Analytical solutions of the problem of violent explosions in a plasma of varying density

Abstract

Analytical solutions of the non-linear problem of violent explosions in a plasma of varying density under power law have been obtained. A critical law for a medium of decreasing density from the source of explosion is determined for which the problem admits a very simple solution but beyond this critical line analytical solutions admit another discontinuity automatically occuring inside a blast wave region. It is assumed that a disturbance caused by violent explosion due to sudden release of immense amount of energy is expanding very rapidly and is headed by a strong MHD shock wave. It is found that the discontinuity appearing inside a blast wave region causes a violation of continuum theory in the physical plane and consequently a cavity is formed. Analytical solutions predict that just before a discontinuity appears, the gas pressure falls to zero and the solution breaks down and can not be extended further. © 1981 Springer-Verlag.