Editing Magnetic reconnection (section)

== Fundamental principles ==

Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "[[Alfvén's theorem]]" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the [[Magnetic Reynolds Number]] is very large: this makes the convective term in the [[induction equation]] dominate in such regions. The frozen-in flux theorem states that in such regions the field moves with the plasma velocity (the mean of the ion and electron velocities, weighted by their mass). The reconnection breakdown of this theorem occurs in regions of large magnetic shear (by Ampére's law these are [[current sheet]]s) which are regions of small width where the [[Magnetic Reynolds Number]] can become small enough to make the diffusion term in the [[induction equation]] dominate, meaning that the field diffuses through the plasma from regions of high field to regions of low field. In reconnection, the inflow and outflow regions both obey [[Alfvén's theorem]] and the diffusion region is a very small region at the centre of the current sheet where field lines diffuse together, merge and reconfigure such that they are transferred from the topology of the inflow regions (i.e., along the current sheet) to that of the outflow regions (i.e., threading the current sheet).  The rate of this magnetic flux transfer is the electric field associated with both the inflow and the outflow and is called the "reconnection rate".<ref>{{Cite encyclopedia |author-last= Priest |author-first= E.R. |title= The Sun and its magnetohydrodynamics |pages= 58–90 |encyclopedia=Introduction to Space Physics |date= 1995 |publisher=Cambridge University press |isbn=0-521-45104-3 |editor-last1=Kivelson |editor-first1=M. G. |editor-last2=Russell |editor-first2=C. T. | location=Cambridge U.K.}}</ref><ref>{{Cite encyclopedia |author-last= Hughes |author-first= J.W. |title= The magnetopause, magnetotail, and magnetic reconnection |pages= 227–285 |encyclopedia=Introduction to Space Physics |date= 1995 |publisher=Cambridge University press |isbn=0-521-45104-3 |editor-last1=Kivelson |editor-first1=M. G. |editor-last2=Russell |editor-first2=C. T. |location=Cambridge U.K.}}</ref> 

The equivalence of magnetic shear and current can be seen from one of [[Maxwell's equations]]

<math display="block">\nabla \times \mathbf{B} = \mu \mathbf{J} + \mu \epsilon \frac{\partial \mathbf{E}}{\partial t}.</math>

In a [[Plasma (physics)|plasma]] (ionized gas), for all but exceptionally high frequency phenomena, the second term on the right-hand side of this equation, the displacement current, is negligible compared to the effect of the free current <math>\mathbf{J}</math> and this equation reduces to Ampére's law for free charges.  The displacement current is neglected in both the Parker-Sweet and Petschek theoretical treatments of reconnection, discussed below, and in the derivation of ideal MHD and [[Alfvén's theorem]] which is applied in those theories everywhere outside the small diffusion region. 

The resistivity of the current layer allows [[magnetic flux]] from either side to diffuse through the current layer, cancelling outflux from the other side of the boundary.  However, the small spatial scale of the current sheet makes the [[Magnetic Reynolds Number]] small and so this alone can make the diffusion term dominate in the [[induction equation]] without the resistivity being enhanced. When the diffusing field lines from the two sites of the boundary touch they form the separatrices and so have both the topology of the inflow region (i.e. along the current sheet) and the outflow region (i.e., threading the current sheet). In magnetic reconnection the field lines evolve from the inflow topology through the separatrices topology to the outflow topology.  When this happens, the plasma is pulled out by [[Magnetic tension force]] acting on the reconfigured field lines and ejecting them along the [[current sheet]].  The resulting drop in pressure pulls more plasma and magnetic flux into the central region, yielding a self-sustaining process. The importance of Dungey's concept of a localized breakdown of ideal-MHD is that the outflow along the [[current sheet]] prevents the build-up in plasma pressure that would otherwise choke off the inflow. In Parker-Sweet reconnection the outflow is only along a thin layer the centre of the current sheet and this limits the reconnection rate that can be achieved to low values. On the other hand, in Petschek reconnection the outflow region is much broader, being between shock fronts (now thought to be [[Alfvén waves]]) that stand in the inflow: this allows much faster escape of the plasma frozen-in on reconnected field lines and the reconnection rate can be much higher.

[[James Dungey|Dungey]] coined the term "reconnection" because he initially envisaged field lines of the inflow topology breaking and then joining together again in the outflow topology. However, this means that [[magnetic monopole]]s would exist, albeit for a very limited period, which would violate [[Maxwell's equation]] that the divergence of the field is zero. However, by considering the evolution through the separatrix topology, the need to invoke [[magnetic monopoles]] is avoided.  Global numerical MHD models of the magnetosphere, which use the equations of ideal MHD, still simulate magnetic reconnection even though it is a breakdown of ideal MHD.<ref name=":0">{{Cite journal |last1=Laitinen |first1=T. V. |display-authors= etal |date=November 2006 |title=On the characterization of magnetic reconnection in global MHD simulations |journal=Annales Geophysicae |volume=24 |issue=11 | pages = 3059–2069 |doi=10.5194/angeo-24-3059-2006 |bibcode=2006AnGeo..24.3059L |doi-access=free }}</ref> The reason is close to [[James Dungey|Dungey's]] original thoughts: at each time step of the numerical model the equations of ideal MHD are solved at each grid point of the simulation to evaluate the new field and plasma conditions. The magnetic field lines then have to be re-traced. The tracing algorithm makes errors at thin current sheets and joins field lines up by threading the current sheet where they were previously aligned with the current sheet. This is often called "numerical resistivity" and the simulations have predictive value because the error propagates according to a diffusion equation.

A current problem in plasma [[physics]] is that observed reconnection happens much faster than predicted by MHD in high [[Lundquist number]] plasmas (i.e. '''fast magnetic reconnection'''). [[Solar flare]]s, for example, proceed 13–14 orders of magnitude faster than a naive calculation would suggest, and several orders of magnitude faster than current theoretical models that include turbulence and kinetic effects.  One possible mechanism to explain the discrepancy is that the electromagnetic [[turbulence]] in the boundary layer is sufficiently strong to scatter electrons, raising the plasma's local resistivity.  This would allow the magnetic flux to diffuse faster.