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Resonant interactions of modes in coronal magnetic flux tubes
Authors:V M Nakariakov and V N Oraevsky
Institution:(1) Applied Mathematics Department, Nizhny Novgorod State Technical University, 603600 Nizhny Novgorod, Russia;(2) IZIMIRAN, Russian Academy of Science, 142092 Troitsk, Moscow Region, Russia
Abstract:Nonlinear resonant interactions of different kinds of fast magnetosonic (FMS) waves trapped in the inhomogeneity of a low-beta plasma density, stretched along a magnetic field (as, for example, in coronal loops) are investigated. A set of equations describing the amplitudes of interactive modes is derived for an arbitrary density profile. The quantitative characteristics of such interactions are found. The decay instability 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 quantitative 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 expressed through Hermitian polynomials. The interaction of kink and sausage waves is investigated. The sausage wave, with a sufficiently large amplitude, may be unstable with respect to the decay into two kink waves, in particular. The spatial scale of a standing wave structure and the time spectrum of radiation are formed due to the nonlinear interactions of loop modes which contain information about the parameters of the plasma slab.
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