Effect of Long-Wavelength Magnetic Field Disturbances on the Generation of Auroral Kilometric Radiation

The effect of long-wavelength magnetic field disturbances typical of the Earth’s auroral region on the generation of auroral kilometric radiation in a narrow three-dimensional plasma cavity in which a weakly relativistic electron flow propagates against the background of cold low-density plasma is analyzed. The dynamics of the propagation and amplification of fluctuation waves with initial group velocities directed toward the higher magnetic field is considered in the geometrical optics approximation. Analysis of wave trajectories shows that the wave amplification coefficients depend on the magnetic field gradient in the reflection region. If the wave reflection point lies in the region where the gradient of the disturbed magnetic field is less than that of the undisturbed dipole field, then the wave amplification coefficients exceed those of waves propagating in the undisturbed field, and vice versa. Thus, the shape of the spectrum of generated waves changes in the presence of long-wavelength disturbances of the dipole magnetic field in such a way that segments with different curvatures can form in the spectrum.     

Effect of the global topology of the interplanetary magnetic field on the properties of impulsive acceleration processes in distant regions of the Earth’s magnetospheric tail

The paper is devoted to a statistical study of high-speed ion beams (beamlets) observed by the Interball-1 and Interball-2 satellites in the boundary region of the plasma sheet of the geomagnetic tail and in the high-latitude auroral regions of the Earth’s magnetosphere. Beamlets result from nonlinear acceleration processes occurring in the current sheet in the distant regions of the geomagnetic tail. They propagate toward the Earth along the magnetic field lines and are detected in the boundary region of the plasma sheet and near the high-latitude boundary of the plasma sheet in the auroral region in the form of short (with a duration of 1–2 min) bursts of high-energy (with energies of about several tens of keV) ions. The sizes of the latitudinal zones where the beamlets are localized in the tail and in the auroral region are determined using the epoch superposition method. The relationship between the frequency of beamlet generation in the boundary region of the plasma sheet and the prehistory of the direction of the interplanetary magnetic field (the magnitude of a clock angle) is investigated. It was established that this direction exerts a global effect on the beamlet generation frequency; moreover, it was found that the beamlet generation frequency in the midnight local time sector of the tail and at the flanks depends differently on the direction of the interplanetary magnetic field. In the midnight sector, the beamlets are observed at almost all directions of the interplanetary field, whereas the frequency of their generation at the flanks is maximal only when the interplanetary magnetic field has a large y component.     

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.     

Conversion of fast magnetosonic waves into Alfvén waves in a longitudinally inhomogeneous gyrotropic plasma

A model is considered of the conversion of running fast magnetosonic waves into Alfvén waves in a longitudinally inhomogeneous gyrotropic plasma in a magnetic field with open field lines. The set of equations for the amplitudes of the interacting modes is obtained and investigated in the Wentzel-Kramers-Brillouin approximation. In the synchronization region, where the wave vectors of the two modes approach one another, most of the energy of fast magnetosonic waves is converted into the Alfvén wave energy. The phases of the waves are matched in such a way that the phase difference is most favorable for wave conversion. The fact that the conversion is resonant in nature may help to explain the onset of quasi-monochromatic signals in the Earth’s magnetosphere and in the magnetospheres of the giant planets.     

Experimental studies of the magnetic structure and plasma dynamics in current sheets (a review)

Based on measurements of magnetic fields in current sheets, spatial distributions of the electric current and electrodynamic forces in successive stages of the sheet evolution are determined. Two new effects manifesting themselves mostly in the late stages of the current sheet evolution have been discovered, namely, expansion of the current flow region at the periphery of the sheet and the appearance of a region with inverse currents, which gradually expands from the periphery toward the center of the sheet. Using spectroscopic methods, generation of superthermal plasma flows accelerated along the sheet width from the center toward the periphery has been revealed and investigated. The measured energies of accelerated plasma ions satisfactorily agree with the Ampère forces determined from magnetic measurements. The excitation of inverse currents additionally confirms the motion of high-speed plasma flows from the center of the current sheet toward its side edges.     

