General Dispersion Relation Research Articles

Jeans instability of rotating plasma with radiative heat-loss function and FLR corrections flowing through porous medium

The effect of rotation, porosity and finite ion Larmor radius (FLR) corrections on the gravitational instability and radiative instability of infinite homogeneous plasma has been explored, accounting for the consequences of radiative heat-loss function and thermal conductivity. The general dispersion relation is obtained by means of the normal mode analysis method with the help of appropriate linearized perturbation equations of the problem. This dispersion relations is further reduced for rotation axis parallel and perpendicular to the magnetic field. The stability of the medium is argued for by the Routh-Hurwitz criterion and it is found that the Jeans criterion establishes the stability of the medium. We acknowledge that the presence of the radiative heat-loss function and thermal conductivity modifies the fundamental Jeans criterion of gravitational instability into a radiative instability criterion. Numerical computations have been executed to show the effect of various parameters on the growth rate of the Jeans gravitational instability. We find that rotation, FLR corrections and medium porosity stabilize the growth rate as regards the structure in both the transverse mode and longitudinal mode or propagation. Our result demonstrates that the rotation, porosity and FLR corrections affect the dense molecular cloud configuration and star formation.

Acoustic Modes of Multi-Ion Dusty Plasmas

In this manuscript, we aim to derive a general dispersion relation applicable to a multi-component dusty plasma including massive negatively charged dust particles, both negative and positive ions, and electrons. Using the fluid treatment of plasma, we derive dispersion relations for dust ion-acoustic waves (DIAWs) and dust acoustic waves (DAWs) in self-gravitating dusty plasmas and collisional dusty plasmas by incorporating multiple species such as electrons, positive/negative ions, etc. Effects that arise in multicomponent dusty plasma due to negative ions are also discussed. The results obtained in this study are applicable in various space environments, such as cometary plasmas, astrophysical situations, planetary rings and interstellar medium.

Magnetoacoustic Waves in a Magnetic Slab Embedded in an Asymmetric Magnetic Environment. II. Thin and Wide Slabs, Hot and Cold Plasmas

Abstract Wave propagation in magnetically structured atmospheres is a thoroughly studied, yet practically inexhaustible, well of investigations in the field of solar magneto-seismology. A simple but powerful example is the examination of wave behavior in a magnetic slab. Our previous study used an analytical approach to derive the general dispersion relation for magnetoacoustic waves in a magnetic slab of homogeneous plasma, which was enclosed in an asymmetric magnetic environment. In the present study, we focus on the analysis of wave propagation in various limiting cases applicable to solar and space plasma physics or astrophysics. The thin- and wide-slab approximations, as well as the limits of low and high plasma β values, are considered. Utilizing the fact that in a weakly asymmetric slab the dispersion relation can be decoupled, the behavior of quasi-sausage and quasi-kink modes is studied in further analytical and numerical detail, and their avoided crossings are described. The results highlight how asymmetry influences the wave properties, e.g., the phase speed of eigenmodes, depending on the ratios of external to internal densities and magnetic fields on the two sides. Notably, the phase speeds of surface modes will converge to different values for the quasi-sausage and quasi-kink modes in the wide-slab limit, and cutoff frequencies are introduced with respect to both surface and body modes, in thin as well as wide slabs, beyond which the solutions become leaky. These obtained properties of MHD wave behavior could be measured with suitable high-resolution instruments in the future.

Optimal local well-posedness theory for the kinetic wave equation

We prove local existence and uniqueness results for the (space-homogeneous) 4-wave kinetic equation in wave turbulence theory. We consider collision operators defined by radial, but general dispersion relations satisfying suitable bounds, and we prove two local well-posedness theorems in nearly critical weighted spaces.

