Plasma Dispersion Relation Research Articles

Generalized Buneman Dispersion Relation in the Longitudinally Dominated Magnetic Field

The generalized Buneman dispersion relation for two-component plasma is derived in the case of nonzero pressure of both plasma components and longitudinally dominated magnetic field. The derived relation is also valid for other field configurations mentioned in the paper. It can be useful in a variety of plasma systems, for example, in the analyses of plasma jet penetrating into background plasma, in beam-plasma physics, and in tests of various magnetohydrodynamics (MHD) and hybrid numerical codes designed for the magnetized plasmas.

ON THE MAGNETIZATION OF COSMIC OUTFLOWS: PLASMA MODES AND INSTABILITIES OF UNMAGNETIZED PLASMA BEAMS

The dissipation of the kinetic energy of cosmic outflows in interactions with ambient collision-free plasmas and the associated generation of electromagnetic plasma turbulence is a fundamental problem of modern astrophysics. Thermalization by elastic two-body Coulomb collisions is orders of magnitudes too slow as compared to interactions with electric and magnetic fields because of the generally low density of cosmic plasmas. Alternative dissipation mechanisms have to be examined such as energy diffusion by second-order Fermi interactions of charged particles with electromagnetic turbulence, which are an intrinsic property of any sufficiently agitated magnetized plasma. We consider the microphysical details of the energy conversion in relativistic and nonrelativistic outflows by investigating the solutions of the linear plasma dispersion relation in an unmagnetized anisotropic beam plasma consisting of two overall-neutral particle beams propagating with arbitrary velocities in the same direction. The general plasma dispersion relation is derived for arbitrary propagation angle θ with respect to the beam propagation direction both in the initial laboratory frame and in the counterstream frame of reference. Solutions of the linear dispersion relation are derived for parallel (θ = π/2) and perpendicular (θ = 0) propagation angle, respectively. For parallel propagation angles, the electrostatic mode is excited and its maximum growth rate depends on the relative bulk Lorentz factor of the flows and their density ratio. For perpendicular propagation angles, the aperiodic filamentation mode is excited and its maximum growth rate depends differently on the relative bulk Lorentz factor of the flow and their density ratio. The respective maximum growth rates indicate that for nonrelativistic flow velocities the electrostatic instability (EI) is excited much faster than the filamentation instability (FI), whereas for relativistic flow velocities the FI has a larger growth rate than the EI. This implies that nonrelativistic flows dissipate their kinetic energy predominantly in electric fields associated with the electrostatic mode, while relativistic flows dissipate their kinetic energy predominantly in magnetic fields. Therefore, initially unmagnetized relativistic flows are more effectively magnetized than initially unmagnetized nonrelativistic flows.

Measurements of Inertial Limit Alfvén Wave Dispersion for Finite Perpendicular Wave Number

Measurements of the dispersion relation for shear Alfvén waves as a function of perpendicular wave number are reported for the inertial regime for which V{A}>V{Te}. The parallel phase velocity and damping are determined as k{ perpendicular} varies and the measurements are compared to theoretical predictions. The comparison shows that the best agreement between theory and experiment is achieved for a fully complex plasma dispersion relation which includes the effects of electron collisions.

Analytical Evaluation of the Fully Relativistic Plasma Dispersion Function Using Binomial Expansion Theorems

In this paper, we propose a new method to calculate the relativistic plasma dispersion (RPD) function for wave propagation perpendicular to the magnetic field in a fully relativistic magnetized Maxwellian plasma. Explicit representations for the RPD function are developed in terms of some relatively more familiar special functions and binomial coefficients. As will be seen, the present formulation yields compact closed-form expressions that enable the ready analytical calculation of the RPD function. Extensive numerical tests and comparisons with some already existing methods show that the approach proposed here is highly efficient and competitive. The convergence rate of the series is estimated and discussed.

Analytic models of warm plasma dispersion relations

The present paper is concerned with analytic models of warm plasma dispersion relations for electromagnetic waves propagating parallel to the ambient magnetic field. Specifically, effects of finite betas on two slow modes, namely, the left-hand circularly polarized ion-cyclotron mode and the right-hand circularly polarized whistler mode, are investigated. Analytic models of the warm plasma dispersion relations are constructed on the basis of conjecture and upon comparisons with numerically found roots. It is shown that the model solutions are good substitutes for actual roots. The significance of the present work in the context of nonlinear plasma research is discussed.

