Acoustic oscillations in a field-free cavity under solar small-scale bipolar magnetic canopy

Observations show the increase of high-frequency wave power near magnetic network cores and active regions in the solar lower atmosphere. This phenomenon can be explained by the interaction of acoustic waves with a magnetic field. We consider small-scale, bipolar, magnetic field canopy structure near the network cores and active regions overlying field-free cylindrical cavities of the photosphere. Solving the plasma equations we get the analytical dispersion relation of acoustic oscillations in the field-free cavity area. We found that the m = 1 mode, where m is azimuthal wave number, cannot be trapped under the canopy due to energy leakage upwards. However, higher ($m \geq 2$) harmonics can be easily trapped leading to the observed acoustic power halos under the canopy.