GiENERALAmMIC DIVISION OF GENERAL DYNAMICS JOHN JAY I-IOPKINS LABORATORY FOR PURE AND APPLIED SCIENCE P.O. BOX 608.S AN OlEGO 12. CALIFORNIA GA -3542 PHYSICS INTEGRAL NEUTRON THERMALIZATION .ANNUAL SUMMARY REPORT October 1, 1961, through September 30, 1962 Contract AT(04-3) -167 Project Agreement No. 2 U. S. Atomic Energy Commission Work done by: Report written by: J. R. Beyster J. Russell J. R. Beyster J. R. Brown G. D. Trimble J. R. Brown H. C. Honeck F. Wikner H. C. Honeck G. K. Houghton J. C. Young D. H. Houston D. H. Houston J. U. Koppel G. D. Joanou W. M. Lopez J. U. Koppel Y. D. Naliboff W. M. Lopez D. E. Parks I Y. D. Naliboff G. D. Trimble M. S. Nelkin F. Wikner D. E. Parks J. C. Young This document is Authorizing official fl6-/25*/2086 II DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. CONTENTS I. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . 1 I1 . RESEARCH EQUIPMENT . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 . 1. Linear Accelerator . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 . 2 . Pressure 'Vessel . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2 . 3 . Cockcroft-Walton Neutron Generator . . . . . . . . . . . . . . 10 . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4. Instrumentation 14 . . . . . . . . . 2 4 1 RCL 256-channel Analyzer, Model 20609 14 2.4. 2 . RCL 256-channel Analyzer, Model 20620 . . . . . . 14 . . . . 2.4. 3 TMC 1024-channel Analyzer, Model CN-1024 14 . . . . . . . . . . . . . . . . . . . . . EXPERIMENTAL TE CHNIQUE S 16 . . . . . . . . . . . . . . . . . . . . . . . 3 1 Experimental Arrangement 16 . . 3 2 Sensitivity Functions of the 16- and 50-meter Detector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Banks 18 . . . . . . . . . . . 3 2 1 Derivation of the Sensitivity Function 18 3 . 3 . Effect of Scatterer on Neutron Spectra . . . . . . . . . . . . . 2 5 3 . 4 . Effect of Location of Pulsed Neutron Source on Spectra . . 27 3 . 5 . Effect of Precollimator Opening and Location on . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Spectra 27 3 . 6 . Effect of Linac Intensity on Spectra . . . . . . . . . . . . . . .3 3 IV. SPATIALLY DEPENDENT. FINITE-MEDIUM SPECTRA IN . . . . . . . . . . . . . . . . . . . . . NONMULTIPLYING SYSTEMS 37 4 . 1. Four-inch- thick Slab . . . . . . . . . . . . . . . . . . . . . . . . . 38 4 . 2 . Two-inch-thick Slab . . . . . . . . . . . . . . . . . . . . . . . . . 47 4 . 3 . Finite-medium (Nonmultiplying) Analysis . . . . . . . . . . . 5 1 . V SPATIALLY DEPENDENT, FINITE-MEDIUM SPECTRA IN . . . . . . . . . . . . . . . . . . . . . . . . MULTIPLYING SYSTEMS 54 5 . 1. Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5. 1. 1. Flux-distribution Measurements . . . . . . . . . . . . 57 5 . 1. 2 . Measurement of Decay Constants. . . . . . . . . . . 5 7 5 . 1. 3 . Spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 5 . 2 . Analysis of Experiments . . . . . . . . . . . . . . . . . . . . . . 63 5 . 2 . 1. Decay Constant of Multiplying Assemblies . . . . . 63 5 . 2 . 2 . Numerical Calculation . . . . . . . . . . . . . . . . . . 7 2 d . . . . . . . . . . . . . . . . . . . . . . . . VI INFINITE-MEDIUM STUDIES 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1. Samarium 73 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. Gadolinium 84 6 . 3 . Polyethylene . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 i . ii . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4. D20 89 6 . 5 . Thermal Spectra in Lithium Hydride . . . . . . . . . . . . . 102 VI1. SCATTERING LAW . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1 Introduction 108 7.2. Graphite . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3 Zirconium Hydride 117 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.4. Water 127 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 5 Lithium Hydride 127 . . . . . . . . . . . . . . . . . . . . . . VI11 NONSTATIONARY PROBLEMS 130 . . . . . . . . . . . . . 8 1 Time-dependent Thermalization Spectra 130 8 . 2 . Diffusion Parameters . . . . . . . . . . . . . . . . . . . . . . . 138 8 . 3 . Eigenvalue Problem Derived from the BoltzmannEqua- tion for Neutrons Approaching Thermal Equilibrium . 138 IX . CODES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.1. THERMOS 140 9 . 1. 1. The Integral Transport Equation . . . . . . . . . . . 