Nonlinear wave damping due to multi-plasmon resonances

Abstract

For short wavelengths, it is well known that the linearized Wigner-Moyal equation predicts wave damping due to wave-particle interaction, where the resonant velocity shifted from the phase velocity by a velocity $v_q=\hslash k/2m$. Here $\hslash$ is the reduced Planck constant, $k$ is the wavenumber and $m$ is the electron mass. Going beyond linear theory, we find additional resonances with velocity shifts $n{v}_q$, $n=2,3,\dots$, giving rise to a new wave-damping mechanism that we term \emph{multi-plasmon damping}, as it can be seen as the simultaneous absorption (or emission) of multiple plasmon quanta. Naturally this wave damping is not present in classical plasmas. For a temperature well below the Fermi temperature, if the linear ($n=1$) resonant velocity is outside the Fermi sphere, the number of linearly resonant particles is exponentially small, while the multi-plasmon resonances can be located in the bulk of the distribution. We derive sets of evolution equations for the case of two-plasmon and three-plasmon resonances for Langmuir waves in the simplest case of a fully degenerate plasma. By solving these equations numerically for a range of wave-numbers we find the corresponding damping rates, and we compare them to results from linear theory to estimate the applicability. Finally, we discuss the effects due to a finite temperature.

Accepted for publication in Plasma Physics and Controlled Fusion

References in corpus (2)

• Exchange effects in Coulomb quantum plasmas: Dispersion of waves in 2D and 3D mediums
• Nonlinear Landau damping of wave envelopes in a quantum plasma

Cited by in corpus (5)

• Wave-particle interactions in quantum plasmas
• Effects of group velocity and multi-plasmon resonances on the modulation of Langmuir waves in a degenerate plasma
• Linear pair creation damping of high frequency plasma oscillation
• Short-scale quantum kinetic theory including spin-orbit interactions
• Landau damping of electron-acoustic waves due to multi-plasmon resonances