Effect of flux surface curvature on the linear coupling of electron cyclotron waves in tokamak plasmas

Specific features of the linear interaction of ordinary and extraordinary electromagnetic waves in the electron cyclotron frequency range in a nonuniform plasma confined in a toroidal magnetic trap are considered. Reduced wave equations taking into account the curvature of the cut-off surfaces in toroidal geometry are formulated. Using these equations, the distributions of the wave fields in the coupling region are analyzed. A method for calculating quasi-optical beams passed through the region of linear wave interaction is proposed.     

Magnetic geometry, plasma profiles, and stability

The history of the stability of short wavelength modes, such as MHD instabilities and drift waves, has been a long and tortuous one as increasingly realistic representations of the equilibrium magnetic geometry have been introduced. Early work began with simple slab or cylindrical models where plasma profiles and magnetic shear were seen to play key roles. Then the effects of toroidal geometry, in particular the constraints imposed by periodicity in the presence of magnetic shear, provided a challenge for theory, which was met by the ballooning transformation. More recently the limitations on the conventional ballooning theory arising from effects such as toroidal rotation shear, low magnetic shear, and the presence of the plasma edge have been recognized. These have led in turn to modifications and extensions of this theory. These developments have produced a continuously changing view of the stability of the “universal” drift wave, for example. After a survey of this background, we describe more recent work of relevance to currently important topics, such as transport barriers characterized by the presence of strong rotation shear and low magnetic shear and the edge localized modes that occur in H-mode. Published in Russian in Fizika Plazmy, 2006, Vol. 32, No. 7, pp. 588–598. Based on an invited talk given at the 11th European Fusion Theory Meeting, Aix-en-Provence, France, September 2005. The text was submitted by the author in English.     

Theory of transverse surface electromagnetic waves propagating along a plasma-metal boundary with a finite radius of curvature in a magnetic field

The spectra of electromagnetic waves propagating perpendicular to the axis of a plasma-filled metal waveguide in a magnetic field are studied with allowance for the effects exerted upon the wave frequency by the radial plasma density variation and by the emission of waves through a narrow axial slit in a waveguide wall. The case of wave propagation along the boundary between a plasma and a cylindrical metal waveguide wall with a periodically varying radius of curvature is also considered. The electromagnetic properties of the plasma are described by a dielectric tensor in the hydrodynamic approximation. The spatial distribution of the wave field is determined by the method of successive approximations. Results are presented from both analytical and numerical investigations. Analytical expressions for the corrections to the wave frequency due to the emission of the wave energy from the waveguide and due to the slight corrugation of the waveguide wall are obtained. The rates of wave damping due to the emission of the wave energy through a narrow axial slit and due to collisions between the plasma particles are found. The correction to the frequency that comes from the periodic variation of the radius of curvature of the plasma surface is calculated to within terms proportional to the square of the small parameter describing the azimuthal corrugation of the waveguide wall. The effect of the radial plasma density variation on the dispersion of the surface modes is examined both analytically and numerically.     

Theory of longitudinal plasma waves with allowance for ion motion

A study is made of the propagation of steady-state large-amplitude longitudinal plasma waves in a cold collisionless plasma with allowance for both electron and ion motion. Conditions for the existence of periodic potential waves are determined. The electric field, potential, frequency, and wavelength are obtained as functions of the wave phase velocity and ion-to-electron mass ratio. Taking into account the ion motion results in the nonmonotonic dependence of the frequency of the waves with the maximum possible amplitudes on the wave phase velocity. Specifically, at low phase velocities, the frequency is equal to the electron plasma frequency for linear waves. As the phase velocity increases, the frequency first decreases insignificantly, reaches its minimum value, and then increases. As the phase velocity increases further, the frequency continues to increase and, at relativistic phase velocities, again becomes equal to the plasma frequency. Finally, as the phase velocity approaches the speed of light, the frequency increases without bound.     

