Abstract. A recent method to obtain short-time propagators for finding path-integral solutions of Fokker–Planck equations is applied here to numerically solve the non-linear kinetic Fokker–Planck equation in plasma physics. Furthermore, we extend the use of this method to solve non-homogeneous equations. Cylindrical geometry in velocity space is used and two-species plasma is considered with no linearization of the exact conservative collisional operator. Numerical singularities in the diffusion tensor determinant are avoided by the splitting of the collisional operator into two parts, each one leading to different multiplicative integral operators which describe electron–electron and electron–ion interactions separately. The accurate advancing path-integral numerical formalism preserves conservative physical properties making this procedure a promising alternative to the classical linearized collisional operators used in kinetic theory. Here, we show the feasibility of the method by giving a new calculation of Spitzer's transport coefficients.

PACS numbers: 02.70.Rw, 52.65.Ff, 31.15.Kb, 52.20.−j, 51.10.+y, 02.70.Rr

Print publication: Issue 41 (14 October 2005)
Received 5 June 2005, in final form 31 August 2005
Published 28 September 2005