1.1 The method of MHD coronal seismology

Despite significant progress in coronal physics over several decades, a number of fundamental questions, for instance, what are the physical mechanisms responsible for the coronal heating, the solar wind acceleration, and solar flares, remain to be answered. All these questions, however, require detailed knowledge of physical conditions and parameters in the corona, which cannot yet be measured accurately enough. In particular, the exact value of the coronal magnetic field remains unknown, because of a number of intrinsic difficulties with applications of direct methods (e.g., based upon the Zeeman splitting and gyroresonant emission), as well as indirect (e.g., based upon extrapolation of chromospheric magnetic sources). Also, the coronal transport coefficients, such as volume and shear viscosity, resistivity, and thermal conduction, which play a crucial role in coronal physics, are not measured even within an order of magnitude and are usually obtained from theoretical estimations. Other obscured parameters are the heating function and filling factors. The detection of coronal waves provides us with a new tool for the determination of the unknown parameters of the corona - MHD seismology of the corona. Measurement of the properties of MHD waves and oscillations (periods, wavelengths, amplitudes, temporal and spatial signatures, characteristic scenarios of the wave evolution), combined with a theoretical modelling of the wave phenomena (dispersion relations, evolutionary equations, etc.), leads to a determination of the mean parameters of the corona, such as the magnetic field strength and transport coefficients. This approach is illustrated in Figure 1

. Philosophically, the method is similar to the acoustic diagnostics of the solar interior, helioseismology. But, MHD coronal seismology is much richer by its very nature as it is based upon three different wave modes, namely, Alfvén, slow, and fast magnetoacoustic modes. These MHD modes have quite different dispersive, polarisation, and propagation properties, which makes this approach even more powerful. A similar method for the determination of physical parameters of laboratory plasmas, MHD spectroscopy, has been successfully used for a decade (see, e.g., the recent review of Fasoli et al., 2002 ). In particular, the measurements of Alfvén eigenmode frequencies and mode numbers and the comparison between the antenna driven spectrum and that calculated theoretically give information on the bulk plasma, allowing for the improved equilibrium reconstruction in terms of radial profiles of density and safety factor. In contrast with the MHD spectroscopy, MHD coronal seismology utilises propagating waves too.

Figure 1:

A scheme of the method of MHD coronal seismology.

Originally, the method of MHD coronal seismology was suggested by Uchida (1970 ) for global and Roberts et al. (1984

) for local seismology, and has recently been applied to obtain estimates of the magnetic field (Roberts et al., 1984

; Nakariakov and Ofman, 2001

), the coronal dissipative coefficients (Nakariakov et al., 1999

), and to probe coronal sub-resolution structuring (Robbrecht et al., 2001

; King et al., 2003

). These implementations are discussed in Sections 3.3, 3.4 and 6.3, respectively.