Magnetohydrodynamic wave modes in relativistic anisotropic quantum plasma

This paper presents an overview of waves and instabilities in relativistic degenerate plasma using magnetohydrodynamic double polytropic laws. The model equations are closed by the double polytropic laws. The general dispersion relation has been derived using the normal mode analysis, which consists of two interesting modes, i.e., shear Alfvén mode and modified magnetosonic modes (both slow and fast). The shear Alfvén mode is significantly modified by anisotropic pressure and relativistic effects and remains unaffected from quantum effects. The shear Alfvén mode develops the firehose instability, which is free from the relativistic factor. The obtained slow and fast magnetosonic modes are further discussed in parallel, perpendicular, and oblique modes of propagation. The Alfvén and sound waves propagate in parallel mode, while only the magnetosonic mode propagates in perpendicular mode. The sound wave and magnetosonic wave modes are found to be modified by relativistic and quantum effects. The oblique wave propagation provides fast and slow modes, which propagate with the combined force of anisotropic pressure, Bohm force, magnetic field, and exchange potential. The applicability of the results obtained from the dispersion relation in the relativistic degenerate anisotropic magnetohydrodynamic model can be to the pulsar magnetosphere environment.

Low-frequency plasma waves in a radiative dusty magnetoplasma

The impact of electromagnetic (thermal) radiation on the dispersive low-frequency waves is examined in a radiative dusty magnetoplasma. For this purpose, a magneto-hydrodynamic model along with the Maxwell equations is employed to describe the three-component radiative dusty plasma that contains inertialess electrons, dynamical positive ions and negatively charged static dust particulates. The behavior of the electrostatic and electromagnetic waves significantly changes in a plasma medium when a radiation pressure is taken into consideration, as compared to the waves in vacuum. After seeking a plane wave solution, a general dispersion relation is obtained to investigate different limiting cases of the low-frequency modes propagating parallel, perpendicular and oblique to the external magnetic field direction both analytically and numerically. The calculations reveal that the usual thermal and acoustic speeds (cT, ca) do not remain constant even if the temperature is kept constant, because of the radiation pressure which strongly depends on the equilibrium number density as well. The present results may prove a useful understanding for the new features of the dispersive dust-ion-acoustic and compressional Alfven waves in astrophysical dusty magnetoplasmas.

Propagation of surface waves in semi-bounded quantum collisional plasmas with electron exchange-correlation effects

The propagation of surface waves in semi-bounded quantum collisional plasmas are investigated by taking into account the quantum Bohm potential, Fermi statistical pressure, electron exchange-correlation effects and collisional effects. The modified quantum hydrodynamic model in conjunction with Maxwell equations are used to obtain the new general dispersion relations of surface waves, and the dispersion relations are discussed in some special cases of interest. It is indicated that the wave frequency spectrum can be down-shifted due to the electron exchange-correlation effects. It is also shown that the growth rate of surface waves instability can be enhanced by increasing the collisional frequency, especially in the short wavelength region. The corresponding results can be helpful for identifying surface waves which transport in intense metallic plasmas.

Radiative and gravitating modes in the partially ionized magnetized dusty plasma

In the present study, fluid theory is used to investigate the gravitational and radiative condensation instabilities of a partially ionized magnetized dusty plasma system. The effects of ion and electron capture by dust grains, the charge variation of dust grains, and the radiative effects of electron species are also taken into account. The dynamics of all four species are considered to derive modified densities that further lead to a general dispersion relation. The general dispersion relation describes the propagation of low frequency electrostatic dust acoustic waves in magnetized self-gravitating partially ionized dusty plasma with ionization-recombination, dust charge variations, and radiative effects. Gravitational modes of propagation and radiative modes of propagation are illustrated separately for both parallel and perpendicular cases. Conditions for instabilities are also derived to explain the gravitational collapse and radiative condensation of the system. The numerical results are presented to signify the role of dust neutral collision frequency, dust charge fluctuation, magnetic field, and recombination ionization effects on both the radiative condensation and gravitational instabilities. The relevance of the present study to interstellar molecular clouds is also discussed and the effect of considered parameters on the critical wavelength, critical wave number, luminosity, etc., has been investigated.

