Spherical and cylindrical imploding and exploding shock waves in plasma system dominated by pair production

Abstract

The propagation of ion acoustic shock waves in cylindrical and spherical geometries has been investigated. The plasma system consists of cold ions, Boltzmannian electrons and positrons. Spherical, cylindrical Korteweg–de Vries–Burger equations have been derived by reductive perturbation technique and their shock behavior is studied by employing finite difference method. Our main emphasis is on the behavior of shock as it moves toward and away from center of spherical and cylindrical geometries. It is noticed, that the shock wave strength and steepness accrues with time as it moves toward the center and shock enervates as it moves away from center. The strength of shock in spherical geometry is found to dominate over shock strength in cylindrical geometry. Positron concentration, kinematic viscosity are also found to have significant effect on the shock structure and propagation. The results may have relevance in the inertial confinement fusion plasmas.