2012ApJ...756...77N

Using a multi-fluid approach, we investigate the streaming and thermal instabilities of electron-ion-cosmic-ray astrophysical objects in which homogeneous cold cosmic rays have a drift velocity perpendicular to the background magnetic field. One-dimensional perturbations along the magnetic field are considered. The induced return current of the background plasma and back-reaction of cosmic rays are taken into account. It is shown that the cosmic-ray back-reaction results in a streaming instability with considerably higher growth rates than that due to the return current of the background plasma. This increase is by a factor of the square root of the ratio of the background plasma mass density to the cosmic-ray mass density. The maximal growth rate and the corresponding wavenumber are then found. Thermal instability is shown to be not subject to the action of cosmic rays in the model under consideration. The dispersion relation for thermal instability includes ion inertia. In the limit of a fast thermal energy exchange between electrons and ions, the isobaric and isochoric growth rates are obtained. The results can be useful for the investigation of electron-ion astrophysical objects such as galaxy clusters, including the dynamics of streaming cosmic rays.