Multigroup Methods Research Articles

Estimates of neutron leakage through penetrations of the cern intersecting storage rings by monte carlo albedo calculations

Abstract The monokinetic and multigroup Monte Carlo albedo methods applicable to estimating neutron leakage through penetrations in the shielding of high-energy accelerators are reviewed. They are used to calculate attenuation factors and dose levels in the tunnels of the CERN intersecting storage rings.

Application of the Probability Table Method to Multigroup Calculations of Neutron Transport

The probability table method, developed for Monte Carlo calculations in the region of unresolved neutron resonances, is demonstrated to be of general use in neutron transport studies since the Boltzmann equation involved can be derived and solved by analogy to multigroup methods. Since the resulting equations can be cast into a form identical to that of the multigroup equations, they can be solved by existing multigroup transport codes. From a set of probability tables and spatially independent, unshielded, neutron cross sections, the method yields correct selfshielding effects, such as equivalent, spatially dependent, multigroup cross sections. Extension of the method and the use of probability tables outside the unresolved region are discussed.

Collision probability criticality calculations

A method is presented for computing the multiplication factor of single region systems which contain fissile material and which may be specified by one, two or three coordinates. The systems are assumed to be unreflected, homogeneous assemblies which have no re-entrant surfaces. The method follows the successive scattered neutron collisions which take place in a system and computes for each interaction the product of the probability of a fission collision and the average number of secondaries per fission. The sum of these products, in the limit as the number of collisions become infinite, is the multiplication factor of the system. The initial energy distribution of the neutron-source density needed to start the calculations, is specified in a sixteen energy-group format. The initial spatial neutron distribution is assumed to be uniform and to remain unchanged as a result of collisions. The source-density amplitudes for each successive collision is taken as the probability of a scattering interaction multiplied by the source-density amplitude for the previous collision. The source-density energy distribution is recomputed after each collision using multigroup methods. Critical sizes are found by obtaining the multiplication factor as a function of the system dimensions and graphically determining the dimensions which make the factor equal unity. The critical dimensions of several plutonium metal and enriched-uranium metal systems are computed and, when possible, the calculated dimensions are compared with experimental values. The computed dimensions are from 2· 1 to 5· 6 per cent higher than the measured values. This discrepancy is due primarily to the assumption of a uniformly distributed source density.

Study of a Slightly Enriched UO2 Lattice with H:U=0.42 — Measurement and Analysis

Parameter measurements in a 1.3% enriched UO2 lattice with H:U = 0.42 have been performed. These measurements are an extension of an experimental program in the TRX critical facility of the Bettis Atomic Power Laboratory. Earlier measurements were made for a wide range of water-to-uranium (H2O:U) volume ratios (1:1 to 8:1) using 4-ft (1.2-m)-high slightly enriched, 0.387-in. (0.98-cm)-diam uranium metal or oxide fuel rods clad with aluminum. The new data have been compared with current analytic techniques, using both P-1 and P-3 multigroup analysis in the epithermal neutron energy range and Monte Carlo multigroup methods for thermal neutrons. This extremely undermoderated lattice provides a very stringent test for both the computational methods and the neutron cross sections used. The quantities measured were: the ratio of epithermal-to-thermal radiative captures in U238 (ρ28); the ratio of captures in U238 to fissions in U235 (the modified conversion ratio, CR*); the ratio of U238 fisions to U235 fissions (δ28); and the ratio of epithermal-to-thermal U235 fissions (δ25). In addition, activations were obtained with thermal-neutron detectors of widely different spectral response.The results indicate that the calculational methods predict the parameters very well, except for δ28. The discrepancy in δ28 may be due to inadequate U238 inelastic scattering cross sections, but this conclusion requires additional study. Monte Carlo calculations of thermal-neutron detector activations show that use of either the Nelkin or Koppel kernel gives results that agree with the data.

Modern Techniques Used in Nuclear Design of Reactors

has made a profound change in the philosophy and methodology of reactor phys ics and analys is. For example, the role of the reactor physicist has change d cons iderably in the last decade. In the early history of development of reactor physics, much of the attention of the reactor physicist was directed toward analytic solutions of the equations describing the behavior of the neutrons in tractable idealized systems. In order to obtain analyt ic soluti ons, it was necessary to ignore some of the more subtle effects and to introduce approximatio ns both in energy and geomet ric details. These expedients were usually justified because accurate differential cross-section data were not avail able to allow more careful de­ tail. The early reactor physics calcu lational models were usually based on one- or two-group age-diffusion the ory. The parameters used in these calcu­ lations were usually obtained from correlations of integral experiments with simple physical models. In 1950, mult igroup methods were already begin ning to be used (1), particularly for intermediate-ene rgy and fast-spectrum reactors, where the simp lified models were not even approximately valid. The se probl ems, which used as many as 15 energy groups and a sph erical geometry, were solved by iterative procedures with the use of a desk calcu­ lator. The solution of a single problem typically required several days of calculation. However, the method all owed the reactor phys icist to calculate diffusio n, absorpti on, and fission events wit h proper attent ion given to the neutron flux inten sities and cross-section values appropriate to different energy groups and at different radial positions in the reactor.

The use of multigroup methods in biological shielding calculations

The article describes a seven-group method and a ten-group method, which are applicable to the design of biological shielding for nuclear reactors.

Use of multigroup methods to compute a biological shield

Use of multigroup methods to compute a biological shield

Few Group Calculations of Thermal Neutron Transport

BS>One-velocity treatments of thermal neutron transport have proved inadequate whereas multigroup methods may be so time consuming as to become impractical. The few thermal-group calculations investigated lie between these extremes. Few-group calculations in typical power peaking and control rod worth studies are found to be both rapid and accurate, particularly when the rods are represented by P-3 and double P-1 approximations are derived and discussed. (auth)

Two-Dimensional (r,z) Multigroup Calculation for an Intermediate Spectrum Critical Assembly

The results of two-dimensional (r,z) multigroup calculations of an experimental low-power reactor (PPA-19) are described. Comparison is made between calculated results and experimental measurements of reactivity, power distribution, and sodium activation. Generally good agreement is observed between calculation and experiment. This calculation was performed in 1954 and represents the first application of Roe's two-dimensional multigroup formulation to the analysis of an operating critical assembly. The over-all objective of such calculations is to ascertain the accuracy of two-dimensional multigroup methods in order to facilitate their application to future problems in reactor design. (auth)