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

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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 ... continued below

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PDF-file: 23 pages; size: 0.4 Mbytes

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Xiong, Z; Cohen, R H; Rognlien, T D & Xu, X Q April 18, 2007.

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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.

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PDF-file: 23 pages; size: 0.4 Mbytes

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  • Journal Name: Journal of Computational Physics, vol. 227, N/A, April 15, 2008, pp. 7192; Journal Volume: 227

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  • Report No.: UCRL-JRNL-230192
  • Grant Number: W-7405-ENG-48
  • Office of Scientific & Technical Information Report Number: 940853
  • Archival Resource Key: ark:/67531/metadc900759

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  • April 18, 2007

Added to The UNT Digital Library

  • Sept. 27, 2016, 1:39 a.m.

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  • Nov. 29, 2016, 12:35 p.m.

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Xiong, Z; Cohen, R H; Rognlien, T D & Xu, X Q. A High-Order Finite-Volume Algorithm for Fokker-Planck Collisions in Magnetized Plasmas, article, April 18, 2007; Livermore, California. (digital.library.unt.edu/ark:/67531/metadc900759/: accessed April 21, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.