  A simple model of the coronal magnetic field prior to the CME eruption on May
12 1997 is developed. First, the magnetic field is constructed by superimposing
a large-scale background field and a localized bipolar field to model the
active region (AR) in the current-free approximation. Second, this potential
configuration is quasi-statically sheared by photospheric vortex motions
applied to two flux concentrations of the AR. Third, the resulting force-free
field is then evolved by canceling the photospheric magnetic flux with the help
of an appropriate tangential electric field applied to the central part of the
AR.
  To understand the structure of the modeled configuration, we use the field
line mapping technique by generalizing it to spherical geometry. It is
demonstrated that the initial potential configuration contains a hyperbolic
flux tube (HFT) which is a union of two intersecting quasi-separatrix layers.
This HFT provides a partition of the closed magnetic flux between the AR and
the global solar magnetic field. The vortex motions applied to the AR interlock
the field lines in the coronal volume to form additionally two new HFTs pinched
into thin current layers. Reconnection in these current layers helps to
redistribute the magnetic flux and current within the AR in the
flux-cancellation phase. In this phase, a magnetic flux rope is formed together
with a bald patch separatrix surface wrapping around the rope. Other important
implications of the identified structural features of the modeled configuration
are also discussed.
