Ultra-relativistic Degenerate Electrons Research Articles

Radiation pressure-driven Rayleigh–Taylor instability in compressible strongly magnetized ultra-relativistic degenerate plasmas

The radiation pressure and strong magnetic fields are prominent in the structures of Rayleigh–Taylor (R–T) instability in the interior of white dwarfs. This paper investigates the radiation pressure-driven R–T instability in a compressible and magnetized ultra-relativistic degenerate strongly coupled plasma. The equation of state has been derived for such systems incorporating ultra-relativistic degenerate electrons with their radiation pressure and ion gas compressibility. The dispersion relation of the density gradients driven R–T instability is analyzed using the generalized hydrodynamic fluid model in the strongly coupled and weakly coupled limits. It is observed that the R–T instability criterion has been modified significantly due to radiation pressure, ion gas compressibility and degeneracy parameters. In the kinetic limit, the instability region is shorter than the hydrodynamic limit due to the dominance of plasma frequency over the viscoelastic relaxation frequency. The outcomes are explored in analyzing the development of R–T instability in the strongly magnetized carbon–oxygen white dwarfs. The radiation pressure, electron temperature and ion density strongly suppress the growth rate of the R–T instability in the interior of white dwarfs. The strong magnetic fields introduce asymmetry to the system by destabilizing the R–T unstable modes. The present results are also useful for understanding the R–T instability in the star formation and dense plasmas in inertial confinement fusion in some limiting cases.

Rayleigh–Taylor instability in compressible ultra-relativistic degenerate strongly coupled plasma

Dense stars (e.g., white dwarfs) are composed of mainly ultra-relativistic degenerate electrons and strongly coupled ions subjected to a gravitational field. Considering the physical conditions of such systems, in this paper, we investigate the linear Rayleigh–Taylor (R–T) instability in a compressible ultra-relativistic degenerate strongly coupled plasma (SCP) using the generalized hydrodynamic fluid model. The electron fluid is assumed to be inertialess, ultra-relativistic degenerate, and weakly coupled, while the ion fluid is treated as non-degenerate and strongly coupled. The compressibility effects are considered for the ion fluid in terms of the Coulomb coupling parameter and internal energy. The dispersion properties of the R–T instability have been analyzed using the normal mode analysis. For short wavelength perturbations, the R–T instability excites in the presence of compressibility and degeneracy of ultra-relativistic electrons; otherwise, the characteristic internal wave propagates in the plasma medium. The compressibility and strong coupling effects play a decisive role in suppressing the R–T modes in dense degenerate SCP. In the high-frequency kinetic limit, the instability region is observed to be shorter than the low-frequency hydrodynamic limit. The effects of ultra-relativistic degenerate electrons are almost negligible on the growth rates. However, they significantly modify the dispersion properties and R–T instability criterion. The astrophysical applications of the present work have been discussed in the high-density ultra-relativistic plasmas in the finite flame thickness near the center of white dwarfs.

Overtaking Interactions of Multi-Ion Acoustic Shock Waves in a Magnetized Degenerate Plasma: An Application in White Dwarfs

Overtaking interactions are examined of multi-ion acoustic shock waves in magnetized degenerate quantum plasmas comprising inertial non-relativistic heavy and light ions having positive charges ultra-relativistic degenerate inertialess electrons. A Burgers’ equation governs the nonlinear excitation of multi-ion acoustic shock waves in a plasma model at hand. The Cole-Hopf transformation and the exponential function have been used to study the overtaking interactions of multi-ion acoustic shock waves in two modes (i.e., the fast and the slow modes). Numerically, the compressive ion-acoustic shock waves exist for the fast mode, but the rarefactive ion-acoustic shock waves exist for the slow mode. A numerical simulation demonstrates that the overtaking interactions of multi-ion acoustic shock waves and their electric fields are remarkably modified with the effectiveness of the charge states of heavy ions and light ions. Furthermore, the amplitude and the steepness of multi-ion acoustic shock waves increase with the decrease in the directional cosines of the multi-ion acoustic shock waves vector along the z-axis. Numerical simulations of overtaking interaction are employed to significantly highlight the physical features of multi-ion acoustic shock waves in astrophysical situations such as white dwarfs and neutron stars.

