Linear and nonlinear waves in quantum plasmas with arbitrary degeneracy of electrons

TL;DR

This review discusses recent advances in understanding linear and nonlinear wave phenomena in quantum plasmas with arbitrary electron degeneracy, deriving relevant equations and identifying physical conditions for various wave modes.

Contribution

It introduces a generalized approach to quantum plasma modeling that accounts for arbitrary electron degeneracy, extending previous dense plasma assumptions.

Findings

Derivation of quantum KdV and Zakharov-Kuznetsov equations for arbitrary degeneracy

Conditions for bright and dark soliton propagation in quantum plasmas

Analysis of wave modes in magnetized and unmagnetized quantum plasmas

Abstract

The purpose of this review is to revisit recent results in the literature where quantum plasmas with arbitrary degeneracy degree are considered. This is different from a frequent approach, where completely degeneracy is assumed in dense plasmas. The general reasoning in the reviewed works is to take a numerical coefficient in from of the Bohm potential term in quantum fluids, in order to fit the linear waves from quantum kinetic theory in the long wavelength limit. Moreover, the equation of state for the ideal Fermi gas is assumed, for arbitrary degeneracy degree. The quantum fluid equations allow the expedite derivation of weakly nonlinear equations from reductive perturbation theory. In this way, quantum Korteweg - de Vries and quantum Zakharov - Kuznetsov equations are derived, together with the conditions for bright and dark soliton propagation. Quantum ion-acoustic waves in unmagnetized and magnetized plasmas, together with magnetosonic waves, have been obtained for arbitrary degeneracy degree. The conditions for the application of the models, and the physical situations where the mixed dense - dilute systems exist, have been identified.