Modeling electrostatic shock waves in kappa-distributed plasmas: overview of recent advancements

The nonlinear properties of electrostatic (ion-acoustic) shock waves are investigated, based on a plasma fluid-dynamical approach. A fluid plasma model is considered, consisting of inertial ions and kappa-distributed electrons. Electron trapping is phase space is taken into consideration. Weak dissipative effects (interactions) are taken into account via a small ad hoc term, due to the kinematic viscosity of the inertial ion fluid.

A hybrid (novel) version of the Korteweg - deVries/Burgers (KdVB) equation is derived for the electrostatic potential via a multiple scales perturbation technique. Shock wave solutions are subsequently obtained analytically and their stability is tested numerically.

This paper summarizes the salient aspects of electrostatic shock models, in the presence of suprathermal electrons, taking into account the combined effect of the ambient field and, where appropriate, particle trapping in phase space. A new type of PDE is derived and its analytical solutions are presented.