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The main goal is to study the dynamics of the gravitationally stratified,field-free cavities in the solar atmosphere, located under small-scale,cylindrical magnetic canopies, in response to explosive events in thelower-lying regions (due to granulation, small-scale magnetic reconnection,etc.).  We derive the two-dimensional Klein-Gordon equation for isothermal densityperturbations in cylindrical coordinates. The equation is first solved by astandard normal mode analysis in order to obtain the free oscillation spectrumof the cavity. Then, the equation is solved in the case of impulsive forcingassociated to a pressure pulse specified in the lower-lying regions.  The normal mode analysis shows that the entire cylindrical cavity of granulardimensions tends to oscillate with frequencies of 5-8 mHz and also with theatmospheric cut-off frequency. Furthermore, the passage of a pressure pulse,excited in the convection zone, sets up a wake in the cavity oscillating withthe same cut-off frequency. The wake oscillations can resonate with the freeoscillation modes, which leads to an enhanced observed oscillation power.  The resonant oscillations of these cavities explain the observed power halosnear magnetic network cores and active regions.

astronomy and astrophysics

Acoustic oscillations in the field-free, gravitationally stratified  Acoustic oscillations in the field-free, gravitationally stratified cavities  under solar bipolar magnetic canopies