Self-similar Piston-Shock and CME

Based on a dimensional analysis, we discuss the existence conditions for one-dimensional self-similar solutions to the problem of a piston extending into an inhomogeneous plasma with magnetic field. In these solutions, the Mach number of a shock wave ahead of the piston is constant. As an application, we consider the SOL2010-06-13 solar eruptive event, where this property was found for a coronal wave at the formation stage of a coronal mass ejection (CME). Using a known wave trajectory in the distance-time plane, it is possible to follow the trajectory of an effective (virtual) piston that is a driver of the wave. The trajectory of the virtual piston originates in an eruptive filament during its impulsive acceleration and terminates at a rim bounding an apparent CME bubble in extreme-ultraviolet images, when the rim appears. The velocity of the rim at that time is approximately equal to the fast-mode speed at this place before the expansion onset, and the shock-front has a speed corresponding to a Mach number of about 1.5. We also discuss an analogy between the shock-wave propagation caused by the eruption of a solar magnetic flux-rope and the inverse-pinch effect as known from laboratory plasma physics.