Dispersion and damping of potential surface waves in a degenerate plasma

TL;DR

This paper investigates electrostatic surface waves in a degenerate plasma half-space, revealing their dispersion relations and weak damping characteristics across a broad wavelength spectrum using a quasi-classical kinetic model.

Contribution

It provides a numerical analysis of surface wave spectra and damping rates in degenerate plasmas, highlighting differences from Maxwellian plasmas and identifying a nonmonotonic damping dependence on wavelength.

Findings

Surface waves approach the cold-plasma limit at long wavelengths.

Surface waves remain weakly damped at all wavelengths.

Maximum damping occurs at wavelength approximately 5π times the Thomas-Fermi length.

Abstract

Potential (electrostatic) surface waves in plasma half-space with degenerate electrons are studied using the quasi-classical mean-field kinetic model. The wave spectrum and the collisionless damping rate are obtained numerically for a wide range of wavelengths. In the limit of long wavelengths, the wave frequency $\omega$ approaches the cold-plasma limit $\omega=\omega_p/\sqrt{2}$ with $\omega_p$ being the plasma frequency, while at short wavelengths, the wave spectrum asymptotically approaches the spectrum of zero-sound mode propagating along the boundary. It is shown that the surface waves in this system remain weakly damped at all wavelengths (in contrast to strongly damped surface waves in Maxwellian electron plasmas), and the damping rate nonmonotonically depends on the wavelength, with the maximum (yet small) damping occuring for surface waves with wavelength of $\approx5\pi\lambda_{F}$, where $\lambda_{F}$ is the Thomas-Fermi length.