141 9 . 1. 2 . Approximate Method for a DiagonalCsl(E’+E) . 143 9 . 1 . 3 . Slowing-down Source (Anisotropic Approximation) . . . . . . . . . . . . . . . . . . . . . 145 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.2. DSN 147 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.3. CORC 148 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.4. ECTOPLASM 150 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9.5. SPAN 151 9 . 5 . 1. Westcott Parameters . . . . . . . . . . . . . . . . . . 152 9 . 5 . 2 . Low-energy Flux . . . . . . . . . . . . . . . . . . . . . 153 9 . 5 . 3 . Smoothing of the Flux . . . . . . . . . . . . . . . . . . 153 9 . 5.4. Integration Table . . . . . . . . . . . . . . . . . . . . . 154 9 . 5 . 5 . Least-squares Fitting . . . . . . . . . . . . . . . . . . 154 9 . 5 . 6 . Quantities Computed by SPAN . . . . . . . . . . . . 155 9 . 5 . 7 . Inclusion in ECTOPLASM . . . . . . . . . . . . . . . 156 . X THE SPATIAL DEPENDENCE OF THE THERMAL-NEUTRON SPECTRA ACROSS A TEMPERATURE AND ABSORPTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . DISCONTINUITY 158 . XI SPECTRA PRODUCED BY A SOURCE WITHOUT A HIGH- . . . . . . . . . . . . . . . . . . . . . . . . ENERGYCOMPONENT 170 Appendixes: 1 . I BUILD-UP OF MODAL AMPLITUDES IN PULSED SUB- 4 . . . . . . . . . . . . . . . . . . . . . . . CRITICAL ASSEMBLY 175 6 I1 . MILNE PROBLEM FOR A MULTIPLYING SYSTEM . . . . . 177 . 111 COMPARISON OF DIFFUSION PARAMETERS OBTAINED FOR WATER BY THE PULSED AND THE POISONING . . . . . . . . . . . . . . . . . . . . . . . . . . . . TECHNIQUES 183 __~~ ~ ~ . . . . . . . ._ ........ . . . . . . _ .... I. INTRODUCTION In September, 1961, a report was issued which contained all results obtained in the Integral Neutron Thermalization program up to that time, In that report (GA-2544),,t he general methods of attack- -experimental, analytical, and theoretical- -were explained. Experimental results and the significance of these results for the common moderators--light water, graphite, polyethylene, zirconium hydride, etc. --were discussed. In general, the work descr:tbed in the present report includes only that which was undertaken during the contract year from October 1, 1961, through September 30, 1962. It is presumed that many of the experimental and analytical procedures are well known by now. Therefore, only new tech- niques and improvements made in the old procedures are discussed here (GA- 2544 contains the background for these discussions). Facility improve- ments and major-equipment performance during the past year are also described for both General Atomic and Atomic Energy Commission equip- ment used in the present research program. In addition to summarizing the work done on thermalization at General Atomic, the present document describes much of the current work at other laboratories for purposes of comparison and discussion of specific problems. In many cases, the inclusion of work from other laboratories has stemmed from a cooperative effort to solve particularly difficult problems which have arisen in the . pr e s ent inve s tigations The motivation for work in neutron thermalization is quite strong at this time. Reactor technology has been progressing in the direction of higher power density and more heavily loaded systems. Detailed knowledge of neutronic behavior has khus become increasingly important in predictions of reactor lifetime (burnup), temperature coefficient, flux peaking, criti- cality, and safety. There has been a general tendency in the past to over- simplify and idealize the assumptions regarding neutron thermalization, much to the detriment of reactor calculational procedures. The pulsed techniques developed here and elsewhere are particularly adaptable to studying these problems experimentally in a precise way. Present-day theoretical tools are also capable of shedding much light on these problems. The current general method of approach in the Integral Neutron Thermalization program includes most of the techniques utilized in the past (experimental and ana1ytic:al). Experimental techniques were improved during the past year, but this constituted only a minor portion of the program because these procedures had been reasonably well in hand previously. 