Main Results

MHD waves in solar partially ionized plasmas: two-fluid approach
We develop two-fluid magnetohydrodynamic (MHD) approach, where ion-electron plasma and neutral particles are considered as separate fluids, and derive the dynamics of MHD waves in the solar atmosphere. We found that two- and single-fluid descriptions give similar results for low-frequency waves. However, the dynamics of MHD waves in the two-fluid approach is significantly changed when the wave frequency becomes comparable with or higher than the ion-neutral collision frequency. Therefore, the two-fluid approximation should be used for the description of relatively fast processes.

Damping of Alfvén waves in partially ionized solar plasma: effect of neutral helium
We use a three-fluid MHD approach, where one component is electron-proton-singly ionized helium and the other two components are the neutral hydrogen and neutral helium atoms. We derive the damping rates of linear Alfvén waves for different plasma parameters. It is shown that the presence of neutral helium significantly enhances the damping of Alfvén waves compared to the damping due to neutral hydrogen at certain values of plasma temperature (10 000-40 000 K) and ionization. Damping rates have a peak near the ion-neutral collision frequency, but decrease for the higher part of the wave spectrum.

Torsional Alfvén waves in partially ionized solar plasma: effects of neutral helium and stratification
We consider an expanded and study the dynamics of linear torsional Alfvén waves in the presence of neutral hydrogen and neutral helium atoms. We start with a three-fluid description of plasma and subsequently derive single-fluid magnetohydrodynamic equations for torsional Alfvén waves. Thin flux tube approximation allows us to obtain the dispersion relation of the waves in the lower part of tubes, while the spatial dependence of steady-state Alfvén waves is governed by a Bessel-type equation in the upper parts of the tubes. Consecutive derivation of single-fluid MHD equations results in a new Cowling diffusion coefficient in the presence of neutral helium, which is different from the previously used one. We find that shorter period (< 5 s) torsional Alfvén waves damp quickly in the chromospheric network owing to ion-neutral collision. On the other hand, longer period (> 5 s) waves do not reach the transition region because they become evanescent at lower heights in the network cores. Therefore, propagation of torsional Alfvén waves through the chromosphere into the solar corona should be considered with caution: low-frequency waves are evanescent owing to the stratification, while high-frequency waves are damped by ion-neutral collisions.

Cut-off wavenumber of Alfvén waves in partially ionized plasmas of the solar atmosphere
Alfvén wave dynamics in partially ionized plasmas of the solar atmosphere shows that there is indeed a cut-off wavenumber, i.e. the Alfvén waves with wavenumbers higher than the cut-off value are evanescent. The cut-off wavenumber appears in single-fluid MHD approximation but it is absent in a multi-fluid approach. Up to now, an explanation for the existence of the cut-off wavenumber is still missing. Beginning with three-fluid equations (with electrons, protons and neutral hydrogen atoms), we performed consecutive approximations until we obtained the usual single-fluid description. We solved the dispersion relation of linear Alfvén waves at each step and sought the approximation responsible of the cut-off wavenumber appearance. We have found that neglecting inertial terms significantly reduces the real part of the Alfvén frequency although it never becomes zero. Therefore, the cut-off wavenumber does not exist at this stage. However, when the inertial terms together with the Hall term in the induction equation are neglected, the real part of the Alfvén frequency becomes zero. The appearance of a cut-off wavenumber, when Alfvén waves in partially ionized regions of the solar atmosphere are studied, is the result of neglecting inertial and Hall terms, therefore it has no physical origin.

Kelvin-Helmholtz instability of kink waves in photospheric twisted flux tubes
We investigate conditions under which kink MHD waves propagating along photospheric uniformly twisted flux tubes with axial mass flows become unstable as a consequence of the Kelvin-Helmholtz instability. We show that the stability of the waves depends upon four parameters, the density contrast between the flux tube and its environment, the ratio of the background magnetic fields in the two media, the twist of the magnetic field lines inside the tube, and the value of the Alfvén-Mach number (the ratio of the jet velocity to Alfvén speed inside the flux tube). At certain densities and magnetic field twists, an instability of the Kelvin-Helmholtz type of kink (m = 1) mode can arise if the Alfvén-Mach number exceeds a critical value. The observed mass flows may trigger the Kelvin-Helmholtz instability of the kink (m = 1) mode in weakly twisted photospheric magnetic flux tubes at critical Alfvén-Mach numbers lower that those in untwisted tubes if the magnetic field twist lies in the range 0.36-0.4 and the flow speed exceeds a critical value.

Further development of equivalent electric circuit models of coronal magnetic loops and related oscillatory phenomena on the Sun
An overall review analysis of the earlier developed by the project participants ‘equivalent electric circuit’ (LCR) models of coronal magnetic loops and their major principles has been undertaken. Primary attention was paid to the possibility of application of LCR models for interpretation of the observed oscillatory phenomena in the solar coronal loops and related radiation. A set of advanced data analysis tools and innovative approaches to the interpretation of the radiative and oscillatory phenomena on the Sun has been developed. According to a basic concept of the 'equivalent electric circuit' (LCR) models, each loop is considered as an equivalent electric LCR-circuit with variable inductive coefficients L, capacitance C, and resistance R, which depend on shape, scale, position of the loop with respect to neighbouring loops, as well as on the plasma parameters in the magnetic tube. Such an approach enables to describe the electric current dynamics in the groups of coronal loops, as well as the related energy release and radiation processes.

