efficiency calibration of the burnup spectrometer, a scheme was designed that utilizes the radiation sources that exist within an irradiated fuel pebble. Specifically, a search was performed to identify appropriate isotopes that emit gamma rays that can be used in the calibration effort. The main criteria that need to be satisfied are: 1) the isotope needs to have a sufficiently long half-life to allow its survival after a pebble leaves the core and until it reaches the detector; 2) it should be of reasonable activity; 3) it should emit intense gamma rays that cover a wide energy range; and, finally, 4) its gamma lines should be free from spectral interference. After examining the large list of radionuclides that are produced upon the irradiation of the fuel (as calculated by the ORIGEN code) and inspecting the simulated MCNP spectra, I-132, Cs-134, and La-140 were chosen as potential relative efficiency calibration standards. task Table 3.6 lists the characteristics of these radionuclides that are relevant to this 59

72 Table 3.6. Relevant data for the nuclides used in relative efficiency calibration. Radionuclide (half-life) Gamma-Ray (kev) & (% Branching Ratio) Single Pass Activity (Ci) MDA (Ci) I-132 (2.30 h) (16) (13.3) (98.7) (75.6) (17.6) 1295 (1.9) 1372 (2.5) (7.0) (1.4) (1.2) (1.1) (0.3) (0.2) Cs-134 (2.06 y) (1.5) (8.4) (15.4) (97.6) (85.5) 802 (8.7) 1163 (1.8) (3.0) La-140 (1.68 d) (20.3) 487 (45.5) (23.3) (6.9) (95.4) (0.9) (3.5) (0.1) (0.02) Notice that, even after 48 hours of cooling during the travel period from the core to the detector location, all these radionuclides are detectable. However, the gamma lines 60

73 of La-140 extend over an energy range from 300 kev to 3000 kev, which would be very convenient for both relative efficiency calibration and quality assurance purposes Absolute Efficiency Monoenergetic source data La140 data Cs134 data I132 data Energy (kev) Fig The Absolute Efficiency Curve of the Gamma-ray Spectrometer. The pebble was assumed to be 100 cm from the detector. The burnup is assumed to be 20,000 MWD/MTU. To further verify the suitability of these radionuclides for efficiency calibration, a computer experiment was performed using the pebble/spectrometer model that was described previously. Initially, an absolute efficiency curve was constructed using monoenrgetic source simulations in the energy range kev. Subsequently, a spectrum similar to ones shown in Fig. 3.3 was used to construct the absolute efficiency curve using the gamma lines of I-132, Cs-134, and La-140. Fig 3.8 shows a comparison 61

74 of the results obtained in both cases. In general, good agreement is observed between the efficiency values obtained using the two different methods. This confirms that the efficiency values derived from the pebble s spectrum did not suffer from any effects that could have been undetected during the analysis of the spectrum (e.g., spectral interference). In addition, the monoenergetic simulations were based on unbroadened spectra, which confirms that the broadening operation and the procedures for the calculation of full energy peak areas that were used to analyze the pebble s spectrum are producing consistent results. Nevertheless, La-140 presents the best coverage of the energy range. Therefore, it was selected as the radionuclide to be used in the relative calibration operation. In all of the above, the peak areas were determined using a simple procedure for summing the channel content of the peak region and accounting for spectral background, which is similar to that given in [39]. Next, the method developed by Hawari et al. was implemented to construct the relative efficiency curve using a radionuclide that emits a series of gamma rays (e.g., La- 140). The details of this method are described elsewhere and are briefly presented here [38, 41]. The general approach is to assume a functional dependence between energy and efficiency that is given by the following expression ε i E ln = f ln i (3.15) ε0 E0 where ε 0 is the full energy peak efficiency for the reference energy E 0. Eq. (3.15) can be expanded to yield the following: 62

