A model of plasma sheath of magnetized planets: Self-similar case

In studying processes during solar flares or during the explosive phase of a substorm, problems of equilibrium and non-equilibrium configurations of magnetized plasma arise. First of all, it is extremely important to know a stationary state of the system in order to further study of it’s evolution. The magnetohydrodynamic approach we have chosen as the main tool. The main task is to solve the Grad-Shafranov equation, that determines an equilibrium configuration with a non-linear distribution of the longitudinal current. Various options for the longitudinal current are considered. The results of the solution in addition to the ”earthly” application can be used in considering physical phenomena in the magnetized planets magnetospheres, in the shells of pulsars, as well as in a laboratory. In this paper, we considered in detail the solutions leading to the dependence of the magnetic flux on the distance in the form of r−1. This dependence is typical for most space objects with a ring structure.