A self-similar solution of exponential shock waves in non-ideal magnetogasdynamics

A self similar method is used to analyze numerically the one-dimensional, unsteady flow of a strong cylindrical shock wave driven by a piston moving with time according to an exponential law in a plasma of constant density. The plasma is assumed to be a non-ideal gas with infinite electrical conductivity permeated by an axial magnetic field. Numerical solutions in the region between the shock and the piston are presented for the cases of adiabatic and isothermal flow. The general behaviour of density, velocity, and pressure profiles remains unaffected due to presence of magnetic field in non-ideal gas. However, there is a decrease in values of density, velocity and pressure in case of magnetogasdynamics as compared to non-magnetic case. It may be noted that the effect of magnetic field on the flow pattern is more significant in case of isothermal flow as compared to adiabatic flow. The effect of non-idealness, specific heat exponent and magnetic field strength on the variation of shock strength across the shock front is also investigated.