Back-reaction instabilities of relativistic cosmic rays

TL;DR

This paper investigates streaming instabilities caused by relativistic cosmic rays in plasma, revealing new instabilities with growth rates comparable to the Bell instability, relevant for astrophysical phenomena like supernova shocks.

Contribution

It derives dispersion relations for cosmic-ray-induced instabilities in a multi-fluid plasma, identifying new instabilities stronger than previously known ones and comparing different plasma return current models.

Findings

New instabilities with growth rates approaching Bell instability.

Identification of instabilities in ultra-relativistic cosmic rays.

Differences between plasma return current models are demonstrated.

Abstract

We explore streaming instabilities of the electron-ion plasma with relativistic and ultra-relativistic cosmic rays in the background magnetic field in the multi-fluid approach. Cosmic rays can be both electrons and ions. The drift speed of cosmic rays is directed along the magnetic field. In equilibrium, the return current of the background plasma is taken into account. One-dimensional perturbations parallel to the magnetic field are considered. The dispersion relations are derived for transverse and longitudinal perturbations. It is shown that the back-reaction of magnetized cosmic rays generates new instabilities one of which has the growth rate that can approach the growth rate of the Bell instability. These new instabilities can be stronger than the cyclotron resonance instability. For unmagnetized cosmic rays, the growth rate is analogous to the Bell one. We compare two models of the plasma return current in equilibrium with three and four charged components. Some difference between these models is demonstrated. For longitudinal perturbations, an instability is found in the case of ultra-relativistic cosmic rays. The results obtained can be applied to investigation of astrophysical objects such as the shocks by supernova remnants, galaxy clusters, intracluster medium and so on, where interaction of cosmic rays with turbulence of the electron-ion plasma produced by them is of a great importance for the cosmic-ray evolution.