ACOUSTIC INSTABILITY DRIVEN BY COSMIC-RAY STREAMING

We study the linear stability of compressional waves in a medium throu gh which cosmic rays stream at the Alfven speed due to strong coupling with Alfven waves. Acoustic waves can be driven unstable by the cosmi c-ray drift, provided that the streaming speed is sufficiently large c ompared to the thermal sound speed. Two effects can cause instability: (1) the heating of the thermal gas due to the damping of Alfven waves driven unstable by cosmic-ray streaming; and (2) phase shifts in the cosmic-ray pressure perturbation caused by the combination of cosmic-r ay streaming and diffusion. The instability does not depend on the mag nitude of the background cosmic-ray pressure gradient, and occurs whet her or not cosmic-ray diffusion is important relative to streaming. Wh en the cosmic-ray pressure is small compared to the gas pressure, or c osmic-ray diffusion is strong, the instability manifests itself as a w eak overstability of slow magnetosonic waves. Larger cosmic-ray pressu re gives rise to new hybrid modes, which can be strongly unstable in t he limits of both weak and strong cosmic-ray diffusion and in the pres ence of thermal conduction. Parts of our analysis parallel earlier wor k by McKenzie & Webb (which were brought to our attention after this p aper was accepted for publication), but our treatment of diffusive eff ects, thermal conduction, and nonlinearities represent significant ext ensions., Although the linear growth rate of instability is independen t of the background cosmic-ray pressure gradient, the onset of nonline ar effects does depend on \delP(C)\ 1. At the onset of nonlinearity th e fractional amplitude of cosmic-ray pressure perturbations is deltaP( C)/P(C) - (kL)-1 much less than 1, where k is the wavenumber and L is the pressure scale height of the unperturbed cosmic rays. We speculate that the instability may lead to a mode of cosmic-ray transport in wh ich plateaus of uniform cosmic-ray pressure are separated by either la minar or turbulent jumps in which the thermal gas is subject to intens e heating.