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PAGE 1 1 A NEW EXPERIMENTAL DESIGN AND METHOD FOR IMPROVED DELAYED NEUTRON DATA OF GROUP ABUNDANCES B Y HEEJUN CHUNG A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY UNIVERSITY OF FLORIDA 201 4 PAGE 2 2 201 4 Heejun Chung PAGE 3 3 This doctoral dissertation is dedicated to my wonderful parents, Jougup Chung and Youngok Kim who have supported me and made all of this possible. I also dedicate this dissertation to my loving and supportive wife Yereum Yun, and particularly to my first baby ( Ja mes T aemin Chung) who is the joy of our lives. PAGE 4 4 ACKNOWLEDGMENTS My special thanks go to Pr ofessor Kelly A. Jordan, my advisor and the supervisory committee chair, for his guidance and support. Without his strong help, this work would not have been possible. I would like to thank my supervisory committee members, Professor Wesley E. Bolch, Sedat Goluoglu, and Heather Ray for their guidance, support, and instruction. I also need to thank my outstanding colleagues at Adelphi Technology Inc. and in my lab, Jason M. Lewis, Lucas M. Rolison, and Ryan P. Kelley, for their support and help on the equipment It has been my pleasure to work with them. Finally, I would like to thank all my family members for their consistent support through the many years of my education I am especially grateful to my older sister, Prof essor Youngjin Chung, for encou raging me to pursue an advanced degree PAGE 5 5 TABLE OF CONTENTS page ACKNOWLEDGMENTS ................................ ................................ ................................ ............... 4 LIST OF TABLES ................................ ................................ ................................ ........................... 7 LIST OF FIGURES ................................ ................................ ................................ ......................... 9 LIST OF ABBREV IATIONS ................................ ................................ ................................ ........ 13 ABSTRACT ................................ ................................ ................................ ................................ ... 14 CHAPTER 1 INTRODUCTION ................................ ................................ ................................ .................. 16 2 LITERATURE REVIEW OF DELAYED NEUTRONS ................................ ....................... 20 Overview of Delayed Neutrons ................................ ................................ .............................. 20 History of Delayed Neutron Experiences and Data Fitting ................................ .................... 30 Six Group Model of Delayed Neutrons ................................ ................................ .......... 33 Eight Group Model of Delayed Neutrons ................................ ................................ ....... 37 Uncertainty on Six and Eight Group Model of Delayed Neutrons ................................ 45 3 NUMERICAL METHODOLOGIES ................................ ................................ ..................... 50 Detector Count Rates as a Function of Fission Yields ................................ ........................... 50 Delayed Gamma Fission Rate Measurement Technique (Gamma Scanning) ........................ 52 Delayed Neutron Fission Rate Measurement Technique ................................ ....................... 54 Combining Fission Rate Measurement Tec hniques to Derive Improved Nuclear Data Parameters ................................ ................................ ................................ ........................... 5 5 Uncertainty Calculation for Longest lived Delayed Neutron Group ................................ ..... 56 4 EXPERIMENTAL DESIGNS AND SETUPS ................................ ................................ ....... 64 Maximizing Fission Rates in a Sample ................................ ................................ .................. 64 Detector Bundle Design ................................ ................................ ................................ .......... 67 Detector Bundle Setup ................................ ................................ ................................ ............ 73 A Sample Handler Design and Setup ................................ ................................ ..................... 76 Integral System Design and Setup ................................ ................................ .......................... 78 5 NEUTRON GENERATOR DESIGN, CONSTRUCTION, TESTING, AND QUALIFICATION ................................ ................................ ................................ ................. 80 Neutron Sources ................................ ................................ ................................ ...................... 80 Neutron Gene rator Design ................................ ................................ ................................ ...... 86 PAGE 6 6 D D Neutron Generator Construction and Testing ................................ ................................ 90 D D Neutron Generator Qualification ................................ ................................ .................... 97 6 SAMPLE FABRICATION AND COMPOSITION ANALYSIS ................................ ........ 102 Sample Fabrication ................................ ................................ ................................ ............... 102 Gamma ray Spectroscopy Method ................................ ................................ ....................... 105 Other Possible Samples ................................ ................................ ................................ ........ 107 7 PARAMETRIC UNCERTAINTY ANALYSIS OF THE DELAYED NEUTRON MEASUREMENT ................................ ................................ ................................ ................ 111 Parametric Studies for Uncertainty Calculation ................................ ................................ ... 112 Irradiation, Cooling, and Acquisition Time, T ................................ .............................. 112 Nuclear Data Library Selection for Delayed Gamma Parameters, b T and A .......... 115 Gamma ray Attenuation and Detector Efficiency, and ................................ ......... 116 Total Number of Delayed Fission Neutrons, d8 ................................ ........................... 118 Result: Uncertainty Calculation for Longest lived Delayed Neutron Group for 238 U .......... 120 Verification of the experimental data ................................ ................................ ............ 123 8 FUTURE WORK ................................ ................................ ................................ .................. 126 Future Work in Nuclear Data Measurement ................................ ................................ ......... 126 Prompt Neutron Fission Rate Measurement with Gas Scintillators ................................ ..... 126 Prompt Neutron Fission Rate Measurement Technique ................................ ....................... 129 9 CONCLUSIONS ................................ ................................ ................................ .................. 132 A PPENDIX A COMPUTER CODE INPUT FILES ................................ ................................ .................... 134 B MEASURED RADIATION DOSES ................................ ................................ ................... 142 LIST OF REFERENCES ................................ ................................ ................................ ............. 145 BIOGRAPHICAL SKETCH ................................ ................................ ................................ ....... 150 PAGE 7 7 LIST OF TABLES Table page 2 1 Thermal fission data from ENDF/B VII.0 showing the fission cross section and the av erage number of fission neutrons produced per thermal fission (at 0.0253 eV) for several fissile isotopes. ................................ ................................ ................................ ....... 22 2 2 The delayed neutron fraction ( ) for thermal and fast fission of several fissionable nuclides, showing the fraction of all fission neutrons that are born delayed. .................... 25 2 3 Approximate diffusion time for several common moderators, taken from J. R. Lamarsh (Introduction to Nuclear Engineering, 2 nd ed., pp. 277, 1983). The uncertainty of these data was not reported. ................................ ................................ ........ 26 2 4 Several important parameters for prompt and delayed fission neutrons from thermal fission of 235 U. ................................ ................................ ................................ .................... 30 2 5 Half life, energy, and yield of delayed neutrons, measured by D. J. Hughes et al in 1948. The uncertainty for each energy value was improperly estimated and showed the same value ( 60 kV). The shortest lived group, with the half life of 0.05 sec, was unable to me measured due to transport time limitations of the rabbit sample transfer system. ................................ ................................ ................................ .................. 31 2 6 Fast and thermal delayed neutron data from 235 U, measured by G. R. Keepin et al in 1957, for each of the six delayed neutron groups. ................................ ............................. 36 2 7 Eight group delayed neutron parameters (relative uncertainties), suggested by G. D. Spriggs and J. M. Campbell in 2002. ................................ ................................ ................. 37 2 8 The dominant precursor and half life of each of the eight delayed neutron groups, as evaluated by LANL. The uncertainty of half life was not reported. ................................ 43 2 9 lives for eight group delayed neutron model. This model applied weighting factor to each of the groups to achieve a lo wer sum of squares of the deviation. The uncertainty of half life was not reported. ........................... 44 3 1 A summary of the errors introduced by the experimental process, grouped by systematic and random errors. ................................ ................................ ........................... 58 4 1 Fission rate from a UO 2 sample with different enrichment was estimated via MCNP simulation [fissions/cm 3 /sec]. ................................ ................................ ............................ 67 4 2 Absolute efficiency for detector b undles in one and two layer geometries. The 3 He detector was about twice as efficiency as the BF 3 in identical geometries. ....................... 70 4 3 Dimensions of a HPGe detector, used for MCNP simulation. ................................ .......... 73 PAGE 8 8 5 1 Characteristics of some alpha particle and neutron reaction sources the average energy and half life. ................................ ................................ ........................ 81 5 2 Ch aracteristics of incident and produced particle. ................................ ................................ .......................... 82 5 3 Current NDA techniques, organized by active and passive interrogation methods. Active interrogation requires the sample irradiation by an external neutron source. ........ 85 6 1 UO 2 pellet fabrication methods and properties of the four UO 2 pellets fabricated and used in this study. ................................ ................................ ................................ ............. 104 6 2 The passive gamma ray signatures from 235 U and 238 U. ................................ .................. 105 6 3 Enrichment values for the UO 2 pelletized samples. These values were calculated through the gamma spectrometry method. ................................ ................................ ...... 106 6 4 Measured and reported specifications of the Mark I slug. ................................ ............... 108 7 1 Parameter values for the relative uncertainty calculation ................................ ................ 111 7 2 Half life and inverse decay constant of each delayed neutron group. ............................. 113 7 3 Available refere nces for delayed neutron yields from 238 U. ................................ ............ 119 7 4 The chosen uncertainty values of parameters from the optimized measurements and simulation. These values were used to calculate the relative uncertainty of the longest lived delayed neutron group from fast fissions of 238 U. ................................ ...... 120 7 5 The correlation between the number of experiments and the relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U. ................................ .... 121 8 1 The total fission neutron yields from major radioactive nuclides ................................ .... 131 PAGE 9 9 LIST OF FIGURES Figure page 2 1 Delayed neutron precursors are produced from fission and undergo beta decay, becoming delayed neutron emitters. These emitters de excite by delayed neutron emission. ................................ ................................ ................................ ............................ 21 2 2 The prompt neutron spectrum for thermal fission of 235 U. Prompt neutrons are born with energies between 0.1 and 10 MeV, with 0.7 MeV being the most probable energy. The average prompt neutron energy is about 2 MeV. ................................ ........... 23 2 3 The rabbit system, consisting of the rapid transfer tube and associated apparatus at Argonne Laboratory in 1948. The sample was drawn toward the reactor by the vacuum pump, and moved back toward the detector by pressuriz ed gas. ......................... 32 2 4 The schematic diagram of the delayed neutron experimental system, Kiva at Los Alamos Scientific Laboratory in 1957 A pneumatic system was used to move the sample between the irradiation and measurement positions. ................................ ............. 35 2 5 The approximation meth ods for position, energy, angle, and time in the transport equation ................................ ................................ ................................ .............................. 39 3 1 A schematic of the experimental process used for this study. A fissile sample is irradiated for time T i transferred and allowed to cool for a time T c and then measured for time T a ................................ ................................ ................................ ......... 50 3 2 The 1032 keV gamma line from the decay of 89 Rb was chosen for this study based on its larger yield, low nuclear data uncertainty, and the ability to isolate the peak in the gamma spectrum. ................................ ................................ ................................ ......... 53 3 3 Diagram showing how the delayed neutron and gamma techniques were combined based on a proportional constant. ................................ ................................ ....................... 56 3 4 The illustration of Central Limit Theorem (n = sample size), showing that a statistical result becomes more accurate as th e sample size increases. .............................. 59 3 5 Several data sets describing the accuracy and precision of a measurement. The mean value of the me ...... 61 3 6 Total counts of three longer lived delayed neutron gro ups versus the cooling time, showing that the contribution of the higher groups drops as cooling time increases due to decay. ................................ ................................ ................................ ...................... 62 4 1 MCNP simulation geometry showing the neutron generator (blue) output as appoint source. The sample (red) was placed 2 cm away and was surrounded by a meta l reflector (grey) in order to increase the neutron flux incident on the sample. ................... 65 PAGE 10 10 4 2 Fission rate from a UO 2 sample as a functi on of reflector thickness for lead and tungsten reflectors. A 30 cm lead reflector was chosen based on the 27 % increase in fission rate. ................................ ................................ ................................ ......................... 66 4 3 The cross sectional view of the two different detector bundle designs, one and two layers. 3 He and BF 3 tubes detectors were considered and compared. ............................... 68 4 4 The detector bundle efficiencies as a function of layer positions in the cylindrical block of polyethylene of 13.54 cm radius. Efficiency was maximized at 6.17 cm from the center of the bundle. ................................ ................................ ............................ 69 4 5 Showing the method for determining the Full Width at Half Maximum (FWHM). The dete ctor energy resolution can be calculated by the ratio, FWHM/E 0 and is a standard measure of detector performance. ................................ ................................ ....... 71 4 6 An NaI d etector has a higher absolute efficiency, and therefore higher count rates, while the Ge(Li) detector offers much better energy resolution. ................................ ....... 72 4 7 The side and cross sectional views (left XY and right YZ) of the detector bundle with a HPGe detector. ................................ ................................ ................................ ........ 73 4 8 The chained 3 He neutron detector bundle with electronics, PDT 10A and 20A MHV modules built by Precision Data Technology. These daisy chained detectors can work as a single counter (Photo: Author, Heejun Chung). ................................ ................ 74 4 9 The cross sectional view of the detector bundle, employing a HPGe gamma ray detector and seven 3 He neutron detector tubes, as shown by the bolded hole s. ................ 75 4 10 The user interface for a pneumatic sample handler, written by a LabView Virtual instrument (VI). ................................ ................................ ................................ .................. 77 4 11 Front and side views of the sample handler. This allows the sample to be transferred in less than 250 ms and rotated duri ng irradiation and acquisition times to ensure homogeneity (Photo: Author, Heejun Chung). ................................ ................................ .. 77 4 12 The left photo shows the sample inserted into the neutron generator port for irradiation. The right photo shows the sample withdrawn to be counted (Photo: Author, Heejun Chung). ................................ ................................ ................................ ..... 78 4 13 Front and side views of the measurement geometry and neutron generator. ..................... 79 5 1 The cross sections for the primary fusion reactions, showing that a D T reaction has the highest cross section, and therefore provides the higher neutron production yield. .... 86 5 2 Time integrated neutron counts for the two longest lived groups of 238 U, which was used to determine the minimum required neutron production yield from a D D neutron generator. ................................ ................................ ................................ .............. 88 PAGE 11 11 5 3 The initial design of the generator head and simpl e working process of neutron production. Deuterium ions are accelerated into the negatively biased titanium target, these ions are captured by the target, and then react with the next incoming deuterium ions. ................................ ................................ ................................ ................... 90 5 4 The cross sectional view of the DD 109X neutron generator. This generator is featured by its sample irradiation holes since the sample can be close to the neutron source. ................................ ................................ ................................ ................................ 91 5 5 The actual whole experimental system, employing the D D generator, the simultaneous measurement system, and the sample han dler (Photo: Author, Heejun Chung). ................................ ................................ ................................ ............................... 92 5 6 The user interface to control voltage, current, time, and gas flow rate of the neutron generator. ................................ ................................ ................................ ........................... 94 5 7 The whole control system. Monitor in upper left controls the sample handler, the monitor in upper right is emp loyed for monitoring and recording the neutron generator, the monitor in lower left controls the HPGe, and the monitor in lower right controls the neutron generator (Photo: Author, Heejun Chung). .............................. 95 5 8 The magnetron and electronics in the mounting box, employed for the DD 109X neutron generator (Photo: Author, Heejun Chung). ................................ ........................... 96 5 9 The simulation geometry of the actual experimental system, drawn by Moritz Geometry Tool. The monitoring detector is used to measure the real time neutr on production yield from the neutron generator, and the detector bundle is used to count delayed neutrons from the sample after irradiation. ................................ .......................... 98 5 10 The correlation between neutron yield from the D D generator and number of counts on a 3 He monitoring detector (linear fitting). ................................ ................................ ..... 99 5 11 The scratched target head of the DD 109X neutron generator as a result of arcing inside the neutron generator (Photo: Author, Heejun Chung). ................................ ........ 100 5 12 The scratched and fuliginous metal body and ceramic jar (Photo: Author, Heejun Chung). ................................ ................................ ................................ ............................. 101 5 13 The scratched metal body which was placed next to the ceramic jar (Photo: Author, Heejun Chung). ................................ ................................ ................................ ................ 101 6 1 UO 2 samples fabricated by the conventional method (left) and the spark plasma sintering method (right) (Photo: Author, Heejun Chung). ................................ ............... 103 6 2 Microstructure of UO 2 sample fabricated by the conventional method (left) and the spark plasma sintering method (right). ................................ ................................ ............ 103 PAGE 12 12 6 3 Impurities from depleted uranium powder, supplied by SPI Chem Chemicals (Photo: Author, Heejun Chung). ................................ ................................ ................................ ... 107 6 4 The Mark I solid slug. The slug contains natural uranium, surrounded by aluminum cladding (Photo: Author, Heejun Chung). ................................ ................................ ....... 108 6 5 ThO 2 sam ples fabricated by the conventional method (Photo: Author, Heejun Chung). ................................ ................................ ................................ ............................. 109 7 1 The relative uncertainty of the longest lived gr oup abundance vs. the cooling time, showing that 170 sec is the optimal cooling time to minimize uncertainty of the longest lived delayed neutron group. ................................ ................................ ............... 114 7 2 The relative uncertainty of the longest lived group of 238 U with different libraries (ENDF vs. JEFF). Both libraries agree that 170 sec is the optimal cooling time to minimize uncertainty of the longest lived delayed neut ron group. ................................ 115 7 3 The expected gamma spectrum from 89 Rb via MCNP. ................................ ................... 117 7 4 The geometry for attenuation and its uncertainty calculations via MCNP. This simulation was used to estimate the self attenuation of gamma rays in the sample. ...... 118 7 5 The measured photo peak of 89 Rb at 1032 keV, measured from a UO 2 sample irradiated by the neutron generator. ................................ ................................ ................. 12 0 7 6 The MATLAB input deck for uncertainty calculation. ................................ ................... 122 7 7 The MCNP geometry with aluminum slug cladding and the expected gamma spectrum from 89 Rb. ................................ ................................ ................................ ......... 124 8 1 The schematic drawing (left, Arktis Radiation Detector Ltd.) and actual photo of a 4 He scintillation detector (right, Photo: Author, Heejun Chung). Incoming fast fission neutrons elastically scatter with the 4 He fill gas, producing scintillation photons that are counted by PMTs at either end. ................................ ................................ ................. 127 8 2 Energy cut off for integrated counts of fission neutrons, 1.6 MeV is the maximum e nergy that can be deposited by an incident 2.45 MeV neutron from the D D neutron generator. ................................ ................................ ................................ ......................... 129 PAGE 13 13 LIST OF ABBREVIATIONS D D Deuterium Deuterium D T Deuterium Tritium UO 2 Uranium Dioxide NDA Non Destructive Assay PANDA PAssive Non Destructive Analysis HPGe Hyper Pure Germanium MCNP Monte Carlo N Particle model (transport code) SPS Spark Plasma Sintering LSF Least Square Fit PPS Personal Protection System JEFF Joint Evaluated Fission and Fusion file ENDF Evaluated Nuclear Data File FWHM Full Width at Half Maximum PAGE 14 14 Abstract of Dissertation Presented to the Graduate School of the University of Florida in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy A NEW E XPERIMENTAL DESIGN AND METHOD FOR IMPROVED DELAYED NEUTRON DATA OF GROUP ABUNDANCES By Heejun Chung May 201 4 Chair: Kelly A. Jordan Major: Nuclear Engineering Sciences The nuclear data on the physics of delayed neutrons coming from fission events are of key importance in reactor kinetics and safeguards applications. The accuracy of reactor kinetics calculations, reactor physics validation studies and techniques for non destructive assay of special nuclear material are all limited by the quality of these data. The uncertainties on the delayed neutron group abundances of the longest lived delayed neutron groups are particularly large up to 13 % for thermal fissions of 235 U, 16 % for fast fission s of 238 U and 38 % for fast fissions of 239 Pu [1] T here are also several competing data sets with significant variation in values Recent work indicates that these already large uncertainties are underestimated due to numerical instabilities in the parametric fitti ng methods [2] A novel approach to experimentally measure delayed neutron group yields has been proposed by Jordan and Perret [3] This approach combines gamma ray scanning and delayed neutron fis sion rate measurement techniques With two independent esti mates of the same fission rate, a higher uncertainty delayed neutron parameters can be linked to lower uncertainty delayed gamma parameters. A n experimental apparatus implementing these techniques ha s been designed, optimized, and built The apparatus con sists of a D D neutron generator a detector bundle, a sample PAGE 15 15 handler, and related electronics. Existing neutron generator technology was unsuitable for these measurements. A D D neutron gen erator (model DD 109X) was newly designed and installed to run at a maximum intensity of up to 4x10 9 neutrons per second with modifications to the accelerator beamline allowing very large solid angle irradiations. A pelletized UO 2 sample was irradiated by a D D generator and delayed neutrons and delayed gamma rays at 1032 keV from 89 Rb from the sample were simultaneously measured. The time was respectively set up 20 min, 170 sec, and 360 sec for irradiation, cooling, and acquisition. The neutron generation yield during the experiment was 1. 1x10 9 neutrons per second at 115 kV. T he relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U using the optimized experimental measurements has been reevaluated and reduced to 8.6 %. This reevaluated uncertainty value is almost a facto r of two lower than the Spriggs and Campbell recommended data set (16 % [1] ). T he system built has shown considerable potential to reduce the large uncertainties of the longest lived delayed neutron group abundances. The neutron generator technology has more widespread applications for nuclear security and safeguards. More accurate fiss ion yield measurements can be carried out by comparison of multiple fission rate measurement models. A new prompt neutron measurement technique with a prototype 4 He scintillator detector is proposed as a third experimental technique for future experimental evaluation of nuclear data PAGE 16 16 CHAPTER 1 INTRODUCTION Fission is the process of importance in a nuclear reactor; from fission, energy is generated. Fission reaction rates depend on the kinetic energy and flux of the fissioning neutrons, fuel material composition, and the location in the reactor core. The process of fission drives fuel material composition changes in a reactor core over time, which in turn alters the neutron flux and fission rates. Estimation of fission rates an d its relative uncertainty over time and position are the essential core of reactor physics. Several computational methods have been developed to solve the neutron transport equation, which governs neutronics. However, the accuracy of computation is limite d by the accuracy and quality of the nuclear data underlying the computational model. Reactor kinetics, describing the changing of overall fission (power) levels in a reactor, is dependent on a property of how neutrons are produced in time from fission ev ents. Whereas most neutrons are emitted immediately, a small fraction (order of 1 %) is released later. These neutrons are delayed and the properties of these delayed neutrons drive the kinetics of the reactor as a whole [4 ] Delayed neutrons are emitte d from decays of certain fission products. There are more than 100 fission product isotopes that give rise to delayed neutrons, each with their own time constant. For mathematical (and experimental) convenience, these isotopes are collected into a series o f groups of similar decay constants and given effective half lives and abundances for the whole group. These group constants are experimentally determined from reactor irradiation measurements of fissile isotopes (described in greater detail in Chapter 2) The relative uncertainties of the longest lived groups are considerably higher than for other groups. These PAGE 17 17 high uncertainties originate either from the statistical quality of the parametric fitting methods or the quantity of the measurement data sets R ecent work indicates that the high uncertainties might be underestimated due to numerical instabilities in the parametric fitting methods used to estimate these relative group parameters [ 2 ]. Another application in which delayed neutrons are important goes to the question of experimental validation of reactor physics parameters and computational models. Gamma scanning techniques have been used for the derivation of fission rates in fresh fuel since the of this technique can suf fer from the long lived delayed gamma precursors or from high background activity in the case of spent (burnt) fuel [ 5 ] In order to overcome this, d elayed neutron measurement techniques can be applied as an alternative method of measuring these reactor re action rates [ 6 ] In both cases, the quality of nuclear data limits the accuracy of measurement. This dissertation implements a novel technique for measuring delayed neutron group parameters first conceptualized by Jordan and Perret [ 3 ]. This method combin es the well established fission rate measurement techniques using delayed gammas and delayed neutrons ( in following chapters). Each technique provides an independent estimate of the fission rate in a well characterized sample. Next the estimate fission rates via two techniques are set equal since fission rates were estimated from the same fissile sample. Thus, one can then solve different parameters in the equations used to derive the individual fission rate estimates. Consequentl y, the high uncertainty delayed neutron data can be expressed in terms of the low uncertainty delayed gamma data and hence, the uncertainty on the parameter of interest can be reduced. However, this technique has never been experimentally implemented. Chap ter 2 provides a basic introduction and background of previous works in delayed neutron PAGE 18 18 experiences and data fitting with uncertainty. Six and eight group delayed neutron models are explained. In Chapter 3, the combined technique is explained, as well as the theoretical background of the delayed gamma scanning and neutron techniques. An apparatus has been designed and built to carry out a proof of concept experiment for improvement of a targeted parameter, namely the first delayed neutron group abu n dance o f 238 U. Chapter 4 introduces the design concepts and the actual experimental apparatuses with a purpose of improvement on the relative uncertainties on the delayed neutron group abundances. Chapter 6 describes UO 2 sample fabrication and the analysis of the material composition (mass ratio) of uranium elements in the fabricated UO 2 samples. Chapter 7 gives the projected results of the relative abundance and its improved uncertainty of the longest lived delayed neutron group for fast fission of 238 U. The sensitivity studies of the relevant parameters in uncertainty calculation were also performed. In addition to the results associated with the originating motivation described above, two significant new developments were realized while pursuing improved nuc lear data measurements: 1) a marked improvement in neutron generator technology; 2) a new fission measurement technique using prompt neutrons and a prototype gas scintillator fast neutron detector. An accelerator drive deuterium deuterium fusion reaction b ased neutron generator was built. These systems are specialized, but commercially available. However, the technology was not sufficiently developed to perform the proposed nuclear data measurements. As a part of the work presented in this dissertation, a n ovel neutron generator design was built in collaboration with Adelphi Technology Inc., a neutron generator manufacturing spinoff from Lawrence Berkeley National Laboratory. The improvements in generator performance from this design PAGE 19 19 neutron flux intensity on target resulted in an order of magnitude increase. The commercial product resulting from this work was awarded an R&D 100 award as one of the 100 most commercially significant research achievements of 2013. Chapter 5 highlights the design, constructi on, testing, and qualification of the newly designed D D generator (DD 109X). In the last offshoot of this main work, the neutron generator has been used to characterize a novel gas scintillator fast neutron detector. Delayed neutron and gamma measurements are used to quantify induced fission rates because there has been no experimental method of differentiating between neutrons produced by a source (in this case a neutron generator), and new fission neutrons induced by the source neutrons. Using delayed em issions, a source can be removed or turned off, and the delayed particles measured. However, with the advent of this new gas scintillator fast neutron detector technology, a technique that differentiates between the energy of neutrons from a neutron genera tor and fission becomes possible. The implications of this technique and measurements demonstrating the feasibility are presented in Chapter 8. This work concludes with a summary of the dissertation and recommendations for future work based on the experime ntal results in Chapter 9 PAGE 20 20 CHAPTER 2 LITERATURE REVIEW OF DELAYED NEUTRONS Overview of Delayed Neutrons When a heavy fissile nucleus undergoes a fission reaction, it breaks apart into various fragment pairs (light nuclei) of unequal mass and energy. A n a verage energy from this fission reaction is about 195 MeV. Most of the energy (about 162 MeV) is carried away by the fragment pairs and the rest (about 33 MeV) produces particles such as neutrinos, prompt neutrons, and photons in the form of gamma rays [ 7 ] The produced fission fragments are unstable due to unbalanced neutron and proton ratios. In order to adjust these unbalanced ratios, the excited fission fragments undergo several beta decays until becoming stable. In some cases, the excitation energy of daughter nuclei formed by beta decays ( ) is higher than the neutron separation energy S n and the daughter nuclei then emit neutrons again sometime after the fission reaction. This decay chain is written as: (2 1) The fission fragment X undergoing a beta decay, is called as a delayed neutron precursor, the daughter nucleus Y emitting a delayed neutron, is called as a delayed neutron emitter and t he emitted neutron n in Equation 2 1 is called as a delayed neutron The total delay time is mainly governed by the half life of a precursor nucl eus since there is no significant time delay from a daughter nucl eus ( a delayed neutron emitter) The daughter nucl eus emit s neutrons nearly immediately after it is formed by beta decay. If the excitation energy is lower than the neutron separation energy, the daughter nucl eus then emit s delayed gamma rays instead of delayed neutrons. The neutron separation energy S n varie s based on the nuclear structure of precursors, and its aver age value can be calculated in terms of mass distribution or binding energy difference between a precursor ( A N 1) and its daughter nucleus ( A N 2) [ 8 ] : PAGE 21 21 ( 2 2 ) ( 2 3 ) w here m(x) is the mass of x element in the unit AMU or kg c is the speed of light in vacuum (2.998x10 8 m/s), and BE(x) is the binding energy of x element in MeV, typically. The calculated value through Equation 2 2 has a unit Joule (J=kg m 2 /s 2 ) but can b e converted to MeV since 1 MeV is equal to 1.6x10 1 3 J. Th e whole decay process es, mentioned above, is described in Figure 2 1. Figure 2 1. Delayed neutron precursors are produced from fission and undergo beta decay, becoming delayed neutron emitters. These emitters de excite by delayed neutron emission From the fission reaction, two different types of neutrons are released Nearly all of fission neutrons (more than 99%) are release d at the instant of fission within the o rder of 10 1 6 seconds PAGE 22 22 or smalle r. These neutrons are prompt neutrons. Relatively long after fission, a small amount of neutrons (less than 1%) are released through beta decay processes There neutrons are delayed neutrons. The average number of neutrons per fission, denoted by varies with the energy of the incident neutron In the case of thermal fissions, the most fission events are caused by 233 U, 235 U, 239 Pu and 2 41 Pu since they have large fission cross section s The observed mean value of the fission cross sections and their aver age number of neutrons per fission obtained from the Evaluated Nuclear Data File ( ENDF/B VII.0 ) standards evaluation, are listed in Table 2 1 [ 9 ]. Table 2 1 Thermal fission data from ENDF/B VII.0 showing the fission cross section and the average number of fission neutrons produced per thermal fission (at 0.0253 eV) for several fissile isotopes. Isotope Fission Cross Section (barn) Average number of fission neutrons ( ) 233 U 531. 22 0.25 % 2.49 7 0.14 % 235 U 58 4 33 0.17 % 2.4 36 0.09 % 239 Pu 750.00 0.24 % 2.884 0.16 % 2 41 Pu 1013.96 0.65 % 2.94 8 0.18 % The (mean) number of neutrons per fission is typically called the yield. The total fission neutron yield is the sum of prompt and delayed neutron yields (2 4) w here d is the delayed neutron yield, and P is the prompt neutron yield per fission. The carried energy by these prompt neutrons is varied based on the mass distribution of fission fragments and the energy of the incident particle that induced the fission reacti on. The distribution of prompt neutron s at a certain energy level E in MeV per fission (E) can be represented by Equation 2 5 [ 4 ] : PAGE 23 23 (2 5 ) Since (E) is a probability density function, (2 6 ) T he prompt neutrons are distributed from 0.1 MeV to 10 MeV. In the case of 235 U the most probable energy of prompt neutrons is about 0. 7 MeV, and the average is about 2 MeV [Figure 2 2]. Figure 2 2. The p rompt n eutron s pectrum for thermal fission of 235 U. Prompt neutrons are born with energies between 0.1 and 10 MeV, with 0.7 MeV being the most probable energy. The average prompt neutron energy is about 2 MeV. In addition to the prompt neutrons in fission, delayed neutrons are often emitted by beta decay processes These delayed neutrons show different physical properties from the properties of prompt neutrons : 1) t he fraction of delayed neutrons is typically less than 1 or 2 % per fission ; 2) they are released usually within the order of seconds (0.07 to 80 sec) and born at a somewhat PAGE 24 24 lower energy in the range of a hundred keV (about 250 to 620 keV) ; and 3) every fissioning isotope has a distinct signature of delayed neutron emission The total fraction of delayed neutrons can be denoted by called the delayed neutron fraction [ 4 ] : ( 2 7 ) This delayed neutron fraction represents the number of emitted delayed neutrons of the total number of fission neutrons per fission. By combining and rearranging above e quation s [Equation 2 4 and 2 7] equations for the yield of prompt P and delayed d neutrons per fission can be written as : ( 2 8) ( 2 9) The delayed neutron fraction depends on the energy of the incident neutron and the target fissile or fertile nuclide which is undergoing the fission reaction. A fissile material is composed of nuclides for which fission is possible with neutrons of any energy level and a f ertile material is composed of nuclides for which can be transformed ( transmuted ) into fissile materials by the bombardment of neutrons [ 10 ]. As t hey eventually induce fission events they can be described as either fissioning or fission nuclides. The d elayed neutron fractions for the major fission nuclides are listed in the Table 2 2 [1 1 ] PAGE 25 25 Table 2 2 The delayed neutron fraction ( ) for thermal and fast fission of several fissionable nuclide s showing the fraction of all fission neutrons that are born delayed. Isotope Fission Type Delayed Neutron Fraction 233 U Thermal 0.00268 0.013 % 235 U Thermal 0.00665 0.021 % 23 8 U Fast 0.01 65 0 0.086 % 239 Pu Thermal 0.00225 0.011 % The total fission neutron yield must be the sum of prompt and delayed neutron yields per fission and s ome references do not really differentiate between the total fission neutron yield and the yield of the prompt neutrons P since the delayed neutron yield is quite small However, t h is small number of delayed neutrons plays a vital role in many applications so the total fission neutron yield should be expressed by the sum of prompt and delayed neutron yields per fission Additionally, the meaning of fraction is mixed with the meaning of yield Later in this study, the fraction is defined as the ratio between delayed and all fission neutrons The yield means the actual ( mean ) number of neutrons per fission The importance of delayed neutrons in reactor kinetics calculations can be easily understood by comparing properties of the above two fission neu trons, prompt and delayed. Delayed neutrons have significantly longer lifetime, compar ed to prompt neutrons, and their longer lifetime plays a vital role in the design and control of a nuclear reactor The longer lifetime of delayed neutrons i ncrease s the total neutron lifetime l in a reactor and consequently leads to a longer reactor period T A longer reactor period s l ows the power growth rate in a reactor and enhances the safety of the system. PAGE 26 26 The total neutron lifetime l can be simply defined as the time between the birth of a neutron from fission and its death A fast neutron is typically moderated (losing its kinetic energy) by the collisions within a moderator such as light water, heavy water, and graphite just after i ts releas e from a fission reaction When it reaches the thermal energy range it is absorbed and causes another fission reaction to occur This repeated process is referred as the nuclear chain reaction. Therefore, the total neutron lifetime can be defined by the sum of times of generation, moderation (slowing down) and thermalization : ( 2 10) The generation time is a releasing time of fission neutrons, the moderation time is a slowing down time into the thermal energy range (about 0.025 eV) of the fission neutrons, and the thermalization time means the average time which the thermal ized neutrons diffuse before being lost in some way The thermalization time can be expres sed by the mean diffusion time. The mean diffu sion time in various moderators that are widely used in a reactor is listed in Table 2 3 [ 4 ]. Table 2 3 Approximate d iffusion time for several common moderators taken from J. R. Lamarsh (Introduction to Nucle ar Engineering, 2 nd ed., pp. 277, 1983 ). T he uncertainty of these data was not reported Moderator Diffusion Time (sec) H 2 O 2.1x10 4 D 2 O 4.3x10 2 Be 3.9x10 3 Graphite 1.7x10 2 The number density of neutrons in a reactor is proportionally changed by the multiplication factor k which accounts for the rate of neutron production from fission reactions and loss PAGE 27 27 through absorptions within reactor materials and leakage from a reactor. Therefore, the neutron population in each generation is written in terms of the multiplication factor k the ratio of the number of fission neutrons in the next generation (n+1 th ) divided by the number of fission neutrons in current n th generation [ 7 ]: (2 11) w here f is the thermal fuel utilization factor is the reproduction factor is the fast fission factor is the resonance escape probability L F is the fast non leakage factor and L TH is the thermal non leakage factor The multiplcation factor can be expressed as the infinite multiplication factor ( k ), only considering neutron production and absortion ( ), and the effective multiplication factor ( k eff ) for a finite reactor, regarding the actual reactor size. As shown in Equation 2 11, the effective multiplication factor is written in terms of the infinite multiplication factor ( k ) and two additional factors ( L F and L TH ) that allow for neutron leakage When the rate of neutron production and loss between a preceding and current generation is balanced, the effective multiplication factor is 1.0, and the reactor is critical or steady state at a constant power level. If k eff is bigger than 1.0, the reactor is supercritical, and the reactor power level is rising. Oppositely, k eff is less than 1.0, the reactor is subcritical, and the reactor power level is decre a sing [ 4 ]. The effective multiplication factor indicates the change of the reactor power level, dir ectly prop ortional to neutron population. The difference between a value of k eff and 1.0 is called the k excess and is represented by k This excess value can be positive or negative, and is a useful quantity in reactivity calculation s R eactivity can be defined as the term explaining the reactor power level (operation condition) or showing a margin from the critical point of a reactor ( k eff = PAGE 28 28 1.0 ) and expressed by (rho). The reactivity is different from the resonance escape probability in Equ ation 2 11 even though the expression symbol is the same. Reactivity is defined as [ 4 ]: ( 2 12) The reactivity is generally expressed in a number or percent, but is also often given in unit s of dollar s ($) or cent s (0.01$). The unit of one dollar was derived in order to express the core reactivity in terms of the delayed neutron fraction The delayed neutron fraction is an important factor in reactor control and will change as the fuel composition changes througho ut change, relative to the delayed neutron fraction. O ne dollar indicates the reactor is critical and t he reactivity is equivalent to the delayed neutr on fraction : (2 13) If the dollar value is larger than one dollar, the n reactor power increases. Oppositely, the reactor power level decreases when the dollar value is less than one dollar. From Equation 2 11, t he number density of neutron s per cm 3 sec at time t and at a certain location in a homogeneous reactor can be written as: ( 2 1 4 ) By rearranging Equation 2 1 4 (2 1 5 ) Intergrating Equation 2 1 5 ( 2 1 6 ) Let, (2 17) PAGE 29 29 Equation 2 1 6 can be simply written with the reactor period T [Equation 2 17], defined as the taken time to exponentially increase the relative reactor power level : (2 1 8 ) Without delayed neutrons, the total neutron lifetime l is the same as the prompt neutron lifetime l P The average lifetime is only in the order of 10 4 seconds nearly equal to the moderation time, since the generation time is within the order of 10 1 6 seconds or smaller Considering a step change in k from 1.0 to 1.001 ( 0.1% ) with th at short lifetime (the order of 10 4 seconds), the reactor period would be 0.1 sec. It means that the number density of neutrons per fission would increase by a factor of e 10 per sec in Equation 2 1 8 Therefore, the design and operation of a reactor would be im possible due to the rapid power changes if only prompt neutrons existed With delayed neutrons, the total neutron lifetime becomes: ( 2 1 9 ) This Equation 2 1 9 can be weighted by the relative yields of prompt and delayed neutron fractions [Equation 2 8 and 2 9], and rewritten as: (2 20 ) The lifetime of delayed neutrons l d is dominated by the half life of delayed neutron precursor nuclei (0.07 to 80 sec) so the mean lifetime of delayed neutrons is much longer than one of prompt neutrons. Therefore, Equation 2 20 is governed by the delayed neutron term l d In the case of thermal fissions o f 235 U, the delayed neutron lifetime is about 0. 