Collisionless Damping of Hydromagnetic Waves in Relativistic Plasma. Weak Landau Damping

The propagation and damping of small-amplitude waves in a plasma of relativistic electrons and/ or protons is studied. As in the analogous nonrelativistic problem, the damping is found to be large except for particular angles of propagation. The results are applied, in the ultrarelativistic limit, to the problem of the heating of the high-energy electrons in the Crab Nebula. Some aspects of the morphology of the propagating disturbances near the center of the nebula can be understood in terms of the magnitude and angular dependence of the calculated damping. Subject headings: Crab Nebula - hydromagnetics - plasmas - relativity