Analytical approximations for the dispersion of electromagnetic modes in slabs of biaxial crystals

Anisotropic crystals have recently attracted considerable attention because of their ability to support polaritons with a variety of unique properties, such as hyperbolic dispersion, negative phase velocity, or extreme confinement. Particularly, the biaxial crystal $\alpha$-MoO$_3$ has been demonstrated to support phonon polaritons, light coupled to lattice vibrations, with in-plane anisotropic propagation and unusually long lifetime. However, the lack of theoretical studies on electromagnetic modes in biaxial crystal slabs impedes a complete interpretation of the experimental data, as well as an efficient design of nanostructures supporting such highly anisotropic polaritons. Here, we derive the dispersion relation of electromagnetic modes in biaxial slabs surrounded by semi-infinite isotropic dielectric half-spaces with arbitrary dielectric permittivities. Apart from a general dispersion relation, we provide very simple analytical expressions in typical experiments in nano-optics: the limits of short polaritonic wavelength and/or very thin slabs. The results of our study will allow for an in-depth analysis of anisotropic polaritons in novel biaxial van der Waals materials.

Magnetoacoustic waves with effect of arbitrary degree of temperature and spin degeneracy in electron‐positron‐ion plasmas

AbstractThe linear properties of magnetosonic waves are studied in nearly degenerate and nearly non‐degenerate quantum plasmas composed of electrons, positrons and ions in the presence of spin‐ effect. Using the fluid equations, a generalized dispersion relation for perpendicular and oblique propagation is derived. It is found that degree of temperature and spin degeneracy modify the dispersive properties of the given modes. The results of analysis are beneficial for understanding the collective phenomena in dense quantum astrophysical plasmas.

The effect of a periodic tangential magnetic field on the stability of a horizontal magnetic fluid sheet

AbstractThe current article aims at investigating the effect of a periodic tangential magnetic field on the stability of a horizontal flat sheet. The media were considered porous, the three viscous‐fluid layers were initially streaming with uniform velocities, and the magnetic field admitted the presence of free‐surface currents. Furthermore, the transfer of mass and heat phenomenon was taken into account. The analysis, in this paper, was followed by the viscous potential theory. Moreover, the stability of the boundary‐value problem resulted in coupled second‐order linear differential equations with damping and complex coefficients. In regard to the uniform and periodic magnetic field, the standard normal mode approach was applied to deduce a general dispersion relation and judge the stability criteria. In addition, several unfamiliar cases were reported, according to appropriate data choices. The stability conditions were theoretically analyzed, and the influences of the various parameters in the stability profile were identified through a set of diagrams. In accordance wth the oscillating field, the coupled dispersion equations were combined to give the established Mathieu equation. Therefore, the governed transition curves were, theoretically, obtained. Finally, the results were numerically confirmed.

Analysis of radiative gravitational modes in magnetized dusty plasma with non-thermal ion distribution

The characteristics of radiative gravitational modes in non-thermal magnetized dusty plasma with charge fluctuation and the polarization force of dust particles are investigated. The electron species are assumed to be radiative and the ions are assumed to be non-thermal. A normal mode analysis is applied to derive the general dispersion relation for radiative magnetized self-gravitating dusty plasma. Modified radiative condensation and self-gravitational instability criteria for both perpendicular and parallel modes of propagation are obtained. Analytically, it is found that the presence of a non-thermal ion population significantly modified the usual radiative condensation instability criterion, and damped the growth rate of the radiative mode. The obtained analytical results are further discussed in the numerical result section. We investigate the fact that the non-thermal ion population acts as a stabilizing source for radiative condensation instability in magnetized self-gravitating dusty plasma fluid, including the dust polarization force and charge fluctuation. The thermal conductivity with non-thermal ion distribution quickly moves the system towards stability. The implications of the results in the region of the interstellar medium (ISM) are discussed.

