RESONANT INTERACTIONS OF MODES IN CORONAL MAGNETIC-FLUX TUBES

Nonlinear resonant interactions of different kinds of fast magnetosoni c (FMS) waves trapped in the inhomogeneity of a low-beta plasma densit y, stretched along a magnetic field (as, for example, in coronal loops ) are investigated. A set of equations describing the amplitudes of in teractive modes is derived for an arbitrary density profile. The quant itative characteristics of such interactions are found. The decay inst ability of the wave with highest frequency is possible in the system. If amplitudes of interactive modes have close values, the long-period temporal and spatial oscillations are in the system. For a quantitativ e illustration, the parabolic approximation of the transverse density profile has been chosen. Dispersion relations of FMS waves trapped in a low-beta plasma slab with a parabolic transverse density profile are found. The transverse structure of the waves in this case can be expr essed through Hermitian polynomials. The interaction of kink and sausa ge waves is investigated. The sausage wave, with a sufficiently large amplitude, may be unstable with respect to the decay into two kink wav es, in particular. The spatial scale of a standing wave structure and the time spectrum of radiation are formed due to the nonlinear interac tions of loop modes which contain information about the parameters of the plasma slab.