On the modulational instability of electrostatic ion cyclotron waves

The instability of electrostatic ion cyclotron waves to low frequency density modulations is considered and nonlinear equations are derived which describe its development in terms of a coherent four wave interaction. A dispersion relation for the linear phase of the instability is obtained and threshold conditions for marginal stability determined. It is shown, using data from recent optical observations, that the conditions necessary for the instability to occur in the auroral plasma would probably be satisfied and that modulational frequencies in agreement with the observations are obtained for plausible wave amplitudes. The nonlinear development of the instability is then studied and it is shown that substantial modulation can occur. It is suggested therefore that this instability could lead to the development of a strongly turbulent state.     

Electromagnetic wave instability in a relativistic electron-positron-ion plasma

By employing the anisotropic plasma distribution function, the stability of circularly polarized electromagnetic (EM) waves is studied in a relativistically hot electron-positron-ion (e-p-i) plasma, investigating two specific scenarios. First, linear dispersion relations associated with the transverse EM waves are analyzed in different possible frequency regimes. The expression of the aperiodic hydrodynamic instability is obtained and numerically the transverse EM modes are shown to grow exponentially. Secondly, we have found that the transverse electromagnetic wave interact with a collisionless anisotropic e-p-i plasma and damp through the nonlinear Landau damping phenomena. Taking the effects of the latter into consideration, a kinetic nonlinear Schrödinger equation is derived with local and nonlocal nonlinearities, computing the damping rates. The present work should be helpful to understand the linear and nonlinear properties of the intense EM waves in hot relativistically astrophysical plasmas, e.g., pulsars, black holes, neutron stars, etc.     

On the generation of modified low‐frequency Farley‐Buneman waves in the solar atmosphere

The possibility of the excitation of Farley‐Buneman turbulence in the solar atmosphere is examined. It is found that the conditions for the generation of the modified Farley‐Buneman instability can be realized in the chromosphere of the Sun 1000 km above the photosphere. While usual Farley‐Buneman waves studied in relation to the Earth's ionosphere are almost electrostatic, the modified Farley‐Buneman waves in the solar atmosphere are electromagnetic ones. This means, that not only the potential electric field caused by the charge distribution, but also the perturbations of the magnetic field and the circularly‐polarized electric field are essential. Although the physical pictures of usual and modified Farley‐Buneman waves are different, their dispersion equations are almost the same. However, the increment of the modified Farley‐Buneman waves is varied by additional electromagnetic effects. It is demonstrated that electromagnetic effects hinder a Farley‐Buneman instability in occurring while ξ < 1, where ξ is the square of the ratio of ion plasma frequency times ion‐neutral frequency to ion‐cyclotron frequency times wave number times speed of light in vacuum. Under the condition ξ > 1, no Farley‐Buneman disturbances appear at all. In weakly‐ionized solar regions, the modified (ξ < 1) and also the usual (ξ ≪ 1) Farley‐Buneman turbulence could make “electromagnetic” contributions to the process of energy dissipation of nonstationary streams of neutral gases. Besides, they may modify the low‐frequency acoustic noise. It seems that the modified Farley‐Buneman turbulence contributes to the sporadic radiation of the Sun. It is possible, that such an effect takes not only place in the chromosphere of the Sun, but also in the atmospheres of other stars.     

Proton cyclotron instability in the drifting magnetoplasma

A general expression for the tensor of the dielectrical susceptibility in an anisotropic plasma with particle drifts is derived, and the dispersion equation is found for waves propagating in arbitrary direction with respect to the mean magnetic field. The dispersion equation is solved for the case of electromagnetic ion‐cyclotron waves. It is found that in the plasma of the auroral magnetosphere strong plasma instability may occur so that the value of the growth rate of the waves is of the order of the wave frequency. Besides, the plasma instability is excited at less values of the wave number if the magnetospheric altitude becomes larger.     

Electrostatic instability excited by an electron beam trapped in the magnetic mirror of the magnetosphere

A dispersion relation which takes into account the nonuniformity of the magnetic field as well as the plasma density along the field lines is obtained for an electrostatic wave propagating parallel to the magnetic field. This dispersion relation is solved for a particular case in which a group of electrons with a monochromatic distribution in magnetic moment is mixed with a low energy plasma. Such electrons are shown to excite ion acoustic waves carried by the low-energy plasma component near multiples of the bounce frequency of these electrons. The theoretical results are applied to explain electrostatic oscillations with a period of approximately fifty seconds observed in the high energy electron fluxes at synchronous altitude.     

