On Reactive Shock in Magnetogasdynamic Flow

In this paper, the behaviour of a detonation wave in a polytropic gas under the influence of an azimuthal magnetic field is investigated. It is assumed that the gas is shocked by an infinite piston moving at a constant velocity. Further, the shock is assumed to be sufficient to start the detonation and the detonation itself takes place rapidly throughout a thin and finite width region. The flow is divided into three domains - the unburnt gas ahead of the detonation, the burning zone in the boundary layer, and the burnt gas zone which extends from the back of the boundary layer to the piston. First, the characteristics of the system and generalised Riemann invariants are obtained, then the solutions in the reaction zone and outside the zone are found. Finally, the solution is obtained by matched asymptotic expansion. It turns out that the piston energy decreases with the increase of the Alfven speed. In the plane case, the activation energy increases (decreases) according to whether the magnetic field increases (decreases).