Non-relativistic Degenerate Electrons Research Articles

Obliquely Propagating Self-Gravitational Shock Waves in Non-Relativistic Degenerate Quantum Plasmas

A rigorous theoretical investigation has been carried out on the propagation of non-linear self-gravitational shock waves (SGSHWs) in a magnetized super dense degenerate quantum plasma system (DQPS) composed of inertia-less non-relativistic degenerate electrons and inertial non-degenerate extremely heavy nuclei/element. The nonlinear propagation of these SGSHWs in the plasma system under consideration is studied by the standard reductive perturbation technique, which is valid for a small finite amplitude limit. The nonlinear dynamics of the SGSHWs are found to be governed by the Burgers equation. The Burgers equation is derived analytically and solved numerically. It has been found that the considered plasma model supports positive potential shock waves only. The fundamental properties (amplitude, steepness, etc.) of these SGSHWs are significantly modified by the variation of kinematic viscosity, obliqueness and number density of the plasma species. The results of our present investigation can be applied to astrophysical compact objects like neutron stars. Journal of Engineering Science 15(1), 2024, 21-29

Numerical simulations and bifurcation analysis of monotonic and oscillatory magnetosonic shock waves in a spin 1/2 degenerate quantum plasma

Nonlinear propagation of monotonic and oscillatory magnetosonic shock waves in a magnetized degenerate quantum plasma consisting of ions and spin 1/2 nonrelativistic degenerate electrons is examined. The well-known reductive perturbation analysis is applied to obtain a Korteweg–de Vries–Burgers equation (KdVBE). The dissipative system of coupled nonlinear, ordinary, differential equations and the equilibrium points are hereby discussed on the basis of the bifurcation analysis. The nonlinear behaviour of shock wave structures is numerically investigated under the fourth order Runge-Kutta method. Numerical simulations show that the behaviour of monotonic and oscillatory magnetosonic shock waves depends essentially on the effects of quantum statistics and the spin magnetization energy. The present results may be helpful for an in-depth understanding of the nonlinear propagation of magnetosonic waves in magnetized degenerate quantum plasma, which occur in the dense astrophysical objects.

Anisotropic pressure in brown dwarf stars

The dynamical nature of the fluid motion in very low-mass and brown dwarf stars indicates that the magnetic field has to be generated in these objects by dynamo action. Pressure in these stars is supported partially by non-relativistic degenerate electrons. It was established that the magnetic field can act on degenerate gas produces pressure anisotropy. Also anisotropy can be generated in rotating stars. Hence magnetic field and rotation may be considered as a source of anisotropy in such stars. This paper addresses the effect of anisotropy in the minimum mass of hydrogen burning and in brown dwarf stars. The results show that the minimum mass of the star needs to be increased to reach the stability condition due to the existence of pressure anisotropy and there was a change in the mass-radius relation for that stars.

Arbitrary amplitude electrostatic wave propagation in a magnetized dense plasma containing helium ions and degenerate electrons

The obliquely propagating arbitrary amplitude electrostatic wave is studied in a dense magnetized plasma having singly and doubly charged helium ions with nonrelativistic and ultrarelativistic degenerate electrons pressures. The Fermi temperature for ultrarelativistic degenerate electrons described by N. M. Vernet [(Cambridge University Press, Cambridge, 2007), p. 57] is used to define ion acoustic speed in ultra-dense plasmas. The pseudo-potential approach is used to solve the fully nonlinear set of dynamic equations for obliquely propagating electrostatic waves in a dense magnetized plasma containing helium ions. The upper and lower Mach number ranges for the existence of electrostatic solitons are found which depends on the obliqueness of the wave propagation with respect to applied magnetic field and charge number of the helium ions. It is found that only compressive (hump) soliton structures are formed in all the cases and only subsonic solitons are formed for a singly charged helium ions plasma case with nonrelativistic degenerate electrons. Both subsonic and supersonic soliton hump structures are formed for doubly charged helium ions with nonrelativistic degenerate electrons and ultrarelativistic degenerate electrons plasma case containing singly as well as doubly charged helium ions. The effect of propagation direction on the soliton amplitude and width of the electrostatic waves is also presented. The numerical plots are also shown for illustration using dense plasma parameters of a compact star (white dwarf) from literature.

New analytical solutions for propagation of small but finite amplitude ion-acoustic waves in a dense plasma

The theoretical and numerical studies have been investigated on the nonlinear propagation of electrostatic ion-acoustic waves (IAWs) in an un-magnetized Thomas–Fermi plasma system consisting of electron, positrons, and positive ions for both of ultra-relativistic and non-relativistic degenerate electrons. Korteweg-de Vries (K-dV) equation is derived from the model equations by using the well-known reductive perturbation method. This equation is solved by employing the generalized Riccati equation mapping method. The hyperbolic functions type solutions to the K-dV equation are only considered for describing the effect of plasma parameters on the propagation of electrostatic IAWs for both of ultra-relativistic and non-relativistic degenerate electrons. The obtained results may be helpful in proper understanding the features of small but finite amplitude localized IAWs in degenerate plasmas and provide the mathematical foundation in plasma physics.