Nonlinear coherent four‐wave interaction in space plasma

According to a widespread point of view, intensive electrostatic structures in the E‐region of the auroral ionosphere can be a consequence of the excitation of the modified two‐stream or Farley‐Buneman (FB) plasma turbulence. But in spite of the successes of the theoretical and experimental research of the auroral radar scattering, it is impossible to explain the existence of auroral echoes with large aspect angles (> 2 deg.), the wave propagation perpendicular to the electron drift velocity and wave scales less than 1 m. In this paper the coherent nonlinear interactions of three and four electrostatic FB‐waves are considered analytically and numerically. The evolution of the nonlinear waves is described by a system of magnetohydrodynamic equations. 1) It is shown that the interaction of three and four coherent waves is the main physical mechanism which leads to the saturation of the FB‐instability. 2) If no dissipative and dispersive effects occur, an explosive instability may be excited. 3) The main result of the interaction of coherent waves is the generation of nonlinear waves and nonlinear structures when the waves are damped linearly and propagate perpendicular to the electron drift velocity. This region corresponds to large aspect angles of the small‐scale waves. 4) Further, the wave interaction causes a nonlinear stabilization of the growth of the high‐frequency waves and a formation of local density structures of the charged particles. The results of the numerical models allow to analyse the possibility of scenarios of the two‐stream plasma instability in the collisional auroral E‐region.     

Dispersion relations in the electrostatic approximation for waves in a magnetic neutral sheet

Dispersion equations in the electrostatic approximation are derived for waves propagating near the centre of a magnetic neutral sheet system. The unperturbed equilibrium is based on the Alfvén-Cowley neutral sheet model, in which the sheet current is carried by accelerated non-adiabatic electrons oscillating about the field reversal, and moving through a cold neutralizing ion background. Detailed account is taken of the non-adiabatic nature of the electron motion. It is also recognized that the zeroth order electron distribution may differ significantly from a convecting isotropic Maxwellian. A companion paper presents a detailed numerical study of the dispersion relations derived here.     

Ulysses observations of nonlinear wave-wave interactions in the source regions of type III solar radio bursts

The Ulysses Unified Radio and Plasma Wave Experiment (URAP) has observed Langmuir, ion-acoustic and associated solar type III radio emissions in the interplanetary medium. Bursts of 50&amp;#x2013;300 Hz (in the spacecraft frame) electric field signals, corresponding to long-wavelength ion-acoustic waves are often observed coincident in time with the most intense Langmuir wave spikes, providing evidence for the electrostatic decay instability. Langmuir waves often occur as envelope solitons, suggesting that strong turbulence processes, such as modulational instability and soliton formation, often coexist with weak turbulence processes, such as electrostatic decay, in a few type III burst source regions.     

Stability of Electrostatic Electron Cyclotron Waves in a Multi-Ion Plasma

We have studied the stability of the electrostatic electron cyclotron wave in a plasma composed of hydrogen, oxygen and electrons. To conform to satellite observations in the low latitude boundary layer we model both the ionic components as drifting perpendicular to the magnetic field. Expressions for the frequency and the growth rate of the wave have been derived. We find that the plasma can support electron cyclotron waves with a frequency slightly greater than the electron cyclotron frequency ω _ce ; these waves can be driven unstable when the drift velocities of both the ions are greater than the phase velocity of the wave. We thus introduce another source of instability for these waves namely multiple ion beams drifting perpendicular to the magnetic field.     

Electrostatic waves at electron gyrofrequency

An attempt to give theoretical foundation for understanding the origin of electrostatic waves at electron gyrofrequency in the magnetosphere is presented. The electrostatic dispersion equation describ- ing wave propagation at electron gyrofrequency is investigated in different limiting cases. It is pointed out that this equation can describe weakly damped waves when the electron plasma frequency is above electron gyrofrequency.     

Dust-acoustic solitary and rogue waves in a Thomas-Fermi degenerate dusty plasma

The formation and propagation of dust-acoustic (DA) solitary and rogue waves are studied in a non-relativistic degenerate Thomas-Fermi thermal dusty plasma incorporating transverse velocity perturbation effects. The electrons and ions are described by the Thomas-Fermi density distributions, whereas the dust grains are taken as dynamic and classical. By using the reductive perturbation technique, the cylindrical Kadomtsev-Petviashvili (CKP) equation is derived, which is then transformed into a Korteweg-deVries (KdV) equation by using appropriate variable transformations. The latter admits a solitary wave solution. However, when the carrier waves frequency is much smaller than the dust plasma frequency, the DA waves evolve into the nonlinear modulation instability, generating modulated wave packets in the form of Rogue waves. For the study of DA-rogue waves, the KdV equation is transformed into a self-focusing nonlinear Schrödinger equation. The variation of dust temperature and the electron density affects the nonlinearity and dispersion coefficients which suppress the amplitudes of the DA solitary and rogue waves. The present results aim to describe the nonlinear electrostatic excitations in astrophysical degenerate dense plasma.     

