Nonlinear mechanism for the generation of electromagnetic fields in a magnetized plasma by the beatings of waves

The modulational instability in a plasma in a strong constant external magnetic field is considered. The plasmon condensate is modulated not by conventional low-frequency ion sound but by the beatings of two high-frequency transverse electromagnetic waves propagating along the magnetic field. The instability reduces the spatial scales of Langmuir turbulence along the external magnetic field and generates electromagnetic fields. It is shown that, for a pump wave with a sufficiently large amplitude, the effect described in the present paper can be a dominant nonlinear process.     

Modulational excitation of low-frequency dust acoustic waves in the Earth’s lower ionosphere

During the observation of Perseid, Leonid, Gemenid, and Orionid meteor showers, stable low-frequency lines in the frequency range of 20–60 Hz were recorded against the radio-frequency noise background. A physical mechanism for this effect is proposed, and it is established that the effect itself is related to the modulational interaction between electromagnetic and dust acoustic waves. The dynamics of the components of a complex (dusty) ionospheric plasma with dust produced from the evolution of meteoric material is described. The conditions for the existence of dust acoustic waves in the ionosphere are considered, and the waves are shown to dissipate energy mainly in collisions of neutral particles with charged dust grains. The modulational instability of electromagnetic waves in a complex (dusty) ionospheric plasma is analyzed and is found to be driven by the nonlinear Joule heating, the ponderomotive force, and the processes governing dust charging and dynamics. The conditions for the onset of the modulational instability of electromagnetic waves, as well as its growth rate and threshold, are determined for both daytime and nighttime. It is shown that low-frequency perturbations generated in the modulational interaction are related to dust acoustic waves.     

Excitation of inertial Alfvén waves via modulational interaction with lower hybrid waves

The concept of modulational instability, which results from the coupling of waves modes of very different time and space scales, was introduced to plasma physics through an elegant paper by Vedenov and Rudakov in 1964 [1]. Our paper is devoted to the theory of modulational instability resulting from the interaction of lower hybrid waves and slow density perturbations associated with inertial Alfvén waves. The nonlinear set of equations describing the modulational coupling of these two types of waves is constructed. The lower hybrid wave trajectories are analyzed within predefined density structures and it is shown that these waves can be trapped in the vicinity of the density extremum. The density modulations, originally being associated with inertial Alfvén waves, deepen due to the trapping of lower hybrid waves; this leads to modulational instability. A dispersion relation describing the modulational instability is constructed and analyzed. The threshold intensity of the lower hybrid waves for the onset of instability is obtained and it is shown that instability can serve as an efficient mechanism for the excitation of inertial Alfvén waves in the auroral ionosphere.     

Nonlinear theory of coupled waves exemplified by beam-plasma instability

The nonlinear stage of instability of an annular electron beam spatially separated from an annular plasma is investigated. The equations describing coupled waves for an arbitrary ratio between the beam and plasma densities are derived. It is shown that instability saturates at distances on the order of several inverse spatial growth rates. The saturation is caused by relativistic nonlinearity, generation of the second harmonic, and low-frequency modulation of the electromagnetic field. At larger distances, resonant generation of low-frequency beam oscillations becomes a dominant factor. In the case of a low-density beam, an expression for the maximum power of the generated plasma wave is obtained in an explicit form.     

Multimode parametric instability during electron cyclotron heating

A study is made of the generation of electron Bernstein waves in the interaction of a microwave field with a magnetized plasma during electron cyclotron heating. Parametric resonance accompanied by simultaneous conversion of microwave-field energy into the energy of numerous waves is analyzed. The relevant dispersion relation is investigated using the Hill method, which has recently been applied for the first time to examine the parametric interaction between high-power microwave radiation and plasmas. It is shown that the dispersion relation can be used to describe the onset of modulational instability at multimode parametric resonance. The growth rate of the modulational instability is obtained. Efficient energy transfer from the microwave field into Bernstein modes and, accordingly, into plasma electrons may be one of the main mechanisms for electron cyclotron resonance plasma heating.     

Low-frequency instability of an ion beam in the field of a high-current REB

A study is made of the linear and nonlinear stages of the low-frequency instability of an ensemble of ions that execute radial oscillations in the electric field of the space charge of an unneutralized high-current relativistic electron beam. Nonlinear mechanisms for stabilizing the low-frequency ion instability are considered. It is shown, in particular, that, under certain conditions, the development of the low-frequency instability can lead to the ejection of ions onto the walls of the drift chamber.     

Effect of the ponderomotive force on the development of beam-plasma instability

The amplitude of the wave generated in a plasma during the development of beam-plasma instability is nonuniform in the longitudinal direction. The ponderomotive force associated with this nonuniformity leads to a redistribution of the plasma density; as a result, the wave amplitude and its spatial distribution change. As the beam current grows, the ponderomotive force plays an increasingly important role and radically changes the mechanism by which the beam-plasma instability saturates. Ion acoustic waves generated by the ponderomotive force propagate in the direction opposite to the propagation direction of the beam, thereby ensuring distributed feedback and giving rise to a strong low-frequency self-modulation of the wave amplitude and phase. Results are presented from experimental investigations of the self-modulation regime of the beam-plasma instability in a magnetized plasma waveguide. Theoretical estimates of the parameters of the low-frequency self-modulation agree well with the experimental data.     

