A new method to derive fluid equations and transport coefficients from equilibrium fluctuations

A simple method to compute the transport coefficients of plasma hydrodynamics or MHD from kinetic theory is developed. It is based on an association between differential phase-space elements of a velocity distribution and the trajectory of test particles. This is utilized to solve an approximate form of the Green-Kubo relations for weakly correlated systems, which relate the fluctuation properties of a system at equilibrium to linear transport coefficients. The only input from kinetic theory is moments of the collision operator for a test charge interacting with a Maxwellian background. 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.