  [..] The change in the magnetic configuration due to the increase/decrease of
electric current for different force-free models (potential, linear and
nonlinear force-free fields) has never been studied in detail before. Here we
focus especially on the evolution of the free magnetic energy, the location of
the excess of energy, and the distribution of electric currents in the corona.
For this purpose, we use an idealised active region characterised by four main
polarities and a satellite polarity allowing us to specify a complex topology
and sheared arcades to the coronal magnetic field but no twisted flux bundles.
We investigate the changes in the geometry and connectivity of field lines, the
magnetic energy and current density content as well as the evolution of null
points. Increasing the photospheric current density in the magnetic
configuration does not dramatically change the energy-storage processes within
the active region even if the magnetic topology is slightly modified. We
conclude that for reasonable values of the photospheric current density (the
force-free parameter alpha < 0.25 Mm-1), the magnetic configurations studied do
change but not dramatically: i) the original null point stays nearly at the
same location, ii) the field-line geometry and connectivity are slightly
modified, iii) even if the free magnetic energy is significantly increased, the
energy storage happens at the same location. This extensive study of different
force-free models for a simple magnetic configuration shows that some
topological elements of an observed active region, such as null points, can be
reproduced with confidence only by considering the potential-field
approximation. This study is a preliminary work aiming at understanding the
effects of electric currents generated by characteristic photospheric motions
on the structure and evolution of the coronal magnetic field.