75 63 = = ε ε N 0 k 0 i k k 0 i E E ln a ln (3.16) Therefore, for any two gamma lines designated i and j, Eq. (3.16) can be written as = = ε ε N 0 k 0 j k 0 i k k j i E E ln E E ln a ln (3.17) Utilizing some algebraic manipulation and applying the binomial expansion to the expression ln k (E i /E 0 )-ln k (E j /E 0 ), Eq. (3.17) can be expressed in the following form: = = ε ε = N 1 k 0 j 0 i k k j i j i E E,ln E E ln f a E E ln ln P (3.18) The functions f k result from the application of the binomial expansion and are given by 1 k j 2 k j i j 2 k i 1 k i k X X X... X X X f = (3.19) where X i = ln(e i /E 0 ) and X j = ln(e j /E 0 ). Explicitly, the expression for the relative efficiency as a function of energy becomes ( ) i X j, X p j i j i E E = ε ε (3.20) where ( ) ( ) = = N k j i k k j i X X f a X X p 1,,. Finally, linear least-squares analysis can be used to obtain the a k coefficients from the set p,f k. The uncertainties in the predicted values of p are obtained using the covariance

76 matrix resulting from the analysis. This allows the propagation of that uncertainty into the calculation of the relative efficiency (i.e., Eq. (3.20)). The above approach was utilized for constructing the relative efficiency curve for the detector using the La-140 gamma lines. Fig. 3.9 shows the efficiency curve relative to the 3119 kev line of La-140 obtained from the calculated absolute efficiency values as compared to the data points obtained using the above fitting approach. This approach resulted in a 4-parameter fit to describe the variation in p, and is given by the following expression P = f f f 4 p (> χ 2 ) = 7% 3 Fit prediction MCNP data Relative Efficiency Energy (kev) Fig The Relative Efficiency Curve of the Gamma-ray Spectrometer. The pebble was assumed to be 100 cm from the detector. 64

77 3.3.2 Cs-134/Co-60 as a Burnup Indicator The two most commonly used isotopic ratios, namely, Cs-134/Cs-137 and Eu-154/Cs-137, were investigated [13, 15]. But, these two ratios failed for the PBR situation by either introducing too much error due to power history variations, or by not having a gamma peak strong enough to be used (for Eu-154, all of its gamma lines are too weak to be identified from the spectrum background). Co-60 has two well known gamma peaks with strong intensities ( kev with 99.97% and kev with 99.98% intensities), and these two peaks can be used in the fuel burnup measurement by doping the fuel pebble with a small amount of Co-59 to utilize the Co-59 (n,γ) Co-60 reaction. To investigate the possibility of using these two characteristic peaks of Co-60, the fresh fuel pebble doped with 100 weight parts per million (ppm) with Co-59 is used to perform the same ORIGEN depletion calculations stated in Section Furthermore, the activity ratio of Cs-134/Co-60 is found to have a correlation with fuel burnup that shows good resistance to power history variation. Cs-134 is produced by neutron capture on the fission product Cs-133; therefore, its production requires two neutron interactions, the first of which is the neutron that causes fission of uranium or plutonium. The second interaction is the Cs-133(n,γ)Cs- 134 reaction. Because these interactions are the primary source of Cs-134, the concentration of Cs-134 within the fuel is approximately proportional to the square of the integrated flux. For Co-60 production from fission is negligible, therefore, the Co-60 65

78 produced within the fuel is primarily from the Co-59(n,γ)Co-60 reaction, which is proportional to the integrated flux. Hence, by dividing the concentration of Cs-134 by the concentration of Co-60, the ratio becomes approximately proportional to the burnup. The correlation of burnup with Cs-134/Co-60 is plotted in Fig high_bound low_bound Burnup (MWD/MTU) Activity Ratio Fig Burnup vs. 134 Cs/ 60 Co activity ratio correlation. The interference check is performed for both Cs-134 and Co-60. The Co kev peak is found to be contaminated by I-132, which also emits kev gammas. However, the Co kev peak and Cs kev peak remain free of interference. These two peaks can be identified clearly from the fuel pebble spectrum. 66

79 Therefore, the 134 Cs/ 60 Co ratio can be used as a burnup indicator. The peak regions of Cs-134 and Co-60 in the fuel pebble spectrum are shown in Fig (a) 20,000MWD/MTU 50,000MWD/MTU 80,000MWD/MTU (b) Fig Co kev Peak (a) and Cs kev Peak (b) in Fuel Pebble Spectra at Different Burnup Steps. The error analysis for using 134 Cs/ 60 Co to predict fuel burnup is performed and listed in Table 3.7. Table 3.7. Error Components for 134 Cs/ 60 Co Ratio. Uncertainty Components 20,000 MWD/MTU 50,000 MWD/MTU 80,000 MWD/MTU Spectral Interference ± 0% ± 0% ± 0% Counting Statistics ± 0.1% ± 0.1% ± 0.1% Relative Efficiency Calibration ± 1.6% ± 1.6% ± 1.6% Branching Ratio ± 0.05% ± 0.05% ± 0.05% Power History ± 2.22% ± 1.18% ± 1.96% Quadrature Sum ± 2.74% ± 1.99% ± 2.53% 67

