Relativistic theory for localized electrostatic excitations in degenerate electron-ion plasmas

Abstract

A self-consistent relativistic two-fluid model is proposed for electron-ion plasma dynamics. A one-dimensional geometry is adopted. Electrons are treated as a relativistically degenerate fluid, governed by an appropriate equation of state. The ion fluid is also allowed to be relativistic, but is cold, nondegenerate, and subject only to an electrostatic potential. Exact stationary-profile solutions are sought, at the ionic scale, via the Sagdeev pseudopotential method. The analysis provides the pulse existence region, in terms of characteristic relativistic parameters, associated with the (ultrahigh) particle density.

Ion-beam/plasma modes in ultradense relativistic quantum plasmas: Dispersion characteristics and beam-driven instability

“…Our description follows closely the electrostatic relativis-tic model proposed in Refs. [29][30], thus extending the analytical framework proposed therein to take into account the ion beam.…”

“…where H = 1 + ξ 2 represents the dimensionless enthalpy of the system [29], where ξ = hne 4mec ; the relativistic factor is redefined as γ j = 1/ 1 − αu 2 j , where α = c 2 s /c 2 = µ e ξ 2 0 and ξ 0 = p F e /(m e c) = hn e0 /(4m e c).…”

“…(4). Within our model, the quantum relativistic pressure term derives from the (1D) equation of state [29,31]:…”

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

“…Both the static electronic response and the long-wavelength (and hence fluid) assumptions are collected in Eq. (27) of [29], reproduced here for convenience:…”

“…Eliasson and Shukla [26] derived certain nonlinear quantum electron fluid equation by taking into account the moments of the Wigner equation and using the Fermi-Dirac distribution function for electrons of arbitrary temperature. 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].…”