Detection of manifestation of coronal loop transverse oscillations in solar microwave emission
Long period (minutes) modulations in microwave emission detected in Metsähovi Radio Observatory (Finland) data during solar flare events were interpreted as signature of large scale transverse oscillations of solar coronal loops. In this case a properly located observer, in addition to the modulation caused by the emission diagram pattern motion at the main frequency of the loop oscillation, may detect a modulation at twice the frequency, produced by the varying magnetic field during each inclination of the loop. Our main result consists in identification of these “modulation pairs” in the dynamic spectra of solar microwave emission and their association with the oscillating coronal loops observed in by TRACE in EUV.

Diagnostics of Supergiant Complexes of Solar Activity and Convection Zone
The global distribution of solar surface activity (active regions) is apparently connected with processes in the convection zone. The large-scale magnetic structures above the tachocline could in a pronounced way be observable in the surface magnetic field. To get the information regarding large-scale magnetic formations in the convection zone, a set of solar synoptic charts (Mount Wilson 1998 - 2004, Fe I, 525.02 nm) have been analyzed. It is shown that the longitudinal dimensions and dynamics of super giant complexes of solar surface activity carry valuable information about the processes in the convection zone of the Sun. A new result is a Kolmogorov-type energy spectrum of the longitudinal variations of solar activity. This spectrum for non-photospheric scales of convection (harmonic number m<100) is a new “fingerprint” of turbulence in the deep layers of the solar convection zone. The preferred scales of longitudinal variations in surface solar activity are revealed. These are: ~24º (gigantic convection cells), 90º, 180º and 360º. By this, similar scales are found in the millimeter radio-images (Metsähovi Radio Observatory 1994-1998, 37 and 87 GHz). Hence, the millimeter radio astronomy has certain prospects for remote sensing of the solar convection zone.

Interpretation of frequency drifts of 3-min oscillations in microwave and EUV emission above sunspots
We analysed 3-min oscillations of microwave and extreme ultraviolet (EUV) emission generated at different heights of a sunspot atmosphere, studied the amplitude and frequency modulation of the oscillations, and its relationship with the variation of the spatial structure of the oscillations. High-resolution data obtained with the Nobeyama Radioheliograph, TRACE and SDO/AIA were analysed with pixelised wavelet filtering (PWF) and wavelet skeleton techniques. Three-minute oscillations in sunspots appear in the form of recurring trains of 8–20 min duration (13 min in average). The typical interval between the trains is 30–50 min. The oscillation trains are transient in frequency and power. The relative amplitude of 3-min oscillations was about 3–8% and sometimes reached 17%. Recurring frequency drifts of 3-min oscillations were detected during the development of individual trains, with the period varying in the range 90–240 s. These structures can be interpreted as waveguides that channel upward propagating waves, which in turn are responsible for the 3-min oscillations. A possible explanation of the observed properties are two simultaneously operating factors: dispersive evolution of the upward propagating wave pulses and the non-uniformity of the oscillation power distribution over the sunspot umbra with different wave sources that correspond to different magnetic flux tubes with different physical conditions and line-of-sight angles.

Observation of standing kink waves in solar spicules
We analyze the time series of Ca II H-line obtained from Hinode/SOT on the solar limb. The time distance analysis shows that the axis of spicule undergoes quasi-periodic transverse displacement at different heights from the photosphere. The mean period of transverse displacement is 180 s and the mean amplitude is 1 arc sec. Then, we solve the dispersion relation of magnetic tube waves and plot the dispersion curves with upward steady flows. The theoretical analysis shows that the observed oscillation may correspond to the fundamental harmonic of standing kink waves.

Excitation of 5-min oscillations in the solar corona
We solve the full set of nonlinear one-dimensional Euler equations numerically for the velocity pulse propagating in the solar atmosphere that is determined by the realistic temperature profile. Numerical simulations show that an initial velocity pulse quickly steepens into a leading shock, while the nonlinear wake in the chromosphere leads to the formation of consecutive pulses. The time interval between the arrivals of two neighboring pulses to a detection point in the corona is approximately 5 min. Therefore, the consecutive pulses may result in the 5-min oscillations that are observed in the solar corona.

Discovery of MHD soliton in the solar atmosphere
Time series of Ca II H line obtained at the solar limb with the Solar Optical Telescope (SOT) on the board of Hinode is analysed. Observations show an intensity blob, which propagates from 500 km to 1700 km above the solar surface with the mean apparent speed of 35 km/s. The blob speed, length to width ratio and relative intensity correspond to slow sausage soliton propagating along a magnetic tube. Propagation of the intensity blob is the first observational evidence of slow sausage soliton in the solar atmosphere.

