Geometry and dynamics of fast magnetosonic wavefronts near magnetic null points

The behavior of two-dimensional fast magnetosonic waves in the vicinity of isolated points where the magnetic field vanishes is studied analytically. The geometry of rays and wavefronts is described, and the curvature of both is found using conformal mapping techniques. These results are applied to the formation of shock waves, obtaining that shock formation is guaranteed at a finite time for any initial condition of the perturbation when the wavefront is concave and the rays tend to focus, whereas otherwise shocks occur only for a certain range of initial conditions.