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Context: .Wave energy dissipation by viscous and resistive damping in magnetic coronal plasmas is addressed. A two and one half dimensional, line-tied magnetic channel is considered whose footpoints are disturbed by buffeting motions of the photosphere. Aims: .The aim of the analysis is to determine how effectively shear Alfvén waves, driven by footpoint motions and resonating in the channel, can be damped by visco-resistive friction. Methods: .The problem is analyzed using a mixture of numerical and analytic techniques. Dynamic simulations, based on a cyclic footpoint driver, show that phase mixing resulting from variations in the magnetic field of the channel is instrumental in setting up a permanent "resonance regime" for the system. Analytic methods are used to analyze the resonance regime and to develop scaling laws for the rate of energy dissipation. Results: .We show that in the general case where the Alfvén velocity profile may be linearized around the resonance, the dissipation rate is "fast" in that it is not limited by small damping coefficients. Although large energies can accumulate within the channel in the limit of very small damping, we show that by tuning the driver to low frequencies, both the energy level and the dissipation rate can be made insensitive to the level of the damping

Rapid dissipation in a current sheet driven by footpoints motions