MHD waves in the solar north polar coronal hole

The effects, hitherto not treated, of the temperature and the number density gradients, both in the parallel and the perpendicular direction to the magnetic field, of O VI ions, on the MHD wave propagation characteristics in the solar North Polar Coronal Hole are investigated. We investigate the magnetosonic wave propagation in a resistive MHD regime where only the thermal conduction is taken into account. Heat conduction across the magnetic field is treated in a non‐classical approach wherein the heat is assumed to be conducted by the plasma waves emitted by ions and absorbed at a distance from the source by other ions. Anisotropic temperature and the number density distributions of O VI ions revealed the chaotic nature of MHD standing wave, especially near the plume/interplume lane borders. Attenuation length scales of the fast mode is shown not to be smoothly varying function of the radial distance from the Sun (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Wave Transformation and Scattering on Stationary Charged Particles in a Magnetoactive Plasma. II

The transformation of upper-hybrid, lower-hybrid, and magnetosonic waves on a heavy charged particle lying at the plane boundary of a magnetoactive plasma is considered. The angular distribution of the radiation resulting from wave transformation is investigated. The transformation of a low-frequency magnetosonic wave is suggested as a possible mechanism for pulsar radio emission.     

Standing slow magnetosonic waves in a dipole-like plasmasphere

A problem of the structure and spectrum of standing slow magnetosonic waves in a dipole plasmasphere is solved. Both an analytical (in WKB approximation) and numerical solutions are found to the problem, for a distribution of the plasma parameters typical of the Earth's plasmasphere. The solutions allow us to treat the total electronic content oscillations registered above Japan as oscillations of one of the first harmonics of standing slow magnetosonic waves. Near the ionosphere the main components of the field of registered standing SMS waves are the plasma oscillations along magnetic field lines, plasma concentration oscillation and the related oscillations of the gas-kinetic pressure. The velocity of the plasma oscillations increases dramatically near the ionospheric conductive layer, which should result in precipitation of the background plasma particles. This may be accompanied by ionospheric F2 region airglows modulated with the periods of standing slow magnetosonic waves.     

Generation of magnetosonic waves and formation of structures in galaxies

We study the generation of magnetosonic waves in galactic gaseous discs taking account of the magnetic field, differential rotation and self-gravity. The special case of perturbations is considered with the wavevector perpendicular to the magnetic field. The necessary condition of the amplification of seed perturbations is the presence of differential rotation and non-vanishing radial component of the magnetic field that can easily be satisfied in galactic discs. Differential rotation stretches the azimuthal field from the radial one and, therefore, we consider the generation of waves on the time-dependent background magnetic field. Basically, an amplification is rather efficient, and seed perturbations become non-linear already after several rotation periods for a wide range of wavelength. The generated magnetosonic waves can be either non-oscillatory or oscillatory depending on the parameters of gas. If perturbations are Jeans stable, then typically non-oscillatory waves are amplified. However, interplay between self-gravity, magnetic field and rotational shear can change qualitatively the classical Jeans instability, so that the latter becomes oscillatory and tends to be suppressed in galaxies.     

Generation and propagation of the ULF planetary-scale electromagnetic wavy structures in the ionosphere

In the present article, the results of theoretical investigation of the dynamics of generation and propagation of planetary (with wavelength 10³ km and more) ultra-low frequency (ULF) electromagnetic wave structures in the dissipative ionosphere are given. The physical mechanism of generation of the planetary electromagnetic waves is proposed. It is established, that the global factor, acting permanently in the ionosphere—inhomogeneity (latitude variation) of the geomagnetic field and angular velocity of the earth's rotation—generates the fast and slow planetary ULF electromagnetic waves. The waves propagate along the parallels to the east as well as to the west. In E-region the fast waves have phase velocities (2-20) km s⁻¹and frequencies (10⁻¹-10⁻⁴) s⁻¹; the slow waves propagate with local winds velocities and have frequencies (10⁻⁴-10⁻⁶) s⁻¹. In F-region the fast ULF electromagnetic waves propagate with phase velocities tens-hundreds km s⁻¹ and their frequencies are in the range of (10-10⁻³) s⁻¹. The slow mode is produced by the dynamoelectric field, it represents a generalization of the ordinary Rossby-type waves in the rotating ionosphere and is caused by the Hall effect in the E-layer. The fast disturbances are the new modes, which are associated with oscillations of the ionospheric electrons frozen in the geomagnetic field and are connected with the large-scale internal vortical electric field generation in the ionosphere. The large-scale waves are weakly damped. The features and the parameters of the theoretically investigated electromagnetic wave structures agree with those of large-scale ULF midlatitude long-period oscillations (MLO) and magnetoionospheric wave perturbations (MIWP), observed experimentally in the ionosphere. It is established, that because of relevance of Coriolis and electromagnetic forces, generation of slow planetary electromagnetic waves at the fixed latitude in the ionosphere can give rise to the reverse of local wind structures and to the direction change of general ionospheric circulation. It is considered one more class of the waves, called as the slow magnetohydrodinamic (MHD) waves, on which inhomogeneity of the Coriolis and Ampere forces do not influence. These waves appear as an admixture of the slow Alfven- and whistler-type perturbations. The waves generate the geomagnetic field from several tens to several hundreds nT and more. Nonlinear interaction of the considered waves with the local ionospheric zonal shear winds is studied. It is established, that planetary ULF electromagnetic waves, at their interaction with the local shear winds, can self-localize in the form of nonlinear solitary vortices, moving along the latitude circles westward as well as eastward with velocity, different from phase velocity of corresponding linear waves. The vortices are weakly damped and long lived. They cause the geomagnetic pulsations stronger than the linear waves by one order. The vortex structures transfer the trapped particles of medium and also energy and heat. That is why such nonlinear vortex structures can be the structural elements of strong macroturbulence of the ionosphere.     