0 84 sec. Taking 0. 0 84 sec into the previous calculation, the number density of neutrons per fission would increase by a factor of e 0.01 per sec. Therefore, it would take about 100 sec to PAGE 30 30 exponentially increase the number density of fissions per sec, and it makes a reacto r designable and controllable [ 4 ]. In summary, prompt and delayed neutrons have their own unique physical properties since they originate from different nuclear processes, fission reacti on s and beta decay process es T he classification of fission neutrons in thermal fissions of 235 U is summarized in Table 2 4 [ 4 ] Table 2 4 Several important parameters for prompt and delayed fission neutrons from thermal fission of 235 U. Fraction Mean Li fetime Origination Average of Energy Prompt Neutrons 99.35 % 10 4 sec Fission Mechanism 2 MeV Delayed Neutrons 0.65 % 0.8 4 sec Beta Decay Process of Precursors 300 to 600 keV To have better results in reactor kinetics calculations, more precursor s should be considered It is currently practical to consider more than 270 precursor nuclei, but possibly more precursors may exist [ 2 ] However their decay scheme s half li ves and yield s are not well known for every precursor. Therefore, delayed neutron s should be separated into groups and numerical fitting methods should also be used for applications. History of Delayed Neutron Experiences and Data Fitting Delayed neutrons were first discovered by Robert et al. in 1939. They bombarded a 100g uranium nit rate bottle with a beam of deuterium, and observed neutrons as long as 1.5 min after the bombardment via a boron lined chamber. B oth the target bottle and the chamber were surrounded by paraffin in order to cut off background radiation [ 1 2 ] After delayed neutrons were discovered, their properties were ex tensively studied PAGE 31 31 The major three components for measuring delayed neutrons are specification (energy and yield) of a neutron source for sample irradiation, a sample transfer system, and a c ounting (measurement) system or good detector efficiency Additionally, the best fitted line, providing lower or minimum uncertainties for each data set, should be required in order to apply measured delayed neutron data to reactor kinetic calculations. H ughes et al. in 194 8 measured the period s yields and energies of the delayed neutrons from 235 U using a heavy water reactor at Argonne Laboratory [ 1 3 ] Early researchers had used the term period to explain the half life of each delayed neutron group sin ce they grouped delayed neutrons with different irradiation periods. Hughes et al measured the longest group first with the longest irradiation time period and tried to find other shorter lived groups by shortening the irradiation period and subtracting the contribution from the previous measured group data. T hey were only able to measure yields and energies of five longer lived groups with half li ves of 55.6, 22.0, 4.51, 1.52, and 0.43 sec [Table 2 5 ] since the sample transfer system, named rabbit was insufficient for the last shortest lived group with a half life of 0.05 sec Table 2 5 Half life, energy, and yield of d elayed neutron s, measured by D. J. Hughes et al in 1948 The uncertainty for each energy value was improperly estimated and showed the same value ( 60 kV). The shortest lived group, with the half life of 0.05 sec, was unable to me measured due to transport time limitations of the rabbit sample transfer system. Half life (sec) Energy (k e V) Relative Yield to Total Neutron Emission (%) 55.6 250 0.025 22.0 560 0.166 4.51 430 0.213 1.52 620 0.241 0.43 420 0.085 0.05 0.025 PAGE 32 32 The rabbit system was designed to move a fissile sample from the reactor to the measurement station in less than 5 min, and its minimum tran sferring time was not reported. Thus, the yield of the shortest lived group was just assumed by subtracting previous measured data sets [ 1 3 ] Their experimental achievements in measuring the delayed neutron energy spectra of 235 U can be highlighted but th e yield data may be over/under estimated since they ignored the contribution from the shortest lived group in t he calculation of other groups. The rabbit transferring system is described in Figure 2 3 [13] Figure 2 3. The rabbit system, consisting of th e rapid transfer tube and associated apparatus at Argonne Laboratory in 1948 The sample was drawn toward the reactor by the vacuum pump, and moved back toward the detector by pressurized gas. After that period, the most extensive studies for delayed neutrons were performed at Los Alamos National Laboratory (LANL) T he most outstanding result was the six group model and the eight group model of delayed neutrons d eveloped by Keepin et al [ 1 4 ] and has been commonly used over the past decades PAGE 33 33 Six Group Model of Delayed Neutrons Keepin et al in 1957 measured delayed neutrons using the Godiva React or the bare spherical uranium metal critical assembly at Los Alamos Scientific Laboratory, and explained their measurement data with the new six group model. Through the six group model, the delayed neutron emission can be described as [ 1 4 ] : ( 2 2 1 ) where n d (t) is the number of delayed neutrons as a function of time t after irradiation and i t can be thought as count rates in the aspect of radiation detection. The index i demotes each delayed neutron group, A i is the activity of group i and i is the corresponding decay constant for each i th group Since the activity [ 7 ] is ( 2 2 2 ) w here i is ( 2 2 3 ) T 1/2 is the half life of a precursor, and t he number of delayed neutrons N i in each group can be defined as: (2 2 4 ) where a i is the group abundance and defined as the ratio between the number of delayed neutrons in each group and all fission delayed neutrons : (2 2 5 ) Taking all above definitions, Equation 2 2 1 can be written in terms of group abundances : ( 2 2 6 ) PAGE 34 34 They measured delayed neutrons from fast and thermal fissions. S ix major nuclide samples ( 232 Th, 233 U, 238 U, 239 Pu, and 240 Pu) and three nuclides ( 233 U, 235 U, and 239 Pu ) were measured for fast and thermal fissions. For thermal fissions, an 8 inch cubic polyethylene block surrounded by cadmium was placed near the Godiva reactor. Evaluating delayed neutron emission re quires consideration of the precursor saturation. Precursor nuclei are formed in the sample from fission and decay with individual half lives. The precursors must be built up to equilibrium (saturation). Both instantaneous (not long enough for precursors to reach saturation) and infinite (long enough for full saturation of the longest lived precursor about 1 min ) conditions were applied [14] In order to measure delayed neutrons, t he BF 3 proportional counter, embedded in a shaped sleeve of boron plasti c, was employed A pneumatic system capable mov ing a 2 5 g s ample in 50 ms was designed and used. The whole experimental apparatus was called Kiva, and is shown in Figure 2 4 [ 1 4 ]. PAGE 35 35 Figure 2 4. The schematic diagram of the delayed neutron experimental system, Kiva at Los Alamos Scientific Laboratory in 1957 A pneumatic system was used to move the sample between the irradiation and measurement positions. There are many methods available to estima te delayed neutron parameters. Traditionally, a Least Square Fit (LSF) method is used to describe and fit delayed neutron nuclear data. In the Equation 2 2 6 the group a bundance a i and decay constant i are free parameters which need to be numerically de cided since the count rate and measurement time t are known parameters. Keepin et al applied LSF to find the solutions to the group abundance a i and decay constant i and finally found that the six group model was sufficient to fit their experimental dat a for 235 U [ 1 4 ] Later Keepin used the inverse matrix method with the solution of the weighted LSF to determine probable error of each relative parameter [ 1 5 ]. periods (regarding the half lives of precursors) and relative abundance with uncertainty for fast and thermal fission of 235 U is listed in Table 2 6 [ 1 4 ] PAGE 36 36 Table 2 6 Fast and thermal delayed neutron data from 235 U, measured by G. R. Keepin et al in 1957 f or each of the six delayed neutron groups DN Group Fast Thermal Half life (sec) Relative Abundance (%) Half life (sec) Relative Abundance (%) 1 54.51 0.94 0.038 0.003 55.72 1.28 0.033 0.003 2 21.84 0.54 0.213 0.005 22.72 0.71 0.219 0.009 3 6.00 0.17 0.188 0.016 6.22 0.23 0.196 0.022 4 2.23 0.06 0.407 0.007 2.30 0.09 0.395 0.011 5 0.496 0.029 0.128 0.008 0.610 0.083 0.115 0.009 6 0.179 0.017 0.026 0.003 0.230 0.025 0.042 0.008 six group model has been show n to be a good approximation for fission estimation s in reactor kinetic s calculation s However, improved representations (higher order delayed neutron models) as well as more accurate group abundance data for delayed neutrons have been demanded as more delayed neutron precursors have been discovered following the availabi lity of experimental apparatus. Additionally, it was found that o n ly a dozen or so precursors contribute d to 82% of the half lives for each delayed neutron gro up regardless of the nucleus being fission (i.e. U, Pu, and Th) [1] These two points suggest a model should be made that uses averaged half lives (using those major precursors) for the groups, for all fissioning isotopes, but at the same time utilize all the known precursors to formulate group abundances for each individual fissioning isotope. This creates a delayed neutron group model that has all fissioning isotopes shar ing life data but has separate group abundance data for each isotop e (as seen in Table 2 6, the following subchapter) A new eight group model was recommended by Spriggs and Campbell in 2002 [ 1 ] This new model was characterized by : 1) the same time set of half lives of precursors f o r all PAGE 37 37 fissioning isotopes and 2) for fission s induced by neutrons of different energ ies (thermal fast high) [ 1 6 ] Eight Group Model of Delayed Neutrons A new concept for delayed neutron groups, expand ing the traditional six group model to eight group model, was pr oposed at an internation al workshop which was held by the Nuclear on delayed neutrons in Russia, 19 9 7. This workshop focused on 1) reviewing the current status of delayed neutron data, and 2) proposing a new model for applications in reactor ph ysics. As a result of the workshop, the eight group model was initially suggested [1]. This initial eight group model was modified with the abundance weighted half lives of precursors, and published in 2002 [ 1 ]. The eight group model for important fiss ile isotopes is given in Table 2 7 Table 2 7 Eight group delayed neutron parameters (relative uncertainties), suggested by G. D. Spriggs and J. M. Campbell in 2002 DN Group Half lives (T 1/2 sec) 235 U (Thermal ) 238 U (Fast ) 239 Pu (Thermal) 1 55.6 0.033 (13%) 0.008 (16%) 0.032 (38%) 2 24.5 0.154 (4%) 0.104 (2%) 0.237 (14%) 3 16.3 0.091 (10%) 0.038 (2%) 0.083 (2%) 4 5.21 0.197 (12%) 0.137 (15%) 0.182 (29%) 5 2.37 0.331 (2%) 0.294 (4%) 0.294 (10%) 6 1.04 0.090 (5%) 0.198 (1%) 0.082 (2%) 7 .424 0.081 (2%) 0.128 (10%) 0.072 (43%) 8 .195 0.023 (41%) 0.093 (4%) 0.018 (2%) PAGE 38 38 T he eight group model was not newly developed. It extended (shifted) group model by the expansion tec hnique, mathematically expanding the measured six group parameters into the equivalent eight group values To optimize the two free parameters of the delayed neutron model [Equation 2 26] the group abundance a i and decay constant i Spriggs and Campbell suggested the expansion technique fo r the group abundance a i and then recommended the fixed (same) half lives for any fissionable isotopes weighted half lives [1]. Spriggs and Campbell summarized the 245 experimentally measured delayed neutron group parameters for twenty different fission isotopes calculated the time behavior of the reactor d the new eight group abundances by using the given (conserved) cr iticality scale for positive reactivities as predicted by the original six group model This technique is called the it is necessary to briefly review the point reactor kinetic equation The rate of chang e in number of neutron s at certain time and volume is simply considered as the difference between production rate and loss rate. ( 2 2 7 ) Production rate in a certain volume is the sum of 1) externa l source production rate, 2) scattering in production rate, 3) flow in production rate, and 4) fission source production rate. Loss rate is the sum of 1) absorption rate, 2) scattering out rate, and 3) flow out rate. Considering e ach term above the neutro n density at a certain time and volume can be written as [1 7 1 8 ] : PAGE 39 39 (2 2 8 ) This Equation 2 2 8 is called as time dependent neutron transport equation or integro differential form of transport equation. This equation is the microscopic transport equation describing each neutron movement with the angular flux In fact, this equation is too c omplicated to directly solve for each neutron. Thus, the macroscopic equation, regarding neutron group movement with flux (r,E) can be rewritten by some approximations. The approximation methods are explained in Figure 2 5 [18] Figure 2 5. The approxi mation methods for position, energy, angle, and time in the transport equation By applying the assumptions for energy and angle, the time dependent diffusion equation in one (energy) group for a non multiplying homogeneous reactor, without delayed neutrons can be written as [1 8 ] : ( 2 2 9 ) w here v (vi) is the one group neutron speed in cm/sec, and it should be identified with the neutron yield (nu) in the last term D is the diffusion coefficient in cm 2 /sec and is defined in Equation 2 30 2 is the Laplacian operator, and x is the cross section on the parameter x in cm 2 The cross section x can be considered with the flux [Equation 2 3 2 ] as a probability that fission or absorption events on the parameter x o ccu r The diffusion coefficient is defined as: PAGE 40 40 ( 2 30 ) tr is the macroscopic transport cross section, and tr is called the transport mean free path. The diffusi on length in a medium totally depends on the atomic density of a medium so t he diffusion coefficient D can be written in terms of the atomic mass number A [ 4 ]: ( 2 3 1 ) The flux is defined as: ( 2 3 2 ) Therefore, Equation 2 2 9 can be written in terms of number of neutrons: ( 2 3 3 ) In a steady state (the left neutron term is equal to 0 in Equation 2 3 3 ) and homogeneous reactor, the Laplacian term 2 can be replaced by the geometrical buck l ing factor B 2 which is a geometrical quantity measuring neutron lea kage and totally depends on the size or shape of a reactor: ( 2 3 4 ) The geometrical bucking factor B 2 is defined as: ( 2 3 5 ) The effective multiplication factor K eff is 1.0 in a steady state (critical ) meaning neutron production rate is equal to loss rate Therefore, Equation 2 3 3 becomes: (2 3 6 ) The source term (the last term in Equation 2 3 6 ) is now rewritten in terms of prompt and delayed neutron : PAGE 41 41 (2 3 7 ) C is the precursor concentration showing the ratio between the production ra te and decay rate so t he delayed neutron term (r,t) can be defined by the radioactive decay law : ( 2 3 8 ) Considering the prompt and delayed neutron terms, Equation 2 3 6 becomes: ( 2 3 9 ) By factorizing the term f v ( 2 40 ) From Equation 2 3 5 the effective multiplication factor under a critical is defined as: ( 2 41 ) The definition of the mean neutron generation time in one ( 2 4 2 ) By applying Equation 2 12 ( ), 2 4 1 ( K eff ), and 2 4 2 ( ), the time dependent neutron density with subdelayed neutron groups in a homogeneous and steady state can be simply written as: ( 2 4 3 ) ( 2 4 4 ) T hese equations can be solved by assuming general solutions of the exponential form: ( 2 4 5 ) ( 2 4 6 ) PAGE 42 42 The n 0 and C 0 result ing from the initial condition (t=0) are constants and is a parameter to be determined. Sub s t itut ing the solution forms into Equation 2 4 3 and 2 4 4 and solving for reactivity we can get: ( 2 4 7 ) This Equation 2 4 7 is known as the inhour equation since the unit of root is typically taken as inverse hour. The root is also called as the inverse period and solved by a graphical determination of the roots to the inhour equation [1 9 ] The root is the corresponding decay constant for each i th delayed neutron group and describes the time behavior of the relative neutron density If there is no reactivity feedback from other factors such as fuel depletion, temperature, pressure, poisons, and control rod movement, the amount of reactivity in a reactor core can be determined by the time change of the neutron population only. Therefore, the reactor power change can be written in terms of only neutron population at certain time period : ( 2 4 8 ) w here ( 2 4 9 ) n(t ) is the relative neutron power j is j th root of the inhour equation, and A is the amplitude. The amplitude A j is related to the relative abundance a i and decay constant i of each delayed neutron group, and also proportional to the system reactivity in dollar unit $ The system reactivity in dollar unit $ is easily defined as dividing Equation 2 4 7 by the effective delayed neutron fraction [Equation 2 13]. In Equation 2 4 8 the free parameters are originally the amplitude A and root of j th transient term. Spriggs inferred these free parameters using the original delayed neutron PAGE 43 43 parameters. The original parameters can be estimated from the previous order model. F or group is the original model in order to produce parameters for the next higher group model [1, 20 ] This Equation 2 4 9 states that the root of j th transient term for a higher order model can be solved by a given set of delayed neutron parameters, a given mean neutron generation time, and a value of the root which is inferred from the original delayed neutron model Spriggs and Campbell notated this inferred root as a and it was used to obtain the rema ining roots j [1]. This step was iterated to form the eight group model with 20 different transient data sets In the calculation, the following quantities were conserved: 1) the time dependent behavior of the system as predicted from the original delayed neutron group model, 2) the reactivity scale for positive periods, and 3) the mean delayed neutron half life. The conserved mean half life was evaluated by LANL based on 28 different isotopes and is shown in Table 2 8 [1]. Table 2 8 The dominant precursor and half life of each of the eight delayed neutron groups, as evaluated by LANL The uncertainty of half life was not reported. DN Group (Dominant) Precursor Half lives (T 1/2 sec) 1 87 Br 55.6 2 137 I 24.5 3 88 Br 16.3 4 89 Br 4.35 5 90 Br 1.91 6 98 Y 0.548 7 95 Rb 0.378 8 96 Rb 0.203 initial eigh t group model with the above fixed half lives for any isotopes was constructed. However, this initial model was PAGE 44 44 lives since it showed lower sum of the squares of the deviation, and was ensure d as a better fit. The lives was calculated by: ( 2 50 ) Equation 2 50 gives the final average half lives of precursors in each group, and the calculated values are presented in Table 2 9 [1 21 ]. Table 2 9 lives for eight group delayed neutron model This model applied weighting factor to each of the groups to achieve a lower sum of squares of the deviation. The uncertainty of half life was not reported. DN Group (Dominant) Precursor Half lives (T 1/2 sec) Spriggs and Cam p bell Piksaikin 1 87 Br 55.6 55.6 2 137 I 24.5 24.5 3 88 Br 16.3 16.3 4 89 Br, 93 Rb, 138 I 4.35 5.21 5 9 4 Rb, 139 I, 85 As, 98m Y 1.91 2.37 6 9 3 Kr, 144 Cs, 140 I 0.548 1.04 7 95 Rb, 91 Br 0.378 0.424 8 96 Rb, 9 7 Rb 0.203 0.195 This new eight group model was constructed by s plitting the original group number (No.) 2 into two groups and the group No. 6 into two groups The most featured improvements of this new eight group model were : 1) recommending more available sets of delayed neutron, 2) invest i gating new delayed group parameters, regarding an explicit function of incident neutron energ ies: thermal, fast