Reconnection and the Ideal Evolution of Magnetic Fields

A magnetic evolution is ideal if it is consistent with the field being embedded in a perfectly conducting fluid. Faraday's law implies the evolution is ideal when the parallel component of the electric field is the derivative of a scalar potential, a condition that generically holds in any local region of space. Reconnection requires the non-existence of such a potential. In systems with two periodic directions, non-existence focuses reconnection onto the surfaces in which the magnetic field lines close on themselves, the rational surfaces. This rational surface effect does not arise in astrophysics but does appear in periodic simulation codes. Effects that could give astrophysical reconnection are discussed.