A theory for the solar type-I radio continuum

The type-I radio continuum may arise from the combination of two electrostatic waves, both directed nearly normal to the magnetic field. One wave, near the upper-hybrid frequency, is generated by gyroresonance with superthermal electrons and comes into equilibrium with these electrons. The other wave, at the lower-hybrid frequency, is generated by the loss-cone instability of trapped superthermal protons in those wave directions for which the lower-hybrid frequency is an exact multiple of the proton gyrofrequency. The brightness temperature of the continuum indicates both the energy of the superthermal electrons and the existance of at least a small number of superthermal protons.     

Wave-particle interaction around the lower hybrid resonance

Wave-particle interaction in the ionosphere is studied theoretically for wave frequencies around the lower hybrid resonance (LHR) frequency. An expression is derived for the growth rate of whistler-mode waves propagating in a magneto-active plasma penetrated by a tenuous beam of nonthermal particles. This expression is an extension of that derived in a previous paper by employing the electrostatic dispersion equation; here, the full-wave dispersion equation is used which reduces to the electrostatic one for large values of refractive index.     

Linearly coupled oscillations in fully degenerate pair and warm pair-ion astrophysical plasmas

In this paper we study the coexisting low frequency oscillations in strongly degenerate, magnetized, (electron-positron) pair and warm pair-ion plasma. The dispersion relations are obtained for both the cases in macroscopic quantum hydrodynamics approximation. In pair-ion case, the dispersion equation shows coupling of electrostatic and (shear) electromagnetic modes under certain circumstances with important role of ion temperature. Domain of existence of such waves and their relevance to dense degenerate astrophysical plasmas is pointed out. Results are analyzed numerically for typical systems with variation of ion concentration and ion temperature.     

Nonlinear generation of ion loss-cone waves by electrostatic turbulence in the magnetosphere

Effects of plasma turbulence on the stability of electrostatic ion loss-cone waves are examined. The turbulence is assumed to be electrostatic with frequencies near 1.5 times the electron gyrofrequency and the frequencies of the generated waves are below the ion plasma frequency ω_pi>. A nonlinear growth rate of the order of 10^?2ω_pi may be obtained, when the amplitude of the turbulence is 20 mV/m. This is comparable to previously found growth rates of the linear ion loss-cone instability, in a plasma with large pitch angle anisotropy. Bounce averaged pitch angle diffusion coefficients are also presented for different models of the ion loss-cone wave spectrum.     

Effect of small-scale bernstein turbulence on low-frequency plasma waves in the preflare solar chromosphere

The studied region is a part of the current circuit of a magnetic loop in a solar active region in the altitude range of 1400–2500 km above the photosphere. At the earliest stage of development of a flare process, the magnetic field of the loop was assumed to be stationary and uniform in the interval corresponding to weak fields (the so-called deca-hectogauss fields). The conditions for emergence and development of instability of the second harmonic of Bernstein modes in this previously unexamined region were determined. This instability (and low-frequency instabilities emerging later) was assumed to be caused by the sub-Dreicer electric field of the loop, while pair Coulomb collisions were considered to be the major factor hindering its development. The obtained extremely low instability thresholds point to the possibility of subsequent emergence of low-frequency instabilities (and plasma waves corresponding to them) with much higher threshold values against the background of saturated Bernstein turbulence. The frequency of electron scattering by turbulence pulsations in this scenario normally exceeds the frequency of pair Coulomb (primarily ion–electron) collisions. Both the quasistatic sub-Dreicer field in the loop and the weak spatial inhomogeneity of plasma temperature and density were taken into account in the process of derivation and analysis of the dispersion relation for low-frequency waves. It was demonstrated that the solutions of the obtained dispersion relation in the cases of prevalent pair Coulomb collisions and dominant electron momentum losses at pulsations of saturated Bernstein turbulence are morphologically similar and differ only in the boundary values of perturbation parameters. In both cases, these solutions correspond to the two wave families, namely, kinetic Alfven waves and kinetic ion acoustic waves. These waves have their own electric fields and may play the important role in the process of preflare acceleration of energetic electrons.     

