  To understand the magnetic fields of the polar crown filaments (PCFs) at high
latitudes near polar regions of the Sun, we perform magnetofrictional numerical
simulations on the long-term magnetic evolution of bipolar fields with roughly
east-west polarity inversion lines (PILs) in a three-dimensional (3D) spherical
wedge domain near polar regions. The Coriolis effect induced vortical motions
at the boundaries of several supergranular cells inject magnetic helicity from
the photospheric boundary into the solar atmosphere. Supergranular-scale
helicity injection, transfer, and condensation produce strongly sheared
magnetic fields. Magnetic reconnections at footpoints of the sheared fields
produce magnetic flux ropes (MFRs) with helicity signs consistent with the
observed Hemispheric Helicity Rule (HHR). The cross-sectional area of MFRs
exhibits an uneven distribution, resembling a "foot-node-foot" periodic
configuration. Experiments with different tilt directions of PILs indicate that
the PCFs preferably form along PILs with the western end close to the polar
region. The bending of PILs caused by supergranular flows, forming S-shape
(Z-shape) PIL segments, promotes the formation of dextral (sinistral) MFRs. The
realistic magnetic models we got can serve as starting points for the study of
the plasma formation and eruption of PCFs.
