Treatment of Scattering Anisotropy of Neutrons Through the Boltzmann-Fokker-Planck Equation

Caro, M.; Ligou, J.

doi:10.13182/nse83-a18217

Cited by 40 publications

(11 citation statements)

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“…A more realistic model, known as the BoltzmannFokker-Planck equation [7,15], allows rare ''catastrophic" collisions resulting in large-angle deflections. In our Flatland model problem, a reasonable first approximation would be to replace the probability density p by…”

Section: Discussionmentioning

confidence: 99%

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An angular multigrid method for computing mono-energetic particle beams in Flatland

Börgers

MacLachlan

2010

Journal of Computational Physics

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Section: Discussionmentioning

confidence: 99%

“…0 by Eq. (7). We present here the formal derivation of the spatial (steady-state) diffusion equation from Eq.…”

Section: The Spatial Diffusion Limitmentioning

confidence: 99%

An angular multigrid method for computing mono-energetic particle beams in Flatland

Börgers

MacLachlan

2010

Journal of Computational Physics

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“…where L BFP , the BFP scattering operator, contains both Boltzmann-like and Fokker-Planck-like scattering terms. 34,35…”

Section: ͑A8͒mentioning

confidence: 99%

Electron dose calculations using the Method of Moments

et al. 1997

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The Method of Moments is generalized to predict the dose deposited by a prescribed source of electrons in a homogeneous medium. The essence of this method is (i) to determine, directly from the linear Boltzmann equation, the exact mean fluence, mean spatial displacements, and mean-squared spatial displacements, as functions of energy; and (ii) to represent the fluence and dose distributions accurately using this information. Unlike the Fermi-Eyges theory, the Method of Moments is not limited to small-angle scattering and small angle of flight, nor does it require that all electrons at any specified depth z have one specified energy E(z). The sole approximation in the present application is that for each electron energy E, the scalar fluence is represented as a spatial Gaussian, whose moments agree with those of the linear Boltzmann solution. Numerical comparisons with Monte Carlo calculations show that the Method of Moments yields expressions for the depth-dose curve, radial dose profiles, and fluence that are significantly more accurate than those provided by the Fermi-Eyges theory.

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“…For highly forwardpeaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the direction variable. For this reason, various approximations of RTE have been proposed in the literature, e.g., the delta-Eddington approximation [13], the Fokker-Planck approximation [20,21], the Boltzmann-Fokker-Planck approximation [22,5], the generalized Fokker-Planck approximation [16], the Fokker-Planck-Eddington approximation and the generalized Fokker-Planck-Eddington approximation [10]. For RTE with high absorption and small geometries, the simplified spherical harmonics (S P N ) method ( [14]) is shown to produce good approximate solutions ( [9]).…”

Section: Introductionmentioning

confidence: 99%

On a family of differential approximations of the radiative transfer equation

2011

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The radiative transfer equation (RTE) arises in a variety of applications and is challenging to solve numerically due to its integro-differential form and high dimension. For highly forward-peaked media, it is even more difficult to solve RTE since accurate numerical solutions require a high resolution of the direction variable. For this reason, various approximations of RTE have been proposed in the literature. In this paper, we study a family of differential approximations of the RTE in three spatial variables. We explain the idea of constructing the differential approximations, and comment on the usefulness of the approximations.

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Treatment of Scattering Anisotropy of Neutrons Through the Boltzmann-Fokker-Planck Equation

Cited by 40 publications

References 0 publications

An angular multigrid method for computing mono-energetic particle beams in Flatland

An angular multigrid method for computing mono-energetic particle beams in Flatland

Electron dose calculations using the Method of Moments

On a family of differential approximations of the radiative transfer equation

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