EMHD theory and observations of electron solitary waves in magnetotail plasmas

A new approach of electron magnetohydrodynamics (EMHD) is developed by including the anisotropy of the electron pressure tensor to take Biermann battery effect into account. Based on the model, the dispersion relation of slow and fast electron magnetosonic modes are derived. A Korteweg‐de Vries equation is then obtained from the wave equation to get a solution of one‐dimensional slow‐mode soliton. Furthermore, according to measurements of Cluster and Time History of Events and Macroscale Interactions during Substorms, we find a good agreement between the theory and observations of magnetic field depression and perpendicular pressure increase.