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A finite element/Fourier treatment of the Fokker-Planck equation

Journal Article · · Journal of Computational Physics
 [1]
  1. Department of Physics, Utah State University, Logan, Utah 84322 (United States)
A method is proposed for a finite element/Fourier solution of the Fokker-Planck (FP) equation describing Coulomb collisions between particles in a fully ionized, spatially homogeneous plasma. A linearized FP equation is obtained by assuming collisions between test particles and a static background are more important than between the test particles themselves. A full 3D velocity space dependence is maintained using cylindrical coordinates (v{sub Double-Vertical-Line },v{sub Up-Tack },{gamma}). When a magnetic field exists, v{sub Double-Vertical-Line} is aligned with it and {gamma} corresponds to gyroangle. Distribution functions are approximated by a Fourier representation in the azimuthal angle, {gamma}, and by a 2D finite element representation in the parallel and perpendicular directions. The FP equation can be solved in a fully implicit manner allowing large, stable timesteps and simulations that arrive quickly at equilibrium solutions. The results of several test problems are discussed including a calculation of the resistivity of a Lorentz plasma, the heating and cooling of a test particle distribution, the slowing down of a beam of test particles and the acquisition of a perpendicular flow for a non-flowing Maxwellian test distribution. Robust convergence upon refinement of the finite element/Fourier representation is highlighted.
OSTI ID:
22192329
Journal Information:
Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 18 Vol. 231; ISSN 0021-9991; ISSN JCTPAH
Country of Publication:
United States
Language:
English