Resonant energy conversion of 3 - minute intensity oscillations into Alfvén waves in the solar atmosphere

Nonlinear coupling between 3-minute oscillations and Alfvén waves in the solar lower atmosphere is studied. 3-minute oscillations are considered as acoustic waves trapped in a chromospheric cavity and oscillating along transversally inhomogeneous vertical magnetic field. It is shown that under the action of the oscillations the temporal dynamics of Alfvén waves is governed by Mathieu equation. Consequently, the harmonics of Alfvén waves with twice period and wavelength of 3-minute oscillations grow exponentially in time near the layer where the sound and Alfvén speeds equal i.e. c s ≈ v A. Thus the 3-minute oscillations are resonantly absorbed by pure Alfvén waves near this resonant layer. The resonant Alfvén waves may penetrate into the solar corona taking energy from the chromosphere. Therefore the layer c s ≈ v A may play a role of energy channel for otherwise trapped acoustic oscillations.