An entropy based thermalization scheme for hybrid simulations of Coulomb collisions

We formulate and test a hybrid fluid-Monte Carlo scheme for the treatment of elastic collisions in gases and plasmas. While our primary focus and demonstrations of applicability are for moderately collisional plasmas, as described by the Landau-Fokker-Planck equation, the method is expected to be applicable also to collision processes described by the Boltzmann equation. This scheme is similar to the previously discussed velocity-based scheme (R. Caflisch, et al., (2008) [7]) and the scattering-angle-based scheme (A.M. Dimits, et al., (2010) [14])], but with a firmer theoretical basis and without the inherent limitation to the Landau-Fokker-Planck case. It gives a significant performance improvement (e.g., error for a given computational effort) over the velocity-based scheme. These features are achieved by assigning passive scalars to each simulated particle and tracking their evolution through collisions. The method permits a formal error analysis that agrees with numerical results. The tests performed are for the evolution of an anisotropic Maxwellian and a bump-on-tail distribution.