Magnetic reconnection around three dimensional (3D) magnetic null points is the natural progression from X-point reconnection in two dimensions. In 3D the separator field lines of the X-point are replaced with the spine line and fan plane (the field lines which asymptotically approach or recede from the null). In this work analytical models are developed for the newly classified torsional spine and torsional fan reconnection regimes by solving the steady state, kinematic, resistive magnetohydrodynamic equations. Reconnection is localized to around the null through the use of a localized field perturbation leading to a localized current while a constant resistivity is assumed. For the torsional spine case current is found to localize around the spine leading to a spiraling slippage of the field around the spine and out along the fan. For the torsional fan case current is found to be localized to the fan plane leading again to a spiraling slippage of the field. In each case no flux is transported across either the spine or the fan. An intermediate twist is then introduced and a link is established between the two regimes. We find that for a general twist plasma flows associated with both torsional spine and fan appear in distinct regions. As such we suggest that the "pure" flows of each are extreme cases. (C) 2010 American Institute of Physics. [doi:10.1063/1.3480639
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