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

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.

Nonlinear ion-acoustic solitons in a magnetized quantum plasma with arbitrary degeneracy of electrons

“…(18), one has either ω = ω ci (the ion cyclotron frequency) or ω = ω 0 . The latter has been discussed in [29]. In the limit kλ D 1 one has ω 0 ≈ c s k, where the ion-acoustic speed contains only quantum degeneracy effects as seen from Eq.…”

“…(5) has been derived from finite-temperature quantum kinetic theory for low-frequency electrostatic excitations in [29],…”

“…(12) applies to MIAWs too. As discussed in [29], in the classical limit (z 1) one has α ≈ 1, while in the full degenerate limit (z 1) one has α ≈ 1/3. The same behavior is seen for α as a function of the chemical potential, as depicted in Fig.…”

“…Finally, to avoid too much complexity and to focus on the interplay between degeneracy and quantum recoil, exchange effects are also ignored. The equation of state can be obtained from the moments of a local Fermi-Dirac distribution function [29,31] of an ideal Fermi gas and reads…”

“…The relativistic description of localized wave packets in electrostatic plasma [27] as well as the associated ZK equation for dense relativistic plasma [28] was obtained, in the limit of a negligible thermodynamic temperature. Recently, the hydrodynamic equations for ionacoustic excitations in electrostatic quantum plasma with arbitrary degeneracy were put forward [29]. The purpose of the present paper is to achieve a notable generalization of this work, obtaining the corresponding fluid theory for quantum magnetized ion-acoustic waves (MIAWs), in both the linear and the nonlinear realms.…”