Theoretical model and experimental diagnostics of nonlinear electrostatic structures in space plasma

The formation of three-dimensional ion-acoustic electrostatic structures in the magnetized magnetospheric plasma is investigated. Basing on the MHD system of equations for three-component plasmas, evolutionary equations, which are the modified Korteweg-de Vries-Zakharov-Kuznetzov equations, are derived. The mathematical methods for the solution of these nonlinear equations with different degree of nonlinearity are developed. In the specific case of the spherical symmetry, numerical solutions of the evolutionary equations with different degree of nonlinearity are found. It is shown that in dependence on the distribution function of the hot electrons solitary structures with positive potential (compressive structures) or with negative potential (rarefactive structures) can be formed. The characteristics of these solitary structures as the ratio of the dimension parallel to the magnetic field to the dimension perpendicular to the field are estimated. The basic results of the numerical models are compared with experimental data obtained by satellites FAST, POLAR and GEOTAIL.