Determination of the magnetic field B in vacuum for general two-dimensional MHD-equilibria

For general two-dimensional MHD-equilibria it is possible, by using complex functions, to obtain the solution of the vacuum magnetic field which fits the boundary conditions at the plasma surface. The solution allows a distinction between the geometry-governed and the plasma-magnetic-field-governed singularities and stagnation points. Several examples, particularly the elliptic-plasma-boundary case, are discussed.