Transport properties of the three-dimensional guiding-centre plasma

Equilibrium and non-equilibrium properties of the three-dimensional guiding-centre plasma (in which the particles move with the guiding-centre drift across constant magnetic field lines, and according to Newton's laws along the field lines) are investigated. In equilibrium, the transverse spatial diffusion and conductivity coefficients are calculated, and are shown to be related via a generalized Einstein relation. The diffusion coefficient consists of a Bohm-like 1/B contribution which tends to zero as the plasma volume tends to infinity, as well as a classical 1/B² contribution, which is independent of the size of the system. The Gibbs ensemble is constructed, and it is seen that thermal equilibrium results for the pair correlation, fluctuation spectra etc. are exactly the same as for the three-dimensional unmagnetized plasma. In the non-equilibrium case the appropriate Liouville equation and BBGKY hierarchy are considered. It is shown that to first order there is no tendency for the system (assumed spatially uniform) to relax towards thermal equilibrium.