Electrostatic solitary waves in the Earth's magnetosheath: An analytical approach

Electrostatic solitary waves (ESWs) are frequently detected by Cluster and Magnetospheric Multiscale missions within Earth's magnetosheath. Recent findings indicate that the observed ESWs exhibit typical parallel half-widths ranging from 10 to 100 m, corresponding to 1–10 Debye lengths, along with typical amplitudes of the electrostatic potential varying from 10 to 200 mV. Motivated by the above observations, in this study, we investigated the formation of ESWs in the Earth's magnetosheath using a theoretical model. In this model, we considered non-Maxwellian electrons (i.e., Cairns and kappa-distributed) and inertial fluid ions. Furthermore, using the reductive perturbation technique, the standard nonlinear Korteweg–de Vries equation is derived to examine the properties of ESWs associated with ion-acoustic waves. Our investigation admits both positive and negative potential structures. It has been found that the non-Maxwellian particle distribution influences the properties of ESWs, such as amplitude and width. We compared our results with those of earlier studies on ESWs in the aforementioned region. Based on this comparison, we found that our results are consistent with the observations.