Alfvén Waves and Shock Wave Formation at an X-Point Magnetic Field Configuration

We present MHD numerical simulations of the propagation of Alfvén waves in inhomogeneous magnetic fields whose topology consists of two-dimensional X-points threaded by a nonvanishing normal component. The coupling of the waves with the background field gradients leads to the development of fast-mode shock trains propagating normal to the average normal magnetic field. The fronts occur with a frequency matching that of the generating Alfvén wave. Energy in the original Alfvén wave packet is channeled via mode transformation to the fast waves and into the shocks,where it is dissipated at a rate independent of the Reynolds number. Such X-point shock trains might therefore play an important role in the heating of the solar corona plasma and,more generally,in cosmic particle acceleration.