Energy Distribution of Thermal in Uranium, Heavy

Energy Distribution of Thermal in Uranium, Heavy

NYO - 10205 MITNE -17 MEASUREMENTS OF THE SPATIAL AND ENERGY DISTRIBUTION OF THERMAL NEUTRONS IN URANIUM, HEAVY WATER LATTICES by P.S. Brown, T.J. Thompson, I. Kaplan, A.E. Prof io Contract AT (30-1) 2344 U.S. Atomic Energy Commission August 20, 1962 -4 Department of Nuclear Engineering 4h~~ Massachusetts Institute of Technology Cambridge, Massachusetts MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF NUCLEAR ENGINEERING Cambridge 39, Massachusetts MEASUREMENTS OF THE SPATIAL AND ENERGY DISTRIBUTION OF THERMAL NEUTRONS IN URANIUM, HEAVY WATER LATTICES by P. S. Brown, T. J. Thompson, I. Kaplan, A. E. Profio August 20, 1962 NYO-10205 AEC Research and Development Report UC-34 Physics (TID-4500, 17th Edition) Contract AT(30-1)2344 U. S. Atomic Energy Commission The contents of this report have been submitted by Mr. Paul S. Brown to the Massachusetts Institute of Technology in partial fulfillment of the require- ments for the degree of Doctor of Philosophy. ABSTRACT Intracell activity distributions were measured in three natural uranium, heavy water lattices of 1. 010 inch diameter, aluminum clad rods on triangular spacings of 4. 5 inches, 5. 0 inches, and 5. 75 inches, respectively, and in a uranium, heavy water lattice of 0. 25 inch 235 diameter, 1. 03% U 2 , aluminum-clad rods on a triangular spacing of 1. 25 inches. The distributions were measured with bare and cadmium- covered foils of gold, lutetium, and europium. The gold was used as a 1/v absorber to measure the thermal neutron density distribution. Because the activation cross sections of lutetium and europium depart considerably from 1/v behavior, their activation depends strongly on the thermal neutron energy spectrum. Hence, they were used to make integral measurements of the change in the neutron energy spectrum with position in the lattice cell. A method was developed for treating the partial absorption, by cadmium covers, of neutrons at the 0. 46 ev europium resonance, and it was found possible to correct the europium activations to energy cutoffs just above and just below the resonance. The measured activity distributions were compared with those computed with the THERMOS code. In the natural uranium lattices, THERMOS gave excellent agreement with the measured gold activity distributions and very good agreement with the lutetium and europium distributions, indicating that THERMOS gives a very good estimate of the spatial and energy distribution of thermal neutrons in these lattices. In the enriched lattice, THERMOS gave a large overestimate of the activity dip in the fuel for all three detectors. The discrepancy was attributed to a breakdown in the Wigner-Seitz cylindrical cell approxi- mation at small cell radii. However, the measured ratios of lutetium and europium activity to gold activity were in good agreement with the THERMOS values, indicating that THERMOS still gave a good estimate of the degree of spectral hardening. Neutron temperature calculations were made from the data by using Westcott effective cross sections. The temperature changes so calculated agreed well with those predicted by THERMOS. Disadvantage factors calculated by the Amouyal-Benoist-Horowitz (ABH) method were in excellent agreement with the measured values in the natural uranium lattices. The agreement was not as good in the enriched lattice because of an expected breakdown in the ABH method at small cell radii. Values of the thermal utilization obtained from experiment, from THERMOS, and with the ABH method were in excel- lent agreement for all the lattices studied. Radial and axial buckling measurements made with lutetium were in excellent agreement with similar measurements made with gold, indicating that the thermal neutron spectrum was uniform throughout the lattice tank. Measurements of intracell gold activity distributions made in off-center cells differed only slightly from those made in the central cell of the lattice, indicating that the radial flux distribution was almost completely separable into a macroscopic J and a microscopic cell distribution. ACKNOWLEDGMENTS The success of the M. I. T. Lattice Project has been due to the contributions of a number of individuals. The results of this particular report are primarily due to the work of its principal author, Paul Sherman Brown, who has submitted substantially this same report in partial fulfillment for the requirements of the Ph. D. degree at M. I. T. He has been assisted by other students working on the project as well as by those mentioned specifically below. Over-all direction of the project and its research is shared by Professors I. Kaplan, T. J. Thompson, and Mr. A. E. Profio. Mr. Joseph Barch has been of invaluable assistance in the setting up of experiments and in the design and construction of the