Linear theory of electron temperature anisotropy instabilities: Whistler, mirror, and Weibel

A collisionless, homogeneous plasma in which the electron velocity distribution is a bi-Maxwellian with T-perpendicular to e > T-parallel to e, where the directional subscripts refer to directions relative to the background magnetic field B-o, can support the growth of two distinct instabilities. Linear dispersion theory predicts that the whistler anisotropy instability is excited with maximum growth rate gamma(m) at k x B-o = 0 and real frequency omega(r) greater than the proton cyclotron frequency, whereas the electron mirror instability is excited at propagation oblique to Bo and zero real frequency. In an unmagnetized plasma with a similarly anisotropic electron distribution the electron Weibel instability may be excited with zero real frequency and maximum growth rate in the direction of the minimum temperature. Here linear theory is used to compare dispersion and threshold properties of these three growing modes. For 0.10 <= beta(parallel to e) <= 1000, the whistler has a larger gamma(m) and a smaller anisotropy threshold than the electron mirror, so that the former mode should dominate in homogeneous plasmas for most physical values of electron beta. Threshold conditions describing electron temperature anisotropies and parallel wave numbers at given maximum growth rates are presented for each instability.