Formation of vortices in the presence of sheared electron flows in the earth's ionosphere

It is shown that sheared electron flows can generate long as well as short wavelength (in comparison with the ion gyroradius) electrostatic waves in a nonuniform magnetplasma. For this purpose, we derive dispersion relations by employing two-fluid and hybrid models; in the two-fluid model the dynamics of both the electrons and ions are governed by the hydrodynamic equations and the guiding center fluid drifts, whereas the hybrid model assumes kinetic ions and fluid electrons. Explicit expressions for the growth rates and thresholds are presented. Linearly excited waves attain finite amplitudes and start interacting among themselves. The interaction is governed by the nonlinear equations containing the Jacobian nonlinearities. Stationary solutions of the nonlinear mode coupling equations can be represented in the form of a dipolar vortex and a vortex street. Conditions under which the latter arise are given. Numerical results for the growth rates of linearly excited modes as well as for various types of vortices are displayed for the parameters that are relevant for the F-region of the Earth's ionosphere. It is suggested that the results of the present investigation are useful in understanding the properties of nonthermal electrostatic waves and associated nonlinear vortex structures in the Earth's ionosphere.     

Effect of parallel electric fields on whistler mode waves in an anisotropic Jovian magnetospheric plasma

The effect of parallel electrostatic field on the amplification of whistler mode waves in an anisotropic bi-Maxwellian weakly ionized plasma for Jovian magnetospheric conditions has been carried out. The growth rate for different Jovian magnetospheric plasma parameters forL = 5.6R _j has been computed with the help of general dispersion relation for the whistler mode electromagnetic wave of a drifted bi-Maxwellian distribution function. It is observed that the growth or damping of whistler mode waves in Jovian magnetosphere is possible when the wave vector is parallel or antiparallel to the static magnetic field and the effect of this field is more pronounced at low frequency wave spectrum.     

Polar observations of plasma waves in and near the dayside magnetopause/magnetosheath

The plasma wave instrument (PWI) on board the Polar spacecraft made numerous passages of the dayside magnetopause and several probable encounters with the magnetosheath during the years 1996 and 1997. During periods of relatively high density, the PWI antenna-receiver system is coupled to the plasma and oscillates. The oscillations have been shown (cf. Radio Sci. 36 (2001) 203) to be indicative of periods of higher plasma density and plasma flows, possibly associated with magnetic reconnection. We have studied the plasma waves observed on three distinct magnetopause passes distinguished by the presence of these oscillations of the PWI receivers, and we report on the data obtained near, but not during, the times of the oscillations and the possible role of these waves in magnetic reconnection. Sweep-frequency receiver and high-resolution waveform data for some of these times are presented. The plasma wave measurements on each of the passes are characterized by turbulence. The most stable waves are whistler mode emissions typically of several hundred hertz that are seen intermittently in these regions. The data indicate the presence of impulsive solitary-like wave structures with strong electric fields both parallel and perpendicular to the magnetic field near, but not always within, suspected reconnection sites. The solitary waves show the highest occurrence when observed with electrostatic electron cyclotron waves. These latter waves have been observed in the past in the cusp, polar magnetosphere, and auroral regions and therefore may represent excursions into the cusp, but also indicate the presence of low-energy electron beams. Turbulence near the lower hybrid frequency, low-frequency EM waves, and impulsive monopolar electrostatic pulses are seen throughout the magnetopause and particularly near regions of large decrease in the local magnetic field and enhanced field-aligned flows, the suspected reconnection sites. The absence of significant solitary wave signatures within suspected reconnection sites may require modifications to some reconnection models.     

Whistler wave instabilities in collisionless current sheet

Instability of whistler wave in collisionless current sheet is studied with numerical solution of the general dispersion relation obtained in Ref.[4] for the physical model A. As revealed by the results, the whistler wave can be directly absorbed by collisionless current sheets. On the neutral sheet (z/d_i = 0) oblique whistler waves over a rather wide range of wave numbers can propagate, while they are basically stable. In the ionic inertial region (z/d_i < 1), the obliquely propagating whistler wave is unstable. On the edge of the ionic inertial region (z/d_i = 1), the whistler wave is still unstable, with an increase in the growth rate, and in the frequency of the unstable wave. The growth rate is larger for the whistler wave propagating towards the neutral sheet (k_zd_i < 0) than away from the neutral sheet (k_zd_i > 0).