80 3.3.3 Built-in Relative Burnup Indicators It is possible to find radionuclide pairs produced within the fuel during irradiation that can give a good correlation with burnup, independent of power history. These radionuclide pairs must also have strong, clear gamma lines to be used in gamma-ray spectroscopy analysis. There are a total of 58,996 radionuclide pairs that can be constructed from the 344 radionuclides generated by the ORIGEN depletion calculation. To investigate the feasibility of using built-in relative burnup indicators, a program called RatioSearch is written in C++ to perform the search on the ORIGEN output. The criteria used to perform the absolute activity burnup indicator search can also be applied here. For each ratio pair, it should have a monotonous increase or decrease with burnup, it should have a difference greater than 5% between each burnup step, and the error introduced by power history variation should be less than 15%. There are a total of 4,570 ratio pairs, constructed by 267 radionuclides, that passed this search. After performing interference and MDA checks on these radionuclides, 24 ratio pairs were identified and are listed in Table 3.8. Table 3.8. Potential activity ratio pairs for burnup measurement. Ba-140 / U-237 I-133 / Sr-91 Nb-97 / Np-239 Pm-151 / Sr-91 Ce-141 / U-237 I-135 / Np-239 Nd-147 / U-237 Sr-91 / Te-131m I-131 / Np-239 I-135 / Sr-91 Np-239 / Sr-91 Sr-91 / Xe-133 I-131 / Sr-91 La-140 / U-237 Np-239 / Xe-133 Sr-91 / Xe-135 I-132 / Np-239 Mo-99 / Np-239 Np-239 / Xe-135 U-237 / Xe-133 I-132 / Sr-91 Mo-99 / Sr-91 Np-239 / Zr-97 U-237 / Xe

81 Among these ratio pairs, Np-239/I-132 was selected as a candidate pair, since each of them has very strong and clean gamma peaks (see Fig below). (a) 20,000MWD/MTU 50,000MWD/MTU 80,000MWD/MTU (b) Fig Np kev Peak (a) and I kev Peak (b) in Fuel Pebble Spectra at Different Burnup Steps. 69

82 follows: The build up and decay schemes for Np-239 and I-132 can be represented as (n, γ) β - β - U-238 U-239 Np-239 (n, γ) (n, γ) fission β - β - Te-132 I-132 (n, γ) (n, γ) Solving the differential equations for the above reaction chains, the activities of Np-239 and I-132 can be expressed as follows: A 239 Np + A = Np λ λ e 239 Np 239 U λ λ 239 t Np 239 U + Φσ Φσ t 239 U a 238 U N Φσ U t 238 U e λ t Φσ 238 t U 239 Np e + Φσ t ( λ 239 +Φσ t Np 239 ) Np t 239 Np Φσ t 238 U e λ t ( λ 239 +Φσ t U 239 ) U 239 Np + Φσ t 239 Np e λ t ( λ 239 +Φσ t Np 239 ) Np 239 U (3.21) Φσ t 239 U A 132 I + A λ = λ I i e λ I I Te t λ 132 Te Φy t + Φσ i Te Te σ f i N Φσ 0 i t i e λ Φσ t 132 I t i ( λ e t + Φσ 132 I 132 I +Φσ t 132 I Φσ ) t t i e λ ( λ Te I +Φσ t 132 Te t + Φσ 132 I ) t e λ ( λ 132 Te 132 I +Φσ t 132 I t Φσ (3.22) 132 ) t Te a where λ α is the decay constant for radionuclide α, σ α is the spectral-averaged absorption cross section for radionuclide α, f σ i is the spectral-averaged fission cross section for i-th t fissile material, σ is the spectral averaged total cross section for radionuclide α; N 0 α is α 70