and high 3) suggesting the same half lives of precursors for any fissionable isotopes [1 6 ]. PAGE 45 45 Different models such as a seven or thirteen model have been suggested by many other studies but they have not been supported since the eight group model shows better prediction in the reactivity calculation than a lower order group model, and a higher order group model also suffer s from assigning sh orter lived delayed neutrons in the frame of milliseconds. Even though the eight group model shows better prediction, some numerical solutions or other group models have to be studied further to find better numerical solutions to explain the delayed neutro n emission and to redu ce its associate d uncertainties. Uncertainty on Six and Eight Group Model of Delayed Neutrons As shown in Table 2 7, the uncertainties on delayed neutron nuclear data are particularly large. These high uncertainties can fundamentally originate either from the statistical quality of the chosen fitting methods or the quantity of the measurement data sets. The measured data sets can be precisely provided by the well designed experimental apparatus but their final solution a nd relative uncertainty (standard derivation) can be different due to the fitting methods. According to Wang and Reece in 2008, the reported parameters in many studies interestingly fit their individual measured delayed neutron data well even though the ex perimental data are significantly different [ 2 ]. As mentioned, the LSF method has been commonly used to describe and fit delayed neutron nuclear data. The LSF is a common mathematical method to find a best fit line or curve by minimizing the sum of the squ ares of the offsets (distance from the experimental value to the expected value). However, the coefficients, the shape of the fitted curve, and the relative error via LSF can be dramatically changed by adding a few more data points or considering the quant ity of the measured data points, so the validation study of coefficients and the error analysis of each parameter have to be performed [ 2 2 ]. PAGE 46 46 The analytical goodness of the LSF method between the measured data set and the fitted group parameters is expresse d by the sum of squared residual notated by the capital S The residual e is the quantity showing the difference between an observed (measured) response y and a predicted response y by the fitting equation. ( 2 5 1 ) The subscript i indicates the order of observation The predicted response y can be defined as: ( 2 5 2 ) w here i is the error in the i th observation, and is the unknown parameter of the least square s line Equation 2 5 2 can be simply rewritten for the linear model by denoting 0 as the intercept and 1 as the slope of the least square s line. ( 2 5 3 ) The linear least squares fitting technique is the simplest applied form of linear regression and d irectly provides a solution by the best fitting straight line Unlike the linear model, the non linear model is complicated and its solution can not be directly provided. Generally, t he possible solution can be provided by iteratively applying the linear l east squares model until unknown parameters in the function f [ Equation 2 5 2 ] is converged to the form of linear [ 2 3 2 4 ] In Equation 2 5 3 the error i create s uncertainty in the estimates 0 and 1 It means that an observed (measured) response y is the same with a predicted response y if there is no error. If the error has small magnitude, and then the difference between an observed (measured) response y and a predicted response y is also small. In the same manner, the large error leads to the big difference [ 23 ]. PAGE 47 47 Most fitting methods, including linear or non linear LSF methods, use one common assumption which each data point is equally precisely provided (measured) It means that each error i has the same variance and is normally distributed but it is undeniably unavailable in real experiences. Therefore, many researchers use the weight function to provide more precise fitting line or curve and its relative uncertainty. The common model of the weight LSF is: ( 2 5 4 ) w her e w is a weighting factor and known constant Applying this factor, data points with low variance (precisely measured) will be given higher weights and points with higher variance (non precisely measured) are given lower weights. The major advantage of thi s weight technique is that the better analytical goodness of the LSF method between the measured data set and the fitted group parameters can be obtained since the prediction line can be significantly shifted to match the data with weights. However, it has to be remembered that thi s weight technique must be performed with the precisely known constants. Otherwise, the final predicted model will be totally distorted. This weight ed least squares model was used to judge the goodness of the fitted six group parameters, the group abundance a i and decay constant i by Keepin [1 5 2 5 ] : ( 2 5 5 ) C i represents the observed counts at the time interval T i x is the unknown parameters in the time dependent function f and the i ndices i and n are respectively represented as time interval corresponding to half lives of precursors in the six group model and data points. The variable x is can be defined by: (2 5 6 ) PAGE 48 48 Keepin used two different instant and infinite For each condition, two different probability density functions were separately written. For the instant condition, ( 2 5 7 ) For the infinite condition, (2 5 8 ) P is a proportional constant depending on the reactor power level, the fissile sample properties, and detector efficiency. As mentioned, the non linear LSF can be solved by iterative processes. For this iteration, the initial estimations (seeds) have to be decided. Traditionally, the Matrix Inverse method, Levenberg Marquardt method, and Quasi Newton method have been widely us ed for this problem [23] However, it is not cl ear which method is precise. Later t he validation study for these numerical algorithms was performed by Wang and Reece in 2011 [2] They compared three different methods, Matrix Inverse with singular value dec omposition, Levenberg Marquardt, and Quasi Newton, with different regularization techniques in order to estimate the parameter values. It was resulted that the Levenberg Marquardt method produced the most acceptable values, but also pointed out that the fi tted delayed neutron decay parameters are very flexible even though they are calculated based on the perfect data sets [ 2 ]. To calculate uncertainties on the new eight group model, Spriggs and Campbell firstly owever, the final result with the conserved data from the expansion technique was unrealistically small. T hey thus calculated the relative uncertainty on the group abundance (free parameter) corresponding to the variance of the reactivity (measured paramet er). The variance of the reactivity is also calculated by the original PAGE 49 49 delayed neutron model. The half life sets were assumed as perfect values since they suggested the fixed specific numbers for them. The error propagation for the new eight group model wa s [1] : ( 2 5 9 ) w here ( 2 60 ) After expand ing the delayed neutron group model, the validation study was performed using experimental data for 237 Np. The relative group abundance and its uncertainty were calculated by the six and eight group models, and the results were compared. In this study, the eight group model showed that the relative abundances are showing a good agreement with the six group model, and uncertainties were also accepted as realistic data since the uncertainty of the reactivity scale was smaller in the eight group model than in the six group model [1]. Even though the relative uncertainties in the eight group model were considered to be acceptable, t he relative uncertainties on the delayed neutron group abundances of the longest lived delayed neutron groups are particularly large up to 13% for thermal fissions of 235 U, 16% for fast fission s of 238 U and 38% for fast fissions of 239 Pu These high uncertainties hinder the accurate estimation of fission rates in a fissile sample PAGE 50 50 CHAPTER 3 NUMERICAL METHODOLOGIES The derivations in this chapter assume the following experimental process: A sample of fissi le material (a single isotope) is irradiated with neutrons during irradiation time t i After the irradiation, the sample is transported to the measurement position; this time between the end of irradiation and beginning of measurement is the cooling time t c After the cooling time, the radiation signatures from the sample are measured with suitable detectors during the acquisition time t a [Figure 3 1]. Figure 3 1 A schematic of the experimental process used for this study. A f issi le sample is irradiated for time T i transferred and allowed to cool for a time T c and then measured for time T a Detector Count Rates as a Function of Fission Yields In a fissile sample undergoing fission, the delayed neutron yield is related to the number density of precursor nuclei produced during the irradiation. The number density of the precursor nuclei ( ) produced can be written as: (3 1) Or in terms of the fission rate F as: PAGE 51 51 (3 2) w here N FP is the number density of precursor nuclei, F ( F ) is the fission rate, is the decay constant of precursor nuclei, and Y FP is the cumulative yield (hence, the average number of precursor nuclei of a certain k ind, coming from one fission reaction). By integrating Equation 3 2 with the initial condition N FP = 0 (at t =0), the equation for the number density of precursor nuclei produced at the end of irradiation for time t i is: ( 3 3) After the irradiation, the sample is transferred to the measurement station. The number density of precursor nuclei at the end of cooling time ( t=t i +t c ): ( 3 4) The change in the number density of precursor nuclei between the beginning and the end of the acquisition time gives the total number of precursors per unit volume that decayed during this time and, hence, can be measured. This can be written as: ( 3 5) By defin ing Eq uation 3 5 is simplified to: ( 3 6) The total counts ( C FP ) for delayed neutrons or delayed gamma rays from the precursor density depend on the detector efficiency ( ) and the attenuation coefficient ( ), and are generally written as: ( 3 7) PAGE 52 52 The count s for delayed neutrons and gamma rays from precursors depend on the incident neutron flux, target nucleus density, sampl e size, detector efficiency, solid angle, and beam attenuation. Delayed Gamma Fission Rate Measurement Technique (Gamma Scanning) The derivation of the delayed gamma fission rate measurement technique (called as the delayed gamma technique in later chapt ers) starts from E quation 3 7. A fissile sample is irradiated by a neutron generator, and delayed gamma rays (gamma lines) from fission products are emitted with energies characteristic of the decaying isotopes. If the fission yields of the isotopes are kn own, the fission rate during the irradiation is calculated and related to the measured signal ( M ) via [5] : ( 3 8) w here is the proportionality factor accounting for physical and geometrical properties of the detection setup, is the detector efficiency, is the attenuation coefficient, b is the gamma ray intensity, and T k accounts for the build up and decay of the ga mma ray emitting isotope during irradiation, cooling and acquisition time (analogous to the definition of T in Eq uation 3 6). A k is the fission yield of the isotopes in the decay chain with relevant half lives (meaning that the half lives are long enough not to completely decay during cooling time and short enough not to remain unchanged over cooling and acquisition time). The index k denotes the different isotopes at each state in the decay chain leading to the emission of the gamma ray of interest. To o btain low uncertainty fission rate estimates from the delayed gamma technique the analyzed gamma ray lines must have certain properties. The criteria for a gamma line to be useful for the analysis are: 1) good peak statistics (and therefore large cumulativ e fission yields, large beta gamma branching ratio, low background), 2) s uitable half lives of all relevant isotopes PAGE 53 53 in the investigated decay chain, 3) small uncertainties on the nuclear data, and 4) isolati on of the peak in the spectrum. The decay chains of the delayed gamma precursors can be quite complex, depending on the half lives and the decay modes involved. For the present experimental setup, however, the considered gamma lines come from decay chains that can be described by a combination of three states: the gamma ray emitter itself, its isomeric state, and its parent. According to the definitions above and its simple decay process, the most promising isotope for this study is 89 Rb. Its decay scheme is shown in Fig ure 3 2 Figure 3 2 The 1032 keV gamma line from the decay of 89 Rb was chosen for this study based on its larger yield, low nuclear data uncertainty, and the ability to isolate the peak in the gamma spectrum. E quations 3 9 to 3 11 are the general decay schemes considering the parent ( p ), the fission product of interest ( FP ), and its isomeric state ( m ) with relevant half lives ( P FP and m ) and branching ratios ( q P and q m ). The Y ind and Y cum terms are the independent and cumulative effective fission yields. If multiple fissile isotopes are present in the sample, their fission yields are summed [ 5 ]. PAGE 54 54 ( 3 9) ( 3 10) ( 3 11) Some parents of the fission products do not decay to the isomeric state but only to the ground state of the fission product like the chosen i sotope 89 Rb Thus, Equation 3 9 and 3 11 were considered for the saturation and decay of 89 Rb with the time corresponding term T k in Equation 3 8. The counts under the selected peaks are integrated, which gives the measured counts ( M ) in E quation 3 8. By dividing the counts by the proportionality factor, the fission rate of the sample during the irradiation can be derived. Delayed Neutron Fission Rate Measurement Technique A delayed neutron fission rate measurement technique (called as the delayed n eutron technique in later chapters) was developed by Jordan and Perret [ 6 ] to measure induced fission rates in spent fuel for reactor physics validation studies. If a neutron generator irradiates the sample, and a detector bundle measures the delayed neut rons, the fission rate during the irradiation can be calculated and related to the measured signal ( M n ): ( 3 1 2 ) w here n is the proportionality factor, T nj accounts for the build up and decay of the delayed neut ron emitting isotopes during irradiation, cooling and acquisition time (analogous to T in the gamma scanning technique), D j is the correction factor for the solid angle and attenuation corrections, and S ni,j is the normalized group wise delayed neutron source. The indices i and j denote the fissioning isotope i and delayed neutron group j PAGE 55 55 The term of the normalized group wise delayed neutron source is given by: ( 3 1 3 ) The term f i indicates fission rates from each isotope, and d and d account for delayed neutron yields and relative abundances, respectively [ 6 ]. The fission rate of the sample at the time of the irradiation can be derived in the same manner as t he gamma scanning technique above. Combining Fission Rate Measurement Technique s to Derive Improved Nuclear Data Parameters The above two techniques each provide an estimate of the total fission rate in a fissile sample. The total counts of both techniques are proportional to the actual fission rate in each fissile or fertile element. The difference is the proportionality constant between them If the same sample is irradiated under the same condition, the fission term F in Equation 3 8 (the delayed gamma t echnique) and Equation 3 1 2 (the delayed neutron technique) can be theoretically set equal shown in Equation 3 1 4 [3] . ( 3 1 4 ) Therefore, the high uncertainty delayed neutron nuclear data can be expressed (via the two fission rate esti mates) as a function of the low uncertainty delayed gamma nuclear data [Fig ure 3 3 ]. PAGE 56 56 Figure 3 3 Diagram showing how the delayed neutron and gamma techniques were combined based on a proportional constant Considering all relative factors, Equation 3 1 4 becomes: ( 3 1 5 ) According to Jordan and Perret t he uncertainties on the first longest lived delayed neutron group can thereby be reduced significantly by a factor of t hree or four through thi s combin ed technique [3] Uncertainty Calculation for Longest lived Delayed Neutron Group As mentioned, the relative uncertainty of the longest lived delayed neutron group is particularly large The main reasons of these high uncertainties are: 1) the number of delayed neutrons emitted by the longest lived group (decay of 87 Br) is smaller than for the other delayed neutron groups and 2) Keepin et al. had the limitation of the data acquisition ( 330 sec) so which led poor statistics [ 3 ] The expanded eight group model also showed the problem of the poor statistics since the half life sets were recalculated, actually recreated, with the assumption that the uncertainty on the reactivity scale was co nstant The expanded model was not evaluated based on the measurement data of the delayed neutron parameters but just reasonably and PAGE 57 57 mathematically expanded. In fact, Spriggs and Campbell pointed out that t he uncertaint y values on the expanded relative ab undances might not be physically [ 1, 3 ] More statistically meaningful (precise) delayed neutron group parameters can be evaluated by the precise measurements and procedures. For that, an experimental apparatus for high accuracy simultaneous measurements for delayed gamma rays and neutrons ha s been designed, optimized, and built Based on the obtained data sets, u ncertainties on the delayed neutron nuclear data were consequently reduced by the combined technique in this study The experimental setups are e xplained in the next chapter, and t he derivation of uncertainty equation from the combined technique is explained in this subchapter. Before going further, the concepts of error or uncertainty analysis are explained. Radiation measurement is not a determin istic process; it is instead probabilistic since the emission of atomic or nuclear radiation obeys the rules of quantum theory, based on the probability of an atomic or nuclear reaction. The mean (average) number of particles can be determined within a cer tain error of the true value [26]. The error refers to the difference between a measured value and the true value. It can be separated into two parts, the systematic error and the random error. The systematic error is often called a bias. Therefore, the me asured value can be written as: (3 16) S ystematic error s in experimental observations usually come from the measuring instrument, physical changes in the environment, and measuring technique. The systematic error in experimental observations does not deviate upon repeated measurements under the same experimental conditions However, it is difficult to determine the exact causes of these PAGE 58 58 systematic errors and therefore can not be separated and quantified from the total error in a measured value (both systematic and random error) The random error in experimental measurements comes from statistical flu ctuations and varies every time. The ca use of occurrence for these type s of error can never be determined but can be evaluated through statistical analysis The random error can be reduced by averaging over a large number of observations [21]. Table 3 1 shows the difference between two types of errors in the experiment. Table 3 1 A summary of the errors introduced by the experimental process, grouped by systematic and random errors. Types of Errors Reasons (causes of errors) Systematic Error M easuring i nstruments (un calibrated devices) E nvironmental c onditions (physical changes with temperature, humidity, airflow and etc.) Measurement technique s/methods Random Error S tatistical f luctuations Neglecting systematic error, the standard deviation of the mean value represents the size of the random error: (3 1 7 ) The standard deviation decreases with larger sample sizes. The Central Limit Theorem (CLT) states that if the sample size (typically denoted by n ) from a population is large enough, then the distribution of the sample mean is approximately normal, no matter what population the sample was drawn from [23] : (3 1 8 ) PAGE 59 59 The more accurate result can be drawn as the sample size increases since the sample mean will approach the expected value of the population mean with the sample variance being approximately equal to the expected value of the population variance 2 divided by each sample's size n [23]. Generally, the CLT provides a reasonable approximation when the sample size is larg er than 30. However, the statistical result becomes more accurate as the sample size grows larger. This statement is well explained by Figure 3 4. Figure 3 4. The illustration of C entral L imit T heorem (n = sample size) showing that a statistical result becomes more accurate as the sample size increases. PAGE 60 60 The standard deviation can be expressed in terms of absolute and relative uncertainty. The absolute uncertainty is the amount of physical uncertainty in a measurement, has the same unit with the measured object as the quantity, and is expressed in the standard form : (3 19 ) The relative uncertainty indicates how good a measurement is relative to the size of the measured object, is commonly expressed as fraction or percent, ha s no units and takes the standard form as: (3 2 0 ) This study aims to reduce the relative uncertainty of the longest lived delayed neutron group so the both expressions, the uncertainty and relative uncertainty, mean only the relative uncertainty. Additionally, the systematic error and the random error are used to show the accuracy and precision of a measurement. The width of the distribution describes the precision of the measurement, and the distance from the true value to the mean value express es the accuracy of the measurement. These concepts in radiation measuring process are well explained by N. Tsoulfanidis, and shows in Figure 3 5 [26]. PAGE 61 61 Figure 3 5. Several data sets describing the accuracy and precision of a measurement. The mean value of In Figure 3 5, t and m separately mean the true value and measured value. With only one parameter, the standard deviation of its mean value is just the square root of the mean. Howe ver, more than two parameters, each with their individual uncertainties have to be considered in radiation detection. For instance, t he total counts for delayed neutrons ( M n ) are resulted from other parameters such as the time setup, the correction factor for the solid angle and attenuation corrections, and the normalized group wise delayed neutron source [Equation 3 12]. Therefore, each parameter and its uncertainty should be combine d to come up with the final result of an experiment M n The general formula to estimate the standard deviation for any parameter u is given [23, 27]: PAGE 62 62 (3 2 1 ) Equation 3 2 1 is called as the multivariate propagation of error formula or simply the error propagation equation. It is only valid when each parameter is independent from each other The delayed neutron signal