Nonlinear excitation of large-amplitude ion acoustic solitary waves in a multispecies warm ion plasma with ultra-relativistic degenerate electrons

Nonlinear excitation of large-amplitude ion acoustic solitary waves in a multispecies warm ion plasma with ultra-relativistic degenerate electrons

Dressed solitons and double layers of ion-acoustic waves in a dusty plasma having ultra-relativistic degenerate two-temperature electrons

Dressed solitons and double layers of ion-acoustic waves in a dusty plasma having ultra-relativistic degenerate two-temperature electrons

Heavy-and light-nuclei acoustic dressed shock waves in white dwarfs

In this investigation, the evolution of heavy-and light-nuclei acoustic (HLNA) dressed shock waves (DSWs) due to the contribution of higher order of nonlinearity and dissipation effects has been examined in a degenerate quantum plasma composed of inertial heavy as well as light nuclei and inertia-less ultra-relativistic degenerate electrons. By employing the reductive perturbation method, the nonlinear Burgers equation is derived. Further, an inhomogeneous Burgers-type equation accounting for the higher order contributions of nonlinearity and dissipation is also derived. With the insertion of higher order effects, a new humped type or dressed shock structures are evolved. The influence of different plasma parameters on the dynamical evolution of the HLNA-DSWs is examined. It is observed that these plasma parameters play significant role on the characteristics of HLNA-DSWs and their corresponding electric fields. The findings of present investigation may be applicable to provide a new insight to understand the evolution of HLNA-DSWs in different dense astrophysical regions such as white dwarfs.

Modulational instability of bright envelope soliton and rogue waves in ultra-relativistic degenerate dense electron-ion-positron plasma

Modulational instability and bright envelope solitons of ion acoustic waves in dense plasma consisting of ultra-relativistic degenerate electrons and positrons, cold and mobile inertial ions, and negatively charged static dust particles have been investigated using Fried and Ichikawa method. Nonlinear Schrodinger equation has been derived and the growth rate of modulationally unstable ion acoustic wave in such plasma is discussed. It has been found that ion acoustic wave will be always modulationally unstable for all possible values of density of positrons, electrons and charged dust particle but there is no instability of the wave for any value of plasma parameters in such plasma. The solutions of ion acoustic envelope- solitons and rogue waves are obtained from the Nonlinear Schrodinger equation. The theoretical results have been analyzed numerically for different values of plasma parameters and the results are presented graphically. It is found that only bright envelope soliton would be excited in the ultra-relativistic plasma. Our results are new and may be applicable for the study of nonlinear wave processes in relativistic degenerate dense plasmas of astrophysical objects, namely, in white dwarfs and neutron stars.

Nonlinear rarefactive isothermal ion acoustic waves in magnetized ultrarelativistic degenerate plasmas

Abstract Nonlinear rarefactive isothermal ion-acoustic periodic travelling waves (RIIAPTWs) are examined in a magnetized ultrarelativistic degenerate plasma, containing warm fluid ions and ultrarelativistic degenerate inertialess electrons as well as positrons and immobile heavy negative ions. In the linear regime, the excitation of an isothermal ion-acoustic mode and its evolution are investigated. The physical behavior of nonlinear rarefactive isothermal ion-acoustic waves (RIIAWs) in this plasma model is governed by a Zakharov–Kuznetsov (ZK) equation. The analytical solutions for the nonlinear rarefactive isothermal ion-acoustic solitary waves (RIIASWs) and RIIAPTWs are performed by the bifurcation analysis. A careful discussion demonstrates the excitations of RIIASWs and RIIAPTWs are amplified (i.e., the amplitudes become deeper), as the chemical potential (or the Fermi energy at zero temperature) of electrons is decreased. It is found physically that the presence of the ultrarelativistic degenerate positrons and stationary heavy negative ions have strong effects on features of nonlinear RIIASWs and RIIAPTWs. The implications of the present finding in compact astrophysical objects, such as white dwarf stars, have been discussed.

