Dispersion Relation For Electrostatic Waves Research Articles

On the frequency spectra of the electrostatic upper hybrid wave and linear Landau damping in a weakly magnetized relativistic electron plasma

On the basis of Vlasov-Kinetic model and using Maxwell-Juttner distribution function, dispersion relation of electrostatic wave in a collisionless homogeneous relativistic electron plasma is derived. The analysis of the oscillation spectra is carried out in a weak magnetic field limit ≥ Ω. Approximate analytic expression for the weakly damped mode is obtained in the subluminal limiting range. It is shown that the relativistic weakly damped mode can be estimated analytically in the range where the wave phase velocity v φ becomes greater than relativistic thermal velocity of the electron but less than speed of light. Results in the non-relativistic and the ultrarelativistic cases are also discussed.

The debye region in astrophysical plasmas: a new access to the problem

We study the consequences of defining the Debye region in astrophysical plasmas as that region where purely stochastic Poissonian density fluctuations must be perturbed by the appearance of unscreened electric Coulomb forces. Here by we test a new definition of the charge screening length requiring that purely statistical density fluctuations in sub-volumes of the system can only be expected, if particle residence probabilities in those volumes are uncorrelated. We find that within Debye spheres where electric micro fields appear, this can evidently not anymore be guaranteed. We introduce a new definition of the charge-screening length based on this requirement. It turns out that the newly defined charge screening length increases compared to its classical Debye value proportional to the so-called Debye number, i.e. the number of particles in the Debye sphere, while the classical Debye length delivers one unique result independent on the Debye number. We discuss the astrophysical relevance of this new definition which has the consequence that the effective screening length increases with the square of the temperature and decreases inversely proportional to the density, instead of with their square roots as in classic representations. Based on this revised Debye concept we furthermore study the general dispersion relation for electrostatic waves and show, that these waves when propagating into the direction of increasing electron temperatures will grow nonlinear and thus dissipate their excess energy to the electrons, with the consequence of heating them further up. This naturally explains the occurence of observed electron temperature increases at space plasma passages over MHD shocks. Furthermore we study the radiowave scattering in a plasma environment due to density-fluctuations which induce dielectricity fluctuations exciting secondary dipolar radio waves which latter serve as a valuable diagnostic tool for plasma investigations.

Kinetic theory for spin-1/2 particles in ultrastrong magnetic fields.

When the Zeeman energy approaches the characteristic kinetic energy of electrons, Landau quantization becomes important. In the vicinity of magnetars, the Zeeman energy can even be relativistic. We start from the Dirac equation and derive a kinetic equation for electrons, focusing on the phenomenon of Landau quantization in such ultrastrong but constant magnetic fields, neglecting short-scale quantum phenomena. It turns out that the usual relativistic γ factor of the Vlasov equation is replaced by an energy operator, depending on the spin state, and also containing momentum derivatives. Furthermore, we show that the energy eigenstates in a magnetic field can be computed as eigenfunctions of this operator. The dispersion relation for electrostatic waves in a plasma is computed, and the significance of our results is discussed.

Gravitational Drift Instability in Quantum Dusty Plasmas

Abstract The dispersion relation of electrostatic waves due to multi-drifts is studied in an ambient magnetic field across three-species quantum dusty plasmas. The quantum hydrodynamic model is applied to analyze the effects of the Lorentz and the gravitational forces. It is found that the instability is excited mainly due to the E 0 × B 0 \({\mathbf{E}_{0}}\times{\mathbf{B}_{0}}\) drift of the plasma species. However, an additional g 0 × B 0 \({\mathbf{g}_{0}}\times{\mathbf{B}_{0}}\) drift associated with dust particles enhances the instability over a wide spectrum of wavevector. The role of a varying magnetic field and the number density of electrons in the wave instability are analyzed graphically. It is noticed that these factors have a significant contribution over the drift instability.

Broken degeneracy of low frequency surface waves in semi-bounded quantum plasmas including the quantum recoil effect

We present a derivation of the dispersion relation for electrostatic waves propagating at the interface of semi-bounded quantum plasma in which degenerate electrons are governed by the Wigner–Poisson system, while non-degenerate ions follow the classical fluid equations. We consider parameters for metallic plasmas in terms of the ratio of plasmon energy to Fermi energy. The dispersion relation is solved numerically and analyzed for various plasmon energies. The result shows that two-mode of waves can be possible: high- and low-mode. We have found that the degeneracy for high-mode wave would be broken when the plasmon energy is larger than the Fermi energy. We also discuss the characteristics of group velocities for high- and low-mode waves.

