Multidimensional ion-acoustic solitary waves and shocks in quantum plasmas

TL;DR

This paper develops a nonlinear theory for two-dimensional ion-acoustic solitary waves and shocks in dissipative quantum plasmas, considering quantum effects and dissipation, and analyzes their properties and transitions.

Contribution

It derives a Kadomtsev-Petviashvili Burgers-type equation for quantum plasmas and explores the conditions for different shock types and their properties.

Findings

KPB equation admits compressive or rarefactive SWS depending on quantum parameter H.

Large-amplitude stationary shocks analyzed numerically, showing transition from monotonic to oscillatory shocks.

Quantum effects significantly influence the nature and properties of ion-acoustic shocks in quantum plasmas.

Abstract

The nonlinear theory of two-dimensional ion-acoustic (IA) solitary waves and shocks (SWS) is revisited in a dissipative quantum plasma. The effects of dispersion, caused by the charge separation of electrons and ions and the quantum force associated with the Bohm potential for degenerate electrons, as well as, the dissipation due to the ion kinematic viscosity are considered. Using the reductive perturbation technique, a Kadomtsev-Petviashvili Burgers (KPB)-type equation, which governs the evolution of small-amplitude SWS in quantum plasmas, is derived, and its different solutions are obtained and analyzed. It is shown that the KPB equation can admit either compressive or rarefactive SWS according to when $H\lessgtr2/3$, or the particle number density satisfies $n_0\gtrless 1.3\times10^{31}$ cm$^{-3}$, where $H$ is the ratio of the electron plasmon energy to the Fermi energy densities. Furthermore, the properties of large-amplitude stationary shocks are studied numerically in the case when the wave dispersion due to charge separation is negligible. It is also shown that a transition from monotonic to oscillatory shocks occurs by the effects of the quantum parameter $H$.