A high-order finite-volume algorithm for Fokker–Planck collisions in magnetized plasmas

✍ Scribed by Z. Xiong; R.H. Cohen; T.D. Rognlien; X.Q. Xu

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 295 KB
• Volume: 227
• Category: Article
• ISSN: 0021-9991
• DOI: 10.1016/j.jcp.2008.04.004

✦ Synopsis

A high-order finite-volume algorithm is developed for the Fokker-Planck Operator (FPO) describing Coulomb collisions in strongly magnetized plasmas. The algorithm uses a generic fourth-order reconstruction scheme on an unstructured grid in the velocity space spanned by parallel velocity and magnetic moment. By analytically mapping between different coordinates, it produces an accurate and density-conserving numerical FPO for an arbitrary choice of velocity space coordinates. A linearized FPO in constants-of-motion coordinates is implemented as an example of the present algorithm combined with a cut-cell merging procedure. Numerical tests include the thermalization of a test distribution with a background Maxwellian at a different temperature, and the return to isotropy for a distribution initialized with a velocity space loss-cone. Utilization of the method for a nonlinear FPO is straightforward but requires evaluation of the Trubnikov-Rosenbluth potentials.