Stationary configurations of the two-dimensional current-carrying plasma sheet: Exact solutions

Possible stationary configurations in the system of the two-dimensional plasma sheet are considered for the case of inhomogeneous boundary conditions. The general form of solution representation has been used. The derived solution is more general than the well-known solution of Kan. It has the inhomogeneous (as a result of the effect of inhomogeneous boundary conditions) spatially oscillating topology of the fields, plasma distribution, and current in the plasma sheet. The derived solution to the stationary problem under inhomogeneous boundary conditions is the exact analytical solution that enables us to use it as the initial state in studying the dynamics of plasma sheets and describing the system's quasi-stationary evolution.