Shear flow instability near the cusp resonance in magnetopause boundary layer

Shear flow instability is studied in the planar magnetopause boundary layer region by treating the plasma as compressible. A necessary criterion for instability near the cusp resonance is obtained analytically. The criterion depends on plasma, Alfvén Mach numberM _A and the ratio of the scale lengths of the gradients in the flow and Alfvén velocities. The instability at the cusp resonance layer can be excited rather easily for the low plasma and for shear flow scale length smaller than the typical scale length over which Alfvén velocity varies. The growth rate for instability is obtained for any from a cubic equation. The unstable modes may contribute to the ULF wave activity at the magnetopause.     

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.     

Alfvén wave plasma turbulence during solar wind-comet interaction

The large differences in drift velocities between the solar wind protons and the picked-up ions of cometary origin cause the Alfvén waves (among others) to become unstable and generate turbulence. A self-consistent treatment of such instabilities has to take into account that these cometary ions affect the solar wind plasma in a decisive way. With the help of a previously developed formalism one finds the correct Alfvén instability criterion, which is here nondispersive, in contrast to recent calculations where the cometary ions are treated as a low-density, high-speed, and non-neutral beam through an otherwise undisturbed solar wind. The true bulk speed of the combined solar wind plus cometary ion plasma clearly shows the mass-loading and deceleration of the solar wind near the cometary nucleus, indicating a bow shock. The instability criterion is also used to determine the region upstream where the Alfvén waves can be unstable, based upon recent observations near comet Halley.     

Low-frequency plasma turbulence during solar wind-comet interaction

The pick up cometary ion distributions are shown to excite Alfvénic mode instabilities, slow ion-acoustic mode instability and a lower hybrid instability during solar wind-comet interaction. The growth rates of all these instabilities become larger as the comet is approached. The lower hybrid instability is shown to account for the low-frequency 0–300 Hz electrostatic turbulence observed near comet Halley. The Alfvén modes can grow to large amplitudes and become modulationally unstable, in the presence of low-frequency density fluctuations, going over to envelope Alfvén solitons. A model consisting of a gas of Alfvén solitons is suggested to explain the hydromagnetic turbulence observed near comet Halley and comet Giacobini-Zinner.     

Resonant Absorption of Alfvén Waves in Steady Coronal Loops

The effect of equilibrium flow on linear Alfvén resonances in coronal loops is studied in the compressible viscous MHD model. By means of a finite element code, the full set of linearised driven MHD equations are solved for a one-dimensional equilibrium model in which the equilibrium quantities depend only on the radial coordinate. Computations of resonant absorption of Alfvén waves for two classes of coronal loop models show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We find that a steady equilibrium shear flow can also significantly influence the resonant absorption of Alfvén waves in coronal magnetic flux tubes. The presence of an equilibrium flow may therefore be important for resonant Alfvén waves and coronal heating. A parametric analysis also shows that the resonant absorption can be strongly enhanced by the equilibrium flow, even up to total dissipation of the incoming wave.     

Gravitational instability of a thermally-conducting plasma flowing through a porous medium in the presence of suspended particles

Magnetogravitational instability of a thermally-conducting, rotating plasma flowing through a porous medium with finite conductivity and finite Larmor radius in the presence of suspended particles has been investigated. The wave propagation has been considered for both parallel and perpendicular axes of rotation. Magnetic field is being taken in the vertical direction. A general dispersion relation has been derived through relevant linearized perturbation equations. It has been observed that the condition of instability is determined by the Jeans's criterion in its modifed form. Thermal conductivity replaces the adiabatic velocity of sound by the isothermal one. Rotation decreases the Larmor radius. Porosity decreases the Alfvén velocity. In case of a viscous medium the effects of FLR, rotation, and suspended particles are not observed in the Jeans's condition, for transverse propagation for rotational axis parallel to the magnetic field. The effects of rotation and FLR are decreased by the porosity and the suspended particles. Finite conductivity removes the Alfvén velocity from Jeans's condition.     

Nonlinear Alfvén wave modulation in the solar atmosphere

Nonlinear interaction of finite-amplitude Alfvén waves with non-resonant finite-frequency electrostatic and stationary electromagnetic perturbations is considered. This interaction is governed by a pair of coupled equations consisting of nonlinear Schrödinger equation for the Alfvén wave envelope and an equation for the plasma slow response that is driven by the ponderomotive force of the Alfvén wave packets. The modulational instability of a constant amplitude Alfvén pump is investigated and some new results for the growth rate of the instability are presented. It is found that a possible stationary state of the modulated Alfvén wave packets could lead to localized structures. The relevance of our investigation to the solar atmosphere is discussed.     