Helicoidal magneto-electron waves in interstellar molecular clouds

We investigate the evolution of the magnetic flux density in a magnetically supported molecular cloud driven by Hall and Ohmic components of the electric field generated by the flows of thermal electrons. Particular attention is given to the wave transport of the magnetic field in a cloud whose gas dynamics is dominated by electron flows; the mobility of neutrals and ions is regarded as heavily suppressed. It is shown that electromagnetic waves penetrating such a cloud can be converted into helicons – weakly damped, circularly polarized waves in which the densities of the magnetic flux and the electron current undergo coherent oscillations. These waves are interesting in their own right, because for electron magnetohydrodynamics the low-frequency helicoidal waves have the same physical significance as the transverse Alfvén waves do for a single-component magnetohydrodynamics. The latter, as is known, are considered to be responsible for the widths of molecular lines detected in dark, magnetically supported clouds. From our numerical estimates for the group velocity and the rate of dissipation of helicons it follows that a possible contribution of these waves to the broadening of molecular lines is consistent with the conditions typical of dark molecular clouds.     

Viscous Damping of Non-Adiabatic MHD Waves in an Unbounded Solar Coronal Plasma

The damping of MHD waves in solar coronal magnetic field is studied taking into account thermal conduction and compressive viscosity as dissipative mechanisms. We consider viscous homogeneous unbounded solar coronal plasma permeated by a uniform magnetic field. A general fifth-order dispersion relation for MHD waves has been derived and solved numerically for different solar coronal regimes. The dispersion relation results three wave modes: slow, fast, and thermal modes. Damping time and damping per periods for slow- and fast-mode waves determined from dispersion relation show that the slow-mode waves are heavily damped in comparison with fast-mode waves in prominences, prominence–corona transition regions (PCTR), and corona. In PCTRs and coronal active regions, wave instabilities appear for considered heating mechanisms. For same heating mechanisms in different prominences the behavior of damping time and damping per period changes significantly from small to large wavenumbers. In all PCTRs and corona, damping time always decreases linearly with increase in wavenumber indicate sharp damping of slow- and fast-mode waves.     

Alfvén Wave Phase Mixing as a Source of Fast Magnetosonic Waves

The nonlinear excitation of fast magnetosonic waves by phase mixing Alfvén waves in a cold plasma with a smooth inhomogeneity of density across a uniform magnetic field is considered. If initially fast waves are absent from the system, then nonlinearity leads to their excitation by transversal gradients in the Alfvén wave. The efficiency of the nonlinear Alfvén–fast magnetosonic wave coupling is strongly increased by the inhomogeneity of the medium. The fast waves, permanently generated by Alfvén wave phase mixing, are refracted from the region with transversal gradients of the Alfvén speed. This nonlinear process suggests a mechanism of indirect plasma heating by phase mixing through the excitation of obliquely propagating fast waves.     

MHD waves in coronal loops with a shell

We consider a model of a coronal loop in the form of a cord surrounded by a coaxial shell. Two slow magnetosonic waves longitudinally propagate within a thin flux tube on the m=0 cylindrical mode with velocities close to the tube velocities in the cord and the shell. One wave propagates inside the cord, while the other propagates inside the shell. A peculiar feature of the second wave is that the plasma in the cord and the shell oscillates with opposite phases. There are two fast magnetosonic waves on each of the cylindrical modes with m>0. If the plasma density in the shell is lower than that in the surrounding corona, then one of the waves is radiated into the corona, which causes the loop oscillations to be damped, while the other wave is trapped by the cord, but can also be radiated out under certain conditions. If the plasma density in the shell is higher than that in the cord, then one of the waves is trapped by the shell, while the other wave can also be trapped by the shell under certain conditions. In the wave trapped by the shell and the wave radiated by the tube, the plasma in the cord and the shell oscillates with opposite phases.     

