Magnetic reconnection
Encyclopedia
Magnetic reconnection is a physical process in highly conducting plasmas
in which the magnetic topology
is rearranged and magnetic energy is converted to kinetic energy
, thermal energy
, and particle acceleration
. Magnetic reconnection occurs on timescales intermediate between slow resistive diffusion of the magnetic field
and fast Alfvénic
timescales.
The qualitative description of the reconnection process is such that magnetic field lines from different magnetic domains (magnetic domains is a misnomer because that applies to solid materials, we are referring to a plasma) 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 flare
s, 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 current
s 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. A separatrix surface may be compared to the fascia
that separate muscle
s 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).
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
,
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 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. 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.
was in attendance at this conference and developed scaling relations for this model during his return travel.
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. The ideal Ohm's law
then yields the relation
where
is the out-of-plane electric field, 
is the characteristic inflow velocity, and 
is the characteristic upstream magnetic field strength. By neglecting displacement current, the low-frequency Ampere's law, 
, gives the relation
where
is the current sheet half-thickness. This relation uses that the magnetic field reverses over a distance of 
. By matching the ideal electric field outside of the layer with the resistive electric field, 
, inside the layer, we find that
we find that
where
is the plasma resistivity. When the inflow density is comparable to the outflow density, conservation of mass yields the relationship
where
is the half-length of the current sheet and 
is the outflow velocity. 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
where
is the mass density of the plasma. Solving for the outflow velocity then gives
where
is the Alfvén
velocity. The dimensionless reconnection rate can then be written as
where the dimensionless Lundquist number
is given by
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. Results from the Magnetic Reconnection Experiment (MRX) of collisional reconnection show agreement with a generalized Sweet-Parker model which incorporates compressibility, downstream pressure, and anomalous resistivity.
This expression allows fast reconnection almost independent of the Lundquist number.
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.
(where 
is the ion plasma frequency), ion
s decouple from electrons and the magnetic field becomes frozen into the electron fluid rather than the bulk plasma. 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 electron
s 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. Two-fluid/collisionless reconnection is particularly important in the Earth's magnetosphere.
, both on the dayside magnetopause
and in the magnetotail. Cluster
is a four-spacecraft mission, with the four spacecraft in a tetrahedron arrangement, to separate spatial from temporal changes as the suite flies through space. Cluster has now also unambiguously discovered 'reverse reconnection' near the polar cusps. 'Dayside reconnection' allows interconnection of the Earth's magnetic field with that of the Sun (the Interplanetary Magnetic Field
), allowing particle and energy entry into the Earth's vicinity. Tail reconnection allows release of energy stored in the Earth's magnetic tail, injecting particles deep into the magnetosphere, causing auroral substorms. 'Reverse reconnection' is reconnection of Earth's tail magnetic fields with northward Interplanetary Magnetic Fields, causing sunward convection in the Earth's ionosphere
. The upcoming Magnetospheric Multiscale Mission
will improve on Cluster results by having a tighter constellation of spacecraft, allowing finer spatial measurements and finer time detail. In this way the behavior of the electrical currents in the electron diffusion region will be better understood.
On 26 February 2008, THEMIS
probes were able to determine, for the first time, the triggering event for the onset of magnetospheric substorms. Two of the five probes, positioned approximately one third the distance to the Moon, measured events suggesting a magnetic reconnection event 96 seconds prior to Auroral intensification. Dr. Vassilis Angelopoulos of the University of California, Los Angeles, who is the principal investigator for the THEMIS mission, claimed, "Our data show clearly and for the first time that magnetic reconnection is the trigger.".
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
in which the magnetic topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...
is rearranged and magnetic energy is converted to kinetic energy
Kinetic energy
The kinetic energy of an object is the energy which it possesses due to its motion.It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes...
, thermal energy
Thermal energy
Thermal energy is the part of the total internal energy of a thermodynamic system or sample of matter that results in the system's temperature....
, and particle acceleration
Particle acceleration
In a compressible sound transmission medium - mainly air - air particles get an accelerated motion: the particle acceleration or sound acceleration with the symbol a in metre/second². In acoustics or physics, acceleration is defined as the rate of change of velocity. It is thus a vector...
. Magnetic reconnection occurs on timescales intermediate between slow resistive diffusion of the magnetic field
Magnetic field
A magnetic field is a mathematical description of the magnetic influence of electric currents and magnetic materials. The magnetic field at any given point is specified by both a direction and a magnitude ; as such it is a vector field.Technically, a magnetic field is a pseudo vector;...
and fast Alfvénic
Alfvén wave
An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field...
timescales.
The qualitative description of the reconnection process is such that magnetic field lines from different magnetic domains (magnetic domains is a misnomer because that applies to solid materials, we are referring to a plasma) 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 flare
Solar flare
A solar flare is a sudden brightening observed over the Sun surface or the solar limb, which is interpreted as a large energy release of up to 6 × 1025 joules of energy . The flare ejects clouds of electrons, ions, and atoms through the corona into space. These clouds typically reach Earth a day...
s, the largest explosions in the Solar System
Solar System
The Solar System consists of the Sun and the astronomical objects gravitationally bound in orbit around it, all of which formed from the collapse of a giant molecular cloud approximately 4.6 billion years ago. The vast majority of the system's mass is in the Sun...