On the minimal set of plasma parameters to determine the dispersion law of electron whistler waves

The minimal sufficient set of plasma parameters is presented to describe the dispersion properties of electron whistler waves (helicons) in a wide frequency range above the ion cutoff frequency, provided that the wave frequency is significantly lower than the electron plasma frequency. When the gyrofrequency of the lightest ions is much higher than those of heavier ions, it is sufficient to know the relative content of the lightest ions, the highest ion cutoff frequency, the lower hybrid resonance frequency, and the electron gyro- and plasma frequencies. In this case, the frequency of electron whistler waves is determined by the upper root of the biquadratic equation derived, whereas the lower root corresponds to a resonant mode with its refractive index increasing when the frequency tends toward the highest ion gyrofrequency from below. The developed approach is also efficient in plasmas containing a substantial amount of negative ions and/or heavy dust particulates. The accuracy of the approximate solution of the total cold plasma dispersion relation is illustrated graphically.

Landau damping in relativistic plasmas with power-law distributions and applications to solar wind electrons

The relativistic plasma dispersion relation is derived for Langmuir waves in a spatially homogeneous unmagnetized plasma in which the electrons have an isotropic power-law distribution in momentum space. The theory is applied to the study of Langmuir waves in the quiescent solar wind near the orbit of the Earth assuming that the electron distribution function can be approximated as a power-law from thermal energies ∼10eV to relativistic energies ≳100keV. Numerical solutions of the dispersion relation show that in the regime of weak Landau damping the phase speeds of the waves match the velocities of the high-energy particles, known in the solar wind literature as the superhalo, which lie in the range 0.09<v∕c<0.8. While this result raises the question of whether wave-particle interactions with a spectrum of Langmuir waves plays a role in the formation of the superhalo, the observed energy density of the waves near the orbit of the Earth at 1AU is so small that active acceleration of superhalo electrons by Langmuir waves, if it occurs at all, has ceased by the time the solar wind reaches the Earth.

Numerical and theoretical study of Bernstein modes in a magnetized quantum plasma

A numerical and theoretical study is presented for the propagation of electron Bernstein modes in a magnetized quantum plasma. The dispersion relation for electrostatic waves is derived, using a semiclassical Vlasov model for Fermi–Dirac distributed electrons. The dispersion relation is checked numerically with direct Vlasov simulations, where the wave energy is concentrated to the Bernstein modes as well as to the zero-frequency convective mode. Dispersion relations in the long wavelength limit are derived, including the upper hybrid dispersion relation for a degenerate quantum plasma.

Oscillation of electron counts at 500 eV downstream of the quasi-perpendicular bow shock

(1) We investigate an event with oscillations of electron counts at 500 eV, with a period of � 3 s measured by the electron drift instrument (EDI) on Cluster. These oscillations are detected at the overshoot of a quasi-perpendicular bow shock and in its downstream region. During this event, the Alfven Mach number is supercritical, and the proton b is >1. The correlation of the electron counts between three pitch angle ranges (� 10, � 90, and � 170) is in-phase. However, the correlation between the electron counts and the magnitude of the magnetic fields is antiphase. As EDI has a higher time resolution than that of conventional particle instruments, the correlation at a period of � 3si s examined for the first time. The oscillations are inferred as mirror mode waves with oblique propagation angles to the magnetic field. The oscillation of electron counts in the parallel direction might indicate the oscillation of the parallel electric potential. We have estimated this electric potential by Liouville's mapping, taking into account the shape of the electron distribution function as well as using the linear hot plasma dispersion relation. We have found that this kind of parallel electric potential is related to heating of particles with a comparable magnitude as the cross-shock potential. The elliptical polarization of these waves indicates a possible interaction with gyrating particles so that the waves would be related to the particle dynamics. Finally, in-phase correlation between parallel and perpendicular counts is explained in terms of Liouville's mapping.

The exact plasma dispersion functions in the complex region

The exact relativistic plasma dispersion functions are continued analytically into the complex plane, on the basis of a general method derived from the theory of singular Cauchy-type integrals. The main analytic properties of the dispersion functions in the complex region are studied and the physical consequences and applications of this method for ITER conditions are discussed.