Wave processes during the interaction of the Earth’s magnetotail with dusty plasma near the lunar surface

The wave processes that take place under the interaction of the Earth’s magnetosphere with dusty plasma near the lunar surface are considered. It is shown that the waves can be excited for the photoelectron parameters corresponding to the quantum yield of the lunar regolith reported by Willis et al. [Photon and Particle Interactions with Surfaces in Space, Ed. by R. J. L. Grard (Reidel, Dordrecht, 1973), p. 389]. Ion-acoustic waves are excited in the regions of the transient magnetic and/or boundary magnetospheric layers due to the onset of linear hydrodynamic instability, whereas dust-acoustic waves are generated due to the onset of linear kinetic instability in the entire region of magnetotail interaction with dusty plasma near the Moon. In both cases, instability is caused by the relative motion of the magnetospheric ions and charged dust grains. The dynamics of the development of ion-acoustic and dust-acoustic turbulence is investigated. Ion-acoustic turbulence is described in terms of strong turbulence theory, while dust-acoustic turbulence is described in terms of weak turbulence theory. The energy density of oscillations, the effective collision frequencies, and the electric fields arising in the system are determined for both ion-acoustic and dust-acoustic turbulences. It is shown that the development of ion-acoustic turbulence in the dusty plasma system near the Moon can lead to the generation of electric fields that are somewhat weaker than those arising near the lunar surface due to the charging of the Moon’s surface under the action of solar radiation, but still sufficiently strong to affect the electric field pattern above the Moon. The obtained effective collision frequencies should be taken into consideration when deriving hydrodynamic equations for dusty plasma ions with allowance for turbulent plasma heating.     

Better Endurance and Load Capacity: An Improved Design of Manta Ray Robot (RoMan-II)

An improved design of a biomimetic underwater vehicle (RoMan-II) inspired by manta ray is presented in this paper. The design of the prototype and the swimming motion control are discussed. Instead of using rigid multiple degree-of-freedom linkages as fin rays in the first version, six flexible fin rays are adopted to drive two sided fins which generate thrust through flapping motions. Furthermore, in order to save the energy for a long distance cruising, a bio-inspired gliding motion is incorporated onto the motion control of the improved prototype. With a closed-loop buoyancy control system, the vehicle can perform gliding locomotion in water, which reduces the overall energy consumption. The vehicle can also perform pivot turning and backward locomotion without turning its body. It can achieve an average velocity of one body length per second. The vehicle is able to carry various sensors or communication equipments, as the payload capacity is about 4 kg. Initial testing shows that the operation time of the buoyancy body is estimated to about 6 hours for free swimming and 90 hours for a pure gliding. The flapping frequency, flapping amplitude, and the number of waves performed across the fin's chord and wave directions can be independently tuned through the proposed control scheme. In general, the present prototype provides a useful platform to study the ray-like swimming motion in a single or combination mode of flapping, undulation and gliding.     

Time Evolution of the Macroscopic Characteristics of a Thin Current Sheet in the Course of Its Formation in the Earth’s Magnetotail

A numerical model is developed that allows tracing the time evolution of a current sheet from a relatively thick current configuration with isotropic distributions of the pressure and temperature in an extremely thin current sheet, which plays a key role in geomagnetic processes. Such a configuration is observed in the Earth’s magnetotail in the stage preceding a large-scale geomagnetic disturbance (substorm). Thin current sheets are reservoirs of the free energy released during geomagnetic disturbances. The time evolution of the components of the pressure tensor caused by changes in the structure of the current sheet is investigated. It is shown that the pressure tensor in the current sheet evolves in two stages. In the first stage, a current sheet with a thickness of eight to ten proton Larmor radii forms. This stage is characterized by the plasma drift toward the current sheet and the Earth and can be described in terms of the Chu–Goldberger–Low approximation. In the second stage, an extremely thin current sheet with an anisotropic plasma pressure tensor forms, due to which the system is maintained in an equilibrium state. Estimates of the characteristic time of the system evolution agree with available experimental data.     

Distinctive features of collisionless gradient drift instabilities in a high-β plasma in a highly nonuniform magnetic field

A set of Vlasov-Maxwell equations for collisionless electromagnetic drift instabilities of high-β plasma configurations with a nonuniform magnetic fields is solved. The effect of the transverse static magnetic field variation and magnetic field line curvature, as well as the plasma temperature and density gradients, is considered. It is shown that, in a nonuniform magnetic field, the behavior of the instabilities differs substantially from that in a uniform field. Electromagnetic modes propagating strictly transverse to the lines of the static magnetic field are analyzed in detail, and unstable solutions are obtained for both extraordinary and ordinary waves. Numerical results show that, in the latter case, instability occurs when the magnetic field decreases toward the periphery and the plasma temperature and density gradients are oppositely directed.     

