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. In two dimensions, 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. 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 first figure. In three dimensions, the geometry of the field lines become more complicated than the two-dimensional case and it is possible for reconnection to occur in regions where a separator does not exist, but with the field lines connected by steep gradients.
The first theoretical framework of magnetic reconnection was established by Peter Sweet and Eugene Parker at a conference in Sweet pointed out that by pushing two plasmas with oppositely directed magnetic fields together, resistive diffusion is able to occur on a length scale much shorter than a typical equilibrium length scale. The Sweet-Parker model describes time-independent magnetic reconnection in the resistive MHD framework when the reconnecting magnetic fields are antiparallel oppositely directed and effects related to viscosity and compressibility are unimportant.
When the inflow density is comparable to the outflow density, conservation of mass yields the relationship. The left and right hand sides of the above relation represent the mass flux into the layer and out of the layer, respectively. Equating the upstream magnetic pressure with the downstream dynamic pressure gives. Solving for the outflow velocity then gives. Sweet-Parker reconnection allows for reconnection rates much faster than global diffusion, but is not able to explain the fast reconnection rates observed in solar flares, the Earth's magnetosphere, and laboratory plasmas.
Additionally, Sweet-Parker reconnection neglects three-dimensional effects, collisionless physics, time-dependent effects, viscosity, compressibility, and downstream pressure. Numerical simulations of two-dimensional magnetic reconnection typically show agreement with this model.
One of the reasons why Sweet-Parker reconnection is slow is that the aspect ratio of the reconnection layer is very large in high Lundquist number plasmas. The inflow velocity, and thus the reconnection rate, must then be very small. In , Harry Petschek proposed a mechanism where the inflow and outflow regions are separated by stationary slow mode shocks. 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. In the Sweet-Parker model, the common assumption is that the magnetic diffusivity is constant.
Nevertheless, if the drift velocity of electrons exceeds the thermal velocity of plasma, a steady state cannot be achieved and magnetic diffusivity should be much larger than what is given in the above. Another proposed mechanism is known as the Bohm diffusion across the magnetic field. Lazarian and Vishniac considered the magnetic reconnection in the presence of a random component of magnetic field in a totally ionized and inviscid plasma assuming that the resistive effects could be described with an Ohmic resistivity. Lazarian and Vishniac showed that, in general, this cannot affect the final result.
In fact, their model is independent of small scale physics which determines the local reconnection rate. This model has been successfully tested by numerical simulations. On these scales, the Hall effect becomes important. Two-fluid simulations show the formation of an X-point geometry rather than the double Y-point geometry characteristic of resistive reconnection. The Battle of Balaklava needs science; search of the Light order. The Battle of Inkerman antes browser. The role of Sevastopol comes.
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