Plasma collective effects and pulsar emission models

Abstract

Several pulsar emission models are based on the fact that plasma instabilities caused by two relativistic particle streams can lead to radio or, in the case of the Crab pulsar, to optical, X-ray, and ..gamma..-ray emission. In this paper we study the unstable eigenmodes that can occur within a pulsar's light cylinder when the plasma consists of two or more relativistic particle streams of different momenta. Behavior of the unstable eigenmodes is investigated by analytical and/or numerical means as a function of parameters pertaining to the relativistic particle streams and the magnetic field. Where possible, all calculations are carried out in the pulsar (observer) frame of reference. The resulting expressions for the fastest growing waves can be easily compared with past or future pulsar models which predict particle steams of different momenta. We discuss the unstable eigenmodes in the context of parameters predicted by the Ruderman and Sutherland pulsar model. Additionally, we discuss conditions under which various unstable eigenmodes will be of importance and the effect of changes in the particle energy distribution on collective processes.