A new formulation and gauge invariance of the MW-CRF method for kinetic equations

The MW-CRF method for kinetic equations was presented by Motta and Wick some years ago. The basic idea of the method consists in rewriting the collision kernel as divergence of a flux and formally to transform the problem in a collisionless one. The flux vector can be computed at each time step for all particles, giving the collision induced force term in the collisionless formulation. One of the open questions of the method was the gauge invariance of the flux function. A detailed proof was not given in the original paper. In this paper, we present a slightly different formulation of the method which is more transparent for computational purposes and we prove the gauge invariance. Finally, we show the MW-CRF algorithm and, for a model kernel, we give an estimate of the computational effort.