Kappa distributions possess an enhanced high‐energy tail characterized by a spectral index κ. Here we consider how kappa distributions influence the whistler mode instability. In a relativistic regime, we analyze the effects of the bi‐kappa and kappa loss‐cone distributions on the linear and nonlinear growth of whistler mode waves. We find that for κ = 2, the linear growth rate corresponding to the bi‐kappa distribution exceeds that for a bi‐Maxwellian distribution (κ = ∞) for electron anisotropies less than a critical value. The threshold wave amplitude for nonlinear growth corresponding to a hot injected bi‐kappa distribution can be sensitively dependent on the value of κ, but also depends crucially on the electron anisotropy, parallel hot electron temperature, and wave frequency. We plot time profiles of the wave magnetic field, frequency, total nonlinear growth rate and local nonlinear growth rate, and examine how these depend on κ. The sweep (chirp) rates of the whistler mode chorus waves are found to be in the range of observed values, for the adopted plasma parameters. For a given value of the loss‐cone parameter σ, realistic whistler mode wave profiles may only exist for a restricted range of κ. For example, for σ ≥ 4, realistic wave profiles require κ ≥ 4 as well as a sufficiently large anisotropy. In summary, this new study finds that the influence of kappa distributions on the whistler mode instability is complex, not least because the instability depends on several system parameters as well as κ.

中文翻译：

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Kappa分布对惠斯勒模式不稳定性的影响

Kappa分布具有增强的高能尾巴，其特征在于光谱指数κ。在这里，我们考虑kappa分布如何影响惠斯勒模式的不稳定性。在相对论体系中，我们分析了双kappa和kappa loss-cone分布对惠斯勒模式波线性和非线性增长的影响。我们发现，对于κ  = 2，当 电子各向异性小于临界值时，与bi-kappa分布相对应的线性增长率超过了bi-Maxwellian分布（κ =∞）。与热注入双kappa分布相对应的非线性增长的阈值波幅度可以敏感地取决于κ的值，但也主要取决于电子各向异性，平行热电子温度和波频率。我们绘制了波磁场，频率，总非线性增长率和局部非线性增长率的时间曲线，并研究它们如何依赖于κ。对于所采用的等离子体参数，发现惠斯勒模式合唱波的扫描（线性调频）速率在观察值的范围内。对于损失圆锥参数σ的给定值，可能仅在κ的受限范围内存在实际的惠斯勒模式波轮廓。例如，对于σ≥4  ，实际波剖面需要κ ≥4以及足够大的各向异性。总而言之，这项新研究发现，κ分布对哨声模式不稳定性的影响非常复杂，这不仅是因为该不稳定性取决于多个系统参数以及κ。