Two-parametric system of equations for MHD equilibrium

The purpose of the paper was to reduce the system of equations describing static MHD-configurations to the minimum possible number of equations and to present the found equations in the form most adequate to the Cauchy problem. It is shown that the system of MHD-equations without symmetry assumption can be reduced to two equations. If the initial magnetic surface is not closed, the Cauchy problem can be solved, i. e. one can find the equilibrium plasma layer resting on the initial magnetic surface. But the situation sharply changes when one passes to closed initial magnetic surfaces especially to the systems with toroidal magnetic fields. In this case the solution is ambiguous. It means formally that the surface geometry and magnetic field can't be assigned simultaneously. In the physical sense it means that plasma filament formation begins, if one assigns the surface and then tries to impose the field on it