The theory of magnetohydrodynamic wave generation by localized sources. III. Efficiency of plasma heating by dissipation of far-field waves

The flux in Alfvén waves derived with Lighthill's method is compared with fast and slow wave emission from a localized source in an isothermal, homogeneous plasma with constant B field. Since a small fraction of the fast and slow flux generated in the solar photosphere is transported to the corona, the ratio of the Alfvén to the total flux sets an upper bound e on the efficiency of coronal heating from waves emitted by photospheric motions. The scaling of the fluxes with β∝ p_gas/B² shows that in the photosphere where β≫ 1, slow and Alfvén emission are comparable and exceed fast radiation by O(́^7/2). These results imply that e is bounded by e ≲ 1/2. For sources with steep gradients in the applied forcing, the efficiency is reduced to e ≲ (γ - l)/(5γ - 1) ≲ 0.1, where γ is the gas constant. In order to investigate the sensitivity of the efficiency to the source structure, a method is developed for comparing MHD fluxes by decomposition of arbitrary source fields into vector harmonics and computing the flux associated with the coupling between individual harmonics. For a simple class of sources in a high-β plasma, this technique shows that slow and Alfvén emission have similar magnitudes, giving e ≲ 1/2. If these spherical sources are adopted as a model for oscillating solar granules with a 5 minute period, the Alfvén fluxes are comparable to those required to heat the active regions. MHD - Sun: corona.