Dispersion relation for electrostatic waves in plasmas with isotropic and anisotropic Kappa distributions for electrons and ions

Velocity distribution functions which feature extended tails with power-law dependence have been consistently observed in the solar wind environment and are frequently modelled by the so-called Kappa distributions. Different forms of Kappa distributions are commonly employed in analytical studies, and despite their similarities, they can produce different effects on the dispersion properties that occur in a plasma. We consider two different and widely used forms of Kappa distributions, in both isotropic and anisotropic cases, and systematically discuss their effects on the dispersion relations of Langmuir and ion-sound waves. It is shown that in the case of Langmuir waves, one of the forms leads to the expression for the Bohm–Gross dispersion relation, valid for plasmas with Maxwellian velocity distributions, while the other form of Kappa functions leads to a dispersion relation with significant difference regarding the Maxwellian case, particularly in the case of small values of the kappa index. For ion-sound waves, the dispersion relations obtained with the different forms of Kappa distributions are different among themselves, and also different from the Maxwellian case, with difference which increases for small values of the kappa index. Some results obtained from numerical solution of the dispersion relations are presented, which illustrate the magnitude of the perceived differences. Some results obtained with relativistic particle-in-cell simulations are also presented, which allow the comparison between the dispersion relations obtained from analytical calculations and the frequency–wavelength distribution of wave fluctuations which are observed in numerical experiments.

Nonlinear Structures in an Ion-Beam Plasmas Including Dust Impurities with Nonthermal Nonextensive Electrons

The properties of dust ion acoustic waves are investigated in an unmagnetized multicomponent plasma system consisting of ion beam, charged positive and negative ions, electrons obeying nonthermal-Tsallis distribution and stationary negatively charged dust grains by the conventional Sagdeev pseudopotential method, through which the condition for existence of several nonlinear structures is analyzed theoretically. The dispersion relation for electrostatic waves is derived and analyzed and an expression of the energy integral equation is obtained. It is reported here that our plasma model supports solitions, double layers and supersoliton solutions for certain range of parameters. Finally, the effects of different physical plasma parameters on these nonlinear structures are studied numerically. The present theory should be helpful in understanding the salient features of the electrostatic waves in space and in laboratory plasmas where two distinct groups of ions and non-Maxwellian distributed electrons are present.

Electron–electron two-stream instability in embedded assembly of nanoparticle (NP) cluster in n-GaAs

The electron–electron two-stream instability has been studied in two-valley n-GaAs embedded with nanoparticle (NP) cluster. We considered polar optical phonon as the dominant intravalley scattering mechanism and drifted Maxwellian to approximate the distribution of carriers between each valley. We derived the dispersion relation for electrostatic wave using hydrodynamic model of plasmas. While investigating temporal behaviour, we found two novel modes of propagation. These two novel modes are found to be evanescent by nature and propagate with equal phase velocities, but in opposite directions. The pre-existing modes retained their profile structures even in the presence of NP cluster. On the other hand, in the case of convective instability, no new modes are obtained but the propagation and gain profiles of the preexisting modes are significantly modified by the presence of NP cluster in the host medium.

Electrostatic ion cyclotron instability in a plasma with q-nonextensive distributions

The general dispersion relation for electrostatic waves in magnetized plasmas is derived using the standard linear Vlasov theory and the q-distribution of Tsallis statistics. The dispersion relation is solved for a plasma that has nonextensive electrons drifting with respect to stationary ions, and satisfies the other conditions for the excitation of electrostatic ion cyclotron waves. The frequency spectrum and growth rate are obtained for the electrostatic ion cyclotron waves. The marginally stable state is investigated for the onset of instability. It is shown that decreasing the non-extensivity parameter of electrons strengthens the instability and decreases the minimum value of the critical drift velocity, whereas larger temperature anisotropy of ions weakens the instability and increases the minimum value of the critical drift velocity.

Dispersion relation of low-frequency electrostatic waves in plasmas with relativistic electrons

AbstractThe 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 parameters kλDe and ZTe/Ti where k is the wavenumber, λDe, the electron Debye length, Te and Ti the electron and ion temperature, and Z, 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.

