Wave production in an ultrarelativistic electron-positron plasma

Abstract

In this paper we calculate the eigenmodes associated with an ultrarelativistic electron-positron beam traversing a low-energy electron-positron plasma under physical conditions that may exist along open magnetic field lines above pulsar polar caps. We assume that both beam and plasma are cold and charge neutral, and that magnetic field strength and particle density decrease as the cube of (1/R). In the superstrong magnetic fields near the stellar surface where cyclotron frequencies exceed plasma frequencies, electrostatic waves and associated transverse low-frequency waves are driven unstable by the two-stream type particle distribution. At larger distances above the stellar surface the slow beam cyclotron wave is driven unstable. At even greater radial distance (approximately when particle energy density exceeds magnetic energy density) both the Ordinary and Alfven modes become unstable. All of these instabilities can lead to generation of radiation. If the particle distribution as generated at the stellar surface, assumed to consist of two streams, is modified only by plasma effects, then electrostatic and associated transverse waves may only be unstable near the stellar surface. The beam cyclotron mode which is driven by a two-stream or an inverted particle distribution may be stable.