Empirical model of whistler anisotropy instability

Empirical formulae for the real frequency and growth rate associated with the whistler anisotropy instability are obtained. The electrons are assumed to have an anisotropic distribution function, with Maxwellian parallel distribution. Under such an assumption complex roots of the dispersion relation depend only on two dimensionless parameters, namely, the temperature anisotropy factor A = T-perpendicular to e/T-parallel to e-1, where T-perpendicular to e and T-parallel to e are the perpendicular and parallel electron temperatures, respectively, and parallel electron beta, beta(parallel to) = (8 pi nT(parallel to e)/B-2)(1/2), where n and B are the plasma density and magnetic field intensity, respectively. Comparison against exact numerical roots show that analytical formulae describe the whistler instability over a wide range of parallel electron beta and temperature anisotropy factor. The present result may be useful for circumstances in which the use of exact numerical roots becomes impractical, such as in the radiation belt quasi-linear transport coefficient calculation. (C) 2011 American Institute of Physics. [doi:10.1063/1.3647504]