Relativistic Degeneracy Research Articles

Weak dissipative ion-acoustic solitons in relativistically degenerate collisional plasma

Using the quantum hydrodynamical model, we study the effect of collisions on the dynamics of nonlinear ion-acoustic waves in a superdense degenerate electron-ion plasma. The electrons are assumed to be moving with relativistic velocities. The standard reductive perturbation technique leads to a dissipative KdV equation, for small amplitude electrostatic potential disturbances. The dynamics of these solitary waves is studied both analytically as well as numerically. It is observed that the system supports both positive as well as negative potential ion-solitary waves. The interplay between the relativistic degeneracy parameter and the ion-neutral collision frequency gives rise to both dispersion and dissipation, such that the soliton energy, amplitude, and velocity decrease exponentially with time, whereas its width increases.

New insight into the dispersion characteristics of electrostatic waves in ultradense plasmas: electron degeneracy and relativistic effects

The dispersion properties of electrostatic waves propagating in ultrahigh density plasma are investigated, from first principles, in a one-dimensional geometry. A self-consistent multispecies plasma fluid model is taken as starting point, incorporating electron degeneracy and relativistic effects. The inertia of all plasma components is retained, for rigor. Exact expressions are obtained for the oscillation frequency, and the phase and group velocity of electrostatic waves is computed. Two branches are obtained, viz. an acoustic low-frequency dispersion branch and an upper (optic-like) branch: these may be interpreted as ion-acoustic and electron plasma (Langmuir) waves, respectively, as in classical plasmas, yet bearing an explicit correction in account of relativistic and electron degeneracy effects. The electron plasma frequency is shown to reduce significantly at high values of the density, due to the relativistic effect. The result is compared with approximate models, wherein either electrons are considered inertialess (low-frequency ionic scale) or ions are considered to be stationary (Langmuir-wave limit).

Effects of quantum statistical pressure on the Washimi-Karpman magnetization and power radiation in degenerate quantum Fermi-Dirac plasmas

The physical properties of the Washimi-Karpman ponderomotive magnetization are investigated in relativistically degenerate quantum Fermi-Dirac plasmas including the influence of quantum statistical degeneracy pressure. The induced magnetization and power radiation due to the Washimi-Karpman ponderomotive interaction are obtained in Fermi-Dirac plasmas. It is found that the ponderomotive magnetization decreases with an increase of the relativistic degeneracy parameter. It is also shown that the quantum statistical degeneracy pressure effect is more significant in small frequency and large wave number domains than that in large frequency and small wave number domains. In addition, it is found that the ponderomotive power radiation decreases with an increase of the relativistic degeneracy parameter in Fermi-Dirac plasmas. The variations of the Washimi-Karpman magnetization and power radiation due to the physical characteristics of degenerate quantum Fermi-Dirac plasmas are also discussed.

Instability Analysis of Positron-Acoustic Waves in a Magnetized Multi-Species Plasma

The nonlinear propagation of electrostatic excitations and their multi-dimensional instability in a magnetized, degenerate electron-positron-ion (EPI) plasma system (containing inertial cold positrons, relativistic degenerate electrons and hot positrons, and negatively charged immobile heavy ions) are theoretically investigated. The reductive perturbation method is employed to derive the Zakharov–Kuznetsov equation which admits a localized solitary wave solution for small but finite amplitude limit, and the multi-dimensional instability of the positron acoustic solitary waves (PASWs) is studied by the small-k perturbation expansion method. It is found that the basic characteristics (viz. phase speed, amplitude, width) of the PASWs are significantly affected by the degree of obliqueness, relativistic degeneracy, and plasma particle number densities. The instability criterion and its growth rate, which are depending on the magnetic field and the propagation directions of both the PASWs, and their perturbation modes are discussed. The present analysis can be helpful in understanding the nonlinear phenomenon in dense astrophysical as well as space plasma systems, especially in pulsar environments.

