Stability of an anisotropic relativistic plasma in a magnetic field

The collisionless relativistic Boltzmann equation is used to investigate the stability of a large-scale two-component plasma containing numerically small anisotropic relativistic populations. Although most permitted waves are stable, Alfvén type waves are found to be unstable whenever the anisotropy exceeds O(v _A/c). Growth times are estimated as days for supernova remnants and millennia for cosmic ray protons.