Jeans surface instability of an electron-ion plasma

The dispersive properties of Jeans surface instability at a charged plane interface of weakly coupled, classical self-gravitating, magnetized electron-ion plasma and vacuum, are investigated. The general dispersion relation is formulated by employing one fluid magnetohydrodynamic (MHD) model and Poisson’s equations for both electrostatic and gravitational potentials. It is shown that both the surface charge and mass density fluctuations are coupled together effectively, to enhance the growth rate of surface Jeans instability, whereas an increase in magnetic field and surface tension tends to stabilize Jeans surface instability. The modified Jeans criterion of gravitational instability is obtained by formulating a new definition of Jeans wavelength. These results may be useful to examine the gravitational collapse of self-gravitating electron-ion plasma, leading to star formation in astro-cosmic environments.

Radiative and Gravitational Modes and Instabilities in an Inhomogeneous Magneto Dusty Plasma with Charge Variation

The Jeans instability of collisional magnetized dusty plasmas is examined incorporating polarization force, charge variation of dust grains, and radiative cooling of ion and electron species. The collisional effects of dust grains with neutrals are considered with sufficient background of neutral particles. A general dispersion relation is obtained using normal mode analysis technique which is found to be modified due to polarization force, dust charge fluctuation, and radiative effects of electrons and ions. The analytical discussion of general dispersion relation is presented in parallel and perpendicular mode of propagation. The Routh Hurwitz criterion is applied to analyze the stability of the considered system. We report the existence of a modified cyclotron mode in parallel propagation and a purely collisional mode in perpendicular propagation along with the gravitational mode. These modes are discussed analytically, as well as numerically, to show the importance of different parameters considering different situations. The implications of the result have been discussed for the molecular clouds.

MHD Waves and Instabilities in Two-Component Anisotropic Plasma

Based on the 16-moment MHD transport equations, the propagation of linear waves in an anisotropic homogeneous cosmic plasma is considered. A general dispersion relation is derived with allowance for two plasma components (electrons and protons) and heat flux along the magnetic field. This dispersion relation is a generalization of the previously studied cases of one-component (ion) plasma. The case in which the effects associated with the heat flux are ignored is analyzed in more detail. In the limit of longitudinal propagation, the wave modes fully consistent with the modes known in the low-frequency kinetic theory of collisionless plasma are classified. Firehose and mirror instabilities are analyzed. It is shown that taking into account the electron component modifies the growth rates and thresholds of instabilities.

Modeling of the beam excited fishbone mode in EAST

Many beam related instabilities have been observed in EAST. This paper reports on detailed calculations of beam driven fishbone and sawtooth instabilities using a general fishbone dispersion relation. The ideal fluid contribution and eigenfunction were calculated with the magnetohydrodynamic code NOVA, the kinetic contribution was evaluated with sample fast ion distributions in the guiding center code ORBIT, and the general inertial term was calculated using experimental data. The sawtooth branch was stabilized both by co-beam injection and balanced injection, but the stable domain for the sawtooth and fishbone modes is wider for balanced injection. The fishbone of the precessional branch is excited by both trapped and passing particles. To widen the stable domain, we propose a modulated balanced beam heating scenario for long pulse, high beta discharges in EAST, with the single beam pulse turn on time shorter than the plasma energy confinement time and longer than the beam ion slowing down time.

Thermionic emission laws for general electron dispersion relations and band structure data

In this article, a thermionic electron emission theory for general electron dispersion relations E(k) is presented, relating electron energy E to wave-vector magnitude k = |k|. This theory does not require the construction of a model Hamiltonian for the electrode's materials, like Dirac or Weyl Hamiltonians. Instead, use is made of the material's band structure data, e.g., the parabolic E(k) approximation for the Richardson–Dushman equation and linear E(k), as used for graphene and 3D Dirac semimetals. This new theory confirms previous findings on parabolic E(k), e.g., that the emission current is independent of effective electron mass in the material as long as it is larger than real electron mass m0. For effective mass lower than m0, the emission is reduced and tends to zero for vanishing effective mass. For materials with negative electron affinity, additional terms arise in the emission current equation. It turns out that the linear E(k) dispersion, e.g., for Dirac semimetals, does not have the potential to surpass the Richardson emission in materials with the same work function. In addition, a more rigorous electron emission theory is established by utilizing real anisotropic band structure data En(k) for electrode materials. For collimated electron emission normal to the surface, the transverse electron velocities tend to zero, i.e., the transverse derivatives of En(k) have to be comparatively small. If stable electrode materials of this kind can be realized, a considerable increase of electron emission by a factor 100 or more can be achieved, compared to the Richardson–Dushman theory, especially for small lattice constants perpendicular to the emission direction.

