Plasma Instabilities in Gamma‐Ray Bursts: Neutral Points and the Effect of Mode Coupling

Abstract

The method of determining neutral points, corresponding to vanishing frequency in wavenumber space, is applied to the case of gamma-ray bursts (GRBs) to determine low-frequency instabilities. If a particular particle distribution function permits the existence of neutral points, instability is guaranteed on one side or the other of the neutral point. By using the rest frame of the GRB jets, only perpendicular particle motion has to be taken into account. The discussion is limited to the cases of a monoenergetic electron-proton plasma with stationary protons and also to a symmetric electron-positron plasma. In the limiting case of wave propagation perpendicular to a homogeneous background magnetic field, taken to be parallel to the streaming direction of the jet, it is shown that to lowest order in the wave frequency, unstable aperiodic fluctuations occur that grow very rapidly on timescales comparable to or smaller than the characteristic times of the GRB, leading to the conclusion that the jets most likely consist mainly of electron-proton plasmas for the cases investigated. Furthermore, high electron Lorentz factors, as well as the coupling effect between longitudinal and transverse modes, are shown to stabilize the system.