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LOS ALAMOS SCIENTIFIC LABORATORY of the University of California LOS ALAMOS ● NEW MEXICO ,!. LA-3612 432● LOS ALAMOS SCIENTIFIC LABORATORY of the University of California LOS ALAMOS ● NEW MEXICO Criticality Data and Factors Affecting Criticality of Single Homogeneous Units —; -!, UNITED STATES * ATOMIC ENERGY COMMISSION ● CONTRACT W-7405 -ENG. 36 LEGAL NOTICE Thisreportwao preparedasanaccountoff30vernmentsponsoredwork.NeitJertheUnited States,northeCommission,noranypersonactingonbehalfof the Comm.hmion: A. Makesanywarrantyorrepresentation,expressedorimplied,withrespecttotheaccu- racy,completeness,orusefulnessoftheinformationcontainedinthis report,orthattheuse ofanyinformation,apparatue,method,orprocessdisclosedinthisreportmay notinfringe privatelyownedrighte;or B. Aeeumesanyliabilitieswithrespecttotheuseof,orfordamagearesultingfromthe useofanyinformation,apparatua,method,orprocessdisclo6edinthisreport. Aa ueedintheabove,“personactingon behalfoftheCommission”includesany em- ployeeor contractoroftbeCommission,oremployeeof euchcontractor,totheextentthat suchemployeeor contractoroftheCommission,oremployeeofsuchcontractorpreparca, diaseminate6,orprovidesaccesato,anyinformationpursuanttohtsemploymentorcontract withtheCommtesion,orhisemploymentwith6uchcontractor. This report expresses the opinions of the author or authors and does not necessarily reflect the opinions or views of the Los Alamos Scientific Laboratory. I 4 LA-3612 UC-46, CRITICALITY STUDIES TID-4500 ● LOS ALAMOS SCIENTIFIC LABORATORY of the University of California LOS ALAMOS ● NEW MEXICO Report written: July 1964 Report distributed: September 22, 1967 Criticality Data and Factors Affecting Criticality of Single Homogeneous Units by W. R. Stratton z 1 ,. — >— ._ , ● CONTENTS Page Abstract 3 I Introduction 3 II Shape Conversion 7 III Influence of Density 9 IV Internal Scattering (Dilution by Nonmoderators) 12 v Internal Moderation (Hydrogen, Carbon, and Oxygen) 14 A. U(93.5): bfetal-Water-Graphite and Oxide- Water Cores 15 B. Uranium Snriched to Thirty Percent, U(30) 22 c. Uranium Enriched to Five Percent, U(5) 25 D. Uranium Snriched to Three Percent, U(3) 27 E. Uranium Enriched to Two Percent, U(2) 28 F. Uranium Enriched to 1.42 Percent, U(l.42) 30 G. Uranium Enriched to 1.03 Percent, U(l.03) 31 233 H. U Systems 31 I. Plutonium Systems 34 VI Internal Moderation (Deuterium, Beryllium, and Oxygen) 37 VII Reflectors 38 A. Thickness, Gaps, Density 38 B. Thick Moderating Reflectors (Metastable Systems) 47 VIII Neutron Poisons 48 IX Summary aridConclusions 50 Acknowledgments 50 References 51 2 CRITICALITY DATA AND FACTORS AFFECTING CRITICALITY OF SINGLE HOMOGENEOUS UNITS by W. R. Stratton ABSTRACT The critical parameters of single homogeneous units are examined and tabulated. The study includes both theoretical and experimental results which are compared extensively in order to establish the accuracy of the theoretical method. The experimental data are reduced to standard conditions to facilitate this comparison and to investigate the consistency of the large number of critical experiments. Given the validity of the calculational scheme, the various affects of diluents (including moderators), reflec- tors, density charges, and poisons are studied. Finally, by application of the theory, results are obtained which are inaccessible or very difficult to obtain by experimental methods. I. INTRODUCTION geneous critical assembly was the Los Alamos ,,LOP0,,(4,5, -- the Low Power Boiler -- which The critical dimensions of mixtures of was a BeO-reflected, 14.95-liter, stainless enriched uranium or plutonium metals with steel sphere filled with a solution of ura- water were first estimated in 1942,(1) and nyl sulfate. The enrichment was 14.67%, byearly 1943 calculations(2) and improved and the critical state was first achieved 235 cross sections suggested that the spherical with a U mass of 565 g on May 9, 1944. 235U and unreflected critical mass of pure Since these early and historic occa- metal was 60 kg, while reflectors of normal sions, critical data for single homogeneous uranium and gold reduced the requirements units, both theoretical and experimental, to 15 and 22 kg, respectively. The uranium from many sources, and of wildly varying reflected number was amazingly good (exper- degrees of precision, usefulness, and ac- (3) imental value = 16.65 kg), while the cessibility have been accumulating at a predicted bare critical radius was larger prodigious rate. In this paper I propose than the best modern value ‘3) by only 7%; to consider a much smaller set, only those the estimate for the gold reflector stands critical data that can be considered “ba- unchallenged. The first experimental homo- sic.” By basic is implied some simplicity 3 in geometry and, hopefully, minimal compo- cylinders. I note, however, that these