Convective intensification of magnetic fields in the quiet Sun
  Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field $B_e$, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field $B_p$ that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, time-dependent, ``granular'' motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than $B_e$, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than $B_p$. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of ``convective collapse'' within a thin flux tube that remains in overall pressure equilibrium with its surroundings. 
P. J. Bushby, S. M. Houghton, M. R. E. Proctor, N. O. Weiss