Observation of kink instability during solar flare
Using multi-wavelength observations of SOHO, Hinode and TRACE , we present the observational signature of a highly twisted magnetic loop in AR 10960 during the period 04:43 UT–04:52 UT on 2007 June 4. We detected clear double structure of loop top during 04:47 UT–04:51 UT 171Å images, which is consistent with simulated kink instability in curved coronal loops.We suggest that the kink instability of this twisted magnetic loop triggered a B5.0 class solar flare, which occurred between 04:40 UT and 04:51 UT in this active region.

Numerical simulations of chromospheric dynamics
We solve two-dimensional time-dependent magnetohydrodynamic equations numerically to find spatial and temporal dynamics of spicules. The numerical simulations show that the strong initial pulse may lead to the quasi periodic rising of chromospheric material into the lower corona in the form of spicules. The periodicity results from the nonlinear wake that is formed behind the pulse in the stratified atmosphere.The two-dimensional rebound shock model may explain the observed speed, width, and heights of type I spicules, as well as observed multi-structural and bi-directional flows.

Instability of twisted magnetic flux tubes with axial mass flows
We study the influence of axial mass flows on the stability of twisted magnetic flux tubes. Two main important results are found. First, the axial mass flow reduces the threshold of kink instability in twisted magnetic tubes. Second, the twist of magnetic tubes leads to the Kelvin-Helmholtz instability of sub-Alfvénic flows for the harmonics with a large enough azimuthal wave number. The observed mass flow may trigger the kink instability in magnetic configurations that are near their stability threshold, leading to solar flares and coronal mass ejections.

Magnetic Rossby waves in the solar tachocline and Rieger-type periodicities
Apart from the 11-year solar cycle, another periodicity around 155-160 days was discovered during solar cycle 21 in high energy solar flares, and its presence in sunspot areas and strong magnetic flux has been also reported. This periodicity has an elusive and enigmatic character, since it usually appears only near the maxima of solar cycles, and seems to be related with a periodic emergence of strong magnetic flux at the solar surface. Therefore, it is probably connected with the tachocline, a thin layer located near the base of the solar convection zone, where strong dynamo magnetic field is stored. We study the dynamics of Rossby waves in the tachocline in the presence of a toroidal magnetic field and latitudinal differential rotation. Our analysis shows that the magnetic Rossby waves are generally unstable and that the growth rates are sensitive to the magnetic field strength and to the latitudinal differential rotation parameters. Variation of the differential rotation and the magnetic field strength throughout the solar cycle enhance the growth rate of a particular harmonic in the upper part of the tachocline around the maximum of the solar cycle. This harmonic is symmetric with respect to the equator and has a period of 155-160 days. A rapid increase of the wave amplitude could give place to a magnetic flux emergence leading to observed periodicities in solar activity indicators related with magnetic flux.

Quasi-biennial oscillations in the solar tachocline caused by magnetic Rossby wave instabilities
Quasi-biennial oscillations (QBO) are frequently observed in the solar activity indices. However, no clear physical mechanism for the observed variations has been suggested so far. Here we study the stability of magnetic Rossby waves in the solar tachocline using the shallow water magnetohydrodynamic approximation. Our analysis shows that the combination of typical differential rotation and a toroidal magnetic field with a strength 100 kG triggers the instability of the m=1 magnetic Rossby wave harmonic with a period of 2~ years. This harmonic is antisymmetric with respect to the equator and its period (and growth rate) depends on the differential rotation parameters and the magnetic field strength. The oscillations may cause a periodic magnetic flux emergence at the solar surface and consequently may lead to the observed QBO in the solar activity features. The period of QBO may change throughout the cycle, and from cycle to cycle, due to variations of the mean magnetic field and differential rotation in the tachocline.

Acoustic oscillations in the field-free, gravitationally stratified cavities under solar bipolar magnetic canopies
We study the dynamics of the gravitationally stratified, field-free cavities in the solar atmosphere, located under small-scale, cylindrical magnetic canopies, in response to explosive events in the lower-lying regions (due to granulation, small-scale magnetic reconnection, etc.). The two-dimensional Klein-Gordon equation is solved for isothermal density perturbations in cylindrical coordinates. The normal mode analysis shows that the entire cylindrical cavity of granular dimensions tends to oscillate with frequencies of 5-8 mHz and also with the atmospheric cut-off frequency. Furthermore, the passage of a pressure pulse, excited in the convection zone, sets up a wake in the cavity oscillating with the same cut-off frequency. The wake oscillations can resonate with the free oscillation modes, which leads to an enhanced observed oscillation power.

Oscillations and waves in solar spicules
Recent high-resolutions and high-cadence space and ground based facilities with superb spatial, temporal and spectral capacities brought new aspects in the research of solar spicule dynamics. We present the progress made in imaging and spectroscopic observations of waves and oscillations in spicules. The observations are accompanied by a discussion on theoretical modelling and interpretations of these oscillations. Finally, we embark on the recent developments made on the presence and role of Alfven and kink waves in spicules.