Whistler (or Helicon) Instability in Plasmas with Electron Beams

Growing whistlers, i.e., transverse electromagnetic waves propagating along the external magnetic field $B_0$, can exist in a gyrotropic plasma for anisotropic velocity distribution of the electrons. A previous analysis is extended to a plasma traversed by electron beams. Two approaches are adopted. In the first, an arbitrary complex phase velocity is assumed and the conditions on the plasma parameters for its existence may be investigated through a numerical procedure. In the second, the Nyquist criterion is employed to determine the wave vector and frequencies of marginally growing waves. Growth rates are obtained for wave vectors not differing appreciably from the marginal wave. An isotropic plasma is susceptible to growing waves in the presence of an electron beam under very weak conditions. It is possible to have situations suitable for the growth of whistlers but not for two-stream, instability.