We investigate the growth rate of field-aligned whistler-mode waves in space plasmas by using a fully relativistic treatment, including a recently developed relativistic kappa-loss-cone (KLC) distribution and a fully relativistic growth rate formula. Numerical calculations are carried out for a direct comparison between the new KLC distribution and the current kappa distribution, respectively. It is found that, in the lower wave frequency (e.g. ω ≲ 0.1Ωe), the wave growth by the KLC distribution is generally higher than that by the kappa distribution, due to a larger fractional number of the resonant electrons ηrel (which controls the wave growth) for the KLC distribution; but is lower in the higher wave frequency. The growth rates, as expected, tend to increase with the thermal anisotropy A, and the peak wave growth increases more rapidly for the kappa distribution. The relativistic anisotropy Arel basically decreases as the thermal parameter θ2 increases; whereas the fractional number of the resonant electrons ηrel is found to be large in the case of θ2 ∼ 150 keV, and results in a large wave growth. This indicates that hot electrons with typical energies of hundreds of keV may play a dominant role on the instability of whistler-mode waves. The results above have applications to plasma wave instability in the outer radiation belts of the Earth, the Jovian inner magnetosphere and other astrophysical plasmas where relativistic electrons are present.
我们研究了空间等离子体中场向哨声模波的增长率，采用了完全相对论的处理方法，包括最近发展的相对论损失锥（KLC）分布和完全相对论的增长率公式。我们对新的KLC分布与当前的kappa分布进行了数值计算直接比较。结果发现，在较低波频率（例如ω ≲ 0.1Ωe）下，KLC分布产生的波增长通常高于kappa分布，这是因为KLC分布中参与共振的电子数分数ηrel更大，而该分数控制着波增长；但在较高波频率下则相反。正如预期，增长率随热各向异性A的增加而增大，且对于kappa分布，峰值波增长增加得更快。相对论各向异性Arel基本上随热参数θ²的增加而减小；而共振电子数分数ηrel在θ² ∼ 150 keV时较大，并导致较大的波增长。这表明能量为数百keV的热电子可能对哨声模波的不稳定性起主导作用。上述结果可应用于地球外辐射带、木星内磁层以及其他存在相对论电子的天体物理等离子体中的波不稳定性研究。