Editing Magnetic reconnection (section)

===Fast reconnection: Petschek model===

The fundamental reason that Petschek reconnection is faster than Parker-Sweet is that it broadens the outflow region and thereby removes some of the limitation caused by the build up in plasma pressure. The inflow velocity, and thus the reconnection rate, can only be very small if the outflow region is narrow.  In 1964, Harry Petschek proposed a mechanism where the inflow and outflow regions are separated by stationary slow mode shocks that stand in the inflows.<ref>Petschek, H. E., Magnetic Field Annihilation, in The Physics of Solar Flares, Proceedings of the AAS-NASA Symposium held 28–30 October 1963 at the Goddard Space Flight Center, Greenbelt, MD, p. 425, 1964</ref>  The aspect ratio of the diffusion region is then of order unity and the maximum reconnection rate becomes
<math display="block">\frac{v_\text{in}}{v_A} \approx \frac{\pi}{8 \ln S}.</math>

This expression allows for fast reconnection and is almost independent of the Lundquist number. Theory and numerical simulations show that most of the actions of the shocks that were proposed by Petschek can be carried out by [[Alfvén waves]] and in particular rotational discontinuities (RDs). In cases of asymmetric plasma densities on the two sides of the current sheet (as at Earth's dayside magnetopause) the Alfvén wave that propagates into the inflow on higher-density side (in the case of the magnetopause the denser magnetosheath) has a lower propagation speed and so the field rotation increasingly becomes at that RD as the field line propagates away from the reconnection site: hence the magnetopause current sheet becomes increasingly concentrated in the outer, slower, RD. 

Simulations of resistive MHD reconnection with uniform resistivity showed the development of elongated current sheets in agreement with the Sweet–Parker model rather than the Petschek model.  When a localized anomalously large resistivity is used, however, Petschek reconnection can be realized in resistive MHD simulations.  Because the use of an anomalous resistivity is only appropriate when the particle mean free path is large compared to the reconnection layer, it is likely that other collisionless effects become important before Petschek reconnection can be realized.