We present a series of numerical simulations of the quiet Sun plasma threaded by magnetic fields that extend from the upper convection zone into the low corona. We discuss an efficient, simplified approximation to the physics of optically thick radia
tive transport through the surface layers, and investigate the effects of convective turbulence on the magnetic structure of the Suns atmosphere in an initially unipolar (open field) region. We find that the net Poynting flux below the surface is on average directed toward the interior, while in the photosphere and chromosphere the net flow of electromagnetic energy is outward into the solar corona. Overturning convective motions between these layers driven by rapid radiative cooling appears to be the source of energy for the oppositely directed fluxes of electromagnetic energy.
The availability of vector magnetogram sequences with sufficient accuracy and cadence to estimate the time derivative of the magnetic field allows us to use Faradays law to find an approximate solution for the electric field in the photosphere, using
a Poloidal-Toroidal Decomposition (PTD) of the magnetic field and its partial time derivative. Without additional information, however, the electric field found from this technique is under-determined -- Faradays law provides no information about the electric field that can be derived the gradient of a scalar potential. Here, we show how additional information in the form of line-of-sight Doppler flow measurements, and motions transverse to the line-of-sight determined with ad-hoc methods such as local correlation tracking, can be combined with the PTD solutions to provide much more accurate solutions for the solar electric field, and therefore the Poynting flux of electromagnetic energy in the solar photosphere. Reliable, accurate maps of the Poynting flux are essential for quantitative studies of the buildup of magnetic energy before flares and coronal mass ejections.
We introduce two new methods that are designed to improve the realism and utility of large, active region-scale 3D MHD models of the solar atmosphere. We apply these methods to RADMHD, a code capable of modeling the Suns upper convection zone, photos
phere, chromosphere, transition region, and corona within a single computational volume. We first present a way to approximate the physics of optically-thick radiative transfer without having to take the computationally expensive step of solving the radiative transfer equation in detail. We then briefly describe a rudimentary assimilative technique that allows a time series of vector magnetograms to be directly incorporated into the MHD system.
