Head-on collision of nonlinear electrostatic shock waves in a relativistically degenerate plasma

Abstract

We present here theoretical investigation of colliding electrostatic shocks in an electron–ion plasma with relativistically degenerate electrons. A set of Korteweg–de Vries Burgers equations has been derived by employing a modified Poincaré–Lighthill–Kuo method for dissipative nonlinear ion acoustic structures. It has been found that relativistically degenerate plasma allows the formation of only compressional shocks. Moreover, the shocks are found to be sub-acoustic for the non-relativistic regime and super-acoustic for ultra-relativistic regime for a certain range of values of the ion kinematic viscosity. We have estimated the spatio–temporal scales, using the parameters generally found in white dwarf stars, for which the shock waves are theoretically anticipated to collide with each other in the relativistically degenerate plasma. The electric field across the shock has also been plotted numerically. The phase shifts of the shock waves resulting from the head-on collision have been estimated. The results may be helpful to understand the collision and dynamics of shock waves in astrophysical objects, such as hydrogen-rich white dwarf stars, and laboratory experiments, such as inertial confinement fusion.