Abstract
Magnetic reconnection in three dimensions (3D) is fundamentally different in many respects from its two-dimensional counterpart. An analytical example of a global 3D general magnetic reconnection process is presented here, in which a magnetic flux tube has its footpoints rotated in different directions. A localized nonideal region is found in the center of the tube where the field lines are twisted as a result of the footpoint counter-rotation. A qualitative analysis demonstrates how the parameters that determine the strength and geometry of the magnetic field depend on the rotational driving velocity. The reconnection rate measures the rate at which field lines within the entire flux tube are changing their magnetic connections, and is shown to be proportional to the driving velocity imposed on its footpoints. The qualitative estimates are confirmed by an exact kinematic 3D magnetohydrodynamic analytical solution, which possesses a localized three-dimensional current and determines the reconnection rate quantitatively.
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