1 2 Studies of neutron spectra under infinite-medium conditions were continued on a reduced scale from that engaged in during other years, since analytical methods have been developed to handle this relatively uncomplex calculation for many practical applications. However, further refinements in our knowledge of the scattering law seem to be necessary before perturbations in neutron spectra due to resonance absorption can be completely described. New moderators and shield materials were studied under infinite-medium conditions to broaden the scope of the program. Specifically, studies of D20, polyethylene, and lithium hydride were begun. The main experimental effort during the year was devoted to studying the problems associated with the spatially dependent neutron spectra in water. One-dimensional geome- tries in which rapid spatial-flux variations were established were studied. This important class of problem is very similar to that which occurs at control rods and fuel-water interfaces in most common reactor designs. Both multiplying and nonmultiplying assemblies were used in the investiga- tions. Theoretical and analytical efforts were intensified considerably, especially regarding evaluation of scattering-law information from the standpoint of its applicability and sensitivity in reactor calculations. Many other problems concerning the time dependence of neutron spectra, energy eigenvalues, heated interfaces, etc. , were investigated. The over-311 result of this integrated effort has been to solve some of the difficult problems concerning neutron thermalization which have existed in the past. In addition, some new and interesting problems have been uncovered, and various approaches to solving these have been adopted. The relevance of these matters to specific reactor problems is pointed out in this report where appropriate. 11. RESEARCH EQUIPMENT This section contains a brief review of changes made during the past year in the General Atomic Linear Accelerator Facility. A more complete discussionof the over-all facility has been presented in GA-2544. 2. 1. LINEAR ACCELERATOR The General Atomic L-band linear accelerator (Linac) shown in Fig. 1 was installed from July through September of 1961 to replace a lower-current S-band accelerator which had been in use for several years. In the first year of actual operation, the new machine has more than equaled its rated specifications. All research performed during the past contract year has benefited greatly from the increased intensities afforded by the new accelerator. The Linac has been used in connection with the high- current, multitarget, beism- switching system which has been developed at General Atomic during the last few years. There are over 12 target areas (see Fig. 2) currently in use in this system, plus a pulsed-magnet system for simultaneous multiple-target experiments and a high-resolution electron- positron spectrometer. The 16- and 50-m neutron flight paths shown in Fig. 2 are being used primarily in the Integral Neutron Thermalization program. From the standpoint of pulsed-neutron research, the important design parameter of this accelerator is the neutron yield per pulse. Average power considerations very seldom dictate experimental feasibility in neutron-thermalization work. Some typical Linac operating conditions which have been attained during the first year of operation are (1) long- pulse mode (1 psec 5 TS. 14 psec) at 30 Mev and 0. 7-amp peak current, (2) short-pulse mode (0.01 psec T -< 1 p sec) at 40 MeV and 2 amp, and (3) variable electron energy from 1 to 50 MeV. (Thermalization studies usually require the long-pulse mode, whereas cross-section investigations often demand short-pulse operation of the Linac. ) Thus, neutron yields 0 attainable from the General Atomic Linac are within a factor of two of the > highest available anywhere today. In addition, beam-spot size (<1 cm in diameter), angular divergence, and energy spectrum in beam extraction P from the Linac are such that the electron beam pipes easily to a small spot 90 ft from the machine. Typical current losses are less than a few per cent for most operations, which minimizes spurious and fluctuating sources of neutron background in the target areas, as well as activation 3 4 iz & #-I I I 2 H c, Id #-I 4 Id c, .A 0 d 0 w 9 0) ti P rd r: a 4 .r( z Id k rd u 0 a, 4 a, k d c, 0 k c a 5