Kelvin-Helmholtz instability in an Alfvén resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfvén resonant layer in an axially bounded, straight cylindrical coronal loop. The physical model employed is an incompressible, reduced magnetohydrodynamic (MHD) model including resistivity, viscosity, and density variation. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfvén driving amplitude and inversely proportional to the width of the Alfvén resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfvén resonant layer width, and decreases at higher m's. (m is the azimuthal mode number.)     

Tunneling and interference of Alfvén waves

The propagation and interference of Alfvén waves in magnetic regions is studied. A multilayer approximation of the standard models of the solar atmosphere is used. In each layer, there is a linear law of temperature variation and a power law of Alfvén velocity variation. The analytical solutions of a wave equation are stitched at the layer boundaries. The low-frequency Alfvén waves (P > 1 s) are able to transfer the energy from sunspots into the corona by tunneling only. The chromosphere is not a resonance filter for the Alfvén waves. The interference and resonance of Alfvén waves are found to be important to wave propagation through the magnetic coronal arches. The transmission coefficient of Alfvén waves into the corona increases sharply on the resonance frequences. To take into account the wave absorption in the corona, a method of equivalent schemes is developed. The heating of a coronal arch by Alfvén waves is discussed.     

Helical waves in type-1 comet tails

Oscillations of type-1 comet tails with plasma compressibility taken into account are studied. A comet tail is treated as a plasma cylinder separated by a tangential discontinuity surface from the solar wind. The dispersion equation obtained in the linear approximation is solved numerically with typical plasma parameters. A sufficient condition for instability of the cylindrical tangential discontinuity in the compressible fluid is obtained. The phase velocity of helical waves is shown to be approximately coincident with Alfvén speed in the tail in the reference system moving with the bulk velocity of the plasma outflow in the tail. The instability growth rate is calculated.This theory is shown to be in good agreement with observations in the tails of Comets Kohoutek, Morehouse and Arend-Roland. Hence we conclude that helical waves observed in type-1 comet tails are produced due to the Kelvin-Helmholtz instability, and the model under consideration is justified. If so, one may estimate comet tail magnetic field from the pressure balance at the tangential discontinuity; it turns out to be of the order of the interplanetary magnetic field.     

Resonant behaviour of MHD waves on magnetic flux tubes

The resonances that appear in the linear compressible MHD formulation of waves are studied for equilibrium states with flow. The conservation laws and the jump conditions across the resonance point are determined for 1D cylindrical plasmas. For equilibrium states with straight magnetic field lines and flow along the field lines the conserved quantity is the Eulerian perturbation of total pressure. Curvature of the magnetic field lines and/or velocity field lines leads to more complicated conservation laws. Rewritten in terms of the displacement components in the magnetic surfaces parallel and perpendicular to the magnetic field lines, the conservation laws simply state that the waves are dominated by the parallel motions for the modified slow resonance and by the perpendicular motions for the modified Alfvén resonance.The conservation laws and the jump conditions are then used for studying surface waves in cylindrical plasmas. These waves are characterized by resonances and have complex eigenfrequencies when the classic true discontinuity is replaced by a nonuniform layer. A thin non-uniform layer is considered here in an attempt to obtain analytical results. An important result related to earlier work by Hollweg et al. (1990) for incompressible planar plasmas is found for equilibrium states with straight magnetic field lines and straight velocity field lines. For these equilibrium states the incompressible and compressible surface waves have the same frequencies at least in the long wavelength limit and there is an exact correspondence with the planar case. As a consequence, the conclusions formulated by Hollweg et al. still hold for the straight cylindrical case. The effects of curvature are subsequently considered.     

Effects of plasma rotation on alfvén solitons in pulsar magnetospheres

Nonlinear Alfvén wave in a hot rotating and strongly magnetized electron-positron plasma is considered. Using relativistic two fluid equations, the dispersion relation for Alfvén wave in the rotating plasma is obtained. Large amplitude Alfvén solitons are found to exist in the rotating pulsar plasma. Rotational effects on solitons are discussed.     

