Double-wells and double-layers in dusty Fermi-Dirac plasmas: Comparison with the semiclassical Thomas-Fermi counterpart

TL;DR

This paper derives a new relationship in ultra-dense quantum plasmas and compares nonlinear wave phenomena in Fermi-Dirac and Thomas-Fermi models, revealing diverse excitations and the impact of relativistic degeneracy.

Contribution

It introduces a novel energy relation for relativistic electrons in quantum hydrodynamics and compares nonlinear wave structures between Fermi-Dirac and Thomas-Fermi plasmas.

Findings

Fermi-Dirac plasma supports various nonlinear excitations including double-wells.

Relativistic degeneracy significantly affects the wave speed range.

Fermi-Dirac and Thomas-Fermi models exhibit distinct nonlinear behaviors.

Abstract

Based on the quantum hydrodynamic model, a new relationship between the electrostatic-potential and the electron-density in the ultra-dense plasma is derived. Propagation of arbitrary amplitude nonlinear ion waves is, then, investigated in a completely degenerate dense dusty electron-ion plasma, using this new energy relation, for the relativistic electrons in the ground of quantum hydrodynamics model and the results are compared to the case of semiclassical Thomas-Fermi dusty plasma. Using the standard pseudo-potential approach it is remarked that the Fermi-Dirac plasma, in contrast to the Thomas-Fermi counterpart, accommodates a wide variety of nonlinear excitations such as positive-/negative-potential ion solitary and periodic waves, double-layers and double-wells. It is also remarked that, the relativistic degeneracy parameter which relates to the mass-density of plasma has significant effects on the allowed matching-speed range in dusty Fermi-Dirac plasmas.