A modulational instability of nonlinearly interacting electron whistlers and magnetosonic perturbations is studied in the present paper. For typical parameters, there is no modulational instability. However, modulational instability appears in special cases. For example, when the whistler wavenumber is small enough, there is modulational instability. Its growth rate decreases as the angle between the external magnetic field and the perturbed wave's direction increases, while it increases as the whistler wavenumber increases. It is also found that there is no modulational instability when the whistler wavenumber is larger than a critical value ( $k_0 > 0.05$ ), in which the perturbed wave frequency increases as the angle between the external magnetic field and the perturbed wave's direction increases when the angle between the external magnetic field and the perturbed wave's direction is large enough. Whereas, the perturbed wave frequency first increases as the whistler wavenumber increases, reaches a peak value and then decreases as whistler wavenumber increases.

中文翻译：

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相互作用的电子哨声和磁声扰动的调制不稳定性

本文研究了非线性相互作用的电子哨声和磁声扰动的调制不稳定性。对于典型参数，不存在调制不稳定性。然而，在特殊情况下会出现调制不稳定。例如，当哨声波数足够小时，就会出现调制不稳定。其增长率随着外部磁场与扰动波方向夹角的增大而减小，而随着哨声波数的增大而增大。研究还发现，当哨声波数大于临界值时，不存在调制不稳定性（ $k_0 > 0.05$ ），其中当外部磁场与扰动波方向之间的角度足够大时，扰动波频率随着外部磁场与扰动波方向之间的角度的增大而增大。而扰动波频率首先随着哨声波数的增加而增加，达到峰值，然后随着哨声波数的增加而减小。