  We re-analyse spectropolarimetric data of AB Dor taken in 1996 December using
a surface imaging code that can model the magnetic field of the star as a
non-potential current-carrying magnetic field. We find that a non-potential
field needs to be introduced in order to fit the dataset at this epoch. This
non-potential component takes the form of a strong unidirectional azimuthal
field of a similar strength to the radial field. This azimuthal field is
concentrated around the boundary of the dark polar spot recovered at the
surface of the star using Doppler imaging. As polarization signatures from the
center of starspots are suppressed, it is unclear whether or not this
non-potential component genuinely represents electric current at the unspotted
surface or whether it results from the preferred detection of horizontal field
in starspot penumbrae. This model contains 20% more energy than the
corresponding potential field model at the surface. This amount of free energy
drops to under 1% about 1R* above the photosphere.
  We use these surface maps to model the coronal structure of the star. The
mixed radial polarities at the pole in the surface maps support closed coronal
loops in the high latitude regions, indicating that a component of the X-ray
emission may originate in this area. Assuming that the field remains closed out
to 5R*, we find stable surfaces where prominences may form out to the observed
distances using this coronal model.
