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There is increasing evidence that magnetohydrodynamic waves play an important role in the propagation and dissipation of energy in the solar atmosphere. Here we investigate how torsional Alfvén waves driven at the photosphere can transport energy to an overlying coronal magnetic loop and explore their ability to heat the plasma. We consider a coronal loop whose feet are embedded in the partially ionized chromosphere. A broadband driver at the photosphere excites torsional Alfvén waves that propagate upward to the coronal loop. By means of numerical computations under the stationary-state assumption, we study the transmission of wave energy to the loop and the heating associated with ohmic diffusion and ion–neutral collisions. We find that wave transmission to the loop is heavily affected by the presence of cavity resonances when the frequency of the driver matches an eigenfrequency of the loop. A tremendous amount of wave energy is channeled to the coronal loop for those particular frequencies. The transmitted energy surpasses by many orders of magnitude the requirements to balance thermal radiation. However, dissipation is so weak in the coronal plasma that only a tiny percentage of the energy budget is converted into heat, which is not enough to compensate for radiative losses. Most of the energy simply leaks back to the chromosphere. Conversely, dissipation is much more efficient in the lower atmosphere, and wave heating can locally balance a significant fraction of radiation in the chromosphere. We argue that nonlinear effects such as turbulence triggered by the Kelvin–Helmholtz instability should enhance the heating efficiency at coronal heights.

Resonances in a Coronal Loop Driven by Torsional Alfvén Waves Propagating from the Photosphere