Linear theory of multibeam parametric instabilities in homogeneous plasmas

Linear theory of parametric instabilities resulting from N overlapping laser beams with an arbitrary beam configuration and polarization in a homogeneous plasma is presented. A general dispersion relation valid for both N-beam stimulated Raman scattering (SRS) and stimulated Brillouin scattering (SBS) is derived. Analytically, we obtain the growth rate for a two-beam system and find the significance of two special geometries by sharing a common decay wave. By virtue of these geometries, the coefficient matrix of the general dispersion relation is decomposable and reducible in dimensions to give relatively simple formulae. Therefore, the most unstable mode is a trade-off among beam number, geometry, and polarization. We have also considered the spatio-temporal evolution of a highly symmetric N-beam shared scattered light (SL) mode, defined by N beams sharing a common scattered wave, and obtained convective gains for SRS and SBS. An estimation shows that both SRS and SBS in a N-beam SL mode may have significant impacts on inertial confinement fusion.

Gravitoelectrostatic excitations in an opposite polarity complex plasma

The linear and nonlinear properties of gravitoelectrostatic mode, in a plasma system consisting of inertial opposite polarity charged dust grains as well as inertialess nonextensively q-distributed ions and electrons (including the effect of polarization force on the massively charged dust grains), have been investigated. A general dispersion relation has been derived yielding only one eigen wave mode. It is found that the polarization force and the nonextensively distributed ions effects play directly a destabilizing role in Jeans instability. Moreover, a new pair of gravitoelectrostatically coupled energy integral equation has been obtained by applying the Sagdeev pseudopotential technique. Also, a small-amplitude approximation is considered for the self-gravitational potential. It is reported that the fluctuations dynamics of the dust grains evolve self-gravitational rarefactive soliton pulses and electrostatic compressive soliton-like patterns. Applying the phase plane analysis, the phase portraits of the dynamical system have been presented and also the corresponding wave solutions. Our results could be applicable for different space and astrophysical plasma systems, particularly for dust molecular clouds of H-II region.

Modified Vlasov equation and dispersion relations for a relativistic radiating electron plasma

A modified Vlasov equation is obtained by developing a covariant statistical mechanics for a system of electrons without considering the effects of the ions and including the Landau–Lifshitz equation of motion. General dispersion relations for the transverse and longitudinal modes for any temperature are expressed. The results are similar to those found by Hakim & Mangeney (Phys. Fluids, vol. 14, 1971, pp. 2751–2781) for both the modified Vlasov equation and the dispersion relations. However, for the longitudinal mode, unlike the development of Hakim and Mangeney, correct expansions are done in order to give a numerical approach to obtain the longitudinal relativistic dispersion relations for any value of the wavenumber. Accordingly, new loop solutions, with turning points, crossing the super-luminous region and the super-thermal region are found. Although the expressions for the Landau damping and the damping due to the radiation reaction force coincide with the Hakim and Mangeney results for some particular cases, in general they are different. A Landau anti-damping appears in the second branch of the loop in a small region between the cutoff point and the intersection with the super-thermal line. The analysis of this effect leads us to a kind of wave pulse. We will call them bipolar waves. The treatment contains the relativistic interactions between all the electrons in the system with retarded effects. This explain the differences with Zhang’s recent work (Phys. Plasmas, vol. 20, 2013, 092112–092132). It is shown that for low densities, the cutoff of the wave is due to the dispersion relations and not due to the radiation reaction force damping. While for both high densities and temperatures, the damping due to the radiation reaction force is important.