Wave transformations near a coronal magnetic null point

Context. Null points are often invoked in studies of quasi-periodic coronal jets and in connection with periodic signals preceding actual reconnection events. Although the periodicity of these events spans a wide range of periods, most show a 2- to 5-min periodicity compatible with the global p-modes.Aims We investigate whether magnetohydrodynamics (MHD) waves, in particular, acoustic p-modes, can cause strong current accumulation at the null points. This can in turn drive localized periodic heating in the solar corona.Methods. To do this, we began with a three-dimensional numerical setup incorporating a gravitationally stratified solar atmosphere and an axially symmetric magnetic field including a coronal magnetic null point. To excite waves, we employed wave drivers mimicking global p-modes. Using our recently developed wave-mode decomposition technique, we investigated the process of mode conversion, mode transmission, and wave reflection at various important layers of the solar atmosphere, such as the Alfven acoustic equipartition layer and transition region. We examined the energy flux distribution in various MHD modes or in acoustic and magnetic components, as the waves propagate and interact with a magnetic field of null topology. We also examined current accumulation in the surroundings of the null point.Results. We found that most of the vertical velocity is transmitted through the Alfven acoustic equipartition layer and maintains an acoustic nature, while a small fraction generates fast waves via the mode conversion process. The fast waves undergo almost total reflection in the transition region due to sharp gradients in density and Alfven speed. There are only weak signatures of Alfven wave generation near the transition region through the fast-to-Alfven mode conversion. Because the slow waves propagate with the local sound speed, they are not much affected by the density gradients in the transition region and undergo secondary mode conversion and transmission at the Alfven-acoustic equipartition layer surrounding the null point. This leads to fast-wave focusing at the null point. These fast waves have associated perturbations in current density and show oscillatory signatures that are compatible with the second harmonic of the driving frequency. This might result in resistive heating and in an enhanced intensity in the presence of finite resistivity.Conclusions. We conclude that MHD waves are a potential source for oscillatory current dissipation around the magnetic null point. We conjecture that in addition to oscillatory magnetic reconnection, global p-modes could lead to the formation of various quasi-periodic energetic events.