Development of electric currents in a magnetic field configuration containing a magnetic null point

Context. In the past the role of magnetic null points in the generation of electric currents was investigated mainly in the close vicinity of the null, with perturbations being applied at nearby boundaries, or for a magnetic null configuration with a dome-shaped fan. In the solar atmosphere, however, electric currents are generated by perturbations originating at the photosphere, far away from coronal 3D nulls, and the occurence of magnetic nulls with a dome-shaped fan is apparently not common. Aims. We investigate the consequences of photospheric motion for the development of electric currents in a coronal magnetic field configuration containing a null, located far away from the boundaries, and the influence of topological structures on the spatial distribution of the currents. Methods. We use a 3D resistive MHD code to investigate the consequences of photospheric plasma motion for the generation of currents in a coronal magnetic field containing a null. The plasma is considered fully compressible and is initially in hydrostatic equilibrium. The initial magnetic field is potential (current free). Results. The photospheric plasma motion causes magnetic field perturbations that propagate to the corona along the field lines at the local Alfven speed. The Alfvenic wave perturbations correspond to a propagating current directed mainly parallel to the magnetic field. Perpendicular currents connect to return currents to close the current system. The magnetic perturbations eventually reach the vicinity of the null. However, the currents forming in and around the null, near the fan surface or near the spine field lines, are not always the strongest currents developing in the simulation box. In our simulation, the strongest currents develop close to the bottom boundary, where the plasma is moved, and below the null point, in a region where field line connectivity considerably changes. Conclusions. Our simulation shows that the presence of a magnetic null point does not necessarily mean that the strongest currents will form in or around the null, at the fan surface or at the spine. Our results indicate that regions of considerable change in field line connectivity are fundamental for the development of strong and thin current sheets. Regions of connectivity change are important because they combine perturbations that are generated at different locations on the Sun. Our results also suggest that it is more important how the perturbations are mapped and combined in regions of considerable connectivity change than what is the driver of the perturbations itself. The driver does not necessarily need to create strong currents where it is applied. However, when the perturbations produced by the driver combine in the regions of considerable connectivity change, they can increase the current in regions for which the length scale is much smaller than the characteristic length scale of the system. The location of regions of connectivity change, combined with the mapping of the perturbations to those regions, can be a useful tool to predict where and when solar flares will occur.