Neutron Transport In Slab Geometry Research Articles

Modified Chebyshev polynomial (U N ) approximation in the neutron transport theory and computation of critical half thicknesses

Abstract A general theoretical scheme for the UN method and the evolution of a general eigenvalue spectrum are described. The applicability of UN method to one dimensional slab geometry neutron transport problems is discussed. The eigenvalue spectrum is calculated for isotropic scattering with different values of the parameter c, the mean number of secondary neutrons per collision, known as the fundamental eigenvalue. Then the critical slab problem has been studied. The critical half thicknesses are computed for different values of c. For the solution, Mark and Marshak boundary conditions are used. Results are obtained for both, UN and PN approximations for comparison.

Some useful properties of Legendre polynomials and its applications to neutron transport equation in slab geometry

In this paper, we describe a new scattering kernel and general theoretical scheme for the evolution of the discrete and continuum eigenvalue spectrum in one-dimensional slab geometry neutron transport equation. Firstly, some useful properties of the Legendre polynomials which revealed during the definition of the new scattering kernel are discussed. By using the scattering kernel in one-dimensional neutron transport equation we obtained an integral equation for angular part of the angular flux. For the solution of this integral equation and eigenvalue equations, some comments are given.

General Eigenvalue Spectrum in a One-Dimensional Slab Geometry Transport Equation

A general theoretical scheme for the evolution of a general discrete eigenvalue spectrum in a one-dimensional slab geometry neutron transport equation is described. To make a general procedure, we described the consistent scattering kernel. By using this scattering kernel, discrete eigenvalues are computed. Three methods are presented for the calculation of discrete eigenvalues, but the simplest one is chosen for the computation. Numerical results are presented in the tables. Results are discussed and compared with those already obtained using various methods available in the literature.

On the spectrum of the one-speed slab-geometry discrete ordinates operator in neutron transport theory

We describe a numerical method applied to the first-order form of one-speed slab-geometry discrete ordinates equations modelling time-independent neutron transport problems with anisotropic scattering, with no interior source and defined in a nonmultiplying homogeneous host medium. Our numerical method is concerned with the generation of the spectrum and of a vector basis for the null space of the one-speed slab-geometry discrete ordinates operator. Moreover, it allows us to overcome the difficulties introduced in previous methods by anisotropic scattering and by angular quadrature sets of high order. To illustrate the positive features of our numerical method, we present numerical results for one-speed slab-geometry neutron transport model problems with anisotropic scattering.

A closed-form analytic solution for the - equations of neutron transport in slab geometry

A closed-form analytic solution for the discrete-ordinates equations of neutron transport is obtained without recourse to integral transforms. The method is applied to the slab-geometry problem in the one-speed approximation using a one-sided set of boundary conditions. The solution is valid for any number of discrete ordinates and all possible orders of anisotropic scattering, and it does not require a priori knowledge of the particular solution. A set of algebraic expressions for the neutron balance at the boundaries of a slab is obtained and used as a basis for one iterative and one non-iterative numerical algorithm that are valid for all homogeneous and heterogeneous slabs. The numerical solutions are error free other than the roundoff of the computing system. The roundoff error is minimized by the Effective Albedo and Transmittance method.

Subcriticality and supercriticality of energy dependent neutron transport in slab geometry

The energy dependent transport system in an anisotropic medium in slab geometry subjecting possible internal source q and incoming fluxes ψ0, ψ1 is discussed. It has been shown in an earlier paper that under certain conditions on the average number of secondary neutrons per collision c, the scattering cross section σ, and the optical slab length 2a, this system has a unique nonnegative solution for all inputs q, ψ0, ψ1. The aim of this paper is to establish analogous conditions on c, σ, a so that the system has no nonnegative solution when there is either internal source or incoming fluxes (or both), and it only has the trivial solution when neither internal source nor incoming fluxes are present in the system. This conclusion together with the earlier results yield explicit conditions for insuring the supercriticality and the subcriticality of the energy dependent system and therefore lead to analytical upper and lower bounds for the critical value c* in terms of σ and a.

N-group neutron transport theory: A criticality problem in slab geometry

The steady-state equation for N-group neutron transport in slab geometry is written as an integral equation. A spectral analysis is made of the integral operator and related to the criticality problem. The method depends on a representation for the resolvent kernel for a subcritical slab and on analytic continuation in a complex parameter to characterize eigenvalues in terms of singularities of the resolvent. The analytic continuation is based on a bifurcation analysis of some nonlinear matrix integral equations whose solutions provide a matrix Wiener-Hopf factorization of the Fourier transform of the kernel of the transport operator.

The jN method for neutron transport problems in multilayer slab systems and its application to the optimization of moderators in pulsed reactors

The newly developed j N method has been further extended to deal with multilayer slab systems with anisotropic scattering of neutrons. In the present article, the complete mathematical formalism for space-angle energy-time dependent neutron transport in slab geometry is given. The time moments of the neutron flux resulting from the incidence of an external delta function source can also be obtained in a simple analytical form similar to the stationary flux and calculated easily with a reasonable accuracy. By the use of this theory, an optimization study of moderators installed in pulsed reactors or accelerator pulsed reactors is carried out with respect to the heterogeneous poisoning. The thermal neutron yield leaking from a water slab and the variance of the leakage time distribution are obtained. The results have shown that heterogeneous poisoning can give a gam m the figure-of-merit for accelerator pulsed reactors by a factor of more than 3 compared to the unpoisoned value.

Parallel Shooting Method for Boundary-value Problems: Application to the Neutron Transport Equation

A direct method is given for the solution of the spherical harmonics approximation to the Boltzmann equation for neutron transport in slab geometry. The roundoff instability of the problem is eliminated by performing linear transformations of the matrices involved, which ensure that the matrix columns are linearly independent. The novelty of the method lies in that only a minimum number of matrix transformations is performed, the precise number being determined dynamically, efficiently, and in a new way by the program itself in the course of the computation.

One-Speed Neutron Transport in Slab Geometry

One-Speed Neutron Transport in Slab Geometry