2 Properties of MHD Modes of Plasma Structures

In MHD, wave and oscillatory phenomena have spatial and temporal scales much longer than the ion gyroradii and gyroperiods, respectively, the conditions which are satisfied well by the coronal observational constrains. The characteristic speeds of the MHD phenomena are associated with plasma compressibility and elasticity connected with the frozen-in magnetic field of strength $B0$ and with gas pressure $p0$ , and with the ion inertia described by the mass density $r0$ . They are the usual sound speed, $1/2 Cs = (gp0/r0)$ with $g$ the adiabatic index, normally taken to be about $5/3$ in the corona, and the Alfvén speed, $1/2 CA = B0/(m0r0)$ , where $m0$ is the permeability of vacuum. It is convenient to introduce also the cusp or tube speed, $CT = CsCA/(C2A + C2s )1/2$ which is a combination of the sound and Alfvén speeds. Typical values of those speeds in coronal active regions vary from a hundred to a few thousand $-1 km s$ .

There are three basic MHD waves: an incompressible Alfvén wave and a fast and slow magnetoacoustic waves, which are both essentially compressible. Properties of MHD waves strongly depend upon the angle between the wave vector and the magnetic field, consequently, MHD waves are highly affected by plasma structuring and filamentation. Structuring of the solar coronal plasma modifies those waves and may lead to their coupling, bringing such interesting features of MHD wave dynamics as phase mixing, resonant absorption, and guided wave propagation, dramatically influencing manifestation of the waves in observations. This makes the theory of MHD wave modes of plasma structures to be the key ingredient of the coronal wave study. Also, the theory provides the necessary classification of wave and oscillatory phenomena in coronal plasmas.

2.1 MHD modes of a straight cylinder
2.2 MHD continua
2.2.1 Resonant absorption
2.2.2 Alfvén wave phase mixing
2.3 Zero plasma- $b$ density profiles
2.4 Effects of twisting