Dust gravitational drift wave in complex plasma under gravity

The dispersion relation of electrostatic waves in a complex plasma under gravity is presented. It is assumed that the waves propagate parallel to the external fields. The effects of weak electric field, neutral drag force, and ion drag force are also taken into account. The dispersion relation is numerically examined in an appropriate parameter space in which the gravity plays the dominant role in the dynamics of microparticles. The numerical results show that, in the low pressure complex plasma under gravity, a low frequency drift wave can be developed in the long wavelength limit. The stability state of this wave is switched at a certain critical wavenumber in such a way that the damped mode is transformed into a growing one. Furthermore, the influence of the external fields on the dispersion properties is analyzed. It is shown that the wave instability is essentially due to the electrostatic streaming of plasma particles. It is also found that by increasing the electric field strength, the stability switching occurs at smaller wavenumbers.

Dust magneto-gravitational drift wave in g×B configuration

The dispersion relation of electrostatic waves in a magnetized complex plasma under gravity is presented. It is assumed that the waves propagate perpendicular to the external fields. The effects of weak electric field, neutral drag force, and ion drag force are also taken into account. The dispersion relation is numerically examined in an appropriate parameter space in which the gravity plays the dominant role in the dynamics of magnetized microparticles. The numerical results show that an unstable low frequency drift wave can be developed in the long wavelength limit. This unstable mode is transformed into an aperiodic stationary structure at a cut-off wavenumber. Furthermore, the influence of the external fields on the dispersion properties is analyzed. It is shown that the instability is essentially due to the E×B drift motion of plasma particles. However, in the absence of weak electric field, the g×B drift motion of microparticles can cause the instability in a wide range of wavenumbers. It is also found that by increasing the magnetic field strength, the wave frequency is first increased and then decreased. This behaviour is explained by the existence of an extremum point in the dust magneto-gravitational drift velocity.

Space-charge waves in magnetized and collisional quantum plasma columns confined in carbon nanotubes

We study the dispersion relation of electrostatic waves propagating in a column of quantum magnetized collisional plasma embraced completely by a metallic single-walled carbon nanotubes. The analysis is based on the quantum linearized hydrodynamic formalism of collective excitations within the quasi-static approximation. It is shown when the electronic de Broglie's wavelength of the plasma is comparable in the order of magnitude to the radius of the nanotube, the quantum effects are quite meaningful and our model anticipates one acoustical and two optical space-charge waves which are positioned into three propagating bands. With increasing the nanotube radius, the features of the acoustical branch remain unchanged, yet two distinct optical branches are degenerated and the classical behavior is recovered. This study might provide a platform to create new finite transverse cross section quantum magnetized plasmas and to devise nanometer dusty plasmas based on the metallic carbon nanotubes in the absence of either a drift or a thermal electronic velocity and their existence could be experimentally examined.

Nonlinear electrostatic excitations in magnetized dense plasmas with nonrelativistic and ultra-relativistic degenerate electrons

Linear and nonlinear electrostatic waves in magnetized dense electron-ion plasmas are studied with nonrelativistic and ultra-relativistic degenerate and singly, doubly charged helium (He+, He++) and hydrogen (H+) ions, respectively. The dispersion relation of electrostatic waves in magnetized dense plasmas is obtained under both the energy limits of degenerate electrons. Using reductive perturbation method, the Zakharov-Kuznetsov equation for nonlinear propagation of electrostatic solitons in magnetized dense plasmas is derived for both nonrelativistic and ultra-relativistic degenerate electrons. It is found that variations in plasma density, magnetic field intensity, different mass, and charge number of ions play significant role in the formation of electrostatic solitons in magnetized dense plasmas. The numerical plots are also presented for illustration using the parameters of dense astrophysical plasma situations such as white dwarfs and neutron stars exist in the literature. The present investigation is important for understanding the electrostatic waves propagation in the outer periphery of compact stars which mostly consists of hydrogen and helium ions with degenerate electrons in dense magnetized plasmas.

