  Solar flares are powered by energy stored in the coronal magnetic field, a
portion of which is released when the field reconfigures into a lower energy
state. Investigation of sunspot magnetic field topology during flare activity
is useful to improve our understanding of flaring processes. Here we
investigate the deviation of the non-linear field configuration from that of
the linear and potential configurations, and study the free energy available
leading up to and after a flare. The evolution of the magnetic field in NOAA
region 10953 was examined using data from Hinode/SOT-SP, over a period of 12
hours leading up to and after a GOES B1.0 flare. Previous work on this region
found pre- and post-flare changes in photospheric vector magnetic field
parameters of flux elements outside the primary sunspot. 3D geometry was thus
investigated using potential, linear force-free, and non-linear force-free
field extrapolations in order to fully understand the evolution of the field
lines. Traced field line geometrical and footpoint orientation differences show
that the field does not completely relax to a fully potential or linear
force-free state after the flare. Magnetic and free magnetic energies increase
significantly ~ 6.5-2.5 hours before the flare by ~ 10^31 erg. After the flare,
the non-linear force-free magnetic energy and free magnetic energies decrease
but do not return to pre-flare 'quiet' values. The post-flare non-linear
force-free field configuration is closer (but not equal) to that of the linear
force-free field configuration than a potential one. However, the small degree
of similarity suggests that partial Taylor relaxation has occurred over a time
scale of ~ 3-4 hours.
