Weibel instability with non-Maxwellian distribution functions

The Weibel instability in an unmagnetized plasma is investigated for non-Maxwellian distribution functions. In particular, analytical expressions are derived for the real and imaginary parts of the dielectric constant for the Maxwellian, kappa (κ), and (r,q) distribution functions under the conditions of ξ=ω∕k‖θ‖⪢1 and ⪡1. The real frequency and the growth rate of the instability now depend upon the values of the spectral indices of the distribution functions. In general, the growth rate is suppressed for small values of κ and q (keeping r fixed) and for negative values of r (keeping q fixed) instability transforms into damping. In the limiting cases (i) κ→∞ and (ii) r=0, q→∞, the results approach to the Maxwellian situation.

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