Modulation of drift-wave envelopes in a nonuniform quantum magnetoplasma

We study the amplitude modulation of low-frequency, long-wavelength electrostatic drift-wave envelopes in a nonuniform quantum magnetoplasma consisting of cold ions and degenerate electrons. The effects of tunneling associated with the quantum Bohm potential and the Fermi pressure for nonrelativistic degenerate electrons, as well as the equilibrium density and magnetic field inhomogeneities are taken into account. Starting from a set of quantum magnetohydrodynamic equations, we derive a nonlinear Schrödinger equation (NLSE) that governs the dynamics of the modulated quantum drift-wave packets. The NLSE is used to study the modulational instability (MI) of a Stoke's wave train to a small plane wave perturbation. It is shown that the quantum tunneling effect as well as the scale length of inhomogeneity plays crucial roles for the MI of the drift-wave packets. Thus, the latter can propagate in the form of bright and dark envelope solitons or as drift-wave rogons in degenerate dense magnetoplasmas.

Quadrupole moment of a magnetically confined mountain on an accreting neutron star: effect of the equation of state

Magnetically confined mountains on accreting neutron stars are promising sources of continuous-wave gravitational radiation and are currently the targets of directed searches with long-baseline detectors like the Laser Interferometer Gravitational Wave Observatory (LIGO). In this paper, previous ideal-magnetohydrodynamic models of isothermal mountains are generalized to a range of physically motivated, adiabatic equations of state. It is found that the mass ellipticity drops substantially, from \epsilon ~ 3e-4 (isothermal) to \epsilon ~ 9e-7 (non-relativistic degenerate neutrons), 6e-8 (relativistic degenerate electrons) and 1e-8 (non-relativistic degenerate electrons) (assuming a magnetic field of 3e12 G at birth). The characteristic mass M_{c} at which the magnetic dipole moment halves from its initial value is also modified, from M_{c}/M_{\sun} ~ 5e-4 (isothermal) to M_{c}/M_{\sun} ~ 2e-6, 1e-7, and 3e-8 for the above three equations of state, respectively. Similar results are obtained for a realistic, piecewise-polytropic nuclear equation of state. The adiabatic models are consistent with current LIGO upper limits, unlike the isothermal models. Updated estimates of gravitational-wave detectability are made. Monte Carlo simulations of the spin distribution of accreting millisecond pulsars including gravitational-wave stalling agree better with observations for certain adiabatic equations of state, implying that X-ray spin measurements can probe the equation of state when coupled with magnetic mountain models.

Relativistic Degeneracy Effect on Propagation of Arbitrary Amplitude Ion-Acoustic Solitons in Thomas-Fermi Plasmas

Arbitrary amplitude ion-acoustic solitary waves (IASWs) are studied using Sagdeev-Potential approach in electron-positron-ion plasma with ultra-relativistic or non-relativistic degenerate electrons and positrons and the matching criteria of existence of such solitary waves are numerically investigated. It has been shown that the relativistic degeneracy of electrons and positrons has significant effects on the amplitude and the Mach-number range of IASWs. Also it is remarked that only compressive IASWs can propagate in both non-relativistic and ultra-relativistic degenerate plasmas.

Influence of the intrinsic magnetic moment of an electron on the filling of energy levels of a nonrelativistic degenerate electron gas in a quantizing magnetic field

The effect of a quantizing magnetic field on the filling of energy subbands of a degenerate nonrelativistic electron gas, whose magnetic moments are parallel and antiparallel to the direction of the field, is studied. Calculations are made under the assumption that the Fermi kinetic energy of the electron system increases as a result of Pauli's paramagnetism as compared to the kinetic energy calculated without taking this effect into account. Numerical values of the electron concentration are calculated as a function of the magnetic moment direction for magnetic fields under which the electrons are in states with given numbers of the Landau quantum level.

Magnetic susceptibility of relativistic Fermi gas

The magnetic susceptibility of a degenerate relativisitc Fermi gas is obtained for charged fermions with anomalous magnetic moments. The expression for the magnetic susceptibility of the non-relativistic degenerate electron gas is well known in the theory of metals (see for example Ziman (1972)). It consists of two parts corresponding to two different physical effects. The first of them is connected with the behaviour of spin moments in the external magnetic field (Pauli paramagnetism (Pauli 1927)). The second is the result of the circular motion of charges in the magnetic field (Landau diamagnetism (Landau 1930)). For non-relativistic fermions the paramagnetic and diamagnetic susceptibilities can be independently calculated. This is not true for the relativistic case. Magnetic properties of the relativistic Fermi gas are of interest because degenerate relativistic electrons and nucleons form white dwarfs and neutron stars (see for example Weinberg (1972)). As is known, the nucleons have anomalous magnetic moments which also contribute to the magnetic susceptibility. In this connection we consider the Lagrangian (Gell-Mann 1956, see also Bjorken and Drell 1965) including the dipole interaction between the fermion 4 and the external electromagnetic field A,,