  The aim of this work is the determination of the twist, writhe, and self
magnetic helicity of penumbral filaments located in an inner Sunspot penumbra.
To this extent, we inverted data taken with the spectropolarimeter (SP) aboard
Hinode with the SIR (Stokes Inversion based on Response function) code. For the
construction of a 3D geometrical model we applied a genetic algorithm
minimizing the divergence of the magnetic field vector and the net
magnetohydrodynamic force, consequently a force-free solution would be reached
if possible. We estimated two proxies to the magnetic helicity frequently used
in literature: the force-free parameter and the current helicity term. We show
that both proxies are only qualitative indicators of the local twist as the
magnetic field in the area under study significantly departures from a
force-free configuration. The local twist shows significant values only at the
borders of bright penumbral filaments with opposite signs on each side. These
locations are precisely correlated to large electric currents. The average
twist (and writhe) of penumbral structures is very small. The spines (dark
filaments in the background) show a nearly zero writhe. The writhe per unit
length of the intraspines diminishes with increasing length of the tube axes.
Thus, the axes of tubes related to intraspines are less wrung when the tubes
are more horizontal. As the writhe of the spines is very small, we can conclude
that the writhe reaches only significant values when the tube includes the
border of a intraspine.
