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 .