Exact solutions for oblique solitary Alfvén waves in plasma

The properties of solitary Alfvén waves are studied for different ratios between the thermal plasma pressure and the magnetic pressure. It is shown that the wave propagation is accompanied by the generation of a nonlinear ion current along the magnetic field, the contribution of which to the Sagdeev potential was previously ignored. An expression for the quasi-potential of Alfvén waves with allowance for this effect is derived. It is found that Alfvén waves are compression waves in the inertial limit, whereas kinetic Alfvén waves are rarefaction waves. In a high-pressure plasma, a solitary wave has the form of either a well or a hump in the plasma density, depending on the relations between the Mach number, angle between the wave propagation direction and the magnetic field, and the value of the plasma beta.     

Broadening of the frequency spectrum of waves forming a low-pressure helicon discharge

It is found experimentally that the spectrum of waves forming a low-pressure RF discharge in a strong magnetic field broadens toward lower frequencies. Such an asymmetric broadening is explained by the scattering of the pump wave by the electron flows escaping from the discharge. A similar effect can take place during the formation of the spectrum of artificial RF radiation in the Earth??s ionosphere.     

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).     

Supersonic and near-sonic solitary ion-acoustic waves in magnetized plasma

The propagation of large-amplitude solitary ion-acoustic waves in magnetized plasma is analyzed. The problem is solved without assuming plasma quasineutrality within the pulse, and the wave potential is described by Poisson’s equation. Solutions in the form of supersonic and near-sonic solitary waves propagating obliquely to the magnetic field are found. The pulses have several peaks and exist for a discrete set of the wave parameters. The amplitude and oscillation frequency of a solitary wave are determined as functions of the Mach number and the propagation angle with respect to the magnetic field.     

Propagation of MHD waves in a plasma in a sheared magnetic field with straight field lines

The propagation of MHD plasma waves in a sheared magnetic field is investigated. The problem is solved using a simplified model: a cold plasma is inhomogeneous in one direction, and the magnetic field lines are straight. The waves are assumed to travel in the plane perpendicular to the radial coordinate (i.e., the coordinate along which the plasma and magnetic field are inhomogeneous). It is shown that the character of the singularity at the resonance surface is the same as that in a homogeneous magnetic field. It is found that the shear gives rise to the transverse dispersion of Alfvén waves, i.e., the dependence of the radial component of the wave vector on the wave frequency. In the presence of shear, Alfvén waves are found to propagate across magnetic surfaces. In this case, the transparent region is bounded by two turning points, at one of which, the radial component of the wave vector approaches infinity and, at the other one, it vanishes. At the turning point for magnetosonic waves, the electric and magnetic fields are finite; however, the radial component of the wave vector approaches infinity, rather than vanishes as in the case with a homogeneous field.     

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.     

Numerical simulations of plasma equilibrium in a one-dimensional current sheet with a nonzero normal magnetic field component

The force balance in a thin collisionless current sheet in the Earth’s magnetotail with a given constant magnetic field component B _z across the sheet is numerically studied for the first time in a self-consistent formulation of the problem. The current sheet is produced by oppositely directed plasma flows propagating from the periphery of the sheet toward the neutral plane. A substantially improved version of a macroparticle numerical model is used that makes it possible to simulate on the order of 10⁷ macroparticles even with a personal computer and to calculate equilibrium configurations with a sufficiently low discrete noise level in the first-and second-order moments of the distribution function, which determine the stress tensor elements. Quasisteady configurations were calculated numerically for several sets of plasma parameters in some parts of the magnetotail. The force balance in the sheet was checked by calculating the longitudinal and transverse pressures as well as the elements of the full stress tensor. The stress tensor in the current sheet is found to be nondiagonal and to differ appreciably from the gyrotropic stress tensor in the Chew-Goldberger-Low model, although the Chew-Goldberger-Low theory and numerical calculations yield close results for large distances from the region of reversed magnetic field.