Implicit and Conservative Difference Scheme for the Fokker-Planck Equation

Abstract

An implicit and fully conservative finite-difference scheme is proposed for solving the Fokker-Planck equation for Coulomb collisions between isotropically distributed like particles in a spatially homogeneous plasma. The scheme extends the standard Chang-Cooper method by providing not only number density conservation, but also energy conservation. As a result, time steps much larger than the thermal collision time can be used to stably and accurately simulate plasmas far from thermal equilibrium. Such a relaxation in time-step constraint has allowed for the successful implementation of the new scheme in multidimensional transport Fokker-Planck codes, with a resulting increase in computational efficiency.