Kinetic theory of MHD instabilities in a nonuniform plasma

Most of the MHD instabilities originating from the nonuniformity of a plasma excite MHD surface wave. When the excited wave has a frequency _s which corresponds to the local shear Alfvén wave resonance (_s = k v _a (x), where v _a is the Alfvén speed and k is the wave number in the direction of the magnetic field), the surface wave resonantly mode converts to the kinetic Alfvén wave, the Alfvén wave having a perpendicular wavelength comparable to the ion gyroradius and being able to propagate across the magnetic field. We discuss various linear and nonlinear effects of this kinetic Alfvén wave on the plasma including particle acceleration and heating. A specific example for the case of a MHD Kelvin-Helmholtz instability is given.     

Filamentation Instability of Nonlinear Alfvén Waves and Plasma Heating associated with Recombination Effect

We investigate plasma heating associated with the effect of recombination and the filamentation instability of Alfvén waves propagating along homogeneous magnetic field in low-beta plasmas, by using an MHD simulation code. The linear instability of Alfvén waves leading to the filamentation is investigated by imposing small density perturbations across a magnetic field. We show results of the nonlinear stage of the above filamentation instability and the plasma heating through a two-dimensional simulation. It is shown that the plasma heating is caused by localized heating and whole heating, which are associated with the filamentation instability and the effect of recombination, respectively. We discuss the implication of these results for plasma heating processes observed in the chromosphere of the Sun.     

Nonlinear wave propagation along a magnetic flux tube

The weakly nonlinear wave propagation of a slow sausage surface wave traveling along a magnetized slab with a thin nonuniform boundary layer is considered. The ideal incompressible MHD equations are used and the nonlinearities are assumed to be due to second harmonic generation. A nonlinear dispersion relation and the related nonlinear Schrödinger equation is derived. The existence of a continuous thin interface leads to sharply peaked field amplitudes due to resonant interaction with local Alfvén waves. It is shown that the nonlinear effects from processes within the thin layer are much more important than those from the main slab. Furthermore, the nonlinear interaction with local Alfvén waves yields a nonlinear damping rate of the wave that is much larger than the linear damping rate when the transition layer is sufficiently thin.     

Excitation of plasma waves in the ionosphere caused by atmospheric acoustic waves

The transformation of atmospheric acoustic waves into plasma waves in the ionosphere is investigated. The transformation mechanism is based on plasma wave exitation by growing acoustic waves, when a frequency/wavelength matching situation is reached. The interaction of acoustic and plasma waves occurs through collisions of neutral particles with ions. For the case of ion-sound waves, oscillations on ion cyclotron frequency and Alfvén waves is considered. A peculiarity of Alfvén waves is the wide frequency band which may be stimulated through wave-wave interaction.     

On the spatial structure and dispersion of slow magnetosonic modes coupled with Alfvén modes in planetary magnetospheres due to field line curvature

The structure of the slow mode coupled with Alfvén mode in the axially symmetric magnetosphere is studied in the paper. Due to the coupling, the slow magnetosonic wave gets dispersion across magnetic shells and becomes not strictly guided. The slow mode is found to be captured between the resonant and cutoff surfaces, where the wave vector radial component goes to infinity and to zero, accordingly. The resonant surface is farther from the Earth than the cutoff surface. The slow mode resonance frequency is much lower than the Alfvén resonance frequency due to small value of the sound velocity near the equator. The maximum of the slow mode amplitude expressed in terms of the parallel magnetic field is concentrated near the equator, but expressed in hydromagnetic terms is concentrated near the ionospheres.     

The role of electrostatic instabilities in the critical ionization velocity mechanism

The role of electrostatic instabilities in the critical ionization velocity mechanism is investigated. The analysis is based on the theory developed by Sherman, which interprets Alfvén's critical velocity in terms of a circular process. This process involves the acceleration of electrons by a two-stream instability modified by the presence of a magnetic field. A general expression for the energy and momentum of ions and electrons associated with an electrostatic mode is derived in terms of the plasma dielectric constant. This is used in the case of the modified two-stream instability to determine the distribution of energy between ions and electrons. An extrapolation from the linear phase then gives an estimate of the energy delivered to the electrons which is compared to that required to ionize the neutral gas.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Modulational instability of finite-amplitude Alfvén waves

A finite-amplitude plane-polarised Alfvén wave is shown to undergo a modulational instability consequent to its trappping in density cavities which are created by the ponderomotive force associated with the Alfvén wave. The instability arises when the density cavity travels at subsonic speeds.