Study of the O-mode in a relativistic degenerate electron plasma (original) (raw)
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Physics of Plasmas, 2018
The study of relativistic degenerate plasmas is important in many astrophysical and laboratory environments. Using linearized relativistic Vlasov–Maxwell equations, a generalized expression for the plasma conductivity tensor is derived. Employing Fermi-Dirac distribution at zero temperature, the dispersion relation of the extraordinary mode in a relativistic degenerate electron plasma is investigated. The propagation characteristics are examined in different relativistic density ranges. The shifting of cutoff points due to relativistic effects is observed analytically and graphically. Non-relativistic and ultra-relativistic limiting cases are also presented.
Physics of Plasmas, 2018
Thermal momentum space anisotropy is ubiquitous in many astrophysical and laboratory plasma environments. Using Vlasov-Maxwell's model equations, a generalized polarization tensor for a collisionless ultra-relativistic unmagnetized electron plasma is derived. In particular, the tensor is obtained by considering anisotropy in the momentum space. The integral of moments of Fermi-Dirac distribution function in terms of Polylog functions is used for describing the border line plasma systems (TeTFe≈1) comprising arbitrary electron degeneracy, where Te and TFe, are thermal and Fermi temperatures, respectively. Furthermore, the effects of variation in thermal momentum space anisotropy on the electron equilibrium number density and the spectrum of electromagnetic waves are analyzed.
Linear wave dispersion laws in unmagnetized relativistic plasma: Analytical and numerical results
Physics of Plasmas, 2001
In this paper dispersion laws for electrostatic and electromagnetic waves in a homogeneous and unmagnetized relativistic Vlasov plasma are derived. From the dispersion laws the relativistic plasma frequency, which is temperature dependent is derived. Using the standard technique of successive approximations, simple but powerful approximate relativistic dispersion laws are derived, resembling the electromagnetic dispersion law and the electrostatic Bohm–Gross dispersion law in the nonrelativistic case. The relation between the relativistic plasma frequency ωpe, Debye wave number kD and the thermal velocity vth,e is established. The approximate dispersion laws are compared with numerical solutions of the full dispersion laws. The full dispersion equations are transformed so that they are well suited for numerical evaluation in the temperature range where a fully relativistic treatment is needed.
High frequency electromagnetic modes in a weakly magnetized relativistic electron plasma
Physics of Plasmas, 2010
Using the linearized Vlasov-Maxwell model, the polarization tensor for a weakly magnetized electron plasma is derived. For isotropic relativistic Maxwellian velocity distribution function, dispersion relations are obtained for both parallel and perpendicular propagations. The integrals ͑called Meijer G functions͒ that arise due to relativistic effects are examined in various limits and dispersion relations are derived for the nonrelativistic, weakly, strongly, and ultrarelativistic Maxwellian velocity distributions. It is generally observed that the propagation domains of the modes are enlarged as one proceeds from the nonrelativistic to the highly relativistic regime. Resultantly, due to the relativistic effects, the Whistler mode is suppressed in the R-wave, the nonpropagation band of X-mode is reduced, and the X-mode itself approaches the O-mode. Further, the results derived in the ultra-and nonrelativistic limits found to be in agreement with the earlier calculations ͓G. Abbas et al.
Kinetic theory of the plasma-dynamical modes and the transport coefficients of a relativistic plasma
Physica A: Statistical Mechanics and its Applications, 1975
The kinetic equation of an inhomogeneous relativistic plasma, consisting of an electron gas and a radiation field, is studied with particular regard to its eigenvalues in the hydrodynamical limit. The treatment is classical for the particles and quantum-mechanical for the field oscillators. After a suitable regularization, the eigenvalues are obtained by a perturbation theory through second order in the strength of the gradients. It is shown that these eigenvalues are in exact correspondence with the macroscopic relativistic plasma-dynamical modes. The important role played by the Vlassov operator in building up the peculiar structure of these modes is underlined. From a comparison of the macroscopic and microscopic eigenvalues we obtain general expressions for the thermal conductivity, the shear viscosity and the bulk viscosity of a relativistic plasma. The contribution of the radiation field to these quantities is a noteworthy feature of these expressions.
