Higher-order approximations for the growth rate of the Weibel instability in strongly anisotropic plasmas

Simple higher-order approximations for the linear growth rate γ(k) of the electron Weibel instability are obtained by using fractional approximations for the plasma dispersion function. Approximate expressions for γ(k) are found that are valid in the regions T/T < 5 and T/T > 120 (where T and T are perpendicular and parallel electron temperatures respectively).