Fundamental limitation of a two-dimensional description of magnetic reconnection

For magnetic reconnection to be possible, the electrons have at some point to ``get free from magnetic slavery,'' according to von Steiger's formulation [1]. Stochasticity may be considered as one possible ingredient through which this may be realized in the magnetic reconnection process. It will be argued that non-ideal effects may be considered as a ``hidden'' way to introduce stochasticity. Then it will be shown that there exists a generic intrinsic stochasticity of magnetic field lines that does not require the invocation of non-ideal effects but cannot show up in effective two-dimensional models of magnetic reconnection. Possible implications will be discussed in the frame of tokamak sawteeth that form a laboratory prototype of magnetic reconnection. \\[4pt] [1] R. von Steiger, Space physics{-}grand challenges for the 21st century. Front. Physics 1:6 (2013).