Dispersion relation of low-frequency electrostatic waves in plasmas with relativistic electrons
Laser and Particle Beams, 2016
The dispersion relation of electrostatic waves with phase velocities smaller than the electron thermal velocity is investigated in relativistic temperature plasmas. The model equations are the electron relativistic collisionless hydrodynamic equations and the ion non-relativistic Vlasov equation, coupled to the Poisson equation. The complex frequency of electrostatic modes are calculated numerically as a function of the relevant parameterskλDeandZTe/Tiwherekis the wavenumber, λDe, the electron Debye length,TeandTithe electron and ion temperature, andZ, the ion charge number. Useful analytic expressions of the real and imaginary parts of frequency are also proposed. The non-relativistic results established in the literature from the kinetic theory are recovered and the role of the relativistic effects on the dispersion and the damping rate of electrostatic modes is discussed. In particular, it is shown that in highly relativistic regime the electrostatic waves are strongly damped.
Propagation of Ordinary and Extraordinary Modes in Ultra-Relativistic Maxwellian Electron Plasma
Progress of Theoretical Physics, 2010
Modes of ultra relativistic electron plasma embedded in a strong magnetic field are investigated for perpendicular propagation. Using Boltzmann-Vlasov equation, a general expression for the conductivity tensor is derived. An ultra-relativistic Maxwellian distribution function is employed to derive different modes for strong magnetic field limit. In particular, the dispersion relations for the ordinary mode and the extra ordinary mode (O-mode and X-mode) are obtained. Graphs of these dispersion relations and the imaginary parts of the frequency are drawn for some specific values of the parameters. It is observed that the damping rate increases gradually, reaches some maximum point and then decreases for larger wavenumbers. Further, increasing the strength of the magnetic field lowers the maximum value of the damping rate.
Variation of average Lorentz factors in degenerate and non-degenerate relativistic plasmas
Academia Letters, 2022
For the relativistic plasma, how to fix the Lorentz factors of the particles is an important but difficult problem. This problem is resolved in present study, both for degenerate and nondegenerate plasmas, by demonstrating the exact relation between the average Lorentz factors and dimensionless factors (aF and ac) in relativistic plasmas. The numerical and graphical analysis has also been performed. An understanding of when electron plasma becomes degenerate and rela-tivistic is important in the theories of many astrophysical objects e.g., in the study of stellar evolution, black hole magnetosphere and active galactic nuclei etc., [1-6]. From the density-temperature diagram one can observe that dense electron gases are degenerate provided they are not too hot and the hot electron gases are classical provided they are not too dense. For the density n0 = 1020-1045 m-3 and thermal temperature T < 109 K; the degeneracy effects are more important and varies from non-relativistic to ultra-relativistic regimes. In such environments, the Fermi temperature (TF) associated with the degener-acy pressure is much greater than the thermal temperature (T) and, as a result, particles obey Fermi Dirac statistics (where TF = EF /kB). Also the equation of state changes with increase in the temperature and density of the electrons. Consequently, the other mathematical modeling for the description of such media must be relativistic associated with the Fermi Lorentz factor, where pF is the Fermi momentum can relativistically be approximated by the electron equilibrium number density (n0) of the plasma through the factor aF such that, where the degenerate factor (ratio of rest
Dispersion relations in ultradegenerate relativistic plasmas
Physical Review D, 2000
The propagation of excitation modes in a relativistic ultradegenerate plasma is modified by their interactions with the medium. These modifications can be computed by evaluating their on-shell self-energy, which gives (gaugeindependent) dispersion relations. For modes with momentum close to the Fermi momentum, the one-loop fermion self-energy is dominated by a diagram with a soft photon in the loop. We find the one-loop dispersion relations for quasiparticles and antiquasiparticles, which behave differently as a consequence of their very different phase-space restrictions when they scatter with the electrons of the Fermi sea. In a relativistic system, the unscreened magnetic interactions spoil the normal Fermi liquid behavior of the plasma. For small values of the Fermi velocity, we recover the non-relativistic dispersion relations of condensed matter systems.
Relativistic Quantum Response of a Strongly Magnetised Plasma. I. Mildly Relativistic Electron Gas
Australian Journal of Physics, 1992
Approximate analytic expressions are derived for the linear response 4-tensor of a strongly magnestised, mildly relativistic electron plasma. The results are obtained within the framework of quantum plasma dynamics, thus the response contains relativistic and quantum effects that are essential in a super-strong magnetic field. The response is obtained in terms of relativistic plasma dispersion functions known as Shkarofsky functions. These functions allow the wave properties of the plasma to be studied without resorting to complicated numerical schemes. The response derived is valid for radiation with frequency up to about the cyclotron frequency and is of use in the theory of spectra formation in X-ray pulsars. In addition, a simple graphical technique is introduced that allows one to visually locate the roots of the resonant denominator occurring in the response, as well as determine the conditions under which both roots are valid and contribute to absorption.