Average Trajectory Method for Computing Magnetohydrodynamic Transport Coefficients

A simple method to compute the transport coefficients of magnetohydrodyamics from kinetic theory is developed. It is based on a Langevin description of the average trajectory of test particles in the presence of Lorentz and friction forces, which are applied to an approximate form of the Green-Kubo relations for weakly correlated systems. The only input from kinetic theory is the friction force on a test charge. Results agree with those of the Chapman-Enskog, or Grad, methods which are obtained by computationally laborious expansions of the phase-space distribution function. The new method trades the purely analytic formulation for one that is conceptually and computationally simpler, but requires solving a differential equation and an integral on a computer. Results are compared to the expected Braginskii transport equations in the weakly magnetized regime. The model is also used to derive transport coefficients in strongly magnetized plasmas where an MHD theory has not yet been developed. Results are benchmarked by comparison with molecular dynamics simulations of the one-component plasma.