  We propose a physical mechanism to explain giant flares and radio afterglows
in terms of a magnetospheric model containing both a helically twisted flux
rope and a current sheet (CS). With the appearance of CS, we solve a mixed
boundary value problem to get the magnetospheric field based on a domain
decomposition method. We investigate properties of the equilibrium curve of the
flux rope when the CS is present in background multipolar fields. In response
to the variations at the magnetar surface, it quasi-statically evolves in
stable equilibrium states. The loss of equilibrium occurs at a critical point
and, beyond that point, it erupts catastrophically. New features show up when
the CS is considered. Especially, we find two kinds of physical behaviors,
i.e., catastrophic state transition and catastrophic escape. Magnetic energy
would be released during state transitions. The released magnetic energy is
sufficient to drive giant flares. The flux rope would go away from the magnetar
quasi-statically, which is inconsistent with the radio afterglow. Fortunately,
in the latter case, i.e., the catastrophic escape, the flux rope could escape
the magnetar and go to infinity in a dynamical way. This is more consistent
with radio afterglow observations of giant flares. We find that the minor
radius of flux rope has important implications for its eruption. Flux ropes
with larger minor radius are more prone to erupt. We stress that the CS
provides an ideal place for magnetic reconnection, which would further enhance
the energy release during eruptions.