Attenuation of small-amplitude oscillations in a prominence–corona model with a transverse magnetic field

Observations show that small-amplitude prominence oscillations are usually damped after a few periods. This phenomenon has been theoretically investigated in terms of non-ideal magnetoacoustic waves, non-adiabatic effects being the best candidates to explain the damping in the case of slow modes. We study the attenuation of non-adiabatic magnetoacoustic waves in a slab prominence embedded in the coronal medium. We assume an equilibrium configuration with a transverse magnetic field to the slab axis and investigate wave damping by thermal conduction and radiative losses. The magnetohydrodynamic equations are considered in their linearised form and terms representing thermal conduction, radiation and heating are included in the energy equation. The differential equations that govern linear slow and fast modes are numerically solved to obtain the complex oscillatory frequency and the corresponding eigenfunctions. We find that coronal thermal conduction and radiative losses from the prominence plasma reveal as the most relevant damping mechanisms. Both mechanisms govern together the attenuation of hybrid modes, whereas prominence radiation is responsible for the damping of internal modes and coronal conduction essentially dominates the attenuation of external modes. In addition, the energy transfer between the prominence and the corona caused by thermal conduction has a noticeable effect on the wave stability, radiative losses from the prominence plasma being of paramount importance for the thermal stability of fast modes. We conclude that slow modes are efficiently damped, with damping times compatible with observations. On the contrary, fast modes are less attenuated by non-adiabatic effects and their damping times are several orders of magnitude larger than those observed. The presence of the corona causes a decrease of the damping times with respect to those of an isolated prominence slab, but its effect is still insufficient to obtain damping times of the order of the period in the case of fast modes.     

Formation of fast magnetosonic shock waves during a two-current-loop collision in solar flares

We present a numerical simulation of the fast magnetosonic shock wave formation during a two-current-loop collision by using a magnetohydrodynamical model. It is shown that the rarefaction waves are generated in the initial stage when the two current loops start to collide. After the rarefaction waves propagate away from the excited region, the fast magnetosonic waves with density enhancement can be produced for the simulation when the current strength of the loop is weak. As the current becomes strong enough, the magnetosonic shock waves can be generated in the direction perpendicular to that of the two-loop collision.     

Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.     

Turbulence Heating for Protons in High-Speed Solar Wind

In high-speed solar wind, propagating Alfvén waves can be transferred into fast magnetosonic waves. When both the magnetic field strength and Alfvén wave velocity approach zero, fast magnetosonic waves will be transferred into ion-acoustic waves. As the phase velocity of ion-acoustic waves is slightly greater than the thermal velocity of protons, the turbulence energy of ion-acoustic waves can largely be absorbed by protons and can cause the mean temperature of protons to be greater than that of electrons by stochastic turbulence heating of ion-acoustic waves for protons.     

Non-linear spherical Alfvén waves

We present a one-dimensional numerical study of Alfvén waves propagating along a radial magnetic field. Neglecting losses, any spherical Alfvén wave, no matter how small its initial amplitude is, becomes non-linear at sufficiently large radii. From previous simulations of Alfvén waves in plane-parallel atmospheres we expected the waves to steepen and produce current sheets in the non-linear regime, which was confirmed by our new calculations. On the other hand we found that even the least non-linear waves were damped out almost completely before 10 R_⊙. A damping of that kind is required by models of Alfvén wave driven winds from old low-mass stars as these winds are mainly accelerated within a few stellar radii.     

Nonlinear magnetosonic waves propagating perpendicular to a magnetic neutral sheet

Nonlinear magnetosonic waves propagating in a magnetic neutral sheet are investigated within the framework of a fluid model. It is shown that the behavior of the magnetosonic waves is governed by a ‘modified Burgers equation’ with an additional termc(η)? due to the relevant slowly varying background plasma parameter (density or magnetic field), $$\frac{{\partial \phi }}{{\partial \eta }}$$ where ?(ξ, η) is the amplitude of the wave, \(\xi = \int {k_x } {\text{d}}x + k_y y - \omega t\) , and η=εx is the coordinate stretched by a smallness parameter ε. When we consider fast magnetosonic waves propagating toward the neutral region across the magnetic field, they grow and undergo rapid steepening after passing through the neutral region; i.e., shock formation is promoted by the background inhomogeneity. By the numerical computation of the above equation, the time evolution is examined for two initial disturbances, the pulse type (gaussian) and the wave train type (sinusoidal wave). The relevance of the interactions between the magnetosonic shock waves and the neutral sheet plasma to a triggering mechanism of sympathetic flares is also suggested.     

