Context. Partially ionized plasma is usually described by a single-fluid approach, where the ion-neutral collision effects are expressed by Cowling conductivity in the induction equation. However, the single-fluid approach is not valid for time-scales less than ion-neutral collision time. For these time-scales the two-fluid description is the better approximation. Aims. We aim to derive the dynamics of magnetohydrodynamic (MHD) waves in two-fluid partially ionized plasmas and to compare the results with those obtained under single-fluid description. Methods. Two-fluid equations are used, where ion-electron plasma and neutral particles are considered as separate fluids. Dispersion relations of linear waves are derived for the simplest case of homogeneous medium. Frequencies and damping rates of waves are obtained for different parameters of background plasma. Results. 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. Alfvén and fast magneto-acoustic waves attain their maximum damping rate at particular frequencies (for example, the peak frequency equals 2.5 times the ion-neutral collision frequency for 50% of neutral hydrogen) in the wave spectrum. The damping rates are reduced for the higher frequency waves. The new mode of slow magneto-acoustic wave appears for higher frequency branch, which is connected to neutral hydrogen fluid. Conclusions. The single-fluid approach perfectly deals with slow processes in partially ionized plasmas, but fails for time-scales shorter than ion-neutral collision time. Therefore, the two-fluid approximation should be used for the description of relatively fast processes. Some results of the single-fluid description should be revised in future such as the damping of high-frequency Alfvén waves in the solar chromosphere due to ion-neutral collisions.

Since their discovery, spicules have attracted increased attention as energy/mass bridges between the dense and dynamic photosphere and the tenuous hot solar corona. Mechanical energy of photospheric random and coherent motions can be guided by magnetic field lines, spanning from the interior to the upper parts of the solar atmosphere, in the form of waves and oscillations. Since spicules are one of the most pronounced features of the chromosphere, the energy transport they participate in can be traced by the observations of their oscillatory motions. Oscillations in spicules have been observed for a long time. However the recent high-resolution and high-cadence space and ground based facilities with superb spatial, temporal and spectral capacities brought new aspects in the research of spicule dynamics. Here we review 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 Alfvén and kink waves in spicules. We also address the extensive debate made on the Alfvén versus kink waves in the context of the explanation of the observed transverse oscillations of spicule axes.

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.

Using multi-wavelength observations of SoHO/MDI, SOT-Hinode/bluecontinuum (4504Å), G-band (4305Å), Ca II H (3968Å) and TRACE 171Å, we present the observational signature of highly twisted magnetic loop in AR 10960 during the period 04:43 UT-04:52 UT at 4 June, 2007. SOT-Hinode/bluecontinuum (4504Å) observations show that penumbral filaments of positive polarity sunspot have counter-clock wise twist, which may be caused by the clockwise rotation of the spot umbrae. The coronal loop, whose one footpoint is anchored in this sunspot, shows strong right-handed twist in chromospheric SOT-Hinode/Ca II H (3968Å) and coronal TRACE 171Å images. The length and the radius of the loop are L ∼80 Mm and a ∼4.0 Mm respectively. The distance between neighboring turns of magnetic field lines (i.e. pitch) is estimated as ≈ 10 Mm. The total twist angle, Φ ∼12π (estimated for the homogeneous distribution of the twist along the loop), is much larger than the Kruskal -Shafranov instability criterion. We detected clear double structure of the loop top during 04:47-04:51 UT on TRACE 171Å images, which is consistent with simulated kink instability in curved coronal loops (Török et al. 2004). We suggest, that the kink instability of this twisted magnetic loop triggered B5.0 class solar flare, which occurred between 04:40 UT and 04:51 UT in this active region.

The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere -a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.

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Aims. The influence of a toroidal magnetic field on the dynamics of Rossby waves in a thin layer of ideal conductive fluid on a rotating sphere is studied in the "shallow water" magnetohydrodynamic approximation for the first time.Methods. Dispersion relations for magnetic Rossby waves are derived analytically in Cartesian and spherical coordinates. Results. It is shown that the magnetic field causes the splitting of low order (long wavelength) Rossby waves into two different modes, here denoted fast and slow magnetic Rossby waves. The high frequency mode (the fast magnetic Rossby mode) corresponds to an ordinary hydrodynamic Rossby wave slightly modified by the magnetic field, while the low frequency mode (the slow magnetic Rossby mode) has new and interesting properties since its frequency is significantly smaller than that of the same harmonics of pure Rossby and Alfvén waves.

Magneto-hydrodynamic (MHD) Alfvén waves 1 have been a focus of laboratory plasma physics 2 and astrophysics 3 for over half a century. Their unique nature makes them ideal energy transporters, and while the solar atmosphere provides preferential conditions for their existence 4 , direct detection has proved difficult as a result of their evolving and dynamic observational signatures. The viability of Alfvén waves as a heating mechanism relies upon the efficient dissipation and thermalization of the wave energy, with direct evidence remaining elusive until now. Here we provide the first observational evidence of Alfvén waves heating chromospheric plasma in a sunspot umbra through the formation of shock fronts. The magnetic field configuration of the shock environment, alongside the tangential velocity signatures, distinguish them from conventional umbral flashes 5 . Observed local temperature enhancements of 5% are consistent with the dissipation of mode-converted Alfvén waves driven by upwardly propagating magneto-acoustic oscillations, providing an unprecedented insight into the behaviour of Alfvén waves in the solar atmosphere and beyond.The solar surface hosts a web of diverse magnetic fields, from sunspots exhibiting sizes that dwarf the Earth, to dynamic bright grains only a few hundred km across. The magnetic nature of the Sun's atmosphere supports the plethora of MHD wave activity observed in recent years 6 . Such wave motion is predominantly generated near the surface of the Sun, with the creation of upwardly propagating MHD waves providing a conduit for the transportation of heat, from the vast energy reservoir of the solar photosphere, to the outermost extremities of the multi-million degree corona.In comparison to other MHD modes, Alfvén waves are the preferred candidates for energy transport since they do not reflect or dissipate energy freely 3 . Observational studies have been limited by the challenging requirements on instrumentation needed to identify the Doppler line-of-sight (LOS) velocity perturbations and non-thermal broadening associated with Alfvén waves, thus there is only tentative evidence of their existence within the Sun's magnetized plasma 7-9 . Given the difficulties associated with resolving the intrinsic wave signatures, to date there has been no observational evidence brought forward to verify the dissipative processes associated with Alfvén waves. Theoretical studies have proposed multiple dissipation methods that would allow the embedded mechanical energy of Alfvén waves to be converted into localized heat 10,11 . Unfortunately, most act on unobservable scales, providing no clear signatures that can be identified with even the largest current solar telescopes. However, one distinct mechanism revolves around the formation of macroscopic shock fronts, which naturally manifest as a result of the propagation of waves through the solar atmosphere 12 . Shock behavior induced by slow magneto-acoustic waves is ubiquitously observed in sunspots, manifesting as umbral flashes 5 (UFs), giv...