Motivated by recent Transition Region and Coronal Explorer (TRACE) observations of damped oscillations in coronal loops, we consider analytically the motion of an inhomogeneous coronal magnetic tube of radius a in a zero-plasma. An initially perturbed tube may vibrate in its kink mode of oscillation, but those vibrations are damped. The damping is due to resonant absorption, acting in the inhomogeneous regions of the tube, which leads to a transfer of energy from the kink mode to Alfvén (azimuthal) oscillations within the inhomogeneous layer. We determine explicitly the decrement (decay time À1 ) for a coronal flux tube whose plasma density varies only in a thin layer of thickness ' on the tube boundary. The effect of viscosity is also considered. We show that, in general, the problem involves two distinct timescales, À1 and ! À1 k R 1=3 , where R is the Reynolds number and ! k is the frequency of the kink mode. Under coronal conditions (when À1 5 ! À1 k R 1=3 ), the characteristic damping time of global oscillations is À1 . During this time, most of the energy in the initial perturbation is transferred into a resonant absorption layer of thickness of order ' 2 =a, with motions in this layer having an amplitude of order a=' times the initial amplitude. We apply our results to the observations, suggesting that loop oscillations decay principally because of inhomogeneities in the loop. Our theory suggests that only those loops with density inhomogeneities on a small scale (confined to within a thin layer of order a=! k in thickness) are able to support coherent oscillations for any length of time and so be observable. Loops with a more gradual density variation, on the scale of the tube radius a, do not exhibit pronounced oscillations.

The details of the mechanism(s) responsible for the observed heating and dynamics of the solar atmosphere still remain a mystery. Magnetohydrodynamic waves are thought to have a vital role in this process. Although it has been shown that incompressible waves are ubiquitous in off-limb solar atmospheric observations, their energy cannot be readily dissipated. Here we provide, for the first time, on-disk observation and identification of concurrent magnetohydrodynamic wave modes, both compressible and incompressible, in the solar chromosphere. The observed ubiquity and estimated energy flux associated with the detected magnetohydrodynamic waves suggest the chromosphere is a vast reservoir of wave energy with the potential to meet chromospheric and coronal heating requirements. We are also able to propose an upper bound on the flux of the observed wave energy that is able to reach the corona based on observational constraints, which has important implications for the suggested mechanism(s) for quiescent coronal heating.

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.

On 14 July 1998 TRACE observed transverse oscillations of a coronal loop generated by an external disturbance most probable caused by a solar flare. These oscillations were interpreted as standing fast kink waves in a magnetic flux tube. Firstly, in this review we embark on the discussion of the theory of waves and oscillations in a homogeneous straight magnetic cylinder with the particular emphasis on fast kink waves. Next, we consider the effects of stratification, loop expansion, loop curvature, non-circular cross-section, loop shape and magnetic twist.An important property of observed transverse coronal loop oscillations is their fast damping. We briefly review the different mechanisms suggested for explaining the rapid damping phenomenon. After that we concentrate on damping due to resonant absorption. We describe the latest analytical results obtained with the use of thin transitional layer approximation, and then compare these results with numerical findings obtained for arbitrary density variation inside the flux tube.Very often collective oscillations of an array of coronal magnetic loops are observed. It is natural to start studying this phenomenon from the system of two coronal loops. We describe very recent analytical and numerical results of studying collective oscillations of two parallel homogeneous coronal loops.The implication of the theoretical results for coronal seismology is briefly discussed. We describe the estimates of magnetic field magnitude obtained from the observed fundamental frequency of oscillations, and the estimates of the coronal scale height obtained using the simultaneous observations of the fundamental frequency and the frequency of the first overtone of kink oscillations.In the last part of the review we summarise the most outstanding and acute problems in the theory of the coronal loop transverse oscillations.

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Aims. We investigate the spatial damping of propagating kink waves in an inhomogeneous plasma. In the limit of a thin tube surrounded by a thin transition layer, an analytical formulation for kink waves driven in from the bottom boundary of the corona is presented. Methods. The spatial form for the damping of the kink mode was investigated using various analytical approximations. When the density ratio between the internal density and the external density is not too large, a simple differential-integral equation was used. Approximate analytical solutions to this equation are presented. Results. For the first time, the form of the spatial damping of the kink mode is shown analytically to be Gaussian in nature near the driven boundary. For several wavelengths, the amplitude of the kink mode is proportional toAlthough the actual value of 16 in L g depends on the particular form of the driver, this form is very general and its dependence on the other parameters does not change. For large distances, the damping profile appears to be roughly linear exponential decay. This is shown analytically by a series expansion when the inhomogeneous layer width is small enough.

Linear dissipative magnetohydrodynamics (MHD) shows that driven MHD waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfvén or slow frequency of a magnetic surface. This near resonant behaviour is confined to a thin dissipative layer which embraces the resonant magnetic surface. Although the driven MHD waves have small amplitudes far away from the resonant magnetic surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. In the present paper we deal with the nonlinear behaviour of driven MHD waves in the slow wave dissipative layer. The method of matched asymptotic expansions is used to obtain the nonlinear equation for wave variables inside the dissipative layer. The concept of connection formulae introduced into the theory of linear resonant MHD waves by Sakurai, Goossens, and Hollweg [Sol. Phys. 133, 227 (1991)] is extended to include nonlinear effects in the dissipative layer for slow resonant waves. The absorption of the slow resonant wave in the dissipative layer generates a shear flow parallel to the magnetic surfaces with a characteristic velocity of the order of ε1/2, where ε is the dimensionless amplitude of perturbations far away from the dissipative layer.

Heliospheric energetic neutral atoms (ENAs) that will be measured by the Interstellar Boundary Explorer (IBEX) originate from the heliosheath. The heliosheath is formed as a result of the interaction of the solar wind (SW) with the circum-heliospheric interstellar medium (CHISM). The expected fluxes of ENAs are strongly dependent on the nature of this interaction. In turn, the interaction of the solar wind with the local interstellar cloud has a complex and multi-component nature. Detailed theoretical modeling of the interaction between the SW and the local interstellar medium is required to understand the physics of the heliosheath and to predict and explain the heliospheric ENAs. This paper summarizes current state-of-art kinetic-gasdynamic models of the SW/CHISM interaction. We shall restrict our discussion to the kinetic-gasdynamic and kinetic-magnetohydrodynamic (MHD) models developed by the Moscow group. This paper summarizes briefly the main results of the first self-consistent, two-component, kinetic-gasdynamic model by Baranov and Malama (J. Geophys. Res. 98:15157-15163, 1993), presents new results obtained from the 3D kinetic-MHD model by Izmodenov et al. (Astron. Astrophys. 437:L35-L38, 2005a), describes the basic formulation and results of the model by Malama et al. (Astron. Astrophys. 445:693-701, 2006) as well as reports current developments in the model. This self-consistent model considers pickup protons as a separate non-equilibrium component. Then we discuss a stochastic acceleration model for pickup protons in the supersonic solar wind and in the heliosheath. We also present the expected heliospheric ENA fluxes obtained in the framework of the models.