Exact solutions and singularities of an X-point collapse in Hall magnetohydrodynamics

Abstract

Magnetic collapse is a basic dynamic scenario forming a current sheet, where magnetic reconnection can take place and convert magnetic energy into other forms. We discuss a self-similar magnetic collapse of a planar X-point configuration in incompressible Hall magnetohydrodynamics. There are two classes of exact solutions: globally regular and singular ones. The structure of solutions provides an exact expression for the time of breakdown in terms of the initial conditions.