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We have analyzed the multipolar magnetic field structure variation at neutronstar surface by means of the catastrophic eruption model, and find that thevariation of the geometry of multipolar fields on the magnetar surface couldresult in the catastrophic rearrangement of the magnetosphere, which providescertain physical mechanism for the outburst of giant flares. The magnetosphericmodel we adopted consists of two assumptions: a helically twisted flux rope issuspended in an ideal force-free magnetosphere around the magnetar, and acurrent sheet emerges during the flux rope evolution. Magnetic energyaccumulates during the flux rope's gradual evolution along with the variationof magnetar surface magnetic structure before the eruption. The two typicalbehaviors, either state transition or catastrophic escape, would take placeonce the flux rope loses equilibrium, thus tremendous accumulated energy isradiated. We have investigated the equilibrium state of the flux rope and theenergy release affected by different multipolar structures, and find structuresthat could trigger violent eruption and provide the radiation approximately0.5$\%$ of the total magnetic energy during the giant flare outburst. Ourresults provide certain multipolar structures of the neutron star's magneticfield with an energy release percentage 0.42$\%$ in the state transition and0.51$\%$ in the catastrophic escape case, which are sufficient for thepreviously reported energy release from SGR 1806-20 giant flares.

Magnetar giant flares in multipolar magnetic fields. III. Multipolar magnetic field structure variations