Energy is required to heat the outer solar atmosphere to millions of degrees (refs 1, 2) and to accelerate the solar wind to hundreds of kilometres per second (refs 2-6). Alfvén waves (travelling oscillations of ions and magnetic field) have been invoked as a possible mechanism to transport magneto-convective energy upwards along the Sun's magnetic field lines into the corona. Previous observations of Alfvénic waves in the corona revealed amplitudes far too small (0.5 km s(-1)) to supply the energy flux (100-200 W m(-2)) required to drive the fast solar wind or balance the radiative losses of the quiet corona. Here we report observations of the transition region (between the chromosphere and the corona) and of the corona that reveal how Alfvénic motions permeate the dynamic and finely structured outer solar atmosphere. The ubiquitous outward-propagating Alfvénic motions observed have amplitudes of the order of 20 km s(-1) and periods of the order of 100-500 s throughout the quiescent atmosphere (compatible with recent investigations), and are energetic enough to accelerate the fast solar wind and heat the quiet corona.

Abstract. Damped quasi-mode kink oscillations in cylindrical flux tubes are capable of explaining the observed rapid damping of the coronal loop oscillations when the ratio of the inhomogeneity length scale to the radius of the loop is allowed to vary from loop to loop, without the need to invoke anomalously low Reynolds numbers. The theoretical expressions for the decay time by Hollweg & Yang (1988) and Ruderman & Roberts (2002) are used to estimate the ratio of the length scale of inhomogeneity compared to the loop radius for a collection of loop oscillations.

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 ID 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 Alfv6n 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.

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A basic procedure is presented for dealing with the resonance problems that appear in MHD of which resonant absorption of waves at the Alfv~n resonance point is the best known example in solar physics. The procedure avoids solving the full fourth-order differential equation of dissipative MHD by using connection formulae across the dissipation layer.

Context. Magnetohydrodynamic (MHD) waves are often reported in the solar atmosphere and usually classified as slow, fast, or Alfvén. The possibility that these waves have mixed properties is often ignored. Aims. The goal of this work is to study and determine the nature of MHD kink waves. Methods. This is done by calculating the frequency, the damping rate and the eigenfunctions of MHD kink waves for three widely different MHD waves cases: a compressible pressure-less plasma, an incompressible plasma and a compressible plasma which allows for MHD radiation. Results. In all three cases the frequency and the damping rate are for practical purposes the same as they differ at most by terms proportional to (k z R) 2 . In the magnetic flux tube the kink waves are in all three cases, to a high degree of accuracy incompressible waves with negligible pressure perturbations and with mainly horizontal motions. The main restoring force of kink waves in the magnetised flux tube is the magnetic tension force. The total pressure gradient force cannot be neglected except when the frequency of the kink wave is equal or slightly differs from the local Alfvén frequency, i.e. in the resonant layer. Conclusions. Kink waves are very robust and do not care about the details of the MHD wave environment. The adjective fast is not the correct adjective to characterise kink waves. If an adjective is to be used it should be Alfvénic. However, it is better to realize that kink waves have mixed properties and cannot be put in one single box.

The linear theory of MHD resonant waves in inhomogeneous plasmas is reviewed. The review starts from discussing the properties of driven resonant MHD waves. The dissipative solutions in Alfvén and slow dissipative layers are presented. The important concept of connection formulae is introduced. Next, we proceed on to non-stationary resonant MHD waves. The relation between quasi-modes of ideal MHD and eigenmodes of dissipative MHD are discussed. The solution describing the wave motion in non-stationary dissipative layers is given. It is shown that the connection formulae remain valid for nonstationary resonant MHD waves. The initial-value problem for resonant MHD waves is considered. The application of theory of resonant MHD waves to solar physics is discussed.

Abstract. The observed coronal loop oscillations and their damping are often theoretically described by the use of a very simple coronal loop model, viz. a straight, longitudinally invariant, axi-symmetric, and pressureless flux tube with a different density inside and outside of the loop. In this paper we generalize the model by including longitudinal density stratification and we examine how the longitudinal density stratification alters the linear eigenmodes of the system, their oscillation frequencies, and the damping rates by resonant absorption.