Electrostatic shock dynamics in superthermal plasmas

Abstract

The propagation of ion acoustic shocks in nonthermal plasmas is investigated, both analytically and numerically. An unmagnetized collisionless electron-ion plasma is considered, featuring a superthermal (non-Maxwellian) electron distribution, which is modeled by a $\kappa$- (kappa) distribution function. Adopting a multiscale approach, it is shown that the dynamics of low-amplitude shocks is modeled by a hybrid Korteweg-de Vries -- Burgers (KdVB) equation, in which the nonlinear and dispersion coefficients are functions of the $\kappa$ parameter, while the dissipative coefficient is a linear function of the ion viscosity. All relevant shock parameters are shown to depend on $\kappa$: higher deviations from a pure Maxwellian behavior induce shocks which are narrower, faster and of larger amplitude. The stability profile of the kink-shaped solutions of the KdVB equation against external perturbations is investigated and the spatial profile of the shocks is found to depend upon and the role of the interplay between dispersion and dissipation is elucidated.