Self-consistent kinetic equations and the evolution of a relativistic plasma in an ambient magnetic field

A kinetic theory is developed for a relativistic, spatially- homogeneous multispecies plasma embedded in a uniform ambient magnetic field. The theory treats individual particle effects and collective effects on equal footing, and thereby describes both stable and weakly unstable plasma. The three-particle correlation, and nonlinear mode-mode coupling terms are neglected and a 'quasi- longitudinal, weak-field' approximation is employed in calculating the electric and magnetic field fluctuations. The final equations for the long time evolution of the particle distribution functions and the plasma wave intensities emphasize that the evolution of particles and their 'self-excited' waves is coupled in a non-linear manner. Specialized equations for a plasma consisting of cold electrons and protons and a relativistic proton 'tail' are given. These are particularly suited to a discussion of cosmic ray propagation through the interstellar medium no matter whether the cosmic ray distribution is stable or unstable.