Stability of two-dimensional ion-acoustic wave packets in quantum plasmas

TL;DR

This paper investigates the stability of two-dimensional quantum ion-acoustic wave packets in dense plasmas, revealing how quantum effects influence modulational instability and wave stability, with implications for laboratory and astrophysical plasmas.

Contribution

It derives a new set of coupled nonlinear equations for 2D quantum ion-acoustic waves and analyzes how quantum parameters affect modulational instability domains.

Findings

Quantum parameter shifts MI domains in the $k heta$-plane.

Ion-acoustic waves become unstable under quantum conditions where they are stable classically.

Obliqueness reduces the growth rate of modulational instability.

Abstract

The nonlinear propagation of two-dimensional (2D) quantum ion-acoustic waves (QIAWs) is studied in a quantum electron-ion plasma. By using a 2D quantum hydrodynamic model and the method of multiple scales, a new set of coupled nonlinear partial differential equations is derived which governs the slow modulation of the 2D QIAW packets. The oblique modulational instability (MI) is then studied by means of a corresponding nonlinear Schroedinger equation derived from the coupled nonlinear partial differential equations. It is shown that the quantum parameter H (proportional to $\hbar$), associated with the Bohm potential, shifts the MI domains around the $k\theta$-plane, where $k$ is the carrier wave number and $\theta$ is the angle of modulation. In particular, the ion-acoustic wave (IAW), previously known to be stable under parallel modulation in classical plasmas, is shown to be unstable in quantum plasmas. The growth rate of the MI is found to be quenched by the obliqueness of modulation. The modulation of 2D QIAW packets along $\mathbf{k}$ is shown to be described by a set of Davey-Stewartson-like equations. The latter can be studied for the 2D wave collapse in dense plasmas. The predicted results, which could be important to look for stable wave propagation in laboratory experiments as well as in dense astrophysical plasmas, thus generalize the theory of MI of IAW propagations both in classical and quantum electron-ion plasmas.