Electrostatic waves in carbon nanotubes with an axial magnetic field

Based on a linearized hydrodynamic model and within the quasi-static approximation, the dispersion relation of electrostatic waves propagating through single-walled carbon nanotubes subject to an axial magnetic field is theoretically explored. In the classical limit, we obtain two main possible waves which in turn are divided into two branches, a low-frequency acoustical and a high-frequency optical plasmon branch. In the quantum case, we have found that the dispersion relation is substantially modified when the electron wavelength becomes large enough compared to the propagation wavelength of the electrostatic waves in the quantum plasma. We also show that the axial magnetic field manifest itself on the perturbed electron density through the quantum term and gives rise to the propagation of the electrostatic waves within the quantum plasma. As a result, the effect of the magnetic field is pronounced in the plasma dispersion relations in such a way that their curves approach to zero when the magnetic field is weak; and for the strong magnetic field, they asymptotically meet the constant lines.

Linear electrostatic waves in two-temperature electron–positron plasmas

AbstractLinear electrostatic waves in a magnetized four-component, two-temperature electron–positron plasma are investigated, with the hot species having the Boltzmann density distribution and the dynamics of cooler species governed by fluid equations with finite temperatures. A linear dispersion relation for electrostatic waves is derived for the model and analyzed for different wave modes. Analysis of the dispersion relation for perpendicular wave propagation yields a cyclotron mode with contributions from both cooler and hot species, which in the absence of hot species goes over to the upper hybrid mode of cooler species. For parallel propagation, both electron-acoustic and electron plasma modes are obtained, whereas for a single-temperature electron–positron plasma, only electron plasma mode can exist. Dispersion characteristics of these modes at different propagation angles are studied numerically.

Electrostatic vortex structures in a rotating magnetized electron-positron plasma with stationary ions

Nonlinear electrostatic vortex structures in the rotating magnetized electron-positron-ion plasmas are investigated. The electrons and positrons are considered to be dynamic while ions are taken to be stationary to neutralize only plasma background. In linear limit, the dispersion relation for electrostatic wave in a rotating electron-positron-ion plasma is discussed for both local and nonlocal cases. It is also found that conditions for the existence of dipolar vortex structures are modified in the presence of stationary ions in a magnetized rotating electron-positron plasma.

Dipolar vortices and collisional instability in rotating electron-positron-ion plasmas

Linear dispersion relation of electrostatic waves is derived for rotating electron-positron-ion (e-p-i) plasmas. The role of the rotational plasma frequency on drift wave through Coriolis force in the pulsar magnetosphere is discussed. This wave can couple with acoustic mode. In the nonlinear regime, stationary solution in the form of dipolar vortices is obtained. At the end we have also found the collisional instability in the presence of neutral-ion collisions for this rotating e-p-i plasma. The importance of the study with respect to astrophysical plasmas is also pointed out.

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.

Low frequency electrostatic waves in weakly inhomogeneous magnetoplasma modeled by Lorentzian (kappa) distributions

Linear dispersion relations for electrostatic waves in spatially inhomogeneous, current-carrying anisotropic plasma, where the equilibrium particle velocity distributions are modeled by various Lorentzian (kappa) distributions and by well-known bi-Maxwellian distribution, are presented. Spatial inhomogeneities, assumed to be weak, include density gradients, temperature gradients, and gradients (shear) in the parallel (to the ambient magnetic field) flow velocities associated with the current. In order to illustrate the distinguishing features of the kappa distributions, stability properties of the low frequency (lower than ion cyclotron frequency) and long perpendicular wavelength (longer than ion gyroradius) modes are studied in detail, and the results are contrasted with those for the bi-Maxwellian distribution. Specific attention is given to the drift waves, the current-driven ion-acoustic waves in the presence of velocity shear, the velocity shear-driven ion-acoustic modes, and the ion temperature-gradient driven modes. Growth rates of the drift wave instability and the current-driven ion-acoustic instability are reduced from their values for bi-Maxwellian distribution due to larger ion Landau damping rates associated with the kappa distributions. For the same reason, excitation conditions for these two instabilities are more stringent in the case of the kappa distributions. Growth rates of the velocity shear-driven ion-acoustic instability and the ion temperature-gradient driven instability are reduced from their values for bi-Maxwellian distribution as a consequence of the reduced adiabatic response of the electrons to the electrostatic potential perturbation. Frequencies of the drift waves and the ion-acoustic waves are also reduced in kappa-distribution plasmas due to the reduced adiabatic response of the electrons.