Collisional power absorption near mode conversion surface in helicon plasmas

Central core heating in helicon plasmas was simulated in some full wave codes considering classical collision without knowing the clear central heating mechanism since the damping rate of helicon wave was known to be low. However, collisional damping of a fast helicon wave may not be negligible when the fast wave approaches mode conversion surface (MCS) in an inhomogeneous plasma. In this study collisional damping rate of a helicon wave is estimated near MCS from the cold plasma dispersion relation. In the presence of sufficient collision, the WKBJ approximation in inhomogeneous helicon plasmas can be applied even near MCS. The collisional damping rate near MCS is found to be high enough to explain the central heating of helicon plasmas by the helicon wave itself. In this heating mechanism, high density near MCS suffices for the helicon mode and it is closely related to operating parameters such as magnetic field, driving frequency and antenna geometry.

Wave kinetic description of quantum pair plasmas

AbstractThe dispersion relation for a quantum pair plasma is derived, by using a wave kinetic description. A general form of the kinetic dispersion relation for electrostatic waves in a two-component quantum plasma is established. The particular case of an electron–positron pair plasma is considered in detail. Exact expressions for Landau damping are derived, and the quasi-classical limit is discussed.

Dust-acoustic dispersion relation in three-dimensional complex plasmas under microgravity

A series of dedicated experiments with the Plasma Kristal Experiment (PKE)-Nefedov (Nefedov et al 2003 New J. Phys. 5 33) set-up were performed on board the International Space Station to measure the dispersion relation (DR) for the longitudinal dust-acoustic (DA) waves in quasi-isotropic three-dimensional (3D) complex plasmas. The waves were excited by applying ac electric modulation of variable frequency to the radio frequency (rf) electrodes. The amplitude of excitation was varied with frequency to ensure a ‘sufficiently linear’ regime of the dust density perturbations. The DR was obtained by measuring the induced density perturbations, revealing fairly good agreement with a simple multispecies theory of DA waves.

Cold plasma dispersion relations in the vicinity of a Schwarzschild black hole horizon

We apply the ADM 3 + 1 formalism to derive the general relativistic magnetohydrodynamic equations for cold plasma in spatially flat Schwarzschild metric. Respective perturbed equations are linearized for non-magnetized and magnetized plasmas both in non-rotating and rotating backgrounds. These are then Fourier analyzed and the corresponding dispersion relations are obtained. These relations are discussed for the existence of waves with positive angular frequency in the region near the horizon. Our results support the fact that no information can be extracted from the Schwarzschild black hole. It is concluded that negative phase velocity propagates in the rotating background whether the black hole is rotating or non-rotating.

Short wavelength electromagnetic propagation in magnetized quantum plasmas

The quantum electrodynamical (QED) short wavelength correction on plasma wave propagation for a nonrelativistic quantum plasma is investigated. A general dispersion relation for a thermal multicomponent quantum plasma is derived. It is found that the classical dispersion relation for any wave mode can be modified to include quantum and short wavelength QED effects by simple substitutions of the thermal velocity and the plasma frequency. Furthermore, the dispersion relation has been modified to include QED effects of strong magnetic fields. It is found that strong magnetic fields together with the short wavelength QED correction will induce dispersion both in vacuum and in otherwise nondispersive plasma modes. Applications to laboratory and astrophysical systems are discussed.

Diffusion plateaus in the velocity distributions of fast solar wind protons

In a collisionless plasma, such as the fast solar wind, wave‐particle interactions play the decisive role in determining the shape of particle velocity distribution functions (VDFs). In this paper we provide observational evidence for cyclotron‐resonant interaction of ion cyclotron Alfvén waves, which propagate outward from the Sun along the interplanetary magnetic field, with fast solar wind protons. According to quasi‐linear theory, the protons thereby diffuse in velocity space, a process leading to the formation of plateaus in the VDF. This diffusion plateau formation naturally explains the observed thermal anisotropies in the core of the proton VDFs. In this respect, we investigated a large number of data from several distinct fast solar wind streams between 0.3 and 1 AU. All measurements were made on Helios 2 during the solar minimum in 1976 and 1977. The proton VDFs as provided by the plasma instrument are modeled by a superposition of multiple Gaussians, such that the plasma dispersion relation for parallel propagating cyclotron waves can readily be solved numerically. Thus the details of the proton VDFs are well represented and are reflected in the dispersion relation, which makes our analysis as self‐consistent as possible. Proton thermal effects on the wave dispersion relation are naturally taken into account.