Acoustic solitons in a magnetized quantum electron-positron-ion plasma with relativistic degenerate electrons and positrons pressure

The obliquely nonlinear acoustic solitary propagation in a relativistically quantum magnetized electron-positron (e-p) plasma in the presence of the external magnetic field as well as the stationary ions for neutralizing the plasma background was studied. By considering the dynamic of the fluid e-p quantum and by using the quantum hydrodynamics model and the standard reductive perturbation technique, the Zakharov-Kuznetsov (ZK) equation is derived for small but finite amplitude waves and the solitary wave solution for the parameters relevant to dense astrophysical objects such as white dwarf stars is obtained. The numerical results show that the relativistic effects lead to propagate the electrostatic bell shape structures in quantum e-p plasmas like those in classical pair-ion or pair species for relativistic plasmas. It is also observed that by increasing the relativistic effects, the amplitude and width of the e-p acoustic solitary wave will decrease. In addition, the wave amplitude increases as positron density decreases in magnetized e-p plasmas. It is indicated that by increasing the strength of the magnetic field, the width of the soliton reduces and it becomes sharper. At the end, we have analytically and numerically shown that the pulse soliton solution of the ZK equation is unstable and have traced the dependence of the instability growth rate on electron density. It is found that by considering the relativistic pressure, the instability of the soliton pulse can be reduced. The results can be useful to study the obliquely nonlinear propagation of small amplitude localized structures in magnetized quantum e-p plasmas and be applicable to understand the particle and energy transport mechanism in compact stars such as white dwarfs, where the effects of relativistic electron degeneracy become important.

Inverse Compton power and cooling time in a quantum Fermi-Dirac plasma including the quantum degeneracy pressure

The inverse Compton power is investigated in relativistically degenerate quantum Fermi-Dirac plasmas including the influence of quantum statistical degeneracy pressure. The ordinary and double Compton scattering cross sections, the inverse Compton power, and the cooling time are obtained in Fermi-Dirac plasmas. It is shown that the differential Compton scattering cross section has a maximum at the small wave number domain. However, the differential Compton scattering cross section increases with an increase of the wave number in the case of a large relativistic degeneracy parameter. It is interesting to note that the differential Compton scattering cross section in the backward scattering region is greater than that in the forward scattering region when the degeneracy pressure is large. It is also shown that the double Compton scattering process is quite suppressed in the forward scattering domain. It is also shown that the inverse Compton power increases with an increase of the relativistic degeneracy parameter. It is also shown that the influence of the relativistic degeneracy on the inverse Compton power is more significant for small plasmon energies. In addition, it is found that the cooling time due to the inverse Compton process decreases with an increase of the relativistic degeneracy parameter.

Electrostatic two-stream instability in Fermi-Dirac plasmas

In this paper the electrostatic two-stream instability is investigated for a large range of plasma number-density using the quantum hydrodynamic model by incorporating the relativistic degeneracy, electron-exchange, quantum diffraction and strong parallel quantizing magnetic field effects. It is found that the electron diffraction effect significantly alters the instability growth rate in a wide range of plasma number density. Two cases of classical and quantum Landau quantization limits are compared and the parametric instability condition is closely inspected. It is remarked that for a given streaming speed the instability is bounded by an upper plasma number-density limit. It is also shown that for a given stream speed there is a maximal growth rate corresponding to specific plasma number-density and perturbation wavelength. Current study can help in better understanding of electron-beam plasma interactions and energy exchange for a wide area of number densities ranging from solid density, inertial confined plasmas, big planetary cores and compact stars. It may also be useful in understanding of electrostatic beam-plasma interactions and origin of large magnitude sustainable electrical currents in super-intense plasmas with critically high magnetic fields such as, pulsars, white dwarf interiors and neutron star crusts.

Dispersive and dissipative nonlinear structures in degenerate Fermi–Dirac Pauli quantum plasma

We study the interplay between dispersion due to the electron degeneracy parameter and dissipation caused by plasma resistivity, in degenerate Fermi–Dirac Pauli quantum plasma. Considering relativistic degeneracy pressure for electrons, we investigate both arbitrary and small amplitude nonlinear structures. The corresponding trajectories are also plotted in the phase plane. The linear analysis for the dispersion relation yields interesting features. The present work is anticipated to be of physical relevance in the study of compact magnetized astrophysical objects like white dwarfs.

