  Our aim is to model the 3D magnetic field structure of the upper solar
atmosphere, including regions of non-negligible plasma beta. We use
high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as
boundary condition for a magneto-static magnetic field model. The high
resolution of IMaX allows us to resolve the interface region between
photosphere and corona, but modelling this region is challenging for the
following reasons. While the coronal magnetic field is thought to be force-free
(the Lorentz-force vanishes), this is not the case in the mixed plasma $\beta$
environment in the photosphere and lower chromosphere. In our model, pressure
gradients and gravity forces are taken self-consistently into account and
compensate the non-vanishing Lorentz-force. Above a certain height (about 2 Mm)
the non-magnetic forces become very weak and consequently the magnetic field
becomes almost force-free. Here we apply a linear approach, where the electric
current density consists of a superposition of a field-line parallel current
and a current perpendicular to the Sun's gravity field. We illustrate the
prospects and limitations of this approach and give an outlook for an extension
towards a non-linear model.
