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**Harvard**

Nyqvist, R., Anderson, D. och Lisak, M. (2009) *Spreading of collimated particle beams within a generalized Fokker-Planck diffusion equation*.

** BibTeX **

@article{

Nyqvist2009,

author={Nyqvist, Robert and Anderson, Dan and Lisak, Mietek},

title={Spreading of collimated particle beams within a generalized Fokker-Planck diffusion equation},

journal={Nuclear Science and Engineering},

issn={0029-5639},

volume={163},

issue={1},

pages={85-90},

abstract={Recently, an expansion of the Boltzmann scattering operator describing the angular spreading of particle beams was given that included the effects of large angle scattering processes, thus generalizing the classical Fokker-Planck equation, valid in the limit of small angle scattering. The present work aims at making an analytical comparison between predictions based on the classical Fokker-Planck equation and those based on a generalized one, which includes a first-order correction term in the expansion of the Boltzmann scattering operator. The analysis is carried out for thin slabs where backscattering effects can be neglected and makes use of a moment approach, which leads to an infinite system of recursively coupled ordinary differential equations. The system is truncated in a consistent manner, and the effects of large angle scattering on the evolution of the moments are determined in explicit analytical form. An approximate similarity solution of the generalized Fokker-Planck equation is also found, and the results of both approaches provide a clear picture of the increased diffusive beam spreading due to large angle scattering. A comparison with previously published Monte Carlo simulation results shows good agreement.},

year={2009},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 98670

A1 Nyqvist, Robert

A1 Anderson, Dan

A1 Lisak, Mietek

T1 Spreading of collimated particle beams within a generalized Fokker-Planck diffusion equation

YR 2009

JF Nuclear Science and Engineering

SN 0029-5639

VO 163

IS 1

SP 85

OP 90

AB Recently, an expansion of the Boltzmann scattering operator describing the angular spreading of particle beams was given that included the effects of large angle scattering processes, thus generalizing the classical Fokker-Planck equation, valid in the limit of small angle scattering. The present work aims at making an analytical comparison between predictions based on the classical Fokker-Planck equation and those based on a generalized one, which includes a first-order correction term in the expansion of the Boltzmann scattering operator. The analysis is carried out for thin slabs where backscattering effects can be neglected and makes use of a moment approach, which leads to an infinite system of recursively coupled ordinary differential equations. The system is truncated in a consistent manner, and the effects of large angle scattering on the evolution of the moments are determined in explicit analytical form. An approximate similarity solution of the generalized Fokker-Planck equation is also found, and the results of both approaches provide a clear picture of the increased diffusive beam spreading due to large angle scattering. A comparison with previously published Monte Carlo simulation results shows good agreement.

LA eng

LK http://publications.lib.chalmers.se/records/fulltext/local_98670.pdf

OL 30