83 the number of atoms of radionuclide α at the beginning of the burnup step, A 0 α is the activity of radionuclide α at the beginning of the burnup step, and it is zero for both Np- 239 and I-132 at the first burnup step, y i α is the cumulative fission yield for radionuclide α from i-th fissile material, Φ is the neutron flux, and t is the time period of irradiation. As shown in Fig. 3.13, and Fig. 3.14, the calculated values of Np-239 and I-132 activities using Eq. (3.21) and Eq. (3.22) are plotted against the result of the ORIGEN simulation. Good agreement with ORIGEN is obtained using Eq. (3.21) and Eq. (3.22). This shows that the physical processes described by these equations form the basis of the activity vs. burnup variation for each of these isotope Np-239 Activity (Ci/MTU) ORIGEN Simulation Equation (3.21) Burnup (MWD/MTU) Fig Np-239 activity verification. 71

84 40x10 6 I-132 Activity (Ci/MTU) 35x x x x x x10 6 ORIGEN Simualtion Equation (3.22) I-132 Produced from U-235 I-132 Produced from Pu 5x Burnup (MWD/MTU) Fig I-132 activity verification. As shown above, Np-239 is produced primarily by the U-238 capture reaction, while I-132 is produced from the decay of the fission product Te-132. Since both Np-239 and I-132 are short-lived isotopes, for each fuel cycle in the core, they are both going to reach their saturation activities. These saturation activities depend on the amount of source nuclides at the beginning of that fuel cycle and the neutron flux the pebble experiences in the core; i.e., the activity of Np-239 is proportional to the U-238 (n,γ) reaction, and the activity of I-132 is proportional to the fission reaction from fissile materials. Therefore, the ratio of Np-239/I-132 is proportional to the amount of U-238 over the amount of fissile material in the fuel pebble. Since the U-238 (n,γ) cross section is very small, the consumption rate of U-238 in the fuel pebble is very slow (less than 5% 72

85 from 0 MWD/MTU ~ 80,000 MWD/MTU); therefore, the amount of U-238, and the activity of Np-239 can be considered as a constant throughout the fuel life cycle. Additionally, the activity of I-132 depends on the fissile material left in the fuel, which is being depleted very quickly. Dividing the Np-239 activity by the I-132 activity represents how much fissile material has been burnt in the fuel pebble, which is the fundamental concept of fuel burnup. It is also important to take the ratio since this cancels out the effect of neutron flux variation on the absolute isotope activity variations, thus making the ratio power history resistant. This effect can be shown in Fig. 3.15, and Fig Activity (Ci/MTU) Np-239 at 200% Power Np-239 at 100% Power Np-239 at 50% Power I-132 at 200% Power I-132 at 100% Power I-132 at 50% Power Burnup (MWD/MTU) Fig The activity vs. burnup correlation for Np-239 and I

86 Np-239/I-132 Ratio at 100% Power Np-239/I-132 Ratio at 200% Power Np-239/I-132 Ratio at 50% Power Burnup (MWD/MTU) Activity Ratio Fig The Np-239/I-132 activity ratio. Although the activity of the individual isotopes is highly sensitive to power history variations the ratio is resistant to such variations. The error analysis is derived for 239 Np/ 132 I, using an approach similar to that for the Cs-137 and 134 Cs/ 60 Co ratio method. Table 3.9. Error Components for Np-239/I-132 Ratio. Uncertainty Components 20,000 MWD/MTU 50,000 MWD/MTU 80,000 MWD/MTU Spectral Interference ± 0% ± 0% ± 0% Counting Statistics ± 0.10% ± 0.10% ± 0.10% Relative Efficiency Calibration ± 1.50% ± 1.50% ± 1.50% Branching Ratio ± 2.27% ± 2.27% ± 2.27% Power History ± 1.76% ± 0.46% ± 0.36% Quadrature Sum ± 3.24% ± 2.76% ± 2.75% 74

