ABSTRACT
In this chapter, the authors extend a fluctuation formalism to a consideration of relaxation processes based on the theory of Brownian motion. They calculate the Fokker-Planck coefficients in terms of the spectral functions of the electric-field fluctuations and the dielectric response function in a magnetic field. The authors use Fourier decompositions of field variables with the periodic boundary conditions appropriate to a cube of a unit volume. They consider a temperature relaxation and a plasma diffusion across the magnetic field. The authors also consider the equipartition rates in energies between electrons and ions and between the parallel and perpendicular degrees of freedom for plasmas in a magnetic field. The behavior of a particle is described by the Fokker-Planck equation, the coefficients of which contain spectral functions of the microscopic electric fields; the rates of various relaxation processes are thereby determined.