M n in the Eq uation 3 12 is a sum over all delayed neutron groups from all fissioning isotopes. The cooling time t c is the interval between the end of the irradiation and the beginning of the measurement. After a minute of cooling, the shorter lived delayed neutron groups have decayed so that their contributions t o the total delayed neutron signal is negligible. Fig ure 3 6 shows the contributions of the three longest lived delayed neut ron groups to the total signal. Figure 3 6 Total counts of three longer lived delayed neutron groups v er s us the cooling time sho wing that the contribution of the higher groups drops as cooling time increases due to decay. PAGE 63 63 The fraction of neutrons coming from the third group i s below 0.55% after a cooling time of 180 s ec If one waits long enough, Eq uation 3 1 2 can be rewritten in t erms of the first and second group (two longest lived groups, half lives of 55.6 s and 24.5 s) only : ( 3 2 2 ) As described before, t he fission rate in Eq uation 3 2 1 can be substituted by F in the gamma ray equation [Equation 3 8] b y using the simultaneous measurement system with the same fissile sample This leads to an expression of the relative abundance of the longest lived delayed neutron group ( ) from a fission isotope i as a function of the measured delayed neutron counts, the measure d delayed gamma counts and the abundance of the second delayed neutron group : ( 3 2 3 ) Let (3 2 4 ) By a pplying the error propagation equation [Equation 3 2 1 ], the relative uncertainty of the longest lived delayed neutron group is given by : ( 3 2 5 ) w here x is the relative uncertainty on the parameter x and the Equation 3 2 5 is called the uncertainty equation in following chapters. PAGE 64 64 CHAPTER 4 EXPERIMENTAL DESIGNS AND SETUPS This chapter presents the design, optimization, and installation of a new experimental apparatus w ith capability of producing high accuracy measurements for delayed gamma rays and neutrons The apparatus consists of a D D neutron generator, a detector bundle, a sample handler, and relat ed electronics The objective of the experimental design is to 1) maximize the fission rate in the sample, 2) optimize the transfer time of the sample from the irradiation position t o the measurement station and 3) maximize the efficiency of both the neutron and the gamma detection system. Each of these objectives is discussed in detail in the following subsections. The system optimization was carried out using various Monte Carlo mod els (MCNP [ 2 8 ]) in conjunction with the nuclear data library named Joint Evaluated Fission and Fusion file version 3.1 ( JEFF 3.1 ) [ 2 9 ]. The design concept is a fission able sample, roughly the size of a fuel pellet, irradiated by a D D neutron generator, w hich emits neutrons of 2.45 MeV. The sample may contain 235 U, 238 U, 239 Pu or 232 Th. The irradiation is initially set up to last 15 min, long enough for the delayed neutron and gamma precursors to saturate. A pneumatic sample handler rotates the sample duri ng the irradiation to achieve a homogeneous fission rate in the sample, and then transfers the sample from the irradiation position to the measurement position. D elayed neutron s and gamma rays are measured simultaneously by an array of neutron detectors an d a gamma detector, r espectively [Figure 4 9] Maximizing Fission Rates in a Sample The strength of the delayed neutron and the delayed gamma source in the sample is proportional to the induced fission rate s After precursor isotopes are saturated, longer irradiation PAGE 65 65 does not increase source intensity since the production rate of precursors achieves equilibrium with the decay p rocess. The source strength can be increased by high incoming neutron flux, induced f ission reaction, or large mass (size) of a fissile target. The fraction of fissions that emit delayed neutrons is small (in the order of 1 %). Hence, a high fission rate in the sample is needed to obtain low statistical uncertainties. In order to increase the incoming flux and thus the fission rate on the target, a neutron generator and a sample were surrounded by different thickness metal reflectors (lead and tungsten) in the MCNP simulation for potential implementation The dimensions of the sample were e quivalent to a fuel pellet (diameter: 0.82 cm, height: 0.99 cm). The simulated geometry is shown in Fig ure 4 1 Figure 4 1. MCNP simulation geometry showing the neutron generator (blue) output as appoint source. The sample (red) was placed 2 cm away and was surrounded by a metal reflector (grey) in order to increase the neutron flux incident on the sample. The generator was placed at the center of the cubic reflector. The sample was placed on top of the generator, 2 cm away from the source point. PAGE 66 66 Fig ure 4 2 shows the calculated fission rates in the above setup, using a U O 2 sample, for different reflector thicknesses. Reflectors beyond 30 cm provide minimal additional fission. Lead increases the fission rate 20 % more than tungsten, therefore, a 30 cm thick lead reflector was chosen. This increases the total fission rate in a UO 2 sample by 27 % Figure 4 2. Fission rate from a UO 2 sample as a function of reflector thickness for lead and tungsten reflectors A 30 cm lead reflector was chosen based on the 27 % increase in fission rate. Fission rates for various samples placed 2 cm away from the generator target with the lead reflector are summarized in Table 4 1 PAGE 67 67 Table 4 1. Fission rate from a UO 2 sample with different enrichment was estimated via MCNP simu lation [fissions/cm 3 /sec] Sample 235 U 238 U UO 2 ( Enriched, 3.5 w/o) 7.7510 4 8.2110 5 UO 2 ( Natural Uranium ) 3.3010 4 1.7110 6 UO 2 ( Depleted Uranium ) 8.9410 3 1.7210 6 This study focuses on the validation of the combined method and improvement of the high uncertainty of the longest lived delayed neutron group yield of 238 U Therefore, the fission rate from a depleted uranium dioxide (UO 2 ) sample was selected due to its h igher content of 238 U and will be used for the further discussions in this paper The chosen depleted uranium dioxide (UO 2 ) sample will be simply mentioned a UO 2 sample in later chapters. Detector Bundle Design The most important factor to consider for the delayed neutron measurement system is how to effectively detect a small amount of neutrons. The expected delayed neutron emission s from the sample will be o n the order of a few hundred counts per second at the end of the irradiation and rapidly decaying t hereafter. The energy distribution of delayed neutrons is weakly dependent on the fissile material. However, all delayed neutron groups have low average energy of emission o n the order of a few hundred keV [ 1 3 ]. The detector bundle design was optimized to achieve high efficiency for delayed neutron detection. Two possible concepts of detector bundles are shown in Fig ure 4 3 PAGE 68 68 Figure 4 3. The cross sectional view of the two different detector bundle designs, one and two layers. 3 He and BF 3 tubes detectors were considered and compared. 3 He and BF 3 tubes are commonly used to indirectly detect n eutrons through a bsorption reactions, ( n p ) and ( n ) respectively [ 2 7 ] The reaction s in each detector are written as: ( 4 1) ( 4 2) 3 He and BF 3 detector tubes of 1 inch diameter were used to form bundles of one and two layers, embedded in a cylindrical block of polyethylene. One and two layer bundles were designed with twelve and twenty four detectors, respectively. In order to maximize the count rates, the detector layers have been placed at different positions in polyethylene cylinders of various diameters and in various configurations. Fig ure 4 4 shows t he results, describing bundle efficiencies as a function of the distance between the bundle center and the detectors in a cylindrical block of polyethylene of 13.54 cm thickness PAGE 69 69 Figure 4 4. The detector bundle efficiencies as a function of layer positions in the cylindrical block of polyethylene of 13.54 cm radius Efficiency was maximized at 6. 1 7 cm from the center of the bundle. MCNP calculations have shown that for a one layer bundle in a 13.54 cm cylinder of polyethylene the ideal detector pos itions are at about 6. 1 7 cm radius from the center. For a two layer detector in a polyethylene cylinder of 19.08 cm radius, the ideal detector positions are at about 6. 1 7 cm and 11.81 cm from the center. To calculate the detector efficiency of the designs above, the pellet size sample wa s placed at the axial center of the detector bundle. The fission rate distribution, calcula ted during the previous steps, wa s used as delayed neutron source distribution inside sample. The results of the simulations for both types of detectors and for one and two layers of tubes (at the optimized distance from the sample) are shown in Table 4 2 PAGE 70 70 Table 4 2 Absolute efficiency for detector bundles in one and two layer geometries. The 3 He detector was about twice as efficiency as the BF 3 in identical geometries. Tube Type Pressure, Diameter Absolute Efficiency 3 He, 1 layer 4 atm, 1 inch 42.3% 3 He, 2 layers 4 atm, 1 inch 51.7% BF 3 1 layer 0.724 atm, 1inch 16.6% BF 3 2 layers 0.724 atm, 1inch 21.2% The absolute efficiency of 3 He tube detectors wa s more than tw ice as high as that of BF 3 (for identical geometries). The addition of a second layer of tubes increased the overall efficiency of the detector by less than 10 % and 5 % for detectors with 3 He t ubes and BF 3 tubes, respectively. Based on these results and operational cost effectiveness, the one single layer detector design, composed of 3 He tubes with a 1 inch diameter, was chosen for the delayed neutron measurements Another important factor of th is measurement system that it is designed to simultaneously measure delayed neutrons and delayed gamma rays from the irradiated sample, so the above detector bundle design has to be modified. Instead of a full circle with twelve 3 He tubes, a partial circle with seven tubes wa s used The remaining space is necessary to accommodate the gamma detector. A germanium detector (a HPGe) for the delayed gamma ray s w as considered due to its high energy resolution. The energy resolution of a detector means the ability of a detector to identify gamma lines which are close together with slightly different energy, and can be defined as the Full Width at Half Maximum (FWHM) of the photo peak at certain energy [Figure 4 5]. PAGE 71 71 Figure 4 5. Showing t he method for d e termining the Full W idth at Half Maximum (FWHM) The detector energy resolution can be calculated by the ratio, FWHM/E 0 and is a standard measure of detector performance. As shown in Figure 4 5, the FWHM is the difference between E 2 and E 1 the value of energy in the full width at half maximum of the photo peak. The energy value is typically expressed by the number of channel s on the gamma ray spectroscopy program. The energy resolution R 0 is written as the ratio of the full width at half m aximum of a given energy peak to the peak height [27] : ( 4 3) Typically, two types of gamma ray detectors are commonly used in gamma ray spectroscopy, a high purity germanium (HPGe) detector and sodium iodide (NaI) detector A germanium detector generally provides better energy resolution than a NaI detector as shown in Figure 4 6 [ 30 ]. PAGE 72 72 Figure 4 6. An NaI detector has a higher absolute efficiency, and therefore higher count rates, while the Ge(Li) detector offers much better energy resolution As mentioned in Chapter 3 the good peak statistics and isolation of the peak in the spectrum are important to obtain better fission rate estimates with low uncertainty from the gamma scanning technique The obtained fission estimates are directly linked to and used for the improvement of the high uncertainty on delayed neutron data. T herefore, a HPGe detector w as employed in the bundle design. The dimensions of the HPGe detector, used in simulation, are listed in Table 4 3. Cross section views of the detector arrangement are shown in Figure 4 7 PAGE 73 73 Table 4 3 Dimensions of a HPGe detector used for MCNP simulation Description Dimension (mm) Germanium Crystal Diameter 65 Germanium Crystal Length 70 Crystal Center hole Diameter 9.2 Crystal Center hole Depth 61.6 Figure 4 7 The side and c ross sectional views ( left XY and right YZ) of the detector bundle with a HPGe detector The altered neutron detection system has a calculated detection efficiency of 23.7%. Detector Bundle Setup Based on the above designs and simulated results the actual detector bundle was built. The bundle is consisted of a HPGe (PopTop 32 TN30642A ORTEC ) gamma detector and seven 3 He neutron detector tubes (4atm, LND 252284). Each neutron tube has the pulse processing electronic modules, built by Precision Data Technology (PDT), attached to its top. The PDT modules are fully featured by their minimized (compact) size and are composed of two different modules, 10A MHV and 20A M HV. The PDT 10A MHV contains the pre amplifier, amplifier, and discriminator in one module. The PDT 20A MHV has the same electronics as the PDT 10A MHV but with a high PAGE 74 74 voltage supplier (HVS). The PDT 20A module generates its own internal high voltage, and this HV can be used to bias each PDT 10A module. The 3 He tubes are daisy chained together by the PDT modules, and work as a single counter [Figure 4 8]. Figure 4 8. The chained 3 He neutron detector bundle with electronics, PDT 10A and 20A MHV modules bu ilt by Precision Data Technology These daisy chained detectors can work as a single counter (Photo: Author, Heejun Chung) The daisy chained tubes are connected to nuclear instrumentation modules (NIM) on the measurement workstation in order to count dela yed neutrons. The modules consist of a quad counter and timer (Ortec 974), a single channel analyzer (Canberra 2030), and a pulser (Ortec 480) to test modules. A high voltage supply is not required since high voltage can be directly supplied to the PDT 20A module from a DC power supplier (Extech 382200). DC +12 V can generate a proper high voltage (about 1.25 kV) to operate the chained 3 He tubes. The HPGe is connected to a digital spectrum analyzer (DSA 1000, Canberra), and the measured spectra are an alyzed by a gamma analysis software (Genie 2000, Canberra). This gamma measurement system was adjusted and calibrated by a certificated Eu Am source. After PAGE 75 75 calibration, the gamma line of 137 Cs peak at 661.7 keV was determined to be within 3 keV and the FWH M value was about less than 0.85. This measured values met the calibration criteria a ccording to the manual of the gamma analysis software [ 31 ]. A new polyethylene block housing was designed to conveniently hold the detectors, since a detector could be placed into any hole. The (n, p) reaction in a 3 He neutron detector tube [Equation 4 1] is significantly high for thermal neutrons (5400 barns at 0.025 e V) so polyethylene (moderator) thickness should be modified based on the target neutron energy. The previous design was well made to detect delayed neutrons but suffered from the change in its configuration. This new design is fundamentally the same with t he previous design, but its shape was changed from half cylindrical to box, and twenty six detector holes are placed to easily change neutron detector configuration [Figure 4 9]. Figure 4 9. The cross sectional view of the detector bundle, employing a HP Ge gamma ray detector and seven 3 He neutron detector tubes as shown by the bolded holes. PAGE 76 76 The detector bundle, when seven detectors are placed at number (No.) 36, 38, 40, 42, 44, 46, and 48 in Figure 4 9, has a calculated efficiency of 15.2 % via MCNP. A S ample Handler Design and Setup The design objective of the sample h andler is to transfer an irradiated sample from the irradiation position near the neutron source to the measuring position in less than 250 ms in order to maximize the available delayed neu trons for measurement. Additionally, the system must rotate the sample to achieve a homogeneous irradiation. A pneumatic pick and pull actuator and a LabView based control system are used. The pick and pull actuator consists of a rod attached to a pneumati c piston, which allows for 12 inches of linear motion, combined with a second pneumatic piston, which allows for independent rotation of the linear rod. Hall sensors are attached at both ends of each piston to provide position indication as well as a flow restriction valve on the rotation piston to allow for adjustment of the rotation speed. Air at 100 psi is used to operate the actuator and is controlled by two dual solenoid operated four way valves. Each valve controls one of the pistons and allows the ai r supply to be sent to one side of the piston while venting the other side, which causes the piston to move. The air is supplied via a pressure regulator from a standard air compressor. The four way valves, as well as the Hall sensors, are connected to a computer using a LabView sixteen channel digital input, digital output card. Additionally, a digital pressure signal is also supp lied to the LabView card. A LabView Virtual instrument (VI) is use d to display the piston positions, indicate pressure, and control the four way valves to operate the system [Figure 4 10] This VI also has the capability to record accurate timing of the motion of the actuator. The sample handler is shown in Fig ure 4 1 1 and Figure 4 1 2 shows the movement of the pick and pull actuator with a sample in the actual experimental system. PAGE 77 77 Figure 4 10. The user interface for a pneumatic sample handler, written by a LabView Virtual instrument (VI) Figure 4 11. Front and side views of the sample handle r. This allows the sample to be transferred in less than 250 ms and rotated during irradiation and acquisition times to ensure homogeneity (Photo: Author, Heejun Chung) PAGE 78 78 Figure 4 12. The left photo shows the sample inserted into the neutron generator port for irradiation. The right photo shows the sample withdrawn to be counted ( Photo: Author, Heejun Chung) Integral System Design and Setup An integral design of the experimental system is shown in Fig ure 4 13 including a D D neutron generator inside the lead reflector, the pneumatic sample handler, the neutron detector b undle including a HPGe detector with the Dewar to cool the germanium crystal The sample handler extends its arm through the lead reflector to the surface of the neutron generator. For the measurement position, the sample handler retreats the arm through the reflector to the center of the detection system. The sample handler is operated by air pressure and is optimized for fast transfer time between irradiatio n and measurement location, considering shorter live d delayed neutron groups. Additionally, the sample holder will be able to rotate the sample, which allows a more homogeneous irradiation and detection. The short transfer time is one of the main advantage s of doing these experiments with a neutron generator instead of with a nuclear reactor. PAGE 79 79 In the detector bundle design seven daisy chained 3 He tubes for the delayed neutrons and a germanium detector (a PopTop HPGe) for the delayed gamma ray s were consider ed due to its high energy resolution Summarizing, the most important features of the detection system being built, are 1) simultaneous measurement for delayed neutrons and gamma rays, 2) rapid transfer of the sample from the irradiation position to the me asurement station, 3) zero or low background unlike in a reactor system, and 4) flexible irradiation time which can easily be controlled. Figure 4 13 Front and side views of the measurement geometry and neutron generator PAGE 80 80 CHAPTER 5 NEUTRON GENERATOR DESIGN, CONSTRUCTION, TESTING, AND QUALIFICATION The new D D neutron generator developed in collaboration with Adelphi Technology Inc., is highlighted in this chapter. This new design allows a sample to be place very close to the emitting neutron target Previously, a sample w as required to be placed at a large distance from the neutron source so the actual flux of fast neutron s to the sample was relatively small A minimum source to sample distance in the new design provides a high flux of fast neutrons t o the sample and the reaction rate in the sample therefore increases. Un iversity of Florida and Adelphi Technology Inc. have received the 2013 R&D 100 award ( known as the Oscars of Innovation) for their development of this neutron generator, the model DD 109X. Neutron Sources A n external neutron source is necessary to induce a nuclear fission reaction Neutrons can be obtained from nuclear disintegrations or reactions Neutron sources, widely used, are: 1) Spontaneous fission source The nuclear binding ene rgy per nucleon decreases as the atomic mass number increases [ 7 ]. Some transuranic heavy nuclides are naturally split into two nearly equal mass fragments and emit some fast neutrons. This nuclear process is known as a spontaneous fission reaction and is a type of radioactive decay. The most common spontaneous fission neutron source is 252 Cf with a half life of about 2.65 y ears 2) ( ) reaction source This type of neutron source is a compound of two different materials, an alpha emitter and a target nuclide. An energetic alpha ( ) particle emitted from alpha emitters such as 210 Po, 226 Ra PAGE 81 8 1 23 9 Pu, or 241 Am breaks through the Coulomb barrier of a target nuclide and is ab sorbed. The Coulomb barrier is the barrier prod uced by the electrical repulsio n and the energetic alpha ( ) particle must overcome this barrier in order to get close enough to the target nucleus in order to undergo an absorption reaction. Since the Coulomb barrier increases with the atomic number a light element such as 7 Li, 9 Be, 10 B, and 19 F is used as a target in order to minimize Coulomb force repulsion between the alpha particle and the target nucleus [ 32 ] The ( ) reaction in the case of 23 6 Pu and 9 Be can be written as: ( 5 1) Some available ( ) reaction sources are also listed in Table 5 1. Table 5 1. Characteristics of some alpha particle and neutron reaction sources including the average energy and half life. E (MeV) Half life Target E n (MeV) 241 Am 5.4 458 y Be 4 226 Ra 4.5 1620 y Be 3.6 210 Po 5.3 138 d Be 4.3 3) ( n) photoneutron source Some nuclei emit neutrons when the energy of incident gamma ray s is greater than the binding energy of a neutron in the nuclei. T he neutron binding energy is typically higher than 6 MeV. Only two nuclei 9 Be and 2 H, are practically available due to their low er binding energy (below 4 MeV) : (5 2) (5 3) These reactions are e ndothermic (Q value is negative). It means that a photon of at least 1.67 and 2.23 MeV is respectively required to liberate a neutron from beryllium and deuterium PAGE 82 82 [3 3 ]. Through this type of a neutron source, mono energetic neutrons can be obtained from the selected mono energetic photons. This is a unique feature of this type of neutron source but some applications are occasionally limited by the presence of high gamma ray backgrounds Some available ( n ) photoneutron sources are listed in Table 5 2. Table 5 2. Characteristics of ( n) photoneutron sources including the average energy of each incident and produced particle. Source Half life E (MeV) E n (MeV) 24 Na + 9 Be 15 h 2.754 0.967 2 4 Na + 2 H (D) 15 h 2.754 0.263 2 8 Al + 9 Be 2.24 min 1.779 0.101 38 Cl + 9 Be 37.3 min 2.168 0.446 The spectrum of bremsstrahlung photons of high energy and i ntensity from accelerators such as a linear particle accelerator (Linac) can be used as a source to induce the ( n ) photoneutron nuclear reaction, but this method can not generate mono energetic neutrons since the energy spectrum of bremsstrahlung photons is continuous. 