Green–Kubo Formulae for a Plasma in an External Magnetic Field

The relation between linearized magnetohydrodynamics and the space and time dependent correlation functions of a plasma in an external magnetic field is derived. The method used is a perturbation technique based on the assumption that the correlation functions can be decomposed into a slow, hydrodynamic, and a rapid, microscopic, part. Using this method, the hydrodynamic modes are determined, and the description of magnetohydrodynamics found in this manner is assumed to be identical to regular magnetohydrodynamics. The resulting correspondence yields a set of correlation function expressions for the transport coefficients and magnetohydrodynamic modes.