facility. Miss Barbara Kelley has been of assistance in the preparation of foils and in many other ways. Staffs of the M. I. T. Reactor, the Reactor Machine Shop, the Reactor Electronics Shop, and the Radiation Protection Office have provided much assistance and advice during the experimental portion of this work. The secretarial staff of the M. I. T. Reactor and Mrs. M. Bosco have given valuable assistance in the typing of this report. The authors are indebted to Dr. Henry Honeck, of the Brookhaven National Laboratory, for providing copies of the THERMOS code and considerable advice on its use. Mr. R. Simms has given much assistance in carrying out the THERMOS computations, which were done at the M. I. T. Computation Center. All of these individuals and groups were essential to the com- pletion of this work. TABLE OF CONTENTS Chapter I. Introduction 1 1. 1 The M. I. T. Heavy Water Lattice Research Program 1 1. 2 Thermal Neutron Behavior in Lattice Cells 1 1. 3 Various Experimental Methods for Measuring Thermal Capture 2 1. 4 Theoretical Methods for Determining Thermal Capture 4 1. 5 Experimental and Theoretical Methods Used at M. I. T. 6 1.6 Contents of the Report 6 Chapter II. Experimental Methods 8 2. 1 The M. I. T. Lattice Facility 8 2.2 The Experimental Program 8 2. 3 Methods of Measuring the Microscopic Distributions 12 2. 3. 1 Foil Fabrication Procedures 12 2.3.2 Foil Holders 14 2. 3.3 Flux Perturbations 19 2.3.4 Counting Methods 20 2. 3.5 Experimental Procedure 23 2. 3.6 Data Processing Procedure 24 2. 4 Separability Experiments 25 2. 5 Transmission Experiment 25 Chapter III. Theoretical and Analytical Methods 26 3. 1 Introduction 26 3. 2 The THERMOS Code 26 3. 3 The Normalization of Theory and Experiment 28 3. 4 Disadvantage Factors 30 3. 5 Temperature Calculations: The Westcott Method 32 3. 6 The Amouyal-Benoist-Horowitz Method 38 Chapter IV. Results 39 4.1 Introduction 39 4. 2 Natural Uranium Lattices 39 4. 2. 1 Gold Activity Distributions 39 4. 2. 2 Lutetium Activity Distributions 49 4. 2. 3 Europium Activity Distributions 62 TABLE OF CONTENTS (Continued) Chapter IV. (Continued) 4. 2. 4 Dependence of Measurements on Position in the Lattice Tank 81 4. 2. 5 Neutron Temperature Calculations 88 4. 2. 6 Comparison of the Amouyal-Benoist-Horowitz Method and THERMOS 97 4. 2. 7 Comparison with Other Results 99 4. 2. 8 Natural Uranium Lattices: Tabulation of Some Useful Parameters 100 4. 3 The Lattice of 0. 25-inch Diameter, Slightly Enriched Uranium Rods with a Spacing of 1. 25 Inches 108 4. 3. 1 Gold Activity Distributions 108 4. 3. 2 Lutetium Activity Distributions 115 4. 3. 3 Europium Activity Distributions 119 4. 3. 4 Disagreement between Theory and Experiment - the Cylindrical Cell Effect 119 4. 3. 5 Amouyal-Benoist-Horowitz Calculations - 1. 25-inch Lattice 130 4. 3. 6 Temperature Calculations - 1. 25-inch Lattice 132 4.3. 7 The 1. 25-inch Lattice: Tabulation of Some Useful Parameters 133 Chapter V. Summary, Conclusions, and Recommendations 138 5. 1 Neutron Density Distributions 138 5.2 Spectral Distributions 139 5. 3 Disadvantage Factors and Thermal Utilization 140 5. 4 Space and Energy Separability 141 5. 5 Effects of Anisotropic Scattering and of Varying the Scattering Kernel 142 5. 6 Experimental Perturbations 142 Appendix Appendix A. Foil Holder Perturbation Experiment 143 Appendix B. Flux Depression by Cadmium 147 Appendix C. Foil Perturbations 151 Appendix D. Lutetium and Europium Foil Fabrication 153 Appendix E. Cadmium Ratios and Resonance Integrals as a Function of Gold Thickness 154 TABLE OF CONTENTS (Continued) Appendix (Continued) Appendix F. A Transmission Method for Measuring Thermal Neutron Spectra 160 F. 1 Theory 160 F. 2 Experimental Method 161 F. 2. 1 Geometric View Factor 163 F. 2. 2 Effective Path Length of Neutrons through the Stack 163 F. 2. 3 Detector Efficiency 165 F. 2. 4 Buildup Factor Due to Scattering of Neutrons 165 F. 3 Gold Transmission Experiment 166 F. 4 Elimination of the Buildup Effect 169 F. 5 Recommendations for Future Work 174 Appendix G. THERMOS Input Data 176 Appendix H. Transmission of Neutrons through Cadmium 178 Appendix I. Nomenclature 181 Appendix J. References 185 Appendi x K. Supplementary Literature Survey 189 LIST OF FIGURES 2. 1 Vertical Section of the Subcritical Assembly 9 2. 2 Plan View of the Subcritical Assembly 10 Lu17 6 2. 3 Activation Cross Section of il Eu 15 2. 4 Activation Cross Section of 13 2. 5 Top View of Foil Holder Arrangement in the Natural Uranium Lattices 15 2. 6 Side View of Foil Holder Arrangement in the Natural Uranium Lattices 16 2. 7 Side View of Foil Holder Arrangement in the 1. 25-in. Lattice 17 2. 8 Block Diagram of Gamma Counting System 21 2. 9 Block Diagram of Beta Counting System 22 4. 1 Gold Activity Distribution No. 1, 4. 5-in. Lattice 40 4. 2 Gold Activity Distribution No.

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