Landau damping of electron-acoustic waves due to multi-plasmon resonances

TL;DR

This paper investigates how multi-plasmon resonances cause Landau damping of electron-acoustic waves in quantum plasmas, revealing a modified KdV equation with nonlocal nonlinearity and demonstrating slow wave amplitude decay.

Contribution

It introduces a novel nonlinear KdV model incorporating multi-plasmon resonances and analyzes their effect on wave damping in quantum plasmas.

Findings

Two-plasmon resonance dominates nonlinear Landau damping.

Wave energy decays over time due to nonlocal nonlinear effects.

Approximate soliton solutions show slow amplitude decay.

Abstract

The linear and nonlinear theories of electron-acoustic waves (EAWs) are studied in a partially degenerate quantum plasma with two-temperature electrons and stationary ions. The initial equilibrium of electrons is assumed to be given by the Fermi-Dirac distribution at finite temperature. By employing the multi-scale asymptotic expansion technique to the one-dimensional Wigner-Moyal and Poisson equations, it is shown that the effects of multi-plasmon resonances lead to a modified complex Korteweg-de Vries (KdV) equation with a new nonlocal nonlinearity. Besides giving rise to a nonlocal nonlinear term, the wave-particle resonance also modifies the local nonlinear coupling coefficient of the KdV equation. The latter is shown to conserve the number of particles, however, the wave energy decays with time. A careful analysis shows that the two-plasmon resonance is the dominant mechanism for nonlinear Landau damping of EAWs. An approximate soliton solution of the KdV equation is also obtained, and it is shown that the nonlinear Landau damping causes the wave amplitude to decay slowly with time compared to the classical theory.