87 3.3.4 Using Np-239/I-132 and Cs-134/Co-60 for the Simultaneous Determination of Burnup and Enrichment Different enrichment fuel pebbles are expected to be used in the PBR before it reaches the equilibrium core. The correlation between the burnup and the burnup indicator could change for the different enrichment fuel pebbles. Under this circumstance, the information obtained from only a single burnup indicator is not sufficient to determine the two unknowns: burnup and enrichment. Combining Np-239/I-132 and Cs-134/Co-60 can provide an effective approach to attack this problem. As stated earlier, the Np-239/I-132 ratio provides information about how much fissile material is left inside the fuel pebble, while Cs-134/Co-60 shows how much fuel has been burnt, combining this information can aid in determining how much fuel was initially put in the fuel pebble, i.e., the enrichment of that pebble. With the enrichment known, the burnup can also be determined from the burnup vs. activity ratio correlations. When a fuel pebble arrives at the burnup monitoring system, both Np-239/I-132 and Cs-134/Co-60 activity ratios can be calculated from the measured gamma spectrum of this pebble. and Table demonstrate the logic of this approach. Table Use of the Np-239/I-132 and Cs-134/Co-60 to determine burnup and enrichment. Enrichment R ( 239 Np/ 132 I) = R ( 134 Cs/ 60 Co) = Consistency Check 6% 22,000 MWD/MTU 55,000 MWD/MTU 8% 46,000 MWD/MTU 46,000 MWD/MTU = 10% 69,000 MWD/MTU 42,000 MWD/MTU 75

88 As can be seen from Table and, the burnups and enrichments determined from the calculated activity ratios of Np-239/I-132 and Cs-134/Co-60, based on the same measured pebble gamma-ray spectrum, should match each other. Due to their opposite physics principles of production in the fuel, assuming a burnup vs. activity ratio correlation at an incorrect enrichment could produce contradictory results from the two different ratios. Only the correct enrichment correlations can provide a consistent burnup prediction. With this knowledge in mind, one can conclude that the pebble demonstrated in Table is an 8% enriched fuel pebble at its 46,000 MWD/MTU burnup level Np-239/I-132 Activity Ratio enrichment variation % enrichment 6% enrichment 8% enrichment Burnup (MWD/MTU) Activity Ratio Fig Enrichment and Burnup Correlations with Np-239/I-132 and Cs-134/Co-60 Ratios. 76

89 Cs-134/Co-60 Activity Ratio enrichment variation % enrichment 8% enrichment 10% enrichment Burnup (MWD/MTU) Activity Ratio Fig Continued. 77

90 4 Experimental Considerations and Verification 4.1 Introduction to PULSTAR Reactor at NCSU The experimental verification is performed on the fuel at the NC State PULSTAR reactor. The PULSTAR Reactor is the fourth nuclear reactor to be operated on the North Carolina State University Campus. The first research reactor on a university campus, built in 1952, was called NCSUR-1. The PULSTAR Reactor (fourth version on NC State campus) became fully operational in The PULSTAR is classified as a swimming pool research reactor, since the reactor core is located at the bottom of a large, open, 15,000-gallon tank of water. The tank is aluminum and is surrounded by high density concrete, providing radiation shielding from the reactor core in the horizontal direction. The pool water acts as a shielding medium in the vertical direction. The reactor core is loaded with 4% enriched, pin-type fuel, consisting of uranium dioxide pellets in zircalloy cladding. The reactor has the capability of operating at any power, from a few watts to a steady-state full power of 1 million watts (1 MW). The technical specifications of the PULSTAR reactor are listed in Table

91 Table 4.1. PULSTAR Reactor Technical Data. Fuel Total Weight 359 kg Uranium Dioxide Enrichment 4% U-235 Core Dimensions (60.96cm 31.1cm 33.02cm) Pool Cladding Volume Outlet Flow Depth Zircalloy II 15,000 gallons (56,775 liters) 500 gpm ( l/m) 26 feet (7.92 meters) Average Temperature 105 o F (40 o C) Temperature Rise Across 1MW 13.8 o F (10.1 o C) Purification Resin Deionized The PULSTAR has a variety of irradiation facilities used for teaching and analytical services. Neutron Activation Analysis (NAA) is provided to academic institutions, federal and state agencies, and commercial companies across the country. Fixed beam facilities are used for prompt neutron capture gamma analysis and neutron radiography. Training services in radiation measurements and isotopic analysis are also provided. In April, 1997, after completing its twentieth year of operation, the PULSTAR was approved and relicensed for an additional 20 years by the Nuclear Regulatory Commission. A spent fuel off-load facility is proposed and will be built to store the first core fuel assemblies; new fuel assemblies are being procured. Fig shows the reactor bay area, and Figure 4.2 shows the reactor pool. 79

