Flow behind magnetogasdynamic exponential shock wave in self-gravitating gas

The propagation of a cylindrical (or spherical) shock wave driven out by a piston moving with time according to an exponential law, in a self-gravitating ideal gas with azimuthal magnetic field is investigated. The initial magnetic field is assumed to be varying according to an exponential law. Solutions are obtained for both the cases of isothermal and adiabatic flows. The effects of variation of ambient magnetic field, gravitational parameter and adiabatic exponent are worked out in detail. It is manifested that the increase in strength of ambient magnetic field has decaying effect on the shock wave however increase in the value of gravitational parameter has reverse effect on the shock strength. The compressibility of the medium is increased in the presence of gravitational field. Also, a comparison between the solutions obtained in the case of isothermal and adiabatic flows is done. Density, pressure, velocity and magnetic field increases, however mass decreases as we move inward from the shock front towards the piston.