Nonlinear Electroacoustic Waves in Fully Relativistic Astrophysical Degenerate Plasmas

The solitary structures associated with the electroacoustic (EA) waves, in which the cold degenerate electron and positron fluids provide the inertia, the hot electrons and positrons following the Maxwellian distribution give rise to the restoring force, and stationary heavy ions maintain the background charge neutrality condition, have been theoretically studied. The fully relativistic hydrodynamic model is utilized to derive the Korteweg-de Vries equation. The stationary solitary wave solution is obtained and numerically analyzed to identify the basic features of the solitary structures that are found to be formed in the astrophysical relativistic degenerate dense plasmas. It is found that the combined effects of electron and positron dynamics, stationary heavy ions, and relativistic degeneracy play a very significant role in modifying the basic properties of the EA waves in such degenerate dense plasmas. The latter usually occurs in the compact astrophysical objects, such as white dwarfs, neutron stars, and so on.

Nonlinear positron-acoustic waves in fully relativistic degenerate plasmas

The nonlinear positron-acoustic (PA) waves propagating in a fully relativistic electron–positron–ion (EPI) plasma (containing degenerate electrons and positrons, and immobile heavy ions) have been theoretically investigated. A fully relativistic hydrodynamic model, which is consistent with the relativistic principle has been used, and the reductive perturbation method is employed to derive the dynamical Korteweg–de Vries equation. The dynamics of electrons as well as positrons, and the presence of immobile heavy ions are taken into account. It is found that the effects of relativistic degeneracy of electrons and positrons, static heavy ions, plasma particles velocity, enthalpy, etc have significantly modified the basic properties of the PA solitary waves propagating in the fully relativistic EPI plasmas. The application of the results of our present work in astrophysical compact objects such as white dwarfs and neutron stars, etc are briefly discussed.

Dust-ion-acoustic envelopes and modulational instability with relativistic degenerate electrons

Amplitude modulated unstable nonlinear structures have been studied in a three component dusty plasma consisting of degenerate relativistic electrons, degenerate ions, and negatively charged static dust grains. Following the multiscale reductive perturbation method, a nonlinear Schrödinger equation is derived, which not only admits the modulational instability but also causes the evolution of unstable excitations, namely, bright solitons and rogons. Numerical analysis illustrates that modulationally unstable wave envelopes are obtained in the limit of long wave number for taking cold and nondegenerate ions (the ratio of ion Fermi-to-electron rest mass energy, g = 0); however, the ionic Fermi pressure leads to stable excitations. It is observed that modulationally unstable wave packets are excited even for ultra small wave number (k≪1) when the dust concentration parameter exists in the range μc1<μ<μc2, where μc1 and μc2 being the critical values. Furthermore, it is revealed that these critical values are quite sensitive to the variation of electron relativistic degeneracy (ηe0) and the carrier wave number. The present results elucidate the important features of localized dust-ion-acoustic excitations due to self interactions in superdense astrophysical plasmas, viz., white dwarf, neutron stars, etc.

Energy exchange in strongly coupled plasmas with electron drift

In this paper, the generalized viscoelastic collisional quantum hydrodynamic model is employed in order to investigate the linear dielectric response of a quantum plasma in the presence of strong electron-beam plasma interactions. The generalized Chandrasekhar's relativistic degeneracy pressure together with the electron-exchange and Coulomb interaction effects are taken into account in order to extend current research to a wide range of plasma number density relevant to big planetary cores and astrophysical compact objects. The previously calculated shear viscosity and the electron-ion collision frequencies are used for strongly coupled ion fluid. The effect of the electron-beam velocity on complex linear dielectric function is found to be profound. This effect is clearly interpreted in terms of the wave-particle interactions and their energy-exchange according to the sign of the imaginary dielectric function, which is closely related to the wave attenuation coefficient in plasmas. Such kinetic effect is also shown to be in close connection with the stopping power of a charged-particle beam in a quantum plasma. The effect of many independent plasma parameters, such as the ion charge-state, electron beam-velocity, and relativistic degeneracy, is shown to be significant on the growing/damping of plasma instability or energy loss/gain of the electron-beam.

