The Earth's magnetosphere's modulational amplitude dust-ion-acoustic waves are studied. When the moon passes through the Earth's magnetotail, its dust grains may interact, causing these waves. The theoretical plasma model for this study includes positive ionospheric ion fluids, isothermal electrons, and fluid-negative dust grains on the moon. A perturbation technique derived the nonlinear Schrödinger equation, which exhibited dispersion and nonlinear effects. The nonlinear and dispersion term coefficients' polarity may predict stable and unstable pulse domains. A numerical study was performed to identify unstable pulse domains and their connections with bright and rogue unstable modes. The effects of critical plasma conditions on these pulses' basic features have been studied. This study showed that increasing the ratio of ions to electrons temperature and density reduces system nonlinearity. Consequently, shorter unstable pulses are formed. Amplification of plasma unstable waves results in an increase in their intensity and energy, potentially impacting any device traveling through the area of impact.

中文翻译：

---

调制尘埃离子声波是由地球磁层和月球电离层相互作用产生的

研究了地球磁层的尘埃离子声波的调制幅度。当月球穿过地球的磁尾时，其尘埃颗粒可能会相互作用，从而引起这些波。这项研究的理论等离子体模型包括月球上的正电离层离子流体、等温电子和负流体尘埃颗粒。微扰技术导出了非线性薛定谔方程，该方程表现出色散和非线性效应。非线性和色散项系数的极性可以预测稳定和不稳定的脉冲域。进行了一项数值研究，以确定不稳定脉冲域及其与明亮和流氓不稳定模式的联系。研究了临界等离子体条件对这些脉冲基本特征的影响。这项研究表明，增加离子与电子的比率、温度和密度可以降低系统非线性。因此，形成较短的不稳定脉冲。等离子体不稳定波的放大导致其强度和能量增加，可能会影响穿过影响区域的任何设备。