92 Fig The PULSTAR reactor bay area. Figure 4.2. A view of the PULSTAR reactor pool at 1 MW power. 80

93 4.2 Gamma-Ray Verification Measurements The schematic of the measurement setup is shown in Fig The design schematic is shown in Fig As it can be seen from Fig. 4.5., the main components of the measurement system are: 1) a 40% n-type coaxial HPGe (resistant to neutron damage); 2) a DSPEC plus digital gamma-ray spectrometer; and 3) a data acquisition computer 40% n-type Coaxial HPGe Detector High Voltage Filter PreAmplifier DSPEC plus Digital Spectrometer Data Acquisition Computer Fig A schematic of the experimental setup. 81

94 Fig A Schematic of the fuel scanning system. To make the measurement system able to scan the irradiated fuel assembly while it is underneath the water, a railway is built which spans the PULSTAR reactor pool, and the detector is placed face down on a cart which rolls over the railway. The detector is surrounded by lead shielding, and a collimator is extended from the detector to the fuel assembly 12 feet underneath the water to reduce background radiation. Figure 4.5 shows the measurement system as it is being used to perform the fuel scans. Two major measurements were performed: 1) using a spent fuel element and irradiating it to simulate high burnup fuel pebbles; and 2) using a fresh fuel element and irradiating it to simulate low burnup fuel pebbles. 82

95 Fig Actual fuel scanning system during operation. For the spent fuel measurement, the fuel assembly was irradiated in the PULSTAR core for 3 hours at a 500 kw power level. Then, the fuel assembly was measured after cooling for about 21 hours. For the fresh fuel assembly measurement, the fresh fuel assembly was irradiated at 250 kw for one hour; then, it was measured after cooling for 2 hours. Fig 4.6. Fig show the gamma peaks of Cs-137, La-140, Np-239, I-132, and Cs-134 in the measured spectrum from the irradiated spent fuel spectrum. Since the irradiation time is short, the irradiated fresh fuel produces little Cs-137 and La-140. However, for the short-lived isotopes, like Np-239 and I-132, their peaks can be seen from the irradiated fresh fuel spectrum. The observations are consistent with simulation 83

96 predictions described in Chapter 3. This includes the Cs-137 interference as observed in Fig. 4.6 and the availability of the La-140 lines for calibration as shown in Fig Fig 4.6. The Cs-137 peak in the irradiated spent fuel spectrum. Also visible are the interfering peaks of Nb-97, I-132, and Ce143 (marker points to the Cs-137 peak). Np-239 ( kev) I-132 ( kev) Cs-134 ( kev) Fig Np-239, I-132, and Cs-134 gamma peaks as observed in the irradiated spent fuel spectrum. 84

97 kev kev kev kev kev kev Fig La-140 Peaks as observed in the irradiated spent fuel spectrum. 4.3 Count Rate Effects and Distortions The gamma spectra simulated by MCNP are ideal, i.e., MCNP simulates photon interactions, assuming photons are coming into the detector well separated in time; therefore, there is no pulse pile-up for these MCNP-simulated spectra. Since the fuel pebbles are expected to have activities on the order of thousands of Ci, the proper design of the measurement system requires an assessment of its performance under high count rate conditions. Under such conditions, if not accounted for, pulse pileup (i.e., random 85

98 summing), will result in distorting the detected gamma-ray spectrum. Consequently, a Monte Carlo computer routine called SUMMING is developed utilizing the random interval distribution function (based on Poisson statistics) to predict the effect of pileup [33]. The random number generator from MCNP5 is incorporated into SUMMING to produce a reliable and unbiased random number sequence. Combined with the pile-up logic, a recursive digital convolution algorithm is implemented to simulate the pile-up behavior of a digital gamma-ray spectrometry system (e.g., the DESPEC plus system of ORTEC). Since digital systems can have throughputs of greater than 10 5 cps, we anticipate that such a system will be the one used in an on-line burnup measurement device. As opposed to traditional analog systems, where the output of an amplifier is digitized to produce the counting signal, digital pulse shaping is based on digitizing the pre-amplifier pulse and using mathematical algorithms (filters) to produce pulse shapes that are difficult to obtain with analog systems. In this work, the digitized preamplifier pulses are passed through filters that produce trapezoidal pulses [42, 43] Probability Distribution Functions (PDFs) for Monte Carlo Simulations The Monte Carlo method can be used to convert an ideal spectrum to a simulated pulse-height spectrum with pulse pile up. Two probability distribution functions must be known in order to perform the Monte Carlo simulation: 1) the time interval distribution 86

