ON THE CALCULATION OF THE FUNDAMENTAL MODE OF THE ONE-VELOCITY NEUTRON TRANSPORT OPERATOR

1967 ◽  
Vol 45 (12) ◽  
pp. 3793-3801
Author(s):  
N. K. Bansal ◽  
A. K. Ghatak
Keyword(s):  
Asymptotic Behavior ◽  
Cross Section ◽  
Fundamental Mode ◽  
Transport Theory ◽  
Neutron Transport ◽  
Anisotropic Scattering ◽  
Laboratory System ◽  
Neutron Pulse ◽  
The One ◽  
Pulsed Neutron

We report here some results on the asymptotic behavior of a neutron pulse injected into a slab using monoenergetic transport theory including the effects of the anisotropic scattering cross section in the laboratory system. The calculations were performed in the P1 and P3 approximations. These results are compared with the exact numerical calculations and with the recent pulsed neutron experiments in fast nonmultiplying nonmoderating assemblies where the decay of an essentially monoenergetic burst of neutrons is studied.

On the Calculation of the Fundamental Mode of the One Velocity Neutron Transport Operator

1975 ◽  
Vol 53 (5) ◽  
pp. 555-557
Author(s):  
Lakshmi Rangaswamy ◽  
Feroz Ahmed
Keyword(s):  
Fundamental Mode ◽  
Neutron Transport ◽  
Eigenvalues And Eigenfunctions ◽  
Transport Operator ◽  
The One

We report here the P1 and P3 solutions (eigenvalues and eigenfunctions) for the case of one velocity pulsed slabs.

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.

Phonon Transport in Anisotropic Scattering Particulate Media

2003 ◽  
Vol 125 (6) ◽  
pp. 1156-1162 ◽  
Author(s):  
Ravi Prasher
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Transport Theory ◽  
Mode Conversion ◽  
Anisotropic Scattering ◽  
Phonon Transport ◽  
Isotropic Scattering ◽  
Radiative Transport ◽  
Particulate Media ◽  
Transport Cross Section

Equation of phonon radiative transport (EPRT) is rewritten to include anisotropic scattering by a particulate media by including an acoustic phase function and an inscattering term which makes EPRT exactly same as equation of radiative transport (ERT). This formulation of EPRT is called generalized EPRT (GEPRT). It is shown that GEPRT reduces to EPRT for isotropic scattering and is totally consistent with phonon transport theory, showing that transport cross section is different from the scattering cross section. GEPRT leads to same formulation for transport cross section as given by phonon transport theory. However GEPRT shows that transport cross section formulations as described by phonon transport theory are only valid for acoustically thick medium. Transport cross section is different for the acoustically thin medium leading to the conclusion that mean free path (m.f.p) is size dependant. Finally calculations are performed for two types of scatterers for acoustic waves without mode conversion: (1) acoustically hard Rayleigh sphere; and (2) large sphere in the geometrical scattering regime. Results show that the scattering from these particles is highly anisotropic. It is also shown that for geometrical scattering case isotropic scattering leads to the conclusion of total internal reflection at the particle/medium interface.

scholarly journals On the spectrum of discrete-ordinates neutron transport problems

2021 ◽  
Vol 9 (2) ◽  
Author(s):  
Jesús Pérez Curbelo
Keyword(s):  
Discrete Spectrum ◽  
Neutron Transport ◽  
Anisotropic Scattering ◽  
Discrete Ordinates ◽  
High Anisotropy ◽  
Linear Transport Equation ◽  
The One ◽  
Transport Problems ◽  
Theoretical Results ◽  
Analytic Problem

Over the last six decades, the discrete spectrum of the neutron transport operator has been widely studied. Important theoretical results can be found in the literature regarding the one-speed linear transport equation with anisotropic scattering. In this work, the discrete-ordinates (SN) transport problem with anisotropic scattering has been considered and the discrete spectrum results in multiplying media have been corroborated. The numerical results obtained for the dominant SN eigenvalues agreed with the ones for the analytic problem reported in the literature up to a triplet scattering order. A compact methodology to perform the spectral analysis to multigroup SN problems with high anisotropy order in the scattering and fission reactions is also presented in this paper.

Phonon Transport in Anisotropic Scattering Particulate Media

2003 ◽  
Author(s):  
Ravi S. Prasher
Keyword(s):  
Cross Section ◽  
Acoustic Waves ◽  
Transport Theory ◽  
Mode Conversion ◽  
Anisotropic Scattering ◽  
Phonon Transport ◽  
Isotropic Scattering ◽  
Radiative Transport ◽  
Particulate Media ◽  
Transport Cross Section

Equation of phonon radiative transport (EPRT) is rewritten to include anisotropic scattering by a particulate media by including an acoustic phase function and an in-scattering term which makes EPRT exactly same as equation of radiative transport (ERT). This formulation of EPRT is called generalized EPRT (GEPRT). It is shown that GEPRT reduces to EPRT for isotropic scattering and is totally consistent with phonon transport theory, showing that transport cross section is different from the scattering cross section. GEPRT leads to same formulation for transport cross section as given by phonon transport theory. However GEPRT shows that transport cross section formulations as described by phonon transport theory are only valid for acoustically thick medium. Transport cross section is different for the acoustically thin medium leading to the conclusion that mean free path (m.f.p) is size dependant. Finally calculations are performed for two types of scatterers for acoustic waves without mode conversion: 1) Acoustically hard Rayleigh sphere 2) large sphere in the geometrical scattering regime. Results show that the scattering from these particles is highly anisotropic. It is also shown that for geometrical scattering case isotropic scattering leads to the conclusion of total internal reflection at the particle/medium interface.

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