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.

中文翻译：

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非热等离子体中韦贝尔不稳定性的解析与数值研究

使用凯恩斯分布函数研究了未磁化、各向异性非热等离子体中平行传播的 Weibel 模式的色散关系和增长率 γ。实数和虚数频率，考虑凯恩斯分布函数在 ξ >> 1 和 ξ > 1) 范围内，得到所考虑的波的实数频率，而在下限 (ξ << 1) 的虚部频率或增长率恢复。实际频率和增长率均取决于各向异性参数 β = T⊥/T∥ 的值、平行热速度 v 和其他相关参数。凯恩斯分布的光谱指数 α 的必要作用也被证明会影响模式的增长率 γ。在 α → 0 的极限情况下，