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Astron. Astrophys. 339, 215-224 (1998)

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1. Introduction

It is well known that the solar atmosphere can be highly structured by the magnetic field depending on the solar cycle activity. Commonly observed features such as photospheric flux tubes, coronal holes, magnetic arcades indicate the existence of pronounced local nonuniformities at their boundaries. The nonuniformities are often in the form of transitional layers that separate regions of larger extent and with different, comparatively uniform, physical characteristics. Many of these configurations remain quasistationary when observed for time spans much shorter than their life time, such as periods of MHD waves or periodic oscillations existing throughout the solar atmosphere (Tsubaki, 1988). Typical periods found from spectral analyses of various coronal lines in the optical and UV domains are around 2-6 min (Liebenberg & Hoffman, 1974; Egan & Schneeberger, 1979; Koutchmy et al. 1983). Perturbations with higher frequencies of several Hz were detected too (Pasachoff, 1991).

Magnetosonic waves can be generated by turbulent motions in the photosphere and in the chromosphere, by global solar oscillations or by local releases of energy in magnetic reconnection events, for example. These waves are an important means of energy transport from sources of their origin into the ambient atmosphere, while the magnetic structures can duct them in specific directions (Nakariakov & Roberts, 1995 and references therein). The carried energy can be deposited in the medium by dissipation through mechanisms with different efficiencies. For example, the classic viscous or resistive damping of Alfvén waves is found to be a very inefficient way to transform the wave energy into heat if the plasma is uniform and weakly dissipative. This is due to the large values of the viscous and magnetic Reynolds numbers typical for the solar atmosphere. However, a highly efficient mechanism for wave dissipation can occur in nonuniform magnetic plasmas if resonant slow and resonant Alfvén waves can be excited locally.

In ideal MHD, these resonant waves are confined to individual magnetic surfaces and do not interact mutually. Since each magnetic surface has its own local slow and local Alfvén frequency, a nonuniform magnetic plasma can have two continuous ranges of frequencies related to resonant slow waves and to resonant Alfvén waves.

Introduction of dissipation results into coupling between the neighbouring magnetic surfaces. This coupling remains weak for large values of the viscous and the magnetic Reynolds numbers, typical for the solar atmosphere. In this case, local resonant slow oscillations and local resonant Alfvén oscillations are characterized by steep gradients across the magnetic surfaces. Their excitation provides a means for dissipating wave energy in a nonuniform and weakly dissipative plasma in a far more efficient way than in classical resistive or viscous MHD wave damping in a uniform plasma.

Resonant MHD wave damping was first put forward as a possible mechanism for heating the solar corona by Ionson (1978) and was further developed and investigated by many authors like Rae & Roberts (1982), Poedts, Goossens & Kerner (1989, 1990), Sakurai, Goossens & Hollweg (1991a,b), Okreti & ade (1991), Goossens & Hollweg (1993), Goossens, Ruderman & Hollweg (1995) and the review paper by Goossens & Ruderman (1996).

The influence of an equilibrium plasma flow on MHD eigenmodes on a transitional layer in presence of the Alfvén resonance was studied by Hollweg, Yang, ade & Gakovi (1990). They considered incompressible perturbations in Cartesian geometry. A theoretical analysis of driven resonant MHD waves on magnetic flux tubes with a plasma flow was done by Goossens, Hollweg & Sakurai (1992) who derived an appropriate treatment of the Alfvén and the cusp singularities in ideal MHD. Their procedure will be applied in our paper too. Further studies of the resonant wave absorption on magnetic flux tubes with flow were done by Erdélyi & Goossens (1996) and Erdélyi (1996). Some of the effects of a nonuniform equilibrium flow in a planar layer were studied by Csík, Erdélyi & ade (1997) who considered resonant absorption of slow MHD waves due to the cusp resonance only. They did not obtain the effect of over-reflection.

In this paper, however, we perform a more complete analysis of resonant absorption in a nonuniform plasma layer with a uniform flow. The incident waves are here slow and fast magnetosonic waves, and they can be absorbed due to Alfvén and slow resonances in the layer. The layer separates two uniform regions, one of which is transparent for the considered MHD waves while the other one is opaque. The difference in amplitudes of the reflected and the incident wave thus results only from processes related to the resonances. The amplitude of the reflected wave may become larger than that of the incoming wave in which case we have over-reflection.

The paper is organized as follows: Introductory statements about MHD waves in a nonuniform medium such as the solar atmosphere, are given in Sect. 1. The equilibrium configuration is described in Sect. 2 while Sect. 3 contains the governing ideal MHD equations and their solutions for linear waves in each of the three distinct regions of our. The computation of the absorption coefficient is presented in Sect. 4, the results with the discussion are given in Sect. 5 while conclusions are found in Sect. 6.

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© European Southern Observatory (ESO) 1998

Online publication: September 30, 1998