Resonant and phase-mixed magnetohydrodynamic waves in the solar atmosphere

The magnetic field in the solar atmosphere is not uniformly distributed but organized in typical configurations: e.g., intense flux tubes in the photosphere, magnetic loops in the corona, plumes in the solar wind. Each of these magnetic configurations can support magnetohydrodynamic (MHD) waves and observations show that this is indeed the case. The intrinsic inhomogeneity of the magnetic configurations enables local (slow and) Alfven waves to exist on individual magnetic surfaces. These local Alfven waves provide a means for dissipating wave energy which is far more efficient in a weakly dissipative plasma than classical resistive or viscous MHD wave damping in a uniform plasma. This property has inspired a lot of work on the dissipation of driven Alfven waves and wave heating in the solar atmosphere by resonant absorption and phase mixing. This review concentrates on the interaction between fast magnetosonic waves, local Alfven waves and quasimodes and discusses recent results on the time evolution of phase mixing of resonant waves driven by footpoint motions