Shock wave generation in plasmas at varying magnetic field

Abstract

By considering the continuity, the Navier-Stokes and Poisson's equations in a nonrelativistic framework for plasmas, we study the behavior of small amplitude ion acoustic solitary waves in plasmas under the influence of a varying magnetic field. The result is a nonlinear wave equation which complies with the modified Korteweg-de Vries-Burgers equation, surprisingly in the absence of thermal pressure or any dissipative effects. We show that the complete set of equations, by considering the varying magnetic field, creates solitary waves which radiate energy during their travel in the medium. An interesting result is the existence of small amplitude localized shock profiles beside the solitary waves. Properties of this solitaire solution are studied by considering different values for the environmental characters.