Commun. Comput. Phys., 7 (2010), pp. 877-903.

Modeling of Long-Range Intra- and Inter-Species Charged Particle Collisions for PIC Simulations

D. D'Andrea 1*, C.-D. Munz 2, R. Schneider 3

1 Forschungszentrum Karlsruhe - in der Helmholtz-Gemeinschaft, Institut fur Kern- und Energietechnik PF 3640, D-76021 Karlsruhe, Germany.
2 Institut fur Aerodynamik und Gasdynamik, Universitat Stuttgart, Pfaffenwaldring 21, D-70550 Stuttgart, Germany.
3 Forschungszentrum Karlsruhe - in der Helmholtz-Gemeinschaft, Institut fur Hochleistungsimpuls und Mikrowellentechnik, PF 3640, D-76021 Karlsruhe, Germany.

Received 26 May 2009; Accepted (in revised version) 5 October 2009
Available online 6 January 2010


In this paper we present the modelling of elastic intra-species electron-electron and inter-species electron-ion scattering in a plasma on the basis of the Fokker-Planck collision operator. Taking into account the equivalence of this operator with a stochastic differential equation, we propose a Particle-in-Cell based approach for the numerical solution of the Fokker-Planck collision term. As we will see, the introduced numerical concept allows the simulation of the collisional relaxation process in a fully self-consistent fashion.

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PACS: 52.20.Fs, 52.27.Aj, 52.65.Ff, 52.65.Rr
Key words: Coulomb collisions in plasmas, collisional relaxation, Fokker-Planck equation, stochastic differential equation, particle-in-cell method.

*Corresponding author.
Email: (D. D'Andrea), (C.-D. Munz), (R. Schneider)

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