4) Spallation neutron source A s pallation reaction is a process in which a light projectile such as a proton, neutro n, or any light nucleus with high kinetic energy interacts with a heavy nucleus such as a lead (Pb) or spalled 4 ]. The neutrons produced in spallation reactions can be characterized by their energy spatial distributions and multiplicity The neutron multiplicity is t he number of neutrons produced per one beam particle [3 5 ]. This technique is advantageous because of higher neutron production rate but the equipment nece ssary to accelerate the projectile particle to such high speeds makes this method extremely costly. PAGE 83 83 5) Nuclear reactor A nuclear reactor can be considered a continuous neutron source. Neutrons are produced by the fission chain reaction; neutrons are emitted by fissioning nuclei repeatedly induc ing fissions in other fissile or fertile materials [ 4 ] A n uclear reactor is mainly based on the fission reaction of 235 U to yield two fission fragments and about 2 .47 neutrons per fission at 2 MeV kinetic energies Fo r instance, (5 4 ) A nuclear reactor is commonly used, but th is source is frequently inappropriate for some medical or research applications which require neutrons of a specific energy or rate without interferences from the distribution of background radiations. In addition, t he accessibility to those sources is also always lim ited by safety issues 6) Fusion reaction neutron source There are two important nuclear reactions in which energy is released : fission and fusion reactions. As explained before, nuclear fission is the splitting of a heavy nuclide into two lighter nuclides. O n the other hand, a fusion reaction involves two light nuclides fusing into one larger nuclide, and this process also results in the release of neutrons Based on the fusion reaction, accelerator based neutron sources ha ve been developed and widely used fo r medical and research applications. The operating concept of a n accelerator based neutron source is normally that the charged projectile particles or ions are accelerated by the strong electromagnetic force T he target materials are bombarded by th e se energetic projectile particles or ions, and nearly mono energetic neutrons are consequently produced from nuclear reactions PAGE 84 84 The widely used accelerator based source is a fusion based neutron generator, based on deuterium deuterium ( D D ) or itium ( D T ) nuclear reactions A D D neutron generator produces fast neutrons of 2.45 MeV and a D T neutron generator produces 14.1 MeV neutrons [E quation 5 5 and 5 6 ], but due to the differences in solid angle and applied voltages, it is also possible to see a ran ge of produced neutron energies: ( 5 5 ) ( 5 6 ) A neutron generator is usually required for active NDA techniques The NDA technique was initially developed to investi gate nuclear fuel materials without any perturbations in their physical or chemical states. It was started from the proposition that the physical p roperties of the emitted radiation by spontaneous or nuclear reactions are unique to the isotope(s) of interest, and the radiation intensity can be related to the mass and content of the fissile isotopes The NDA techniques are characterized as passive or active interrogation methods The passive interrogation method measur es radiation from the spontaneous decay process of the nuclear material and the active interrogation method measur es radiation induced by an external source [3 6 ]. The current NDA techniq ues deriving their signals predominantly from the induced fission from Uranium (U) and Plutonium (Pu) isotopes, were reviewed by S. J. Tobin et al., and are listed in Table 5 3 [3 7 ]. PAGE 85 85 Table 5 3 Current NDA techniques organized by active and passive int errogation methods. Active interrogation requires the sample irradiation by an external neutron source. T ype T echnique Description Active Californium Interrogation with Prompt Neutron (CIPN) A relatively low cost and light weight instrument Fission chambers for neutron measurement are c ombined with an active interrogation source ( 252 Cf) Delayed Gamma (DG) Measuring delayed gamma rays emitted from the decay process of fission products. Preliminary data on the delayed gamma decay Delayed Neutron (DG) Same as DG, except for delayed neutrons Differential Die Away (DDA) Measuring the induced fast fission neutrons between generator pulses The number of detected neutrons between pulses is proportional to the mass of fissile material Passive Passive Neutron Albedo Reactivity (PNAR) M easurement of time correlated neutrons from a spent fuel assembly with / without a Cadmium (Cd) layer surrounding the nuclear fuel assembly To draw better conclusion s from th e active NDA technique, an important factor to consider is the neutron yield since it is directly related to the induced fission rate. Typically, a D T generator has higher yields than a D D generator, roughly twice as high since the fusion cross section of a D T reaction is larger than a D D reaction [ 3 8 ]. The cross sections for the primary fusion reactions are shown in Figure 5 1 [ 8 ]. PAGE 86 86 Figure 5 1 The cross sections for the primary fusion reactions showing that a D T reaction has the highest cross section, and therefore provides the higher neutron production yield. For a better fission estimation, a D T neutron generator would be chosen due to its higher fusion cross section. However, tritium gas is radioactive so its possession or use is always limited by safety and nuclear regu latory concerns Neutron Generator Design In the early stage s of th e project, a new experimental design and method for improved delayed neutron data, a Kaman A 711 D T generator was considered as a neutron source. The Kaman A 711 generator is a miniature sealed tube type accelerator that produce s 14.1 MeV PAGE 87 87 neutrons from the collision of a mixed beam of deuterium and tritium ions with a deuterium tritium loaded target. It had a maximum intensity of 0. 5 x10 11 neutrons per second and the capability of rapid sta rtup and shutdown for non repetitiv e pulses below 1 sec duration [3 9 ]. The generator intensity and capability of a pulse d and continuous working (CW) operation mode made it to be a suitable neutron source for this study However, the generator tube in the head was no longer viable, the cooling unit needed to be replaced and the power supply tank no longer met the current American Society of Mechanical Engineers ( ASME ) regulatory requirements In addition, fast neutrons of 14.1 MeV emitted from a D T generator have to be thermalized for this study since 14 .1 MeV neutron s w ere classified as high energy in the eight group model. As mentioned in Chapter 2 Spriggs and Campbell used three neutron energies: thermal, fast, and high [1]. F or the fast neutron experiments with the Kaman A 711 D T generator, a moderator is supposed to b e designed and installed around the generator head but due to the previous experimental setups, there was not enough space to do so. Considering the high cost o f refurbishment and inconvenience in re designing other experimental devices for delayed gamma ray and neutron measurements from fast fission a new D D generator was designed and developed with Adelphi Technology Inc. T he generator design concepts focused on 1) high neutron intensity, 2) minimized distance from the source to a fissile sample, 3 ) operation in both pulse d and continuous working (CW) modes, 4 ) compactness of the whole system, and 5) easy access to the source The signal strength of the delayed neutron s from the two longest lived groups highly depends on the fission density (the number of fission events per sec) in a fissile sample since other parameters in Equation 3 13 are almost fixed (constan t) PAGE 88 88 Based on the delayed neutron group abundance in the eight group model, the required generator intensity was calculated [Figure 5 2] Figure 5 2. Time integrated neutron counts for the two longest lived groups of 238 U which was used to determine the minimum required neutron production yield from a D D neutron generator. The initial time setups for irradiation, cooling, and acquisition were each 180 sec T he sample was placed next to a generator, and the detector efficiency was assumed to be 20%. According to Figure 5 2, the minimum required neutron yield must be higher than 2 .0 x10 8 neutrons per sec. Obviously the accuracy of delayed neutron parameters increases with higher neutron flux intensity from a generator so a neutron production yield of 4 .0 x10 9 neutrons per sec was initially planned Th is initial goal was higher than any other current commercial products that use a D D fusion reaction. Another way to increase the fission rate is to minimize the d istance from the source to a sample Typic ally, a sample had to be placed relative ly far away from the generator, and the PAGE 89 89 actual neutron flux incident on the sample was small. In order to utilize the high intensity of a generator, a generator head was designed to be able to inject a sample close t o the source. The purpose of this study is to design experiments to improve delayed neutron group yields and abundances. It is not limited to only the longest lived delay ed neutron group. T he other group parameters will be analyzed based on the same experimental system Thus, a generator should be operated in pulse d and CW modes since the saturation time of other shorter lived groups is s mall The compact design of a generator is highly sought after by many medical and nuclear applications due to its relative portability and convenience. The compact design refers to not only the generator itself but also all the associated electronic equipment Since the size of the Kaman A 711 D T generator was a problem it was important to try and minimize the whole system while maintaining a higher neutron yield. The final consideration in the design was easy access to a source. The generator head is typically sealed so it is difficult to maintain and repair. Adelphi Technology Inc. developed the open vaccum system, allowing disassembly for maintenance or re configuration of the system without being returned to the company. The generator head uses a serviceable stainless steel housing with conflate copper gasket seals that can be easily removed, permitting most of th e components in the generator head to be easily maintained and replaced. The initial design of the generator head, describing the neutron production, was shown in Figure 5 3. PAGE 90 90 Figure 5 3. The initial design of the generator head and simple working proces s of neutron production Deuterium ions are accelerated into the negatively biased titanium target, these ions are captured by the target, and then react with the next incoming deuterium ions. The basic process of neutron pro duction is that the plasma ion source supplies deuterium ions which are accelerated across a high electric potential to a negatively biased titanium target T he energized ions hit the titanium target and are captured by the target lattice, and the next incoming deuterium ions collide (react) with the captured ions, resulting in a D D fusion reaction. D D Neutron Generator Construction and Testing Based on the design concepts, t he D D generator (DD 109X) has been built and tested with Adelphi Technology Inc. It was designed t o achieve the maximum output of 4.0x10 9 neutrons per sec using up to 30 mA of beam current and 125 kV of acceleration voltage The final design was almost the same as the initial design [Figure 5 3] but t wo sample ports were designed into the housing of the generator to allow multiple sample experiments at the same time and a minimum distance from the source to a sample [Figure 5 4] PAGE 91 91 Figure 5 4. The cross sectional view of the DD 109X neutron generator This generator is f eatured by its sample irradiation holes since the sample can be close to the neutron source. The full neutron generator system consists of three main parts: the generator body a cooling unit, and a power rack. The entire system is controlled by a computer program 1) Generator body The generator body is composed of a generator head, a microwave driven plasma source a deuterium gas supply, a turbo molecular high vacuum pump which was designed to reach up to 1.0x10 6 mbar, and a pre vacuum pump. 2) Cooling unit T he generator p roduces nearly 4 kW of heat during operation so sufficient fluorinert an electrically insulating and ideal for use in many single phase heat transfer applications is PAGE 92 92 required. F luorinert liquid ( 3M FC 3283) was used and its level is continuously monitored by a personal protection system (PPS) since over time the fluid can evaporate 3) Power rack The power r ack consists of a h igh v oltage power supply running up to 12 5 kV (maximum) and the main control panel to control all the subsystems of the generator body. The h igh v oltage power supply can be separated into two parts, Glassman PK and EK series. The PK and EK series respectively control high voltage and current on the generator head and a microwave driven plasma source The actual expe rimental system employing the generator system, detector bundle, and sample handler, was built and is shown in Figure 5 5. Figure 5 5 The actual whole experimental system, employing the D D generator the simultaneous measurement system, and the sample handler (Photo: Author, Heejun Chung) PAGE 93 93 To ensure human safety from the 2.45 MeV fast neutrons that are generated, the generator becomes disabled when any interlock switches are open. These safety feature s are controlled by the PPS The PPS consists of three built in interlock systems to prevent failures from a fluorinert cooler, a magnetron, and a high voltage supplier bin. Additionally, three highly visible multi tiered warning devices were installed, al ong with an emergency kill switch to immediately de energize the entire system by personnel in the room The generator was placed in a secured room, surrounded by 2 foot concrete walls. High density polyethylene blocks, 2.5 inches thick and 60 inches long, were attached to the inner wall This secured room is called the generator room in following chapters. Two warning devices with sound are placed in the generator room for radiation work er s, and one warning light, in conjunction with an electromagnetic doo r lock, was installed in the hall way for the public. These warning devices are controlled by the PPS and a controller. The main control room is located next to the generator room. Th is room was designed to monitor the generator room in real time and to c o ntrol the entire experimental setup the DD 109X neutron generator, the sample handler, and the detector bundle. To operate the generator, the user interface of the DD 109X was written to control high voltage and current limit on the accelerator and on the magnetron in kV and mA, generator running time in sec, and deuterium gas flow rate in sccm (standard cubic centimeters per minute). The user interface is shown in Figure 5 6. PAGE 94 94 Figure 5 6. The user interface to control voltage, current, time, and gas flow rate of the neutron generator. The control room is monitored by two B onner ball detector s ( M odel No. 12 4 count ratemeter LUDLUM ). The measured radiation dose in the room was 1 mrem/hr and below 0. 6 mrem/hr around all other side walls Detailed information of the measured radiation dose is available in Appendix B To ensure safety and also to check operating conditions in the generator room, four digital high resolution cameras were employed for monitoring and recording. The installed e ntire control system is shown in Figure 5 7 PAGE 95 95 Figure 5 7 The whole control system Monitor in upper left controls the sample handler, the monitor in upper right is employed for monitoring and recording the neutron generator, the monitor in lower left con trols the HPGe, and the monitor in lower right controls the neutron generator (Photo: Author, Heejun Chung) The above safety features and measured values meet regulatory requirements given in the Code of Federal Regulation Title 10 Part 2 0 (10CFR20) and part IV of Florida Administrative Code The state registration (license) number is JR 22505000. To consistently produce neutrons i n the system, t he delivered deuterium gas is ionized when appropriate gas pressure and microwave coupling are achieved in the microwave driven plasma source T he microwave driven plasma source can consistently deliver deuterium ions and also does not produce metallization inside the vacuum envelope When inappropriate microwave coupling is resulted, the metal in the ion source can be sputtered by the energized ions The sputtered metal is then deposited on the inner surface of the plasma ion source wall. If th is sputtering phenomen on occurs continu ously for some time it PAGE 96 96 results in a fully metalized inner surface of the plasma ion source [ 40 ] This phenomenon is known as the metallization and it finally leads to tube (system) failure. The microwave driven plasma source consists of a magnetron (LG 2M213 Series, 2.54 GHz), the mass flow controller to supply appropriate gas pressure, and related electronics The employed magnetron and electronics in the mounting box are shown in Figure 5 8. Figure 5 8. The magnetron and electronics in the mounti ng box employed for the DD 109X neutron generator (Photo: Author, Heejun Chung) T he deuterium ions are extracted from the plasma energized to about 100 125 kV, and accelerated toward a titanium target by the high voltage supply. The energized deuterium ions hit the titanium target and are captured by the target lattice and the next incoming ions collide (react) with the captured ions. Since the ratio between the captured and incoming ions is not balanced, the neutron generation y ield is unstable in early stages. However, a fter some time (about 50 60 min), the amount of the captured and reacted deuterium ions on the titanium layers are in equilibrium The neutron generation yield from the D D generator becomes stable with 5 10 % va riation and reached the designed neutron yield in early testing. PAGE 97 97 D D Neutron Generator Qualification A ccurate calculat ion o f the neutron generation yield from the D D generator is most important since t he number of counted delayed neutrons and gamma rays is increased only by the high incoming flux or the sample properties such as the amount or composition of fission material. To evaluate neutron yield from the generator, Adelphi Technology Inc. performed the activation foil technique with other electronic neutron gauges They then found response functions from neutron yield to dose rates on a bonner ball neutron detector, and built a neutron yield equation : ( 5 7 ) where mRem is the do se rate from a B onner ball neutron detector, and r is the distance from the generator to the bonner ball neutron detector However, the calculated yield via Equation 5 7 was mismatched to count rates of delayed neutrons and gamma rays. Lower number of dela yed neutrons and gamma rays were measured than expected count rates, academically calculated. Thus, one 3 He detector which is embedded in a block of polyethylene was placed 1.65 m away from the generator in order to monitor the yield in real time The neutron yi eld then can be calculated via: ( 5 8 ) The absorption rate was calculated via MCNP [ Figure 5 9 ] and the whole detector volume is known T he correlation between the neutron yield and number of counts is shown in Figure 5 10 PAGE 98 98 Figure 5 9 The simulation geometry of the actual experimental system, drawn by Moritz Geometry Tool [ 41 ] The monitoring detector is used to measure the real time neutron production yield from the neutron generator, and the detector bundle is used to count delayed neutrons from the sample after irradiation. PAGE 99 99 Figure 5 10 The c orrelation between n eutron y iel d from the D D generator and n umber of c ounts on a 3 He monitoring d etector (linear fitting) The neutron yield from the D D generator gradually increases and becomes stable over time since the high voltage supply and metallic parts are unstably biased fr om 100 kV to 125 kV in the beginning. The imbalanced amount of captured and reacted deuterium ions on the titanium layers also causes the lower neutron yield at the beginning. Additionally, the unstably biased parts lead many number of arcing. The rate of arcing in the initial stage is high, and i t usually occur s between two ceramic jars and a metal body, or the ceramic part of the high voltage supplier. Melted or scratched parts can also produce arcing in the system since they can create shape points in the high voltage regions. To reduce these high rate s of arcing the system should be conditioned using high voltage and lower current limit s, such as 70 kV and 0. 