Nonlinear Right-Hand Polarized Wave in Plasma in the Electron Cyclotron Resonance Region

The propagation of a nonlinear right-hand polarized wave along an external magnetic field in subcritical plasma in the electron cyclotron resonance region is studied using numerical simulations. It is shown that a small-amplitude plasma wave excited in low-density plasma is unstable against modulation instability with a modulation period equal to the wavelength of the excited wave. The modulation amplitude in this case increases with decreasing detuning from the resonance frequency. The simulations have shown that, for large-amplitude waves of the laser frequency range propagating in plasma in a superstrong magnetic field, the maximum amplitude of the excited longitudinal electric field increases with the increasing external magnetic field and can reach 30% of the initial amplitude of the electric field in the laser wave. In this case, the energy of plasma electrons begins to substantially increase already at magnetic fields significantly lower than the resonance value. The laser energy transferred to plasma electrons in a strong external magnetic field is found to increase severalfold compared to that in isotropic plasma. It is shown that this mechanism of laser radiation absorption depends only slightly on the electron temperature.     

Instability of a magnetic drift wave in the vicinity of the dust-ion hybrid resonance

Low-frequency electromagnetic waves propagating perpendicular to the gradients of the density and magnetic field in an inhomogeneous dusty plasma whose mass density is determined primarily by the dust component are analyzed. It is shown that, in analyzing the dispersion properties of inhomogeneous plasma, it is important to take into account the dynamic properties of ions in the vicinity of the dust-ion hybrid resonance. The conditions for the onset of instability of a magnetic drift wave are investigated for different relations between parameters of the inhomogeneity and the value of the Alfvén velocity. The differences from the previous results, as well as possible astrophysical applications, are discussed.     

Progress in theory of instabilities in a rotating plasma

A review is given of the basic results of modern theory of instabilities in a rotating plasma. Both axisymmetric and nonaxisymmetric perturbations are considered. Main attention is given to the magnetorotational instability (MRI), discovered earlier by Velikhov, and the rotational-convective instability (RCI) discussed in a number of papers of astrophysical trend. For qualitative explanation of the results, a local approach is used which, with equilibrium plasma pressure gradient and/or nonsymmetry of perturbations, requires operation with nonlocal azimuthal perturbed magnetic field. The gravity and effects of pressure anisotropy are taken into account. In addition to hydrodynamic, the electrodynamic approach is formulated. The drift effects are considered. Analyzed are the ideal instabilities and those depending on the dissipative effects: viscosity and heat conductivity. The MRI is considered at presence of the charged dust particles. Besides the local approach, the nonlocal approach is formulated for the plasma model with a steplike profile of angular rotation frequency. Alongside with perturbations which frequencies are small compared to the ion cyclotron frequency, the perturbations are analyzed with frequencies larger than the ion cyclotron frequency. The latter corresponds to the Hall regime and subregime of nonmagnetized plasma.     

Saturation of two-stream instability of an electron beam in plasma

The development and nonlinear saturation of two-stream instability of a warm nonrelativistic electron beam in a cold plasma are investigated numerically in the framework of a one-dimensional model. It is shown that, for a sufficiently large velocity spread of the electron beam, instability develops and saturates according to a universal law, the wave phase velocity remains the same in the saturation stage, and the maximum field is somewhat lower than that predicted by classical estimates and depends in a different way on the growth rate. The damping of plasma oscillations not only changes the instability growth rate, but also substantially decreases the maximum wave field.     

Radio-frequency stabilization of a nonequilibrium plasma accelerator

Results of experimental studies of the effect of an external RF field on the excitation of oscillations in a magnetoplasmadynamic plasma accelerator are presented. It is found that applying an RF field can suppress the drift component of low-frequency oscillations in the ejected plasma flow. The experimental data agree with the concept of stabilization of the plasma accelerator by the magnetic component of the field generated by the RF current loop. The conditions under which the RF field stabilizes the generation of the plasma flow are determined, and the factors limiting the stabilization efficiency are revealed.     

Reversal of the hall current and amplification of the magnetorotational instability in a weakly ionized plasma

A criterion for the development of a magnetorotational instability in a weakly ionized dusty plasma is considered. A dispersion relation for the wavenumber and the growth rate of an unstable perturbation is derived for an arbitrary angle between the wave vector and magnetic field. It is shown that the presence of dust grains can reverse the direction of the Hall current in the plasma and can shift the instability threshold to shorter wavelengths. Under certain conditions, Alfvén fluctuations of arbitrary scale can be unstable. The Hall current reversal is found to have a strong effect on the development of a magnetorotational instability when the Alfvén resonance frequency in a weakly ionized plasma is close to the rotation frequency of the accretion disk.     

