Bernstein‐Greene‐Kruskal analysis of electrostatic solitary waves observed with Geotail

Electrostatic solitary waves (ESW) relevant to the high‐frequency component of broadband electrostatic noise spectra observed by Geotail spacecraft in the magnetotail are analyzed. A general description of the ESW, as stationary solutions of Vlasov‐Poisson equations, is developed on the basis of the Bernstein‐Greene‐Kruskal (BGK) technique. It is shown that the structure and relationships among basic parameters of a localized perturbation are primarily determined by resonant and nonresonant plasma screenings of bunched electrons trapped by a potential pulse moving in a plasma. The dependence of the typical width of the pulse on its drift velocity and pulse amplitude is found, which can be treated as a nonlinear dispersion relation for the localized perturbation. The theoretical results are compared with the Geotail data and a particle simulation.