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.
