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Context. High resolution magnetic field measurements are routinely done onlyin the solar photosphere. Higher layers like the chromosphere and corona can bemodeled by extrapolating the photospheric magnetic field upward. In the solarcorona, plasma forces can be neglected and the Lorentz force vanishes. This isnot the case in the upper photosphere and chromosphere where magnetic andnon-magnetic forces are equally important. One way to deal with this problem isto compute the plasma and magnetic field self-consistently with amagnetohydrostatic (MHS) model.  Aims. We aim to derive the magnetic field, plasma pressure and density ofAR11768 by applying the newly developed extrapolation technique to theSUNRISE/IMaX data.  Methods. An optimization method is used for the MHS modeling. The initialconditions consist of a nonlinear force-free field (NLFFF) and agravity-stratified atmosphere.  Results. In the non-force-free layer, which is spatially resolved by the newcode, Lorentz forces are effectively balanced by the gas pressure gradientforce and the gravity force. The pressure and density are depleted in strongfield regions, which is consistent with observations. Denser plasma, however,is also observed at some parts of the active region edges. In the chromosphere,the fibril-like plasma structures trace the magnetic field nicely. Brightpoints in SUNRISE/SuFI 3000 {$\AA$} images are often accompanied by the plasmapressure and electric current concentrations. In addition, the average of anglebetween MHS field lines and the selected chromospheric fibrils is $11.8^\circ$,which is smaller than those computed from the NLFFF model ($15.7^\circ$) andlinear MHS model ($20.9^\circ$). This indicates that the MHS solution providesa better representation of the magnetic field in the chromosphere.

Magnetohydrostatic modeling of AR11768 based on a SUNRISE/IMaX vector magnetogram