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Buildup and Release of Magnetic Twist during the X3.4 Solar Flare of December 13, 2006

We analyze the temporal evolution of the three-dimensional (3D) magnetic structure of the flaring active region (AR) NOAA 10930 by using the nonlinear force-free fields extrapolated from the photospheric vector magnetic fields observed by the Solar Optical Telescope on board {\it Hinode}. This AR consisted mainly of two types of twisted magnetic field lines: One has a strong negative (left-handed) twist due to the counterclockwise motion of the positive sunspot and is rooted in the regions of both polarities in the sunspot at a considerable distance from the polarity inversion line (PIL). In the flare phase, dramatic magnetic reconnection occurs in those negatively twisted lines in which the absolute value of the twist is greater than a half-turn. The other type consists of both positively and negatively twisted field lines formed relatively close to the PIL between two sunspots. A strong CaII image began to brighten in this region of mixed polarity, in which the positively twisted field lines were found to be injected within one day across the pre-existing negatively twisted region, along which strong currents were embedded. Consequently, the central region near the PIL distributed with a mix of differently twisted field lines and the strong currents may play a prominent role in flare onset.