Modulational instability of fast magnetosonic waves emitted from a pinching current sheet

We investigate how fast magnetosonic waves can be produced from a pinching current sheet, by using 3-D MHD code. We show that after magnetic pinch of the current sheet due to pressure imbalance, the current sheet begins to expand by an excess of plasma pressure at the center of the current sheet. During the expansion phase, strong fast magnetosonic waves can be created at the steep region of the density gradient and propagate away from the current sheet. It is shown that the fast magnetosonic waves become unstable against modulational instability, as found by Sakai (1983). After the emission of the fast magnetosonic waves, the current sheet will relax to a new equilibrium state, where the current sheet can be heated by adiabatic compression. The emission processes of the fast magnetosonic waves from the current sheet, as well as the modulational instability of these waves that can lead to effective plasma heating through the Landau damping of the slow waves, are important for an understanding of coronal heating and coronal transient brightening.     

Interaction of particles with ion cyclotron waves and magnetosonic waves. Observations from GEOS 1 and GEOS 2

Coordinated observations involving ion composition, thermal plasma, energetic particle, and ULF magnetic field data from GEOS 1 and 2 often reveal the presence of electromagnetic ion cyclotron and magnetosonic waves, which are distinguished by their respective polarization characteristics and frequency spectra. The ion cyclotron waves are identified by a magnetic field perturbation that lies in a plane perpendicular to the Earth's magnetic field B₀ and propagate along B₀. They are associated with the abundance of cold He⁺ in the presence of anisotropic pitch angle distributions of ions having energies E > 20 keV, and were observed at frequencies near the He⁺ gyrofrequency. The magnetosonic waves are characterized by a magnetic field perturbation parallel to B₀ and thus seem to be propagating perpendicular to the Earth's magnetic field. They often occur at harmonics (not always including the fundamental) at the proton gyrofrequency and are associated with phase-space-density distributions that peak at energies E ～ 5–30 keV and at a pitch angle of 90°. Such a ring-like distribution is shown to excite instability in the magnetosonic mode near harmonics of the proton gyrofrequency. Magnetosonic waves are associated in other cases with sharp spatial gradients in energetic ion intensity. Such gradients are encountered in the early afternoon sector (as a consequence of the drift shell distortion caused by the convection electric field) and could likewise constitute a source of free energy for plasma instabilities.     

Dissipating the energy of magnetoacoustic waves in a structured atmosphere

The distances over which magnetohydrodynamic waves will propagate in a non-ideal, magnetic, compressible medium, representing the solar corona structured by the presence of loops of denser material, are considered. The waves are damped by ion viscosity and electron heat conduction in a radiating, optically thin atmosphere. Waves which lose their energy of propagation in distances of less than our criterion value of 4 × 10⁹ cm are regarded as candidates for contributing towards coronal heating. Alfvénic-type waves only dissipate in this way in weak ( 15 G) magnetic fields and when they have periods of a few seconds (210 s). Acoustic-type waves can also be dissipated and we give typical values of magnetic field strength, density and temperature for which the dissipation could occur. Dissipating acoustic-type waves have periods that range from tens to hundreds of seconds (15–225 s).Calculations show that reliable measurements of velocity amplitudes will be invaluable in deciding whether these dissipating waves can contribute to heating the corona. We suggest that the waves that survive dissipation may account for some of the observed coronal oscillations.     

Mode identification of terrestrial ULF waves observed by Cluster: A case study

Using multipoint measurements from the Cluster mission wave identification techniques are applied to observations of ULF waves made in the terrestrial foreshock with the aim of identifying the modes and properties of the waves taking into account the effects of a high beta plasma. The wave properties in the spacecraft and plasma rest frames are experimentally derived using minimum variance analysis. Two waves with periods of 30 and 3 s dominate the dynamic frequency spectrum. The results indicate that these waves propagate in the fast magnetosonic and Alfvén/Ion Cyclotron modes, respectively. Both waves propagate in the upstream direction in the plasma rest frame but are convected downstream in the spacecraft frame. The measured wave properties in the plasma rest frame are in good agreement with those obtained from the theoretical kinetic dispersion relation taking into account the effects of different plasma beta. The dispersion results show a rather significant deviation from fluid model, especially when high beta plasma conditions occur. These experimentally derived foreshock ULF wave properties are in good agreement with previous results but when the effects of a high beta plasma are considered it is not as straight forward to choose the correct wave mode branch.