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 the average trajectory of test particles computed from moments of a kinetic equation, which are applied to an approximate form of the Green-Kubo relations for weakly correlated systems. 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 need to solve the distribution function iteratively as a perturbation from equilibrium (as in the Chapman-Enskog or Grad methods) for the need to solve time integrals of correlation functions. 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 were an MHD theory has not yet been developed. Results are benchmarked by comparison with molecular dynamics simulations of the one-component plasma.