nents and complexity in the experiments. convergence patterns are most significant In addition, prejudice is shown in favor of for small (or thin) cores and that the num- experiments which can be generalized, i.e., ber of space points in a core may be of which can be correlated by varying one or equal or greater importance in determining two parameters to form a part of an inter- accuracy. I also observe ’15) that, since . nally consistent set. Unless we are des- S4 and S8 are the most commonly used ap- perate for experimental data, those experi- proximations, choice of cross sections may , ments that are not simple in reflection, have been prejudiced, though not conscious- core composition, etc., will not be consid- ly or conspicuously, in favor of S4 or S8. ered. Experiments may be most carefully The number of significant figures retained performed, but be so highly specialized as in the several tables for the critical pa- to be quite useless for our Purposes. Gen- rameters represents not precise knowledge erally a core will be required to be a sim- so much as use of a computer. Calculated ply connected volume with plane or convex results should be internally consistent to surfaces, even though the more complicated the precision quoted. shapes are often of much practical impor- Such computed data, as obtained by ap- tance. plication of an elaborate theory, are rele- The presentation will, in large part, vant to the real world of reactors, criti- be organized around the results of a theo- cal assemblies, chemical processing plants, retical parametric survey of critical data, storage and transportation problems, etc. , and, indeed, many of the critical dimen- only if a comparison of calculational re- sions given in the tables will be from this sults to experimental data is convincingly source. The calculation is the Carlson Sn done. This is attempted throughout, but ~ode(6-9) as prepared for the IRM 7094 com- primarily in the latter sections, and, when- puter, while the neutron cross-section set ever possible, the deviation of theoretical is that of 16 energy groups created by Han- data from experiment will be noted. This (lo) sen and Roach. Other theoretical sur- comparison not only serves to measure the veys of critical data have been published accuracy of such calculations with the cross (see as examples, References 11 through sections needed for input to the theory, 14), but these will not be discussed; com- but also casts some light upon the internal parison will be made only to experiments. consistency of the vast body of experimen- In this article, mention of theory, unless tal data. Given the validity of the scheme, otherwise modified, invariably implies the additional benefits which may now be be- Carlson method and Hansen-Roach cross sec- lievable arise from the possibility of cal- tions. culating critical (or supercritical) points The cross-section set was designed for that are either impossible or most diffi- fast and intermediate critical assemblies, cult to reproduce experimentally and of but, as will be developed, is equally ap- conducting parametric studies at a substan- plicable to thermal systems. Generally the tially reduced cost. Given an internally S4 approximation was utilized, except for consistent set of data, one can hope to un- thin slab calculation in which the better cover simple regularities which can lead to representation of S8 was sometimes needed. additional generalizations, seriously needed ● The S4 - S8 - S16 . convergence pattern in this field. I note that final recourse was investigated to a limited extent. Tbe must always be to experiment. pattern for the extant code seems similar In the most general terms, the criti- ● to that found in 1958(9) for spheres and cal size of a given system is sensitive to slabs, but qualitatively dissimilar for the allowable neutron leakage, moderation, 4 and poison. Neutron leakage is often sub- graphite cores; and a fairly painstaking divided into the effects of shape, density, comparison of theoretical and experimental internal scattering (including dilution results will be presented with this inform- effects), and external scattering (reflec- ation. Following this section, some spe- tion) . These several items are most diffi- cial characteristics and effects of reflec- cult to disentangle completely, and a fully tors will be given, and miscellaneous de? logical presentation in which no prior tails passed over earlier will be discussed. knowledge of critical data is assumed seems Finally, some information on poisons will to be nearly impossible. As minimum pre- be offered, but this coverage will be some- requisites, an awareness of the capabili- what arbitrary and cursory. ties of experimental methods and a feeling The basic critical data referred to for the power of modern computational
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