Similarity transformation for explosions in two-component plasmas with thermal energy and heat-flux relaxation

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Abstract
The nonlinear partial differential equations describing plane, cylindrical, and spherical explosions in a fully ionized electron-ion plasma with heat-flux relaxation and thermal relaxation are reduced to ordinary differential equations by means of novel similarity transformations. The resulting ordinary boundary-value problem for the plasma explosion, with the strong shock conditions as boundary values at the moving shock front, is formulated mathematically. The scaling laws for the plasma fields are presented which show how the plasma properties change with time during the course of the explosion. The importance of electron and ion heat-flux relaxation, which enhances the concentration of thermal energy behind the shock front, is stressed for the understanding of the shock-heating mechanism in fast processes. It is concluded that heat-flux relaxation is an important process for short-time plasma explosions, which determines the discontinuity of the electron and ion temperature fields at the shock front.

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