Non-resonant Alfv\'enic instability activated by high temperature of ion beams in compensated-current astrophysical plasmas

Abstract

Context: Compensated-current systems are established in response to hot ion beams in terrestrial foreshock regions, around supernova remnants, and in other space and astrophysical plasmas. Aims: We study a non-resonant reactive instability of Alfv\'en waves (AWs) propagating quasi-parallel to the background magnetic field $\mathbf{B}_{0}$ in such systems. Methods: The instability is investigated analytically in the framework of kinetic theory applied to the hydrogen plasmas penetrated by hot proton beams. Results: The instability arises at parallel wavenumbers $k_{z}$ that are sufficiently large to demagnetize the beam ions, $k_{z}V_{Tb}/\omega_{Bi}\gtrsim $ $1$ (here $V_{Tb}$ is the beam thermal speed along $\mathbf{B}_{0}$ and $\omega _{Bi}$ is the ion-cyclotron frequency). The Alfv\'en mode is then made unstable by the imbalance of perturbed currents carried by the magnetized background electrons and partially demagnetized beam ions. The destabilizing effects of the beam temperature and the temperature dependence of the instability threshold and growth rate are demonstrated for the first time. The beam temperature, density, and bulk speed are all destabilizing and can be combined in a single destabilizing factor $\alpha_{b}$ triggering the instability at {$\alpha _{b}>$ $\alpha _{b}^{\mathrm{thr}}$}, where the threshold varies in a narrow range $2.43\leq $ $\alpha _{b}^{\mathrm{thr}}\leq $ $4.87$. New analytical expressions for the instability growth rate and its boundary in the parameter space are obtained and can be directly compared with observations. Two applications to terrestrial foreshocks and foreshocks around supernova remnants are shortly discussed. In particular, our results suggest that the ions reflected by the shocks around supernova remnants can drive stronger instability than the cosmic rays.