Relaxation of Velocity Distribution of Ions in a Plasma

A relaxation process which is characterized by many relaxation constants is studied in connection with the magnetic pumping. A relaxation equation is derived from two ways, the one is to use the Boltzmann equation and the other the thermodynamics of irreversible processes. The solution is expressed as a sum of many decaying modes and shown in general to have an oscillatory nature about the Maxwellian distribution. Convergence of a series of approximate relaxation constants is shown to be slow. Applicability of the solution is briefly mentioned. In case of an initially elliptic velocity distribution, excitation of neighboring modes cannot be neglected.