Self-Gravitational Shock Structures in Self-Gravitating, Super-Dense, Degenerate Quantum Plasmas

The nonlinear propagation of self-gravitational shock structures (SGSSs) in a self-gravitating, super-dense, degenerate quantum plasma system (containing non-degenerate extremely heavy nuclei and ultra-relativistic degenerate electrons) has been investigated. The well-known reductive perturbation technique, which is valid in the small but finite amplitude limit, has been used to examine the nonlinear propagation of these SGSSs in such degenerate quantum plasma systems. The nonlinear dynamics of these SGSSs has been found to be governed by the Burgers equation, which is derived analytically and solved numerically in planar coordinates. These SGSSs in such plasma systems are shown to be formed due to the presence of a viscous force (which is the source of dissipation) acting on inertial extremely heavy nuclei species of the plasma system. The fundamental properties (viz., amplitude, width, speed, etc.) of these SGSSs are influenced in the ultra-relativistic limit. Our considered plasma model and the numerical analysis of the Burgers equation can be applied to astrophysical compact objects like neutron stars.

Three-Dimensional Isothermal Ion Acoustic Shock Waves in Ultra-Relativistic Degenerate Electron–Positron–Ion Magnetoplasmas

The modifications, which arise from ultra-relativistic and degenerate effects of electrons and positrons as well as the chemical potentials in the basic features of three-dimensional isothermal ion acoustic shock waves (IIASWs) propagating in magnetized electron–positron–ion (e–p–i) plasmas are studied. The cold ions are considered to be magnetized and inertial, while the small particles (i.e., electrons and positrons) are taken to obey the Fermi–Dirac statistics. The well-known reductive perturbation analysis is applied to obtain the nonlinear Zakharov–Kuznetsov–Burgers equation (NZKBE). The analytical shock wave solution is obtained by employing the tanh technique. Furthermore, the asymptotic behavior and the stability of the shock structures are discussed. In the current model, the disturbances of nonlinear isothermal ion acoustic waves are found to exhibit only monotonic IIASWs. The consequences of the chemical potential, the presence of ultra-relativistic degenerate electrons and positrons, and magnetic field on the essential properties of three-dimensional IIASWs are numerically examined. The numerical investigations give rise to significant high lights on the propagation and the dynamic behavior of IIASWs. It is found that the amplitudes of the monotonic IIASWs decrease with chemical potentials of ultra-relativistic degenerate electrons and positrons increase.

Effects of chemical potentials on isothermal ion-acoustic solitary waves and their three-dimensional instability in a magnetized ultra-relativistic degenerate multicomponent plasma

The three-dimensional instability of isothermal ion-acoustic (IIA) solitary waves is examined in a magnetized ultra-relativistic degenerate multicomponent plasma, comprising nondegenerate inertial warm ions and ultra-relativistic degenerate inertialess electrons as well as positrons, by applying a small-k (long wavelength) expansion method. The nonlinear dynamics of IIA solitary waves in such a plasma model are governed by the nonlinear Zakharov–Kuznetsov equation. To perform the analysis, the instability criterion and the growth rate of the instability of IIA solitary waves have been obtained. A careful investigation shows that the amplitude, the width, the growth rate, and the instability of IIA solitary waves increase with the increasing chemical potential of electrons. The stable region of IIA solitary waves increases with the increasing fermion population and the angle between the directions of propagation and the uniform magnetic field. The present study may be helpful for elucidating the physical nature of nonlinear waves in compact objects such as white dwarfs and neutron stars where the concentration of degenerate ultra-relativistic electrons and positrons and their chemical potentials play a crucial role.

