Extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect

The propagation of extraordinary and upper-hybrid waves in spin quantum magnetoplasmas with vacuum polarization effect is investigated. Based on the quantum magnetohydrodynamics model including Bohm potential, arbitrary relativistic degeneracy pressure and spin force, and Maxwell's equations modified by the spin current and vacuum polarization current, the dispersion relations of extraordinary and upper-hybrid waves are derived. The analytical and numerical results show that quantum effects (Bohm potential, degeneracy pressure and spin magnetization energy) and the vacuum polarization effect modify the propagation of the extraordinary wave. Under the action of a strong magnetic field, the plasma frequency is obviously increased by the vacuum polarization effect.

POSSIBLE ENERGY SPECTRUM OF THE TWO DIMENSIONAL SPATIAL KLEIN-GORDON OSCILLATOR EQUATION

In the present article, one had found a complete energy spectrum and eigen-function of the solution of two dimensional (2D) spatial Klein-Gordon oscillator equation which shows that its relativistic degeneracy energy is related to the eigen-function.

Modulationally stable envelope solitons in astrophysical magnetoplasmas with degenerate relativistic electrons

The formation and propagation characteristics of small-amplitude magnetoacoustic dark/grey solitons are investigated in a semi relativistic degenerate magnetoplasma whose constituents are electrons and singly ionized positive ions. For this purpose, the electrons are assumed to follow the degeneracy pressure law through the Chandrasekhar equation of state, while the inertial cold ions are taken as non-degenerate and magnetized. By solving the one-fluid quantum magnetohydrodynamic (QMHD) model with the aid of a reductive perturbation technique, a nonlinear Schrödinger (NLS) equation is derived for weakly nonlinear envelope magnetoacoustic solitons. The NLS equation admits the existence of stable excitations, e.g. dark and grey solitons for which the condition $P/Q<0$ holds. Numerical results reveal that the variation of plasma number density, magnetic field strength, relativistic parameter $({\it\eta}_{e0})$ and the quantum parameter $(H)$ significantly modify the profiles of the envelope magnetoacoustic solitons. The present results are important to understanding of the nonlinear dynamics of magnetoacoustic solitons in astrophysical dense magnetoplasmas (viz., white dwarfs, magnetars, neutron stars, etc.), where the relativistic degeneracy effects play a vital role in collective interactions.

Low-dimensional relativistic degeneracy in quantum plasmas

In this work we investigate the effect of relativistic degeneracy on different properties of low-dimensional quantum plasmas. Using the dielectric response from the conventional quantum hydrodynamic model, including the quantum diffraction effect (Bohm potential) on free electrons, we explore the existence of the Shukla–Eliasson attractive screening and possibility of the ion structure formation in low-dimensional, completely degenerate electron–ion plasmas. A generalized degeneracy pressure expression for arbitrary relativity parameter in two-dimensional case is derived, indicating that change in the polytropic index (change in the equation of state) for the two-dimensional quantum fluid takes place at the electron number-density of n0 ≃ 1.1 × 1020cm−2 whereas this is known to occur for the three-dimensional case in the electron density of n0 ≃ 5.9 × 1029cm−3. Also, a generalized dielectric function valid for all dimensionalities and densities of a degenerate electron gas is calculated, and distinct properties of electron–ion plasmas, such as static screening, structure factor and Thomson scattering, are investigated in terms of plasma dimensionality.