Magnetohydrodynamic waves with relativistic electrons and positrons in degenerate spin-1/2 astrophysical plasmas

Linear properties of high and low frequency waves are studied in an electron-positron-ion (e-p-i) dense plasma with spin and relativity effects. In a low frequency regime, the magnetohydrodynamic (MHD) waves, namely, the magnetoacoustic and Alfven waves are presented in a magnetized plasma, in which the inertial ions are taken as spinless and non-degenerate, whereas the electrons and positrons are treated quantum mechanically due to their smaller mass. Quantum corrections associated with the spin magnetization and density correlations for electrons and positrons are re-considered and a generalized dispersion relation for the low frequency MHD waves is derived to account for relativistic degeneracy effects. On the basis of angles of propagation, the dispersion relations of different modes are discussed analytically in a degenerate relativistic plasma. Numerical results reveal that electron and positron relativistic degeneracy effects significantly modify the dispersive properties of MHD waves. Our present analysis should be useful for understanding the collective interactions in dense astrophysical compact objects, like, the white dwarfs and in atmosphere of neutron stars.

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.

Nonlinear ion-acoustic waves in a degenerate plasma with nuclei of heavy elements

The ion-acoustic (IA) solitary waves propagating in a fully relativistic degenerate dense plasma (containing relativistic degenerate electron and ion fluids, and immobile nuclei of heavy elements) have been theoretically investigated. The relativistic hydrodynamic model is used to derive the Korteweg-de Vries (K-dV) equation by the reductive perturbation method. The stationary solitary wave solution of this K-dV equation is obtained to characterize the basic features of the IA solitary structures that are found to exist in such a degenerate plasma. It is found that the effects of electron dynamics, relativistic degeneracy of the plasma fluids, stationary nuclei of heavy elements, etc., significantly modify the basic properties of the IA solitary structures. The implications of this results in astrophysical compact objects like white dwarfs are briefly discussed.

D-Dimensional relativistic energies for silver dimer

We study solutions of the Dirac equation with the improved Tietz potential model in higher spatial dimensions. Under the condition of the spin symmetry, we obtain the bound state energy equation. It has been found that there exists a relativistic inter-dimensional degeneracy: under the transformation of a decrease in the spatial dimension by two and an increase in the orbital angular momentum by one, the relativistic rotation-vibrational energy for a diatomic molecule is invariant. We observe that the behavior of the relativistic vibrational energies for the Ag2 B-11Πu state in higher dimensions remains similar to that of the three-dimensional system.

Electrostatic Solitary Waves in Relativistic Degenerate Electron–Positron–Ion Plasma

The linear and nonlinear properties of ion acoustic excitations propagating in warm dense electron–positron–ion plasma are investigated. Electrons and positrons are assumed relativistic and degenerate, following the Fermi–Dirac statistics, whereas the warm ions are described by a set of classical fluid equations. A linear dispersion relation is derived in the linear approximation. Adopting a reductive perturbation method, the Korteweg–de Vries equation is derived, which admits a localized wave solution in the form of a small-amplitude weakly super-acoustic pulse-shaped soliton. The analysis is extended to account for arbitrary amplitude solitary waves, by deriving a pseudoenergy-balance like equation, involving a Sagdeev-type pseudopotential. It is shown that the two approaches agree exactly in the small-amplitude weakly super-acoustic limit. The range of allowed values of the pulse soliton speed (Mach number), wherein solitary waves may exist, is determined. The effects of the key plasma configuration parameters, namely, the electron relativistic degeneracy parameter, the ion (thermal)-to-the electron (Fermi) temperature ratio, and the positron-to-electron density ratio, on the soliton characteristics and existence domain, are studied in detail. Our results aim at elucidating the characteristics of ion acoustic excitations in relativistic degenerate plasmas, e.g., in dense astrophysical objects, where degenerate electrons and positrons may occur.

