A finite element/Fourier treatment of the Fokker-Planck equation
Journal Article
·
· Journal of Computational Physics
- 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
Similar Records
Numerical solutions of the Fokker-Planck charged-particle-transport equation
Numerical solutions of the Fokker-Planck charged particle transport equation
Implicit and conservative difference scheme for the Fokker-Planck equation
Technical Report
·
Tue Sep 01 00:00:00 EDT 1981
·
OSTI ID:5786713
Numerical solutions of the Fokker-Planck charged particle transport equation
Thesis/Dissertation
·
Wed Dec 31 23:00:00 EST 1980
·
OSTI ID:5981519
Implicit and conservative difference scheme for the Fokker-Planck equation
Journal Article
·
Wed Jun 01 00:00:00 EDT 1994
· Journal of Computational Physics; (United States)
·
OSTI ID:7197294