Modulation Instability of Bright Envelope Soliton and Rogue Waves in Ultra-relativistic Degenerate Dense Electron–Ion–Positron Plasma

Modulation instability, bright envelope soliton, and rogue waves of ion acoustic waves in dense plasma consisting of ultra-relativistic degenerate electrons and positrons, cold and mobile inertial ions, and negatively charged static dust particles have been investigated using Fried and Ichikawa method. Nonlinear Schrodinger equation has been derived and the growth rate of modulationally unstable ion acoustic wave in such plasma are discussed. It has been found that ion acoustic wave will be always modulationally unstable for all possible values of density of positrons, electrons, and charged dust particle. The solutions of envelope solitons and rogue waves are obtained from the nonlinear Schrodinger equation. The theoretical results have been analyzed numerically and graphically for different values of plasma parameters. It is found that only bright envelope soliton would be excited in the ultra-relativistic degenerate plasma. Our results are new and may be applicable for the study of nonlinear wave processes in relativistic degenerate dense plasmas of astrophysical objects, namely, in white dwarfs and neutron stars.

Permanent mean spin source of the chiral magnetic effect in neutron stars

We suggest the generalization of the Anomalous Magneto-Hydro-Dynamics (AMHD) in the chiral plasma of a neutron star (NS) accounting for the mean spin in the ultrarelativistic degenerate electron gas within the magnetized NS core as a continuing source of the chiral magnetic effect. Using the mean field dynamo model generalized in AMHD, one can obtain the growth of a seed magnetic field up to 1018 G for an old non-superfluid NS at its neutrino cooling era t < 106 yr, while neglecting any matter turbulence within its core and assuming the rigid NS rotation. The application of the suggested approach to the evolution of magnetic fields observed in magnetars, B∼ 1015 G, should be self-consistent with all approximations used in the suggested laminar dynamo, at least, up to the jumps of growing fields.

Nonlinear nucleus-acoustic waves in strongly coupled degenerate quantum plasmas

We report the evolutionary dynamics of nonlinear nucleus-acoustic wave patterns excitable in a strongly coupled self-gravitating complex quantum degenerate plasma (QDP) systems. It is inertially composed of strongly correlated non-degenerate heavy nuclei and weakly coupled degenerate light nuclei treated classically. It is thermally constituted of non-relativistic and ultra-relativistic degenerate lighter electrons behaving quantum mechanically. Application of nonlinear perturbation analysis results in a conjugated pair of extended Korteweg-de Vries (e-KdV) equations of unique mathematical shape. The constructed numerical tapestry shows the collective excitations of a new conjugational pair of nonlinear eigenmode structures of gravito-electrosatic origin. The electrostatic potential fluctuations evolve as a distinct family of stable periodic symmetric waves resembling regular soliton-antisoliton pulse-trains; in contrast, the gravitational counterparts evolve as a unique extended class of asymmetric oscillatory solitons and non-monotonous compressive dispersive asymmetric pulse-trains. The microphysical influential dependencies of the eigenstructural patterns on various sensible plasma multi-parametric factors are illustratively analyzed in both the non-relativistic (NR) and ultra-relativistic (UR) limits of the non-local quantum electronic dynamics. The applicability of the explored results in wave kinetic phenomenological processes naturalistically relevant in diversified compact astro-objects and their ambient hydrodynamic atmospheres is summarily outlined.