Amplitude modulation of quantum-ion-acoustic wavepackets in electron-positron-ion plasmas: Modulational instability, envelope modes, extreme waves

A semirelativistic fluid model is employed to describe the nonlinear amplitude modulation of low-frequency (ionic scale) electrostatic waves in an unmagnetized electron-positron-ion plasma. Electrons and positrons are assumed to be degenerated and inertialess, whereas ions are warm and classical. A multiscale perturbation method is used to derive a nonlinear Schrödinger equation for the envelope amplitude, based on which the occurrence of modulational instability is investigated in detail. Various types of localized ion acoustic excitations are shown to exist, in the form of either bright type envelope solitons (envelope pulses) or dark-type envelope solitons (voids, holes). The plasma configurational parameters (namely, the relativistic degeneracy parameter, the positron concentration, and the ionic temperature) are shown to affect the conditions for modulational instability significantly, in fact modifying the associated threshold as well as the instability growth rate. In particular, the relativistic degeneracy parameter leads to an enhancement of the modulational instability mechanism. Furthermore, the effect of different relevant plasma parameters on the characteristics (amplitude, width) of these envelope solitary structures is also presented in detail. Finally, the occurrence of extreme amplitude excitation (rogue waves) is also discussed briefly. Our results aim at elucidating the formation and dynamics of nonlinear electrostatic excitations in superdense astrophysical regimes.

Minimal dielectric polarization stopping power in white dwarfs

In this paper, we investigate the energy loss of ions by arbitrarily degenerate electron fluid, in the framework of hydrodynamic model by incorporating the generalized relativistic degeneracy pressure, Wigner–Seitz cell Coulomb interactions, and electron spin-exchange pressures for a wide range of electron number-density regimes relevant to the solid density (SD), inertial confinement fusion (ICF), warm dense matter (WDM), and super-dense astrophysical objects, such as white dwarf (WD) stars. It is found that the use of non-relativistic degeneracy pressure for electron fluid, instead of the exact Chandrasekhar relativistic degeneracy pressure, for the ICF density regime and beyond can introduce significant relative error to the stopping power calculation. Therefore, current study may introduce a significant change to the ICF scheme of super-compressed fuel. It is further revealed that the relativistic degeneracy parameter, R0, and the atomic number of constituent ions, Z, significantly affect the maximum stopping power velocity of ions. We also discover that the velocity-averaged energy loss function becomes minimal in electron number density typical of white dwarf stars, n0≃2×1030 cm−3. It is found that the characteristic density for the minimal ion beam energy loss does not depend on the value of other plasma parameters, such as the ion–electron collision rate and the ion temperature or its atomic number. The latter finding, in particular, may help in better understanding of fusion-burning waves in dense compact stars and their cooling mechanisms.

Generalized charge-screening in relativistic Thomas–Fermi model

In this paper, we study the charge shielding within the relativistic Thomas-Fermi model for a wide range of electron number-densities and the atomic-number of screened ions. A generalized energy-density relation is obtained using the force-balance equation and taking into account the Chandrasekhar's relativistic electron degeneracy pressure. By numerically solving a second-order nonlinear differential equation, the Thomas-Fermi screening length is investigated, and the results are compared for three distinct regimes of the solid-density, warm-dense-matter, and white-dwarfs (WDs). It is revealed that our nonlinear screening theory is compatible with the exponentially decaying Thomas-Fermi-type shielding predicted by the linear response theory. Moreover, the variation of relative Thomas-Fermi screening length shows that extremely dense quantum electron fluids are relatively poor charge shielders. Calculation of the total number of screening electrons around a nucleus shows that there is a position of maximum number of screening localized electrons around the screened nucleus, which moves closer to the point-like nucleus by increase in the plasma number density but is unaffected due to increase in the atomic-number value. It is discovered that the total number of screening electrons, (Ns∝rTF3/rd3 where rTF and rd are the Thomas-Fermi and interparticle distance, respectively) has a distinct limit for extremely dense plasmas such as WD-cores and neutron star crusts, which is unique for all given values of the atomic-number. This is equal to saying that in an ultrarelativistic degeneracy limit of electron-ion plasma, the screening length couples with the system dimensionality and the plasma becomes spherically self-similar. Current analysis can provide useful information on the effects of relativistic correction to the charge screening for a wide range of plasma density, such as the inertial-confined plasmas and compact stellar objects.