  Recent advances in theory and computational experiments have shown the need
to refine the previous categorisation of magnetic reconnection at
three-dimensional null points -- points at which the magnetic field vanishes.
We propose here a division into three different types, depending on the nature
of the flow near the spine and fan of the null. The spine is an isolated field
line which approaches the null (or recedes from it), while the fan is a surface
of field lines which recede from it (or approach it).
  So-called "torsional spine reconnection" occurs when field lines in the
vicinity of the fan rotate, with current becoming concentrated along the spine,
so that nearby field lines undergo rotational slippage. In "torsional fan
reconnection" field lines near the spine rotate and create a current that is
concentrated in the fan with a rotational flux mismatch and rotational
slippage. In both of these regimes, the spine and fan are perpendicular and
there is no flux transfer across spine or fan. The third regime, called
"spine-fan reconnection", is the most common in practice and combines elements
of the previous spine and fan models. In this case, in response to a generic
shearing motion, the null point collapses to form a current sheet that is
focused at the null itself, in a sheet that locally spans both the spine and
fan. In this regime the spine and fan are no longer perpendicular and there is
flux transfer across both of them.