0 5 mA The applied voltage should then be gradually increased up to the designed experimental levels. The current limit shou ld decrease as voltage increases. PAGE 100 100 Huge amounts of sparking can damage some parts o f the system, so the parts suspected to cause the arcing were inspected a fter running the generator for about 100 hours As expected, evidences of arcing were found in these locations, including the ceramic jar and metal body [Figure 5 1 1 to 5 1 3 ]. The scra tched and fuliginous parts were cleaned and polished. Figure 5 1 1 The scratched target head of the DD 109X neutron generator as a result of arcing inside the neutron generator (Photo: Author, Heejun Chung) PAGE 101 101 Figure 5 1 2 The scratched and fuliginous metal body and ceramic jar (Photo: Author, Heejun Chung) Figure 5 1 3 The scratched metal body which was placed next to the ceramic jar (Photo: Author, Heejun Chung) PAGE 102 102 CHAPTER 6 SAMPLE FABRICATION AND COMPOSITION ANALYSIS Different research approaches can lead to different definitions of a well defined sample. People who focus on material properties may be interested in microstructure in terms of grain size, porosity distribution or stoichiometry of a sample. However, for research based on N DA analysis like this study, a well defined sample means that the density and material composition (mass ratio) of fissile elements in the sample are clearly defined. Many methods to analyze the isotopic composition of a n uranium sample c ompo sed of 234 U, 235 U, and 238 U have been developed and reviewed From the early 19 50 t he mass spectrometry [ 4 2 ] alpha spectrometry [ 4 3 ] gamma spectrometry [ 4 4 4 5 ] and photographic spectral [ 4 6 ] techniques have been developed and used for measuring the mass ratios also known as the signature isotopic ratio, for each type of uranium sample S ome advanced techniques have been developed by combining earlier methods such as the chromatographic separation technique [4 7 ] which is derived from the mass spectrometric and thermal ionization mass spectrometry techniques, as well as mass spectrometry with ionization in inductively coupled plasma (ICP MS) techniques [ 4 8 ] As mentioned, many techniques are currently available but gamma spectrometry was chosen for this research since it has been w ell validated for so long Sample Fabrication The pelletized samples of depleted uranium dioxide ( UO 2 ) were fabricated by the conventional powder process method (conventional method) [ 4 9 ] and the spark plasma sintering method (SPS) [ 50 ] An example of samples fabricated by each of these methods is in Figure 6 1, and their microstructure pictures are also shown in Figure 6 2 on a scale of hundreds of microns PAGE 103 103 Figure 6 1. UO 2 samples fabricated by the conventional method ( left ) and the spark plasma sintering method ( right ) (Photo: Author, Heejun Chung) Figure 6 2. Microstructure of UO 2 sample fabric ated by the conventional method ( left ) and the spark plasma sintering method ( right ) The c onventional powder process method is widely used in nuclear reactor s In the conventional method, UO 2 powder was pressed into green body pellets after milling and then sintered at 1600C in an alumin um tube furnace for 5 hours with a high purity argon and hydrogen gas atmosphere. The gas flow rate was 2 liter/min during the sintering process. The total duration of this work is about 12 hours. PAGE 104 104 SPS is a newly developed sintering process using a microscopic electric discharge between the particles under high pressure The SPS fabrication process is very similar to the conventional method but has a much shorter sintering time typically lasting only a few minutes Us ing the SPS system UO 2 powder was sintered at 1600C for only 5 min. In principle, the pellet sintered by the SPS process shows small grain size, reduced chemical formation, higher density, and enhanced interfacial con t act compared to the pellet fabricated by the conventional powder process [51 ] By employing both the conventional method and SPS processes, four UO 2 p ellets were finally fabricated. Each pellet density was measured b y the Archimedean Immersion Method: ( 6 1) w here M P/air is the mass of a pellet in air, M P/water is the mass in water, and water is density of water (10.242 g/cm 3 ). The measured pellet properties are shown in Table 6 1. Table 6 1. UO 2 pellet fabrication methods and properties of the four UO 2 pellets fabricated and used in this study. No. Fabrication Hei ght [cm] Diameter [cm] Density [g/cm 3 ] 1 SPS 0.654 1.224 10.24 2 Conventional 0.888 1.088 9.698 3 Conventional 0.906 0.998 10.74 4 SPS 0.627 1.242 10.48 For this research improving delayed neutron group abundance data fo r each isotope determining the isotopic composition of a fabricated UO 2 sample is important in order to know the fission rates from each isotope indicated by t he term f i i n Equation 3 14. The passive nondestructive analysis (PANDA) for gamma rays is widely used to det ermine the uranium isotopic composition ratio ( 235 U/ 238 U). The PANDA for gamma rays is sub PAGE 105 105 classified into total photon counting, spectroscopy, and imaging methods [3 6 ] The passive gamma ray signatures from 235 U and 238 U are listed in Table 6 2 Table 6 2. The passive gamma ray signatures from 235 U and 238 U Isotope Gamma ray Energy [keV] Intensity [%] 235 U 143.8 10.95 185.7 57.10 238 U 766.4 0.319 In equilibrium with 234m Pa 1001.0 0.835 The gamma ray spectroscopy method was employed to determine the isotopic ratio of the fabricated UO 2 samples. Gamma ray Spectroscopy Method The gamma ray spectroscopy method using a HPGe detector ( GEM 30185 P, EG&G ORTEC ) in a lead shield was used for the analysis of the activity ratio of 235 U and 238 U in the fabricated samples. The target gamma lines are 185.7 keV for 235 U and 1001.0 keV for 234m Pa, a daughter nuclide of 238 U. The number of counts ( C ) can be converted to the activity values by: (6 2) w here BR is the branching ratio or the gamma ray emission rate (intensity), is the detector efficiency, and t is counting time (24 h ou r s for this analysis). From the calculated activity ratio, the enrichment values of the pellets were decided. The enrichment val ue can be calculated by [ 4 4 ]: ( 6 3) w here A U8 is activity of 238 U and A U5 is activity of 235 U in Bq PAGE 106 106 The Equation 6 3 can be rewritten in terms of the count rate: ( 6 4) With the same condition s for both measurement s the detector efficiency term and the counting time term t are canceled in Equation 6 4. 238 U can be precise ly estimated by the photopeak at 1001.0 keV since there are no overlapped photopeaks at that energy range with in 3 However, the photopeak at 185.7 keV for 235 U suffers from interference from t he 186.1 keV gamma line of 226 Ra and this interference must be consi dered before conducting further analysis According to Ebaid in 2009, the interference between 185.7 keV (57.1%) from 235 U and 186.1 keV (3.5%) from 226 Ra can be removed by a simple equation [ 4 5 ] : ( 6 5) w here CR T is the total count rate in the photopeak at 185.7 keV. With the subtracted count rate at 185.7 keV for 235 U and the total count rate at 1001.0 keV for 238 U, the enrichment value can be calculated through Equation 6 4 and 6 5 The enrichment values for fou r fabricated samples are listed in Table 6 3. Table 6 3. Enrichment values for the UO 2 pelletized samples These values were calculated through the gamma spectrometry method. No. 235 U 238 U 1 0.00096 0.99904 2 0.00094 0.99906 3 0.00244 0.99756 4 0.00282 0.99718 PAGE 107 107 The sample s No. 1 and 2 ha ve lower 235 U content since two different powders were used to make the sample s The powder for sample s No. 1 and 2 was supplied by SPI Chem C hemicals and another powder for sample s No. 3 and 4 was obtained from Areva, Hanford, WA. They showed different purity levels during the milling process with the powder from SPI Chem C hemicals being the least pure, as shown in Figure 6 3 Figure 6 3. Impurities from depleted uranium powder, supplied by SPI Chem C hemicals (Photo: Author, Heejun Chung) Other Possible Samples In a sample, o ne of the most important factor s in induc ing more fission events and eventually produc ing a larger number of delayed neutrons and gamma rays is the sample size. The fabricated UO 2 samples in the previous subchapter were well made and defined but it was impossible to increase their size due to the limitation of the size of the sintering supplies and equipment. For that reason, a natural uranium slug was prepared and its physical characteri stics were measured The slug was distributed to sixty five universities in the U.S.A. by Westinghous e PAGE 108 108 Savannah River Company for use in subcritical assemblies for R&D and educational aids in nuclear engineering program s The University of Florida received Mark I slugs (solid slug s ) and Mark IV slugs (hollow slug s ), but the Mark IV slugs were returned and only the Mark I slugs are currently kept. The Mark I slugs contain natural uranium (0.0054 % 234 U, 0.7204 % 235 U, and 99.2742 % 238 U) clad in cylindrical shaped aluminum [Figure 6 4] The measured weight of each slug is 1931.4 g The other measured and reported specification s of the Mark I slug are shown in Table 6 4 [ 52 ] Figure 6 4. The Mark I solid slug The slug contains natural uranium, surrounded by aluminum cladding (Photo: Author, Heejun Chung) Table 6 4. Measured and reported specification s of the Mark I slug Description Dimension (cm) and Volume (cm 3 ) Slug Radius 1.350 Slug Length 21.273 Slug Volume 121.709 Natural Fuel Slug Radius, Clad in Aluminum 1.254 Natural Fuel Slug Length, Clad in Aluminum 21.081 Natural Fuel Slug Volume, Clad in Aluminum 104.144 PAGE 109 109 The exact specification s of this slug are important to derive or simulate accurate delayed neutron parameter s as discussed in later chapters. Th e slug will be used to validate the results of this study, which aims to reduce the uncertainties of the l ongest lived d elayed n eutron g roup for 238 U However, d ue to its bigger size and heavier weight, the experimental setups should be slightl y modified. Another possible sample is a ThO 2 pellet The pelletized samples of thorium dioxide (ThO 2 ) were fabricated by the conventional method [Figure 6 5]. Figure 6 5. ThO 2 samples fabricated by the conventional method (Photo: Author, Heejun Chung) The s e were fabricated in almost the same manner as the UO 2 pellet, except slightly modified based on the reference [ 5 3 ]. Thorium powder was pressed into the green body pellets after milling and then sintered at 1550C in an alumin um tube furnace for 10 hou rs with a high purity argon and hydrogen gas atmosphere. The gas flow rate was exactly the same as a UO 2 pellet. The total duration of this sintering process is about 18 hours. PAGE 110 110 Unlike the reference, the two fabricated ThO 2 pellets in Figure 6 5 showed the different conditions of the surface with cracks and two color layers (black and light brown). From the point o f view of those focused on material properties these pellets have fail ed structures However, they can be successfully used for NDA research like this study since their density and material composition can be clearly identified. PAGE 111 111 CHAPTER 7 PARAMETRIC UNCERTAINTY ANALYSIS OF THE DELAYED NEUTRON MEASUREMENT With regards to the designed setup and the combined technique, a new evaluation of the relative abundance and uncertainty of the longest lived delayed neutron group for fast fissions of 238 U were calculated The calculated result (based on Equation 3 9, 10, 11 and 2 3 with the optimized time setups) showed almost same value with the recommended value (0.008) in the eight group model. The parameters used in the calculation are listed in Table 7 1 [29] T able 7 1 Parameter values for the relative uncertainty calculation Parameters Value Reference 0.002 MCNP and Experiment Results Y cum, K r 89 0.0 3008 7.841 x10 4 JEFF 3.1 Nuclear Library q P 1 JEFF 3.1 Nuclear Library T 1/2 Kr 89 189 2.4 sec JEFF 3.1 Nuclear Library b 89 0.636 0.011 JEFF 3.1 Nuclear Library Y cum, Rb 89 0.0 30349 7.895 x10 4 JEFF 3.1 Nuclear Library Y ind, Rb 89 2.6848x10 4 9.5198 x10 5 JEFF 3.1 Nuclear Library T 1/2 Rb 89 924 12 sec JEFF 3.1 Nuclear Library D j 0.152 MCNP Results PAGE 112 112 The gamma ray detector efficiency was evaluated with a 60 Co standard source, emitting two gamma rays at 1.173 and 1.333 MeV. Th ese energies are close to the promised gamma line of 89 Rb at 1 032 M eV The uncertainty equation [Equation 3 2 5 ] can be written for only the 1 st and 2 nd groups of 238 U : ( 7 1) As mentioned in the previous subchapter, the terms D 1 and D 2 were canceled out due to the same experimental geometry in Equation 7 1 The parameters with non negligible contributions are the time term T the ga mma ray summation term S and the delayed neutron yield term di Parametric Studies for Uncertainty Calculation In the following subsections the parameters with non negligible contributions to the uncertainty of the delayed neutron group yields are studi ed in detail. The objective is to optimize the experimental parameters in order to maximally reduce the uncertainty Irradiation, Cooling, and Acquisition Time, T In the uncertainty calculation [Equation 7 1 ] the most sensitive factor is the time ratio T n2 /T n1 By previous definition, the time dependent term T can be written as: ( 7 2 ) It strongly depends on the half lives of the delayed neutron precursors and the chosen irradiation, cooling and acquisit ion times. The decay constants are fixed nuclear data parameters. To reduce the total uncertainty, the irradiation, cooling and acquisition times must be optimized. Table 7 2 shows the delayed neutron precursor half lives and the inverse decay constants (1 / j ) in the eight group model [ 1 ] PAGE 113 113 T able 7 2 Half l ife and i nverse d ecay constant of each delayed neutron group. DN Group Half lives (sec) 1/ j (sec) 1 55.6 80 2 24.5 35.3 3 16.3 23.5 4 5.21 7.53 5 2.37 3.4 6 1.04 1.5 7 .424 0.6 8 .195 0.3 To maximize the delayed neutron count rate, the sample must be irradiated long enough so that the delayed precursors can saturate. Thus, the irradiation time should be long enough relative to half life of the longest lived group. For the current simulation an irradiation time of 180 s ec is chosen, which leads to a saturation of the precursors of the first delayed neutron group of 89 % Similarly, the acquisition time should be chosen long enough to capture as many delayed neutrons as possible. This is part icularly important for the longer lived groups, since later in the measurement process the ratio of delayed neutrons coming from the longer lived groups increases, reducing uncertainties. If irradiation and acquisition times are long enough, the correspond ing terms are close to 1 .0 in Eq uation 7 2 Th is equation can therefore be simplified to: ( 7 3 ) The uncertainty of the longest lived group can be reduced due to increasing the cooling time, since the contributions from other groups are cut off by their short half lives. However, a long cooling time also results in fewer delayed neutrons being counted which therefore increases PAGE 114 114 measurement uncertainty Thus, the o ptimal cooling time minimizes the contributions to the delayed neutron signal from the shorter lived groups without sacrificing the signal of the longest lived delayed neutron group. The relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U was assessed, based on MCNP simulations and the system configurations described above. The estimated fission rate from a depleted uranium sample was chosen to simulate the total counts (as a function of time) during the acquisition tim e (180 s ec ). In accordance with the optimization of the detection system described in Chapter 4 the detector efficiency was set to 20 % for the delayed neutron as well as the delayed gamma detection system. The nuclear data were taken from the JEFF 3.1 li brary [ 2 9 ]. The correlation between cooling time and the relative uncertainty of the longest lived group is shown in Fig ure 7 1 Figure 7 1. The relative uncertainty of the longest lived group abundance vs. the cooling time showing that 170 sec is the o ptimal cooling time to minimize uncertainty of the longest lived delayed neutron group. PAGE 115 115 Fig ure 7 1 shows that the optimal cooling time to minimize the uncertainty of the delayed neutron group yield of the longest lived group is 170 sec after the end of the irradiation. Nuclear Data Library Selection for Delayed Gamma Parameters b T and A Based on the criteria for a gamma line described in Chapter 3 and in combination with the optimized irradiation, cooling and acquisition times, the 1032 k eV gamma line of 89 Rb was chosen as the fission rate estimator. Its activity and uncertainty were cal culated, using E quation 3 1 1 This line is well suited due to the involved half lives in the decay chain being similar to the irradiation and acquisition times. The calculated total gamma activity of 89 Rb at a certain time depends on the nuclear cross sect ion library that is being used. Thus, the correlation between cooling time and the relative uncertainty of the longest lived group with different libraries was calculated [Fig ure 7 2 ] Figure 7 2. The relative uncertainty of the longest lived group of 23 8 U with different libraries (ENDF vs. JEFF) Both libraries agree that 170 sec is the optimal cooling time to minimize uncertainty of the longest lived delayed neutron group. PAGE 116 116 The difference is caused by the different decay data, fission yields and uncertai nties in the JEFF 3.1 [ 2 9 ] and ENDF/B VII.0 [ 9 ] libraries. However, the optimal cooling time, with regards to the relative uncertainty of the longest lived group, remains 170 sec With regards to the optimized cooling time, the calculated uncertainty of 89 Rb wa s 3.11 %. Gamma ray Attenuation and Detector Efficiency, and The relative uncertainty of detector efficiency ( ) and self attenuation ( ) for delayed gamma rays were estimated via MCNP simulations. The efficiency can be defined as the probabil ity of measurement for each quantum of radiation which interacts within the active volume of a radiation detector and two types of efficiency are generally referred as an absolute and intrinsic efficiency [2 7 ] : ( 7 4) ( 7 5) Efficiencies are also classified by the fraction of the energy deposited: full and partial energy deposition from the incident radiation. The energy deposition within a detector is depending on types of interactions involv ed with each radiation particle. Mostly, isotopes can be identified by their full energy deposition peak if the fraction of the full energy deposition is well known. If the fraction of the full energy deposition is unknown then all peaks on a detector shou ld be considered. Based on the fraction of the energy deposited, the detector efficiency can also be referred to as the total (all pulses) or full energy peak efficiency [2 7 ] T he full energy peak efficiency and uncertainty of the chosen gamma line at 1031 .92 keV from 89 Rb were simulated via MCNP. The gamma spectrum from 89 Rb is shown in Figure 7 3. PAGE 117 117 Figure 7 3. The expected gamma spectrum from 89 Rb via MCNP Figure 7 3 is drawn by the normalized count rate in number of interactions per a unit source. Therefore, the actual count rate can be estimated by multiplying the actual source intensity. Based on the MCNP results, t he uncertainty of the full energy peak of 89 Rb at 1031.92 keV resulted in 0.01 % at 1.02 to 1.04 MeV. Photons are attenuated through a sample based on sam pl e size, shape, density, and chemical com position. The attenuation rate and its uncertainty through a pelletized UO 2 sample were calculated by using mesh tall ies of MCNP. For this, two MCNP models were written. The first one was to fin d exact fission positions in the sample since fission rates are directly related to number density of the target precursor 89 Rb. In the second simulation, t he gamma energy distribution of 89 Rb in a sample, found in the first simulation, was considered as a source term A sample was meshed by ten coarse mesh PAGE 118 118 points in z direction (height) and four coarse mesh points in theta direction ( 90 degree) [Figure 7 4] The uncertainty of gamma self attenuation was then calculated and was less than 0. 01 % Figure 7 4. The geometry for attenuation and its uncertainty calculations via MCNP This simulation was used to estimate the self attenuation of gamma rays in the sample. In both cases for the chosen gamma lines the calculated uncertainties (about or less than 0. 01 %) would be negligible The efficiency of neutron detectors ( D j ) was also not considered in the uncertainty equation since they can be canceled out with the same experimental geometry. Total Number of Delayed Fission Neutrons d8 For the total number of delayed fission neutrons d8 many different sources of data are available [ 1 1 21 5 4 60 ] Interestingly, the values for the yields of delayed neutron emissions are very similar, but the values for their uncertainties differ significa ntly [Table 7 3 ]. PAGE 119 119 T able 7 3 Available references for delayed neutron yields from 238 U Reference (Year) Yield Relative Uncertainty (%) Tuttle (1979) 0.0439 2.28 Piksaikin et al. (2002) 0.0457 3.50 Fort at al. (2002) 0.0471 3.99 Keepin et al. (1965) 0.0412 4.13 James at al. (1990) 0.0406 4.91 JEFF 3.1 (2006) 0.0465 5.16 Blachot at al. (1990) 0.0416 5.77 Blachot (1997) 0.0431 5.80 JEFF 2.2 (2000) 0.0468 6.41 Brady et al. (1989) 0.0405 7.16 England et al. (1983) 0.0354 7.69 Rudstam (1982) 0.0324 8.33 Manevich et al. (1983) 0.0425 12.0 F or this study, Keepin data (1965) and Tuttle data (1 979 ) w ere chosen and compared since they have been widely used in the nuclear industry [ 6 1 ] and give the best agreement with integral reactor experimental data Furthermore, it is close to the recommended value from A. 5 9 ]. Based on the above analyses, values for the various parameters in the uncertainty equation were chosen for the calculation of the relative uncertainty of the long est lived delayed neutron group from fast fission of 238 U, and listed in Table 7 4 PAGE 120 120 T able 7 4 The chosen uncertainty values of parameters from the o ptimized measurements and simulation. These values were used to calculate the relative uncertainty of the longest lived delayed neutron group from fast fissions of 238 U. Parameters Value Reference T c 170 (sec) MCNP Results 2.28 (%) and 4.13 (%) Tuttle (79) and Keepin (65) Data 3.11 (%) JEFF 3.1 Nuclear Library Negligible, ~ 0.01 (%) MCNP Results Negligible, > 0.01 (%) MCNP Results Result: Uncertainty Calculation for Longest lived Delayed Neutron Group for 238 U The fabricated UO 2 sample s were initially irradiated by a D D generator and delayed neutrons and gamma rays ( 89 Rb at 1031.92 keV) were simultaneously measured. The measured photo peak of 89 Rb via the GINIE 2000 Gamma analysis software is shown in Figure 7 5. Figure 7 5. The measured ph oto peak of 89 Rb at 1032 keV, measured from a UO 2 sample irradiated by the neutron generator. PAGE 121 121 Times were chosen as 20 min, 170 sec, and 360 sec for irradiation, cooling, and acquisition, respectively. The neutron generator yield during the experiment was 1 .1x10 9 neutrons per sec at 115 kV. The chosen uncertainty values of relative parameters from the optimized measurements and simulation [Table 7 3] were applied for the uncertainty calculation of the longest lived delayed neutron group for fast fission of 2 38 U. The estimated uncertainty was initially about 11 %. More than 100 measurements had been performed but some measured data sets had shown unacceptable output arising from radiation induced electronics issues. Measurements were accepted or rejected based on the stability and lack of arcing in the D D generator. Arcing interrupts neutron production, so estimates of total output and precursor saturation in the sample become unreliable. In total, 43 data sets were obtained under these criteria and the esti mated uncertainty was about 9.8 %. Further measurement trials will reduce the uncertainty, as we are not yet near the asymptotic limit. The correlation of measurement trials between the number of experiments and the relative uncertainty of the longest live d delayed neutron group for fast fission of 238 U is shown in Table 7 5 T able 7 5 The correlation between the number of experiments and the relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U No. of Experiment 1 st Group Uncertainty with d Data (%) 1 st Group Uncertainty with d Data (%) 25 10.8 11.8 50 8.52 9.78 75 7.63 9.01 100 7.14 8.60 PAGE 122 122 Repeatedly taking other samples into the experimental system, the relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U can be reduced by a factor of two lower than the Spriggs and Campbell recommended data set (16 % [ 1 ]) For convenience, this uncertainty calculation was performed using MATLAB scripts shown in Appendix A The count rates of delayed neutrons and gamma rays, experimental time setups in sec, 238 U enrichment in %, and sample dimension s in cm are the input parameters to the code [Figure 7 6 ] Figure 7 6 The MATLAB input deck for uncertainty calculation The output contains fission rates and uncertainties via the delayed gamma technique, and the calculated the longest lived group abundance and its uncertainty via the combined technique In conclusion, the final improved value for the relative abundance and its uncertainty of the longest lived delayed neutron groups for 238 U was resulted in 0.0082 8 delayed neutron yield data (19 65 ) or alternatively 0.0075 7 .14 % wit h Tuttle data set (1979) in this study The experimental agreement with the Keepin parameters combined with the lower PAGE 123 123 assessed uncertainty values indicates that there is an unidentified systematic error in the original Tuttle data. Verification of the exp erimental data A larger sample volume will result in a greater quantity of delayed neutrons and gamma rays. Using the Mark I slug, the experimental result in the previous subchapter was verified. C onsidering its larger volume (104.144 cm 3 ), an irradiation time of 1 h ou r wa s chosen The cooling and acquisition times were 170 sec and 20 min respectively. Assuming all values of the relative parameters are the same as the previous calculation, the relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U was calculated to be 6. 