MHD EQUILIBRIA WITH CUSPED PLASMA-VACUUM INTERFACES

The free-boundary MHD equilibrium is considered in the case of plane symmetry and constant current profile. We prove the existence of solutions in a neighbourhood of cusp singularities of the plasma-vacuum interface. In both cases - the ''plasma'' and ''vacuum cusps'' - we derive a power law describing the asymptotic shape of the cusps; the allowed exponents are half-integers. This leads to a natural classification of cusps. The solutions are classified accordingly and their asymptotic behaviour close to the cusp is found to depend only on the class to which the solution belongs.