Magnetic reconnection
Magnetic reconnection is a physical process occurring in electrically conducting plasmas, in which the magnetic topology is rearranged and magnetic energy is converted to kinetic energy, thermal energy, and particle acceleration. Magnetic reconnection involves plasma flows at a substantial fraction of the Alfvén wave speed, which is the fundamental speed for mechanical information flow in a magnetized plasma.
The concept of magnetic reconnection was developed in parallel by researchers working in solar physics and in the interaction between the solar wind and magnetized planets. This reflects the bidirectional nature of reconnection, which can either disconnect formerly connected magnetic fields or connect formerly disconnected magnetic fields, depending on the circumstances.
Ron Giovanelli is credited with the first publication invoking magnetic energy release as a potential mechanism for particle acceleration in solar flares. Giovanelli proposed in 1946 that solar flares stem from the energy obtained by charged particles influenced by induced electric fields within close proximity of sunspots. In the years 1947-1948, he published more papers further developing the reconnection model of solar flares. In these works, he proposed that the mechanism occurs at points of neutrality within structured magnetic fields.
James Dungey is credited with first use of the term "magnetic reconnection" in his 1950 PhD thesis, to explain the coupling of mass, energy and momentum from the solar wind into Earth's magnetosphere. The concept was published for the first time in a seminal paper in 1961. Dungey coined the term "reconnection" because he envisaged field lines and plasma moving together in an inflow toward a magnetic neutral point or line, breaking apart and then rejoining again but with different magnetic field lines and plasma, in an outflow away from the magnetic neutral point or line.
In the meantime, the first theoretical framework of magnetic reconnection was established by Peter Sweet and Eugene Parker at a conference in 1956. 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. Parker was in attendance at this conference and developed scaling relations for this model during his return travel.
Fundamental principles
Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "Alfvén's 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 reconnection breakdown of this theorem occurs in regions of large magnetic shear 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 to that of the outflow regions. 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".The equivalence of magnetic shear and current can be seen from one of Maxwell's equations
In a plasma, 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 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 and the outflow region. 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 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.
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 monopoles 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. The reason is close to 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. 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. 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.
Properties
Physical interpretation
The qualitative description of the reconnection process is such that 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, called Alfvén's theorem 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 has been 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.
Types of reconnection
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.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. These regions are known as quasi-separatrix layers , and have been observed in theoretical configurations and solar flares.