Khan Khalid, Algahtani Obaid, Irfan Muhammad, Ali Amir
Department of Mathematics, University of Malakand, Dir (L), Khyber Pakhtunkhwa, Pakistan.
Department of Mathematics, College of Sciences, King Saud University, P. O. Box 2455, Riyadh, 11451, Saudi Arabia.
Sci Rep. 2022 Sep 7;12(1):15175. doi: 10.1038/s41598-022-19206-4.
The linear/nonlinear propagation characteristics of electron-acoustic (EA) solitons are examined in an electron-ion (EI) plasma that contains negative superthermal (dynamical) electrons as well as positively charged ions. By employing the magnetic hydrodynamic (MHD) equations and with the aid of the reductive perturbation technique, a Korteweg-de-Vries (KdV) equation is deduced. The latter admits soliton solution suffering from the superthermal electrons and the streaming flow. The utility of the modified double Laplace decomposition method (MDLDM) leads to approximate wave solutions associated with higher-order perturbation. By imposing finite perturbation on the stationary solution, and with the aid of MDLDM, we have deduced series solution for the electron-acoustic excitations. The latter admits instability and subsequent deformation of the wave profile and can't be noticed in the KdV theory. Numerical analysis reveals that thermal correction due to superthermal electrons reduces the dimensionless phase speed [Formula: see text] for EA wave. Moreover, a random motion spread out the dynamical electron fluid and therefore, gives rise to [Formula: see text]. A degree enhancement in temperature of superthermal (dynamical) electrons tappers of (increase) the wave steeping and the wave dispersion, enhancing (reducing) the pulse amplitude and the spatial extension of the EA solitons. Interestingly, the approximate wave solution suffers oscillation that grows in time. Our results are important for understanding the coherent EA excitation, associated with the streaming effect of electrons in the EI plasma being relevant to the earth's magnetosphere, the ionosphere, the laboratory facilities, etc.
在包含负超热（动力学）电子和带正电离子的电子 - 离子（EI）等离子体中，研究了电子 - 声学（EA）孤子的线性/非线性传播特性。通过采用磁流体动力学（MHD）方程，并借助约化摄动技术，推导出了一个科特韦格 - 德弗里斯（KdV）方程。后者允许存在受超热电子和流动影响的孤子解。改进的双拉普拉斯分解方法（MDLDM）的应用得到了与高阶摄动相关的近似波解。通过对定态解施加有限摄动，并借助MDLDM，我们推导出了电子 - 声学激发的级数解。后者允许波型的不稳定性和随后的变形，而这在KdV理论中是无法注意到的。数值分析表明，超热电子引起的热修正降低了EA波的无量纲相速度[公式：见原文]。此外，随机运动会使动态电子流体扩散，因此，导致[公式：见原文]。超热（动力学）电子温度的升高程度会抑制（增加）波的陡峭程度和波的色散，增强（降低）EA孤子的脉冲幅度和空间扩展。有趣的是，近似波解会出现随时间增长的振荡。我们的结果对于理解与EI等离子体中电子的流动效应相关的相干EA激发很重要，这种激发与地球磁层、电离层、实验室设施等有关。
