Analytical and Numerical Study of Weibel Instability in Non-thermal Plasma

Abstract

The dispersion relation and growth rate γ of the parallel propagating Weibel mode in an unmagnetized, anisotropic non-thermal plasma are investigated using Cairns distribution function. The real and imaginary frequencies, considering Cairns distribution function in the limits of ξ >> 1 and ξ > 1), the real frequency of the wave under consideration is obtained, while in the lower limit (ξ << 1) the imaginary part of the frequency or growth rate is recovered. The real frequency and the growth rate both are shown to depend on the values of anisotropy parameter β = T⊥/T∥, parallel thermal speed v, and other parameters involved. The imperative role of spectral index α of Cairns distribution is also shown to affect the growth rate γ of the mode. In the limiting case when α → 0, the results obtained using the Cairns distribution approach those obtained with the Maxwellian distribution.