Covariant Kinetic Theory with an Application to the Coma Cluster

In this paper, we introduce a novel solution to the covariant Landau equation for a pure electron plasma. The method conserves energy and particle number, and reduces smoothly to the Rosenbluth potentials of non-relativistic theory. In addition, we find that a fully relativistic plasma equilibrates in only 1/100th of a Spitzer time--much faster than in the non-relativistic limit--a factor of significant import to situations in which distortions to a Maxwellian distribution are produced by anomalous methods of acceleration. To demonstrate the power of our solution in dealing with hot, astrophysical plasmas, we use this technique to show that one of the currently considered models--continuous stochastic acceleration--for the hard X-ray emission in the Coma cluster actually cannot work because the energy gained by the particles is distributed to the {\it whole} plasma on a time scale much shorter than that of the acceleration process itself.