Unstable Magnetosonic Waves in a Relativistic Plasma

Abstract

Linearized equations are set up to describe the effect of a circularly polarized electromagnetic wave on a plasma composed of thermal electrons and protons and also containing an anisotropic relativistic proton component. The unperturbed composite plasma is taken to be imbedded in a homogeneous, uniform magnetic field and the wave is taken to propagate along the unperturbed magnetic field. For wave frequencies very much less than the electron cyclotron frequency it is shown that the relativistic proton plasma will be unstable provided only that P|| > P x , where P\\ and P x denote the relativistic plasma pressures parallel and perpendicular to the ambient magnetic field, respectively. The minimum ^-folding time is estimated and upon inserting numerical parameters appropriate to the cosmic-ray gas in the galactic disk it is shown that parallel anisotropy (P|| > P x) will be destroyed in a time short compared to the mean lifetime of cosmic rays in the disk (^6 X 10 5 years).