Constraints on finite-time current sheet formation at null points in two-dimensional ideal incompressible magnetohydrodynamics

It is shown rigorously that, under the conditions of two-dimensional ideal incompressible magnetohydrodynamics, finite time singularity formation (including finite-time collapse to a current sheet) cannot occur at a magnetic null point of any type unless driven by a pressure singularity occurring outside a neighborhood of the null point. The proof is based on the depletion of nonlinearity at a two-dimensional magnetic null point. (C) 1998 American Institute of Physics.