Linear and nonlinear ion-acoustic waves in non-relativistic quantum plasmas with arbitrary degeneracy

TL;DR

This paper investigates ion-acoustic waves in non-relativistic quantum plasmas with arbitrary electron degeneracy, deriving dispersion relations and soliton solutions that incorporate quantum effects and electron degeneracy.

Contribution

It introduces a comprehensive fluid model for quantum plasmas with arbitrary electron degeneracy, deriving new dispersion relations and nonlinear soliton solutions.

Findings

Ion-acoustic speed varies with plasma density and degeneracy.

Quantum effects influence soliton structures and phase velocities.

Results agree with quantum kinetic theory in the long wavelength limit.

Abstract

Linear and nonlinear ion-acoustic waves are studied in a fluid model for non-relativistic, unmagnetized quantum plasma with electrons with an arbitrary degeneracy degree. The equation of state for electrons follows from a local Fermi-Dirac distribution function and apply equally well both to fully degenerate or classical, non-degenerate limits. Ions are assumed to be cold. Quantum diffraction effects through the Bohm potential are also taken into account. A general coupling parameter valid for dilute and dense plasmas is proposed. The linear dispersion relation of the ion-acoustic waves is obtained and the ion-acoustic speed is discussed for the limiting cases of extremely dense or dilute systems. In the long wavelength limit the results agree with quantum kinetic theory. Using the reductive perturbation method, the appropriate Korteweg-de Vries equation for weakly nonlinear solutions is obtained and the corresponding soliton propagation is analyzed. It is found that soliton hump and dip structures are formed depending on the value of the quantum parameter for the degenerate electrons, which affect the phase velocities in the dispersive medium.