Neutron Transport with Anisotropic Scattering

1961 ◽  
Vol 11 (4) ◽  
pp. 415-427 ◽  
Author(s):  
Janusz R. Mika
Keyword(s):  
Neutron Transport ◽  
Anisotropic Scattering

Two-Group Neutron Transport Theory with Anisotropic Scattering

1970 ◽  
Vol 25 (5) ◽  
pp. 587-594
Author(s):  
K. O. Thielheim ◽  
K. Claussen
Keyword(s):  
Integral Equation ◽  
Transport Theory ◽  
Neutron Transport ◽  
Full Range ◽  
Completeness Theorem ◽  
Anisotropic Scattering ◽  
Neutron Transport Theory ◽  
Coeffi Cients ◽  
Group Transport ◽  
Homogeneous Media

Abstract Two-group transport theory with anisotropic scattering in infinite homogeneous media is pre-sented in this paper. The kernel of the integral equation is expanded into a finite series of Legendre polynomials. Eigenfunctions and eigenvalues of the transformed integral equation are found and the number of discrete eigenvalues is calculated. The full-range completeness theorem as well as the orthogonality and normalization relations are presented. As an example the expansion coeffi-cients of the infinite-medium Green's function are explicitly calculated.

Development of Code, PNFENT, Based on Using Finite Elements for Neutron Transport

2009 ◽  
Author(s):  
Ahmad Zolfaghari ◽  
Hamid Minuchehr ◽  
Mohammadreza Abbasi
Keyword(s):  
Finite Element ◽  
Neutron Transport ◽  
Anisotropic Scattering ◽  
Free Form ◽  
Group Method ◽  
Maximum Principles ◽  
Finite Element Program ◽  
Boltzman Equation ◽  
Variational Treatment ◽  
Element Program

A variational treatment of the finite element method for neutron transport is used based on a version of the even parity Boltzman equation for the general case of anisotropic scattering and sources. The theory of maximum principles is based on the Cauchy-Schwartz inequality and the properties of a leakage operator G and a removal operator C. For system with extraneous sources a maximum principle is used in boundary free form to ease finite element computations. The global error of an approximate variational solution is shown. The energy dependence of the angular flux is treated by the multi-group method. In this paper the spatial dependence of the angular flux is given in a finite element representation. The directional dependence of angular flux is represented preferably by a spherical harmonic expansion. The above method has been developed and implemented in the finite element program PNFENT. A homogenous slab of a pure absorber along edge-cell and a two dimensional problems are solved with an accuracy as good as the best problem techniques.

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