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Magnetic reconnection

Magnetic reconnection is the process whereby magnetic field lines from different magnetic domains are spliced to one another, changing their patterns of connectivity with respect to the sources. It is a violation of an approximate conservation law in plasma physics, and can concentrate mechanical or magnetic energy in both space and time. Solar flares, the largest explosions in the solar system, may involve the reconnection of large systems of magnetic flux on the Sun, releasing in minutes energy that is stored in the magnetic field over a period of hours to days. Magnetic reconnection in Earth's magnetosphere is one of the mechanisms responsible for the aurora, and it is important to the science of controlled nuclear fusion because it is one mechanism preventing magnetic confinement of the fusion fuel.

In an electrically conductive plasma, magnetic field lines are grouped into 'domains' – bundles of field lines that connect from a particular place to another particular place, and that are topologically distinct from other field lines nearby. This topology is approximately preserved even when the magnetic field itself is strongly distorted by the presence of variable currents or motion of magnetic sources, because effects that might otherwise change the magnetic topology instead induce eddy currents in the plasma; the eddy currents have the effect of canceling out the topological change.

The most common type of magnetic reconnection is separator reconnection, in which four separate magnetic domains exchange magnetic field lines. Domains in a magnetic plasma are separated by separatrix surfaces: curved surfaces in space that divide different bundles of flux. A separatrix surface may be compared to the fascia that separate muscles in an organism: field lines on one side of the separatrix all terminate at a particular magnetic pole, while field lines on the other side all terminate at a different pole of similar sign. Since each field line generally begins at a north magnetic pole and ends at a south magnetic pole, the most general way of dividing simple flux systems involves four domains separated by two separatrices: one separatrix surface divides the flux into two bundles, each of which shares a south pole, and the other separatrix surface divides the flux into two bundles, each of which shares a north pole. The intersection of the separatrices forms a separator, a single line that is at the boundary of the four separate domains. In separator reconnection, field lines enter the separator from two of the domains, and are spliced one to the other, exiting the separator in the other two domains (see the figure).

Separatrices often (but not always) coincide with current sheets that mark a sudden change in the direction of the magnetic field, but a current sheet is not necessary to the formation of a separatrix, or to magnetic reconnection. As a limiting case, refrigerator magnets moved near one another in Earth's atmosphere cause nearly continuous magnetic reconnection, although no electrical current flows through the air (it is an insulator).

According to simple resistive magnetohydrodynamics (MHD) theory, reconnection happens because the plasma's electrical resistivity near the boundary layer opposes the currents necessary to sustain the change in the magnetic field. The need for such a current can be seen from one of Maxwell's equations,

$\nabla \times \mathbf{B} = \mu \mathbf{J} + \mu \epsilon \frac{\partial \mathbf{E}}{\partial t}.$

The resistivity of the current layer allows magnetic flux from either side to diffuse through the current layer, cancelling out flux from the other side of the boundary. When this happens, the plasma is pulled out by magnetic tension along the direction of the magnetic field lines. The resulting drop in pressure pulls more plasma and magnetic flux into the central region, yielding a self-sustaining process.

A current problem in plasma physics is that observed reconnection happens much faster than predicted by MHD: solar flares, 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. There are two competing theories to explain the discrepancy. One posits 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.

A second explanation, from Hall MHD states that the ions decouple from that magnetic field at a distance comparable to the ion skin depth, $\frac{c}{\omega_{pi}}$. The electrons are then accelerated to very high speeds by Whistler waves. Because the ions can move through a wider "bottleneck" near the current layer and because the electrons are moving much faster in Hall MHD than in standard MHD, reconnection may proceed more quickly.

References

• Eric Priest, Terry Forbes, Magnetic Reconnection, Cambridge University Press 2000, ISBN 0521481791, contents and sample chapter online