Generation of auroral kilometric radiation by a finite-size source in a dipole magnetic field

Generation, amplification, and propagation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron beam propagates is studied in the geometrical optics approximation. It is shown that the waves that start with a group velocity directed earthward and have optimal relation between the wave vector components determining the linear growth rate and the wave residence time inside the amplification region undergo the largest amplification. Taking into account the longitudinal velocity of fast electrons results in the shift of the instability domain toward wave vectors directed to the Earth and leads to a change in the dispersion relation, due to which favorable conditions are created for the generation of waves with frequencies above the cutoff frequency for the cold background plasma at the wave generation altitude. The amplification factor for these waves is lower than for waves that have the same wave vectors but are excited by the electron beams with lower velocities along the magnetic field. For waves excited at frequencies below the cutoff frequency of the background plasma at the generation altitude, the amplification factor increases with increasing longitudinal electron velocity, because these waves reside for a longer time in the amplification region.     

Theory of the acoustic instability and behavior of the phase velocity of acoustic waves in a weakly ionized plasma

The amplification of acoustic waves due to the transfer of thermal energy from electrons to the neutral component of a glow discharge plasma is studied theoretically. It is shown that, in order for acoustic instability (sound amplification) to occur, the amount of energy transferred should exceed the threshold energy, which depends on the plasma parameters and the acoustic wave frequency. The energy balance equation for an electron gas in the positive column of a glow discharge is analyzed for conditions typical of experiments in which acoustic wave amplification has been observed. Based on this analysis, one can affirm that, first, the energy transferred to neutral gas in elastic electron-atom collisions is substantially lower than the threshold energy for acoustic wave amplification and, second, that the energy transferred from electrons to neutral gas in inelastic collisions is much higher than that transferred in elastic collisions and thus may exceed the threshold energy. It is also shown that, for amplification to occur, there should exist some heat dissipation mechanism more efficient than gas heat conduction. It is suggested that this may be convective radial mixing within a positive column due to acoustic streaming in the field of an acoustic wave. The features of the phase velocity of sound waves in the presence of acoustic instability are investigated.     

Spectra of langmuir waves in a magnetized plasma with low-frequency turbulence

A study is made of the formation of the spectra of Langmuir waves excited as a result of the development of beam-plasma instability in a collisionless magnetized plasma with low-frequency turbulence. Equations are derived that describe the dynamics of the formation of spectra in the quasilinear statistical approximation.The equations obtained account for small-and large-angle scattering of the electron-beam-excited waves by given background plasma density fluctuations. The scattering of Langmuir waves leads to the redistribution of their energy in phase space and, under appropriate conditions, to the appearance of a characteristic dent in the wave spectra in the frequency range where the spectral intensity is maximum. Numerical simulations carried out for plasma parameters typical of the polar cap of the Earth’s magnetosphere help to explain the shape of the spectra of Langmuir waves that were recorded by the Interball-2 satellite when it was flying through this magnetospheric region.     

Low-frequency instabilities of collisionless plasma and the 16-moment approximation

Using the 16-moment equations that take into account heat fluxes in anisotropic collisionless plasma, the properties of magnetohydrodynamic (MHD) instabilities are investigated. For all instabilities occurring in the MHD approach (the normal incompressible firehose instability, the second compressible almost longitudinal firehose instability, and the almost transverse mirror instability of slow magnetosonic modes, as well as thermal instability caused by the heat flux directed along the magnetic field), their kinetic analogs are considered. The kinetic dispersion relation in the low-frequency range in the vicinity of the ion thermal velocity is analyzed. The flow of plasma ions along the magnetic field is taken into account. The thresholds and instability growth rates obtained in the MHD and kinetic approaches are found to be in good agreement. This indicates that the 16-moment MHD equations adequately describe the dynamics of collisionless plasma.     

Amplification of surface waves in a plasma waveguide by a straight relativistic electron beam in a finite magnetic field

The problem of the excitation of electron waves in a thin-walled annular cold plasma in a cylindrical waveguide by a straight relativistic electron beam in a finite magnetic field is considered. The dispersion properties of a waveguide system with parameters close to the experimental ones are investigated. It is shown that the growth rate of the excited high-frequency plasma wave is comparable to that of the low-frequency wave, which is weakly sensitive to the strength of the longitudinal magnetic field.     

Decay instability of a lower hybrid wave

A study is made of the decay instability of a lower hybrid wave with a finite wave vector (k ₀≠0) and a large amplitude such that the oscillatory velocity of the electrons with respect to the ions cannot be neglected. It is shown that, depending on the angle between the propagation direction of the lower hybrid wave and the external magnetic field and the angle through which the wave is scattered, the decay instability is primarily governed either by the oscillatory electron motion with respect to the ions or by the nonlinear response of the plasma to the lower hybrid wave propagating in it. The role of the nonlinear frequency shift in the saturation of the lower hybrid decay instability is clarified.