  One of the puzzling features of solar magnetism is formation of long-living
compact magnetic structures; such as sunspots and pores, in the highly
turbulent upper layer of the solar convective zone. We use realistic radiative
3D MHD simulations to investigate the interaction between magnetic field and
turbulent convection. In the simulations, a weak vertical uniform magnetic
field is imposed in a region of fully developed granular convection; and the
total magnetic flux through the top and bottom boundaries is kept constant. The
simulation results reveal a process of spontaneous formation of stable magnetic
structures, which may be a key to understanding of the magnetic
self-organization on the Sun and formation of pores and sunspots. This process
consists of two basic steps: 1) formation of small-scale filamentary magnetic
structures associated with concentrations of vorticity and whirlpool-type
motions, and 2) merging of these structures due to the vortex attraction,
caused by converging downdrafts around magnetic concentration below the
surface. In the resulting large-scale structure maintained by the converging
plasma motions, the magnetic field strength reaches ~1.5 kG at the surface and
~6 kG in the interior; and the surface structure resembles solar pores. The
magnetic structure remains stable for the whole simulation run of several hours
with no sign of decay.
