Fluctuations in guiding center plasma in two dimensions

Statistical mechanics is developed for a two-dimensional guiding center plasma. Because there is no kinetic energy associated with guiding center motion, this development is unconventional. Thermal equilibrium is discussed, and an interesting limiting case is noted. Using the random phase assumption, a kinetic equation for the density fluctuations is obtained, which has thermal equilibrium and its limiting form as the only stationary states. However, despite the phase averaging this kinetic equation is reversible and when disturbed the system oscillates about equilibrium. Similar oscillatory behavior appears in the microscopic correlation function of the fluctuations, and the oscillation frequencies are obtained explicitly; however, these oscillations do not significantly change the macroscopic diffusion coefficient derived earlier by McNamara and Taylor.