Magnetohydrodynamic plasma instability driven by Alfven waves excited by cosmic rays

Hydrodynamical equations describing the mutual interaction of cosmic rays, thermal plasma, magnetic field and Alfven waves scattering the cosmic rays used in cosmic ray shock acceleration theory are analysed for long-wavelength linear compressive instabilities. The Alfven wave field may contain a pre-existing component as well as a component excited by the cosmic ray streaming instability. The conditions under which the instabilities occur are delineated, and sample calculations of growth rates given. Possible applications of the instabilities to astrophysical situations are briefly discussed. (author)