Energy-dependent Diffusion Equation Research Articles

04/01289 Introducing the migration mode method for the solution of the space and energy dependent diffusion equation: Dall'Osso, A. Annals of Nuclear Energy, 2003, 30 (18), 1829–1845

04/01289 Introducing the migration mode method for the solution of the space and energy dependent diffusion equation: Dall'Osso, A. Annals of Nuclear Energy, 2003, 30 (18), 1829–1845

Introducing the migration mode method for the solution of the space and energy dependent diffusion equation

The most usual method to take into account energy dependence in whole core spatial neutronics calculation is the multigroup method. In thermal spectrum reactors as PWR, two-group theory is sufficient to describe accurately the neutron spectrum variation among spatial regions. When the spectrum hardens the precision of two-group theory decreases and more groups are necessary to keep a good accuracy. The aim of the computation method presented here is to represent with a good accuracy the spectral transitions which appear in these situations, without increasing the number of unknowns (i.e. the number of energy groups). The neutron spectrum is considered as a combination of base shapes corresponding to the different modes of migration of the neutrons in the energy dimension. The resulting energy flux distribution is a continuous function that fits the real one. The spatial discretization leads to matrices having the same structure of the ones obtained with multi-group theory. Then the method can be easily applied to existing codes solving the diffusion equation on the whole core in 3D. A methodological comparison between the migration mode method and the multigroup (few-group) method as well as a numerical comparison is presented.

Some Exact Solutions in Energy Dependent Transport Theory

Some exact solutions are obtained for energy dependent slowing down problems with energy dependent cross sections. The transport equation is solved using the backward-forward model of Fermi. Also studied is the energy dependent diffusion equation. Using these models, and a novel technique involving difference equations, it has been possible to find explicit, and numerically useful, solutions for slowing down from a plane, monoenergetic source in an infinite medium. The slowing down density and the energy deposition function are obtained which are of value in reactor physics and radiation damage calculations.

Time Dependent Neutron Spectra in Graphite

An experiment is described in which the 28-Mev electron linac at Harwell was used as a neutron source to produce 1 mu sec bursts of 10/sup 11/ electrons 160 times per second. A natural uranium target was placed centrally against one face of a 60 x 62.2 x 71.1 cm graphite block, and a neutron beam extracted from a channel running into the center of the block. This beam was interrupted by a slow chopper running in synchronism with the pulses from the accelerator. In this way 100 mu sec time samples'' of the neutrons in the block were taken and their spectrum determined by the time-of-the-flight method. The instant of the time sample relative to the fast neutron pulse could be varied by an electronic delay circuit. Neutron spectra are presented for the time varying between 300 and 1000 mu sec after the pulse. These spectra differ from the Maxwellian shape but approach asymptotically to a cooled Maxwellian'' from which they are indistinguishable after 1000 mu sec. Detailed calculations of the spectra were made using an IBM 7090 computer to obtain a numerical solution of the time and energy dependent diffusion equation using a scattering kernel based on themore » scattering measurements made at Chalk River. The experimental results are also compared with spectra using a scattering kernel based on the heavy gas model with a fictitious mass of 33. (auth)« less

Thermal Neutron Flux Spectrum in a Medium with a Temperature Discontinuity

The energy-dependent diffusion equation in the heavy gas approximation is considered for the case of a medium which has absolute temperature T/sub 1/ in one halfspace and T/sub 2/ in the other. The steady-state solution for F(x,E), the neutron flux per unit energy, is obtained in the absence of sinks and sources. Although the formal series solution diverges under certain conditions, it can be summed by means of the Euler transformation. Two approximation schemes giving sample analytical results are discussed. Numerical results for flux spectra and the total neutron density are presented for the case in which the temperature ratio is 2:1. The connection between this work and the theory of irreversible processes is briefly indicated. (auth)