99 function between adjacent photons; and 2) the energy distribution function of incident photons. The distribution function for time intervals between adjacent random events follows Poisson distribution. The probability distribution function is given by the following equation: r t f ( t) dt = r e dt, (4.1) where r is the true counting rate. The cumulative distribution function (CDF) can be obtained by integrating the PDF from 0 to t, which gives t t r t r t F( t) = f ( t) dt = r e = 1 e = R, (4.2) 0 0 where R is the uniform random number generated corresponding to randomly chosen time intervals. Thus, the time interval can be calculated as 1 t = ( ) ln(1 R). (4.3) r For the energy distribution function, the MCNP simulated spectrum can be used as the input true spectrum. The PDF h(e) of the pulse-height energy is just the F8 tally value in each energy bin; and the CDF H(E) can be easily calculated from the spectrum; therefore, the pulse-height energy produced by each individual incident photon is sampled from this distribution function in the analog mode of Monte Carlo simulation, significant computational time is wasted by sampling single pulses that are free of pulse 87

100 pile up. For these single pulses, their output is exactly the same as the input from the true spectrum. By forcing every pulse to be piled up with its previous pulse (forcing pile-up mode), one can only simulate the pulse sequence with two or more pulses piled up, thus avoid sampling pile-up free pulses and improve the simulation efficiency [44]. The formulation for this mode is given in Appendix D, section 7.4. For each pulse emanating from the detector, whose energy is sampled from the energy distribution of true spectrum, it is represented as an exponential decay long-tail pulse based on the preamplifier decay time constant input by a user. These pulses are placed in sequence based on the time intervals sampled from the Poisson distribution. A recursive digital filter algorithm with user specified parameters (shaping time, and flattop time) is performed through this pulse train. As described in [42, 43], a trapezoidal pulse shape can be produced in real-time implementation, using efficient recursive algorithms. The recursive algorithm for trapezoidal shaping is implemented by the following equations: d k, l p( n) = r( n) = = v( n) v( n k) v( n l) + v( n k l), p( n 1) + d p( n) + Md k, l k, l ( n), n 0, ( n), s( n) = s( n 1) + r( n), n 0 (4.4) The parameter M is given by: 1 M =, (4.5) T exp( clk ) 1 τ 88

101 where T clk is the sampling period of the digitizer, which is assumed to be 25 ns; τ is the decay time constant of the exponential pulse from preamplifier; k is the rising (falling) edge of the trapezoidal shape; l is defined as the length of convolution function; and l-k is the flattop of the trapezoidal shape. The output signal for a pulse train is a series of shaped trapezoidal pulses, either piled up or free of pile up, depending on the interval with the adjacent preamplifier pulses. For a sequence of piled up pulses, only the first local peak is recorded by the detection system; the rest of the pulse train is ignored until the base line voltage is restored Random Summing Simulation Results To investigate the random summing effects on the measured gamma-ray spectrum, a 10 5 cps throughput rate is assumed. This throughput rate is the maximum allowed by typical digital systems such as ORTEC s DSPEC plus. The random summing convoluted gamma-ray spectra are simulated using different detection system dead times (pulse width time), which is mostly determined by the shaping time of the amplifier in analog systems and by the convolution function length in the digital filter. Specifically, the simulations for dead times of 1 µs, and 2 µs, are performed. As the dead time increases, the spectrum is distorted more, since the probability of the occurrence of random summing also increases. Many counts in the low energy range of the true spectrum are lost, due to pile up, contributing counts to the high energy part of the spectrum, where they should not be. For the 1 µs dead time simulation, only the part with energy greater than 1.5 MeV is drastically distorted. As for the 2 µs dead time simulation, the effect 89

102 becomes more noticeable. Fig. 4.9 and Fig show these results for a fuel pebble at a burnup level of 50,000 MWD/MTU. Fig Summing effect using 1 µs pulse width at 10 5 cps throughput rate. Fig Summing effect using 2 µs pulse width at 10 5 cps throughput rate. 90