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Streaming cold cosmic ray back-reaction and thermal instabilities

We investigate the streaming and thermal instabilities of the electron-ion plasma with homogeneous cold cosmic rays drifting perpendicular to the background magnetic field in the multi-fluid approach. 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 the streaming instability having considerably larger 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 rates and corresponding wave numbers are found. The thermal instability is shown to be not subject to the action of cosmic rays in the model under consideration. The dispersion relation for the thermal instability includes ion inertia. In the limit of fast thermal energy exchange between electrons and ions, the isobaric and isochoric growth rates are derived. The results obtained can be useful for the investigation of the electron-ion astrophysical objects such as galaxy clusters including the dynamics of streaming cosmic rays.