Effects of group velocity and multi-plasmon resonances on the modulation of Langmuir waves in a degenerate plasma

TL;DR

This paper investigates how group velocity and multi-plasmon resonances influence the nonlinear modulation of Langmuir waves in degenerate plasmas, revealing unique quantum effects on wave damping and stability.

Contribution

It derives a modified nonlocal nonlinear Schrödinger equation incorporating quantum resonances, highlighting the role of multi-plasmon processes in wave damping in degenerate plasmas.

Findings

Group velocity resonance does not necessarily cause damping in strong quantum regimes.

Three-plasmon processes dominate nonlinear Landau damping in certain quantum regimes.

Wave decay rates are higher in regimes where multi-plasmon effects are significant.

Abstract

We study the nonlinear wave modulation of Langmuir waves (LWs) in a fully degenerate plasma. Using the Wigner-Moyal equation coupled to the Poisson equation and the multiple scale expansion technique, a modified nonlocal nonlinear Schr{\"{o}}dinger (NLS) equation is derived which governs the evolution of LW envelopes in degenerate plasmas. The nonlocal nonlinearity in the NLS equation appears due to the group velocity and multi-plasmon resonances, i.e., resonances induced by the simultaneous particle absorption of multiple wave quanta. We focus on the regime where the resonant velocity of electrons is larger than the Fermi velocity and thereby the linear Landau damping is forbidden. As a result, the nonlinear wave-particle resonances due to the group velocity and multi-plasmon processes are the dominant mechanisms for wave-particle interaction. It is found that in contrast to classical or semiclassical plasmas, the group velocity resonance does not necessarily give rise the wave damping in the strong quantum regime where $ \hbar k\sim mv_{F}$ with $\hbar$ denoting the reduced Planck's constant, $m$ the electron mass and $v_F$ the Fermi velocity, however, the three-plasmon process plays a dominant role in the nonlinear Landau damping of wave envelopes. In this regime, the decay rate of the wave amplitude is also found to be higher compared to that in the modest quantum regime where the multi-plasmon effects are forbidden.