Abstract
Linearized equations are set up to describe transverse waves in a relativistic plasma embedded in a magnetic field and in the presence of a nonrelativistic plasma. The waves are taken to propagate at right angles to the unperturbed field. Unstable waves are found to exist when the momentum distribution is taken to be of the cosmic ray type, but anisotropic. The instability exists only when relativistic particles are present and is a consequence of the mass of a fast particle being different from its rest mass. The maximum amplification rate is found for this case and is illustrated numerically by assuming physical values appropriate to the case of galactic cosmic ray electrons. It is shown that any anisotropy is rapidly destroyed and for cosmic ray electrons which are more than about a million years old isotropy is to be expected.
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