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.