6 %. Even though the Mark I is surrounded by an aluminum clad ding t he assumption for using exactly the same parameters was a good approximation since the thickness of the aluminum clad ding is only 0.096 cm [Table 6 4] To better understand the effects of the aluminum slug cladding on the attenuation of gamma rays, two MCNP models were simulated: one with cladding and one without. The simulation g eometry with clad ding and the expected gamma spectrum from 89 Rb were drawn in Figure 7 7 PAGE 124 124 Figure 7 7 The M CNP geometry with aluminum slug cladding and the expected gamma spectrum from 89 Rb Since Figure 7 3 and 7 7 were drawn by the normalized count rate, t wo spectra can be directly compared in order to know the material attenuation of the aluminum clad ding Comparing those two figures, only low energy gamma rays are significantly attenuated, and the full energy peak of 89 Rb at 1031.92 keV still shows good agreement between the two figures. This effectiveness from the material attenuation can be easily verified by the simple attenuation equation [ 4 ] : ( 7 7) w here I denotes the intensity of a gamma ray, i s the attenuation coefficient and t is a material thickness. The value of the attenuation coefficient for an aluminum cladding of 6.049x10 2 cm 2 /g was found [ 6 2 ] The density of aluminum is 2.7 g/cm 3 and the cladding thickness i s 0.096 cm. Inserting these values into Equation 7 7, the uncollide d fraction was calculated to be alm ost 98 %. This means the material attenuation of aluminum cladding can be neg lected PAGE 125 125 In the same manner as the previous attenuation calculation, the uncertainty of gamma self attenuation was also simulated and resulted in less than 0.01 %. The relative uncertainty of the longest lived delayed neutron group for fast fission of 238 U (6.6 %) in the Mark I natural uranium slug is lower than the measurement value in a pelletized UO 2 sample ( 8.60 % with delayed neutron yield data or alternatively 7.14 % with Tu ttle data set ) However, the relative parameters in the uncertainty calculation were assumed to be the same as the chosen values of relative parameters for a pelletized UO 2 sample. Additionally, the Mark I slug was manually handled since the experimental apparatus was optimized for only a pelletized sample. Therefore, the parametric optimization study and modification of the experimental apparatus is required f or the Mark I slug This verification study implies that another mostly sensitive factor in the uncertainty calculation is the sample size. With the parametric optimization study and modification of the experimenta l apparatus for the Mark I slug, better re sults in the uncertainty calculation can be expected. PAGE 126 126 CHAPTER 8 FUTURE WORK Future Work in Nuclear Data Measurement This study showed that the system designed, employing a D D neutron generator and the combined delayed neutron and gamma ray method, has co nsiderable potential to reduce the large uncertainties of the longest lived delayed neutron group abundances. Further steps will be to try to reduce the uncertainties of the shorter live d delayed neutron groups and for the different fissile materials. The limitations of the existing measurement methods lead to a search for improved ways of analyzing nuclear fuel. The details of a promising new technique using prompt neutrons and a new kind of detector are outlined in this chapter. Prompt Neutron Fission Rate Measurement w ith Gas Scintillators Delayed neutrons represent less than 1 % of the total neutron emission from fission. To measure delayed neutrons, the precursors must be saturated through an ~15 min irradiation before measurem ent. In this way we are blind to both the 99 % of neutrons that are promptly emitted, as well as the irradiation time. If there were a method to measure prompt neutrons during irradiation, we could improve the available signal by more than a factor of 1000. A 4 He fast neutron scintillation detector has recently been developed by Arktis Radiation Detectors. The 4 He scintillation detector is characterized by its low electron density, leading to excellent gamma rejection. This detector also has a fast resp onse time on the order of nanoseconds and most importantly, preserves some neutron energy information. [6 3 ]. The 4 He scintillation detector consists of a cylindrical high pressure vessel, filled with 150 bar of 4 He, and two photomultiplier tubes (PMTs) wit h associated electronics for recording data [6 3 ]. PAGE 127 127 Figure 8 1. The schematic drawing ( left, Arktis Radiation Detector Ltd.) and actual photo of a 4 He scintillation detector ( right, Photo: Author, Heejun Chung) Incoming fast fission neutrons elastically s catter with the 4 He fill gas, producing scintillation photons that are counted by PMTs at either end. A 4 He scintillation detector can be placed in a high intensity radiation area due to its excellent gamma rejection; fast fission neutrons can be directly measured without any moderation processes, unlike the general proportional neutron counters ( 3 He and BF 3 ). In a few previous studies, the detector has been used for fission rate measurements to determine the plutonium content in Mixed Oxide (MOX) reactor f uel [6 4 ]. However, the feasibility of active neutron interrogation of a fissile sample has been not proved, so a new, prompt neutron measurement technique, using a D D neutron generator for active interrogation, was developed to try and leverage the increa sed signal availability. The primary challenge is to differentiate between the prompt fission neutrons and the irradiation source. In a delayed neutron measurement, the time emission behavior of delayed PAGE 128 128 neutrons is used as a separation criterion. For prom pt neutrons, we can use energy separation between source and fission neutrons as provided by the elastic scatter signal in the 4 He detector. Neutron elastic scattering is typically notated by (n, n). This physical process in a 4 He scintillation detector can be explained as a neutron collides and transfers some energy to the 4 He nucleus and finally is reflected in a different direction. The collided (recoiling) 4 He nucleus gains the energy from the incident neutron depend ing on the angle of impact and th en increases speed. The recoiling 4 He nucleus loses energy through excitation or ionization in proportion to its initial energy, providing a (somewhat) proportional signal. To distinguish the fission neutron signal, an energy threshold method using these d etectors is proposed. The interrogation neutrons are mono energetic and the e nergy distribution of prompt fission neu trons is according to the Watt fission spectrum typically distributed from 0.1 MeV to 10 MeV [Figure 2 2] From basic kinetics, a n inciden t neutron can transfer up to 64 % of its energy to 4 He nucleus by elastic scattering, so the maximum energy deposited by a 2.45 MeV interrogation neutron will be 1.6 MeV Therefore, any energy deposit ion greater than 1.6 MeV in the detector must be from a fission neutron rather than an interrogating neutron [65 ] PAGE 129 129 Figure 8 2. Energy cut off for integrated counts of fission neutrons 1.6 MeV is the maximum energy that can be deposited by an incident 2.45 MeV neutron from the D D neutron generator. Prompt Neutron Fission Rate Measurement Technique Applying the energy threshold, the total counts from only prompt fission neutrons detected by a 4 He scintillation detector ( M P ) can be written as : (8 1) where P is t he proportionality factor, P is the detector efficiency, T is the acquisition time and V is the sample volume. The exponential term accounts for the attenuation in a sample, t is the macroscopic total cross section and d is the distance between a fissi on position and the end of a sample. S i is the normalized neutron source and can be defined as : (8 2) w here f i /F are the proportion of fission due to the fissioning isotopes i and P account s for prompt fission neutron yields PAGE 130 130 Since the fission proportion relates the amount of fissile material in a sample and its fission cross section, it can be written as: (8 3) Equation 8 1 can be simplified and approximated by: (8 4) The approximation of Equation 8 4 is reasonable if the sample size is relatively small since the macroscopic total cross section is defined as multiplying the number density of a fissile material by the microscopic total cross section in the unit of barn (1 barn is equal to 10 24 cm 2 ). If the fission yields of the isotopes are known the most sensitive parameter in Equation 8 4 is the normalized source term, depending on nuclear data of the prompt neutron yield per fission P since other parameters can be precisely measured. The prompt neutron yield per fission P can be calculated in Equation 2 8 if the total fission neutron yield is known. A few source s of da ta for the total fission neutron yield are available but mostly values and uncertainties are based on ENDF nuclear data. The current ENDF nuclear data for the total number of fission neutrons were evaluated by T. R. England and B. F. Rider, and shown in Table 8 1 [6 6 ]. PAGE 131 131 Table 8 1. The total fission neutron yields from major ra dioactive nuclides Nuclide Type Yield Relative Uncertainty (%) 235 U Thermal 2.42 4.96 235 U Fast 2.47 4.86 23 5 U High 4.38 5.02 23 8 U Fast 2.79 5.02 23 8 U High 4.42 4.98 23 9 Pu Thermal 2.88 4.86 23 9 Pu Fast 2.94 5.10 23 9 Pu High 4.90 5.10 Three different fission rate measurement techniques have been introduced so far, and can be rewritten in terms of fission rate. Currently, the new proposed study for fission rate estimates from the same uranium sample via three techniques is ongoing, a bet ter estimation of fission rate or an accurate assessment of a fissile material can be obtained. PAGE 132 132 CHAPTER 9 CONCLUSIONS The uncertainties of the longest lived delayed neutron groups for important fissile isotopes such as 235 U, 238 U, 239 Pu or 232 Th are large. These high uncertainties are caused by systematic uncertainties in measurements and mathematical instabilities in the par ameters fitting methods. Prior experiments and studies have laid the groundwork for a new measurement approach of the delayed neutron group yields. This is achieved through the combination of the widely used delayed gamma technique and a recently developed delayed neutron technique to measure fission rates in nuclear fuel. However, the combined method for data measurements had not been previously implemented The work presents the design, optimization and measurement results from a newly built system for simultaneous measurement of the delayed neutron and the delayed gamma signals emitted by an irradia ted sample of fissile material. Design studies were made with the objective to maximize the delayed neutron and the delayed gamma signals in the detectors. Based on the design studies, the actual system was built, tested, and compared with the simulation results. The most important result associat ed with the originating purpose the improvement of t he relative uncertainties of the longest lived delayed neutron groups was the newly developed D D neutron generator (DD 109X) in collaboration with Adelphi Technology Inc. Th is neutron generator uses an optimized plasma source and a unique target and chamber design, allowing for increased neutron production and for a higher aspect ratio for irradiation samples. With th e chamber design, samples may be placed extremely close to the neutron target, thereby drastically increasing the neutron flux incident on the sample. University o f Florida and Adelphi Technology Inc. have received the 2013 R&D 100 award for their developm ent of this DD 109X model. PAGE 133 133 Various parametric studies have been conducted to find the optimal combination of experimental and calculative settings to reduce the uncertainty of the first delayed neutron group as much as possible. Irradiation, cooling, and a cquisition times have been optimized. The nuclear data library in general (ENDF/B and JEFF were tested) does n o t have a large effect with the optimized time setups However, the data set that is chosen for the total number of delayed neutrons d8 can c hange the results considerably. The data from Keepin (1965) and Tuttle (1 979 ) w ere selected since they have been widely used in the nuclear industry T he relative value of the longest lived delayed neutron group for fast fission of 238 U using the previousl y used values for relative parameters in the uncertainty equation taken from the optimized measurement and simulation, has been reevaluated and shown consistent with the Spriggs assessed value of 0.008, and the uncertainty has been reduced in this new evaluation from 16 % to 8.6 %. S imilar improvements of the uncertainty of the first delayed neutron group are expected for the other relevant fissile isotopes. A second reevaluation using data obtained from Tuttle resulted in 0.0075 7.14 % which is inconsistent with the new experimental measurement, indicating an unidentified systematic error in the Tuttle measurements Finally a prompt neutron fission rate measurement techniqu e was proposed for fast neut ron interrogation using a D D neutron generator with 4 He gas scintillation fast neutron detectors, newly developed by Arktis Radiation Detectors. PAGE 134 134 APPENDIX A COMPUTER CODE INPUT FILES This appendix contains all of the MCNP and MATLAB input files used to calculate the fission rate s detector efficiency, and relative uncertaint ies PAGE 135 135 MCNP Input File for Fission Rates Neutron Irradiation via Generator (UO2 3.5%) C Cell Card 1 1 11.34 1 2 3 4 5 6 7 8 9 10 11 IMP:N=1 $Lead 2 1 11.34 8 IMP:N=1 $Lead 3 1 11.34 9 IMP:N=1 $Lead 4 0 7 11 IMP:N=1 $Void 5 0 7 10 IMP:N=1 $Void 6 2 10.46 11 IMP:N=1 $UO2 7 0 1:2: 3:4: 5:6 IMP:N=0 $Outside C Surface Card 1 PZ 15 2 PZ 15 3 PY 15 4 PY 15 5 PX 15 6 PX 15 7 RCC 0 0 0.1 0 0 3.9 1 8 RCC 0 0 4 0 0 9 1 9 RCC 0 0 13 0 0 2 2 10 RCC 0 15 0 0 16.5 0 2 11 RCC 0 0 2 0 0 1 0.41 C Materia l Card C 3.5 w/o Converted to a/o M1 82000 1 $Lead M2 8016 2 $UO2 92238 0.964566 92235 0.0354323 C Mode Card MODE N C Source Definition SDEF par=1 POS=0 0 0 ERG=2.45 C Tally Card M235 92235 1.0 M238 92238 1.0 C FC4 Flux in the UO2 F4: N 6 C FC14 Total Fission reaction rates in the UO2 F14: N 6 FM14 ( 1 2 6) C FC24 Fission reaction rates in U 235 F24: N 6 FM24 (8.26797E 04 235 6) C FC34 Fission reaction rate s in U 238 F34: N 6 C PAGE 136 136 FM34 (2.25077E 02 238 6) E0 0 0.0025E 6 1E 6 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 2 3 4 5 6 7 8 9 10 C CutOff Card NPS 1E8 PAGE 137 137 MCNP Input File for Efficiency of Detector Bundle New Design for Detector Bundle C Detector Angles: 15, 40, 65, 90, 115, 140, 165 C Cell Card 1 1 0.92 1 2 ( 3: 4) 12 13 14 15 16 17 18 IMP:N=1 $Poly 2 2 0.00054 5 IMP:N=1 $He3 3 2 0.00054 6 IMP:N=1 $He3 4 2 0.00054 7 IMP:N=1 $He3 5 2 0.00054 8 IMP:N=1 $He3 6 2 0.00054 9 IMP:N=1 $He3 7 2 0.00054 10 IMP:N=1 $He3 8 2 0.00054 11 IMP:N=1 $He3 9 3 2.70 5 12 I MP:N=1 $Al 10 3 2.70 6 13 IMP:N=1 $Al 11 3 2.70 7 14 IMP:N=1 $Al 12 3 2.70 8 15 IMP:N=1 $Al 13 3 2.70 9 16 IMP:N=1 $Al 14 3 2.70 10 17 IMP:N=1 $Al 15 3 2.70 11 18 IMP:N=1 $Al 16 3 2.70 19 20 I MP:N=1 $Al Case (out ) 17 0 20 21 22 IMP:N=1 $Void 18 4 1.848 21 IMP:N=1 $Be Window 19 3 2.7 22 23 IMP:N=1 $Al Case (in) 20 5 5.323 24 25 IMP:N=1 $Ge 21 0 23 24 IMP:N=1 $Void 22 0 25 IMP:N=1 $Void 23 0 ( 1:2:3) ( 1:2:4) 19 26 IMP:N=1 $Void 24 0 26 IMP:N=0 $Outside C Surface Card C POLY 1 RCC 0 0 1 0 0 21.32 1 2 RCC 0 0 1 0 0 21.32 15.54 3 P 0.188654 1 0 0.18865 4 4 P 0.188654 1 0 0.188654 C Detectors (Effective Length) 5 RCC 7.022 1.882 0 0 0 20.32 1.181 6 RCC 5.569 4.673 0 0 0 20.32 1.181 7 RCC 3.072 6.589 0 0 0 20.32 1.181 8 RCC 0 7.27 0 0 0 20.32 1.181 9 RCC 3.072 6.589 0 0 0 20.32 1.181 10 RCC 5.569 4.673 0 0 0 20.32 1.181 11 RCC 7.022 1.882 0 0 0 20.32 1.181 C Detector Cases 12 RCC 7.022 1.882 0 0 0 20.32 1.27 13 RCC 5.569 4.673 0 0 0 20.32 1.27 14 RCC 3.072 6.589 0 0 0 20.32 1.27 15 RCC 0 7.27 0 0 0 20.32 1.27 16 RCC 3.072 6.589 0 0 0 20.32 1.27 17 RCC 5.569 4.673 0 0 0 20.32 1.27 18 RCC 7.022 1.882 0 0 0 20.32 1.27 C HPGe 19 RCC 0 1 10.16 0 13.4 0 3.5 $Ortec GEM 70 (Poptop) PAGE 138 138 20 RCC 0 1.05 10.16 0 13.3 0 3.4 21 RCC 0 1.45 10.16 0 0.005 0 3.326 $Be Window 22 RCC 0 1.455 10.16 0 10.045 0 3.326 $Al Can (in) 23 RCC 0 1.455 10.16 0 9.725 0 3.25 $Al Can (in) 24 RCC 0 1.455 10.16 0 7 0 3.25 $Ge 25 RCC 0 2.2 95 10.16 0 6.16 0 0.46 $Hole in Ge 26 SO 100 C Material Card M1 1001 2 6000 1 $Poly M2 2003 1 $He3 M3 13027 1 $AL (2.70 g/cc) M4 4009 1 $Be M5 32070 0.2123 32072 0.2766 32073 0.0773 32074 0.3594 32076 0.0744 $Ge C Mode Card MODE N C Source Definition SDEF par=1 POS=0 0 10.16 ERG=d1 SI1 L 0.25 0.56 0.43 0.62 0.42 SP1 D 0.00025 0.00166 0.00213 0.00241 0.00085 C Tally Card FC4 Flux in the He3 F4: N 2 3 4 5 6 7 8 T C24 Count rates in cubic cm in the He3 F24: N 2 3 4 5 6 7 8 T FM24 ( 1 2 2) C C utOff Card NPS 1E8 PAGE 139 139 MATLAB Input File for Uncertainty Calculation clear all clc % Notice: This program was written based on: % 1. Rb 89 at 1032 keV % JEFF Nuclear Data %% Input Prompt prompt={ 'Enter Delayed gamma Counts:' 'Enter Delayed Neutron Counts:' 'Irradiation Time [in sec]:' 'Cooling Time [in sec]:' 'Acquisition Time [in sec]:' 'Fractional Fission Rate [No unit]:' 'Sample Radius [in cm]:' 'Sample Height [in cm]:' }; % Create all your text fields with the questions specified by the variable prompt. title= 'Fission Rate Estimator' ; % The main title of your input dialog interface. answer=inputdlg(prompt,title); Mr = str2num(answer{1}); Mn = str2num(answer{2}); TS1 = str2num(answer{3}); TS2 = str2num(answer{4}); TS3 = str2num(answer{5}); FFR = str2num(answer{6}); SR = str2num(answer{7}); SH = str2num(answer{8}); %% Estimated Fission Rate via the Delayed Gamma Technique % EAG = Efficiency and Attenuation for Gamma rays EAG = 0.002; % IG = Intensity of Gamma rays IG = 0.636; % CYKr = Cumulative Yield of Parent, Kr89 CYKr = 0.03008; % BrKr = Braching Ratio of Parent, Kr89 BRKr = 1; % HFKr = Halflife of Parent, Kr89 [in sec] HFKr= 189; % RKr = L amda of Kr89 LKr = log(2)./HFKr; % IYRb = Individual Yield of Rb89 IYRb = 0.00026848; % CYRb = Cumulative Yield of Rb89 CYRb = 0.030349; % HFRb = Halflife of Rb89 [in sec] HFRb = 924; % RKr = Lamda of Rb89 LRb = log(2)./HFRb; % TKr = Time accounts for the build up and decay of Kr89 TKr = 1./LKr.*(1 exp( LKr.*TS1)).*exp( LKr.*TS2).*(1 exp( LKr.*TS3)); % TRb = Time accounts for the build up and decay of Rb89 TRb = 1./LRb.*(1 exp( LRb.*TS1)).*exp( LRb.*TS2).*(1 exp( LRb.*TS3)); PAGE 140 140 % AKr = Activity of Kr, corresponding to TKr AKr = (BRKr.*LRb.*CYKr)./(LRb LKr); % AKr = Activity of Rb, corresponding to TRb ARb = IYRb+(BRKr.*LKr.*CYRb)./(LKr LRb); % CF = Total Activity CF = ARb.*TRb+AKr.*TKr; % V = Sample Volume V = pi.*SR^2.*SH; % FR = Estimated Fission Rate via the Delayed Gamma Technique FR= (Mr./(V.*CF.*EAG.*IG)) %% Evaluate a New Relative Abundance Ddata via the Combined Method % A2 = Relative Abundance of 2nd Group (Spriggs) A2 = 0.104; % D = The correctional Factor for the Solid Angle and Attenuation D=0.152; % vd = The Total Delayed Neutron Yield (Keepin, 65) vd = 0.0412; % vd2 = The Total Delayed Neutron Yield (Tuttle, 79) vd2 = 0.0439; % LG1 = Lamda of Group 1 LG1 = log(2)/55.6; % LG2 = Lamda of Group 2 LG2 = log(2)/24.5; % TG1 and TG2 = Time accounts for Delayed Neutron Group 1 and 2 TG1=1./LG1.*(1 exp( LG1.*TS1)).*exp( LG1.*TS2).*(1 exp( LG1.*TS3)); TG2=1./LG2.*(1 exp( LG2.*TS1)).*exp( LG2.*TS2).*(1 exp( LG2.*TS3)); A1 = (Mn FR.*vd. *D.*TG2.*A2.*V)/(F.*vd.*D.*TG1.*V) % Keepin A1_1 = (Mn FR.*vd2.*D.*TG2.*A2.*V)/(F.*vd2.*D.*TG1.*V) % Tuttle %% Uncertainty Evaluation for the 1st Group (A1) % RU2 = Relative Uncertain of 2nd Group % Spriggs RU2 = 0.02; % Relative Uncertainty on the Total Counts RUMn = sqrt(Mn)/(Mn); RUMr = sqrt(Mr)./(Mr); % Relative Uncertainty on the Gamma Activity (JEFF) RUA = 0.0313; % Relative Uncertainty on Keepin (RUKvd) and Tuttle (RUTvd) RUKvd = 0.0413; RUTvd = 0.0228; % Uncertainty for 1st group (A1) with Keepin RUA1_sq = (1+A2/A1.*TS2/TS1)^2*(RUMn.^2+RUA.^2+RUMr.^2+RUKvd.^2)+(A2/A1.*TS2/TS1)^2*A2.^2; RUA1 = sqrt(RUA1_sq) PAGE 141 141 % Uncertainty for 1st group (A1) with Keepin RUA1_sq_1 = (1+A2/A1_1.*TS2/TS1)^2*(RUMn.^2+RUA.^2+R UMr.^2+RUTvd.^2)+(A2/A1_1.*TS2/TS1)^2*A2.^2; RUA1_1 = sqrt(RUA1_sq_1) PAGE 142 142 APPENDIX B MEASURED RADIATION D OSES This appendix contains results of radiation survey of a neutron generator in nuclear science building. The D D neutron generator was operated at 30 mA beam current and 100 kV potential. Neutron production yield was 2.0x10 9 neutrons/sec. 1) Neutron Survey Instrument: Eberline neutron REM counter model PNR 4 (serial number 2750), Ludlum neutron survey meter Model 12 4 (serial number 38389) 2) X ray and Gamma ray Survey Instrument: Bieron microRem survey meter (serial number B791W) 3) Survey Location: PAGE 143 143 PAGE 144 144 4) Survey Results: Location Ne utron Dose (mrem/hr) X ray/Gamma Dose First Floor 1. Control Room* 0.4 1600 2. Hallway 0.4 50 3. Shop* 1 200 4. Drop Tower < 0.2 20 5. End of Shielded Maze* 1.25 420 6. Hallway 0.5 70 7. Office < 0.2 3 8. General Area 0.4 75 9. General Area 0.6 160 10. General Area 0.4 75 11. General Area < 0.2 20 12. Outdoors < 0.2 30 Second Floor 1. Computer Lab < 0.2 20 2. Computer Lab < 0.2 25 3. Computer Lab < 0.2 25 4. Office < 0.2 20 5. Office < 0.2 25 6. Hallway < 0.2 10 7. Hallway < 0.2 10 indicates the radiation restricted area. 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Rider, Evaluation and Compilation of Fission Product Yields, Los Alamos National Laboratory R eport LA UR 94 3106 1994 PAGE 150 150 BIOGRAPHICAL SKETCH Heejun Chung was born in Seoul, Republic of Korea (S. Korea) on April 4 197 7 He received the Bachelor and Master of Engineering degrees in Nuclear Engineering from the Kyunghee University in S. Korea in 2004 and 2006 respectively, and enrolled in Ph. D. Program of the Nuclear and Radiological Engi neering at the University of Florida in August of 2009. While pursuing his Ph. D. degree, He has served as a research assistant for developing a new micro pocket sized fission detector designing a neutron generator laboratory and improving high uncertain ties on the delayed neutron nuclear data He has also served as a teaching assistant for reactor analysis and radiation detection classes. With his achievements at the University of Florida he was awarded the R&D 100 Award (the Oscars of Innovation) with his supervisor, Dr. Kelly A. Jordan, in 2013 He is scheduled to graduate with a Doctor of Philosophy degree in May 20 1 4 