Numerical Solution of an Ionic Fokker--Planck Equation with Electronic Temperature

We describe a numerical scheme for dealing with an ion/electron collision operator of the Fokker--Planck type; for that purpose, we introduce the notion of the entropic average of two positive quantities. This scheme has the property to be entropic in the sense of Boltzmann's H-theorem under a CFL criteria. Moreover, we prove that the solution of the semidiscrete scheme converges towards a unique Maxwellian equilibrium state when the time grows. Numerical applications are given and show that our scheme is more precise than the classical Chang--Cooper one.