Ion-Scale Excitations in a Strongly Coupled Astrophysical Plasma with Nuclei of Heavy Elements

The linear and nonlinear propagation of ultrarelativistic and nonrelativistic analysis on modified ion-acoustic (MIA) waves in a strongly coupled unmagnetized collisionless relativistic space plasma system is carried out. Plasma system is assumed to contain strongly coupled nonrelativistic ion fluids, both nonrelativistic and ultrarelativistic degenerate electron and positron fluids, and positively charged static heavy elements. The restoring force is provided by the degenerate pressure of the electron and positron fluids, whereas the inertia is provided by the mass of ions. The positively charged static heavy elements participate only in maintaining the quasineutrality condition at equilibrium. The well-known reductive perturbation method is used to derive the Burgers and Korteweg–de Vries equations. Their shock and solitary wave solutions are numerically analyzed to understand the localized electrostatic disturbances. The basic characteristics of MIA shock and solitary waves are found to be significantly modified by the effects of degenerate pressures of electron, positron, and ion fluids, their number densities, and various charge state of heavy elements. The implications of our results to dense plasmas in compact astrophysical objects (e.g., nonrotating white dwarfs, neutron stars, etc.) are briefly discussed.

Parallel propagating modes and anomalous spatial damping in the ultra-relativistic electron plasma with arbitrary degeneracy

The dispersion relations of parallel propagating modes (Langmuir mode, right and left handed circular polarized waves) in the weak magnetic field limit |ω − κ · ν| ≫ Ω are considered for ultra-relativistic arbitrary degenerate electron plasma. The results are presented in terms of moments of Fermi–Dirac distribution. The increase in the electron equilibrium number density from negative large (weakly degenerate) to positive large (highly degenerate) values of μ/Te is observed (where μ is the electron chemical potential and Te is the electron thermal energy). As a result, shifting of the cutoff points in all the real dispersion branches towards the higher values and increasing in the band gap between unmagnetized longitudinal and transverse modes in k-space are examined. Also, the suppression of the weak magnetic field effects in weakly magnetized right handed and left handed circular polarized waves and a decrease in the longitudinal and transverse screening effects are observed in the graphical patterns due to an increase in the equilibrium number density.

Arbitrary electron acoustic waves in degenerate dense plasmas

A theoretical investigation is carried out of the nonlinear dynamics of electron-acoustic waves in a collisionless and unmagnetized plasma whose constituents are non-degenerate cold electrons, ultra-relativistic degenerate electrons, and stationary ions. A dispersion relation is derived for linear EAWs. An energy integral equation involving the Sagdeev potential is derived, and basic properties of the large amplitude solitary structures are investigated in such a degenerate dense plasma. It is shown that only negative large amplitude EA solitary waves can exist in such a plasma system. The present analysis may be important to understand the collective interactions in degenerate dense plasmas, occurring in dense astrophysical environments as well as in laser–solid density plasma interaction experiments.

Magnetosonic Shocks in Ultra-Relativistic Dissipative Degenerate Plasmas

Magnetosonic shock structures in dissipative magnetized degenerate electron ion plasma are studied. The two fluid quantum magnetohydrodynamic equations for non-degenerate ions and ultra-relativistic degenerate electron fluids with the Maxwell equations are presented. Using the reductive perturbation technique the Korteweg de Vries Burgers (KdVB) equation is derived and its solution is presented with the tanh method. Astrophysical plasma parameters are used to study the effects of variation of plasma density, magnetic field intensity and kinematic viscosity on the propagation characteristics of nonlinear shock structures in such plasma systems.

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.

Ion Acoustic Solitary Waves in Degenerate Electron-Ion Plasmas

Employing the reductive perturbation method, a rigorous study of ion acoustic solitary waves (IASWs) in dense electron-ion plasmas is carried out leading to two evolution equations. Both the nonrelativistic and ultrarelativistic degenerate electron cases are considered. It is found that the relativistic parameter $R_{0}$ affects the IASW phase velocity. Stationary solutions of the derived evolution equations are estimated. The higher order contributions of the nonlinear and dispersion terms are calculated. It has been shown that it is more important to be included in the case of nonrelativistic electrons. These findings are devoted to explaining the observed solitary waves propagating in the outer periphery of compact dense stars, which mostly consists of hydrogen and helium ions with degenerate electrons.