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Title: A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas

Abstract

A high-order finite volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm is based on a general fourth-order reconstruction scheme for an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. The method provides density conservation and high-order-accurate evaluation of the FPO independent of the choice of the velocity coordinates. As an example, a linearized FPO in constant-of-motion coordinates, i.e. the total energy and the magnetic moment, is developed using the present algorithm combined with a cut-cell merging procedure. Numerical tests include the Spitzer thermalization problem and the return to isotropy for distributions initialized with velocity space loss cones. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Rosenbluth potentials.

Authors:
; ; ;
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
940853
Report Number(s):
UCRL-JRNL-230192
Journal ID: ISSN 0021-9991; JCTPAH; TRN: US0807225
DOE Contract Number:
W-7405-ENG-48
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Computational Physics, vol. 227, N/A, April 15, 2008, pp. 7192; Journal Volume: 227
Country of Publication:
United States
Language:
English
Subject:
70 PLASMA PHYSICS AND FUSION; 99 GENERAL AND MISCELLANEOUS; ALGORITHMS; EVALUATION; ISOTROPY; LOSS CONE; MAGNETIC MOMENTS; THERMALIZATION; VELOCITY

Citation Formats

Xiong, Z, Cohen, R H, Rognlien, T D, and Xu, X Q. A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas. United States: N. p., 2007. Web.
Xiong, Z, Cohen, R H, Rognlien, T D, & Xu, X Q. A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas. United States.
Xiong, Z, Cohen, R H, Rognlien, T D, and Xu, X Q. Wed . "A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas". United States. doi:. https://www.osti.gov/servlets/purl/940853.
@article{osti_940853,
title = {A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas},
author = {Xiong, Z and Cohen, R H and Rognlien, T D and Xu, X Q},
abstractNote = {A high-order finite volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm is based on a general fourth-order reconstruction scheme for an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. The method provides density conservation and high-order-accurate evaluation of the FPO independent of the choice of the velocity coordinates. As an example, a linearized FPO in constant-of-motion coordinates, i.e. the total energy and the magnetic moment, is developed using the present algorithm combined with a cut-cell merging procedure. Numerical tests include the Spitzer thermalization problem and the return to isotropy for distributions initialized with velocity space loss cones. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Rosenbluth potentials.},
doi = {},
journal = {Journal of Computational Physics, vol. 227, N/A, April 15, 2008, pp. 7192},
number = ,
volume = 227,
place = {United States},
year = {Wed Apr 18 00:00:00 EDT 2007},
month = {Wed Apr 18 00:00:00 EDT 2007}
}