We determine the entire electrical current density vector in a geometrical 3D volume of the inner penumbra of a sunspot from an inversion of spectropolarimetric data obtained with Hinode/SP .
Significant currents are seen to wrap around the hotter , more elevated regions with lower and more horizontal magnetic field that harbor strong upflows and radial outflows ( the intraspines ) .
The horizontal component of the current density vector is 3-4 times larger than the vertical ; nearly all previous studies only obtain the vertical component J _ { z } and thus strongly underestimate the current density .
The current density \vec { J } and the magnetic field \vec { B } form an angle of about 20 ^ { \circ } .
The plasma \beta at the 0 km level is larger than 1 in the intraspines and is one order of magnitude lower in the background component of the penumbra ( spines ) .
At the 200 km level , the plasma \beta is below 0.3 nearly everywhere .
The plasma \beta surface as well as the surface optical depth unity are very corrugated .
At the borders of intraspines and inside , \vec { B } is not force-free at deeper layers and nearly force free at the top layers .
The magnetic field of the spines is close to being potential everywhere .
The dissipated ohmic energy is five orders of magnitudes smaller than the solar energy flux and thus negligible for the energy balance of the penumbra .