Properties of the Fokker-Planck Equation

Abstract

It is shown that the stochastically derived Fokker-Planck collision term, JF, satisfies the conservation equations regardless of the form of the interparticle force law. The form of JF for inverse power potential laws is obtained, and is compared with the form obtained from the expansion of the Boltzmann collision integral about grazing collisions. The two expressions are equal for the Coulomb case only. The expanded Boltzmann operator fails to satisfy the conservation laws for any other inverse power potential law. The relation between the ``diffusion'' coefficient b and the ``friction'' coefficient a, ▿·b = a, is found to hold only for the r−1 interparticle potential. An H-theorem is presented for the Fokker-Planck collision term.