Dispersion and damping of potential surface waves in a degenerate plasma

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 ω approaches the cold-plasma limit ω = ω p / √ 2 with ω 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 ≈ 5πλ F , where λ F is the Thomas-Fermi length.

A new type of surface waves in a fully degenerate quantum plasma

“…15, of which perhaps the most critical ones are the neglect of the quantum recoil (which does not play a significant role unless the wavelengths are extremely short), and the assumptions of collisionless plasma and of the sharp perfectly reflecting boundary confining the plasma. Relaxing the first two assumption should not change the results qualitatively, 26 and there should still be two types of the surface waves when the quantum recoil is retained in the model.…”

“…(2) Contribution of singularities of 1/e(X, K) in the lower half of complex X plane, of two types: (i) residues at the poles of 1/e(X, K), which give the volume plasma oscillations, 19 and (ii) integrals along branch cuts (if any) of 1/e(X, K) in the lower half-plane of complex X, which can lead to non-exponential attenuation of the volume plasma oscillations. 23,24 (3) Contribution into (7) of singularities of 1/f(X, K k ) in the lower half of complex X plane, of two types: (i) residues at the poles of 1/f(X, K k ), corresponding to the surface wave solutions of the initial value problem in the considered system 15,19 and (ii) integrals along branch cuts (if any) of 1/f(X, K k ) in the lower half-plane of complex X.…”

“…Since the maximum growth rate is small, the surface oscillations due to the poles of 1/f(X, K k ) are weakly damped at all wavelengths. 15 B. Contribution of branch cuts of 1/f(X, K k )…”

“…13 This can affect the properties of SPW in a non-trivial way, via modification of analytic properties of the medium response. In particular, quantum effects (due to Pauli blocking and overlapping wave functions of free charge carriers in the medium 14 ), when significant, can modify the dispersion, damping, 15 and spatial attenuation of SPW (Ref. 16) supported by a bounded medium.…”

“…15 In particular, the effects of quantum recoil and quantum degeneracy of plasma electrons on SPW properties have been analyzed.…”