Calculation of dispersion relation and radiation pattern of plasma antenna

We investigated some important plasma antenna parameters, such as the transmission characteristics of a microwave propagating along the cylindrical symmetric plasma antenna, dispersion relations, radiation pattern and gain. By analyzing the dielectric constant of the tube material, the outer and inner radius, the density of the plasma and the collision frequency, we found that to minimize the attenuation of wave propagation along the plasma antenna, one should increase the density of the plasma, decrease the collision frequency, increase the radius of the plasma, increase the thickness of tube，and decrease the dielectric constant. We also calculated the radiation pattern of the plasma antenna and the change of gain under different conditions. These results are useful for the design of plasma antenna.

Laboratory modeling of nonlinear trapping of Langmuir waves inside a small-scale magnetoplasma irregularity

Laboratory studies modeling the small-scale plasma filamentation under the conditions relevant to the ionospheric heating experiments are presented. Filamentation is caused by nonlinear interaction of the short-wavelength quasi-electrostatic waves of the Z-mode with the plasma. This interaction occurs due to thermal plasma nonlinearity, i.e. due to local plasma heating and consequent thermodiffusion, which results in the formation of a narrow magnetic-field-aligned density depletion. The quasi-electrostatic plasma waves, in their turn, are trapped inside the depletion due to their specific dispersion properties. Such nonlinear wave trapping have been observed only at the critical plasma density ( ω = ω p). The trapped eigenmode has been associated with magnetized Langmuir waves, whose dispersion properties are analyzed using the kinetically modified plasma dispersion relation. Threshold of the nonlinear wave trapping exhibits significant growth in the vicinity of harmonics of the electron gyrofrequency.

Relativistic quantum plasma dispersion functions

Relativistic quantum plasma dispersion functions are defined and the longitudinal and transverse response functions for an electron (plus positron) gas are written in terms of them. The dispersion is separated into Landau-damping, pair-creation and dissipationless regimes. Explicit forms are given for the RQPDFs in the cases of a completely degenerate distribution and a nondegenerate thermal (J\"uttner) distribution. Particular emphasis is placed on the relation between dissipation and dispersion, with the dissipation treated in terms of the imaginary parts of RQPDFs. Comparing the dissipation calculated in this way with the existing treatments leads to the identification of errors in the literature, which we correct. We also comment on a controversy as to whether the dispersion curves in a superdense plasma pass through the region where pair creation is allowed.

Stochastic Acceleration of3He and4He in Solar Flares by Parallel‐propagating Plasma Waves: General Results

We study the acceleration in solar flares of $^3$He and $^4$He from a thermal background by parallel propagating plasma waves with a general broken power-law spectrum that takes into account the turbulence generation processes at large scales and the thermal damping effects at small scales. The exact dispersion relation for a cold plasma is used to describe the relevant wave modes. Because low-energy $\alpha$-particles only interact with small scale waves in the $^4$He-cyclotron branch, where the wave frequencies are below the $\alpha$-particle gyro-frequency, their pitch angle averaged acceleration time is at least one order of magnitude longer than that of $^3$He ions, which mostly resonate with relatively higher frequency waves in the proton-cyclotron (PC) branch. The $\alpha$-particle acceleration rate starts to approach that of $^3$He beyond a few tens of keV nucleon$^{-1}$, where $\alpha$-particles can also interact with long wavelength waves in the PC branch. However, the $^4$He acceleration rate is always smaller than that of $^3$He. Consequently, the acceleration of $^4$He is suppressed significantly at low energies, and the spectrum of the accelerated $\alpha$-particles is always softer than that of $^3$He. The model gives reasonable account of the observed low-energy $^3$He and $^4$He fluxes and spectra in the impulsive solar energetic particle events observed with the {\it Advanced Composition Explorer}. We explore the model parameter space to show how observations may be used to constrain the model.