, may involve the reconnection of large systems of magnetic flux on the Sun
Sun
The Sun is the star at the center of the Solar System. It is almost perfectly spherical and consists of hot plasma interwoven with magnetic fields...
, releasing, in minutes, energy that has been stored in the magnetic field over a period of hours to days. Magnetic reconnection in Earth
Earth
Earth is the third planet from the Sun, and the densest and fifth-largest of the eight planets in the Solar System. It is also the largest of the Solar System's four terrestrial planets...
's magnetosphere
Magnetosphere
A magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the intrinsic magnetic field of a planet or similar body. Earth is surrounded by a magnetosphere, as are the other planets with intrinsic magnetic fields: Mercury, Jupiter,...
is one of the mechanisms responsible for the aurora
Aurora (astronomy)
An aurora is a natural light display in the sky particularly in the high latitude regions, caused by the collision of energetic charged particles with atoms in the high altitude atmosphere...
, and it is important to the science of controlled nuclear fusion
Nuclear fusion
Nuclear fusion is the process by which two or more atomic nuclei join together, or "fuse", to form a single heavier nucleus. This is usually accompanied by the release or absorption of large quantities of energy...
because it is one mechanism preventing magnetic confinement of the fusion fuel.
In an electrically conductive plasma
Plasma (physics)
In physics and chemistry, plasma is a state of matter similar to gas in which a certain portion of the particles are ionized. Heating a gas may ionize its molecules or atoms , thus turning it into a plasma, which contains charged particles: positive ions and negative electrons or ions...
, 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 current
Eddy current
Eddy currents are electric currents induced in conductors when a conductor is exposed to a changing magnetic field; due to relative motion of the field source and conductor or due to variations of the field with time. This can cause a circulating flow of electrons, or current, within the body of...
s in the plasma; the eddy currents have the effect of canceling out the topological change.
Fascia
A fascia is a layer of fibrous tissue that permeates the human body. A fascia is a connective tissue that surrounds muscles, groups of muscles, blood vessels, and nerves, binding those structures together in much the same manner as plastic wrap can be used to hold the contents of sandwiches...
that separate muscle
Muscle
Muscle is a contractile tissue of animals and is derived from the mesodermal layer of embryonic germ cells. Muscle cells contain contractile filaments that move past each other and change the size of the cell. They are classified as skeletal, cardiac, or smooth muscles. Their function is to...
s 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).
According to simple resistive magnetohydrodynamics
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
(MHD) theory, reconnection happens because the plasma's electrical resistivity
Resistivity
Electrical resistivity is a measure of how strongly a material opposes the flow of electric current. A low resistivity indicates a material that readily allows the movement of electric charge. The SI unit of electrical resistivity is the ohm metre...
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
Maxwell's equations
Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits. These fields in turn underlie modern electrical and communications technologies.Maxwell's equations...
,
The resistivity of the current layer allows magnetic flux
Magnetic flux
Magnetic flux , is a measure of the amount of magnetic B field passing through a given surface . The SI unit of magnetic flux is the weber...
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
Physics
Physics is a natural science that involves the study of matter and its motion through spacetime, along with related concepts such as energy and force. More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves.Physics is one of the oldest academic...
is that observed reconnection happens much faster than predicted by MHD in high Lundquist number
Lundquist number
In plasma physics, the Lundquist number is the dimensionless ratio of an Alfvén wave crossing timescale to a resistive diffusion timescale...
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. There are two competing theories to explain the discrepancy. One posits that the electromagnetic turbulence
Turbulence
In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic and stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time...
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.
The Sweet-Parker Model
At a conference in 1956, Peter 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. Eugene ParkerEugene Parker
Eugene N. Parker is an American solar astrophysicist who received his B.S. degree in physics from Michigan State University in 1948 and Ph.D. from Caltech in 1951. In the mid 1950s Parker developed the theory on the supersonic solar wind and predicted the Parker spiral shape of the solar magnetic...
was in attendance at this conference and developed scaling relations for this model during his return travel.
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. The ideal Ohm's law
Ohm's law
Ohm's law states that the current through a conductor between two points is directly proportional to the potential difference across the two points...
then yields the relation
where
is the out-of-plane electric field, is the characteristic inflow velocity, and is the characteristic upstream magnetic field strength. By neglecting displacement current, the low-frequency Ampere's law, , gives the relation
where
is the current sheet half-thickness. This relation uses that the magnetic field reverses over a distance of . By matching the ideal electric field outside of the layer with the resistive electric field, , inside the layer, we find thatwe find that
where
is the plasma resistivity. When the inflow density is comparable to the outflow density, conservation of mass yields the relationship
where
is the half-length of the current sheet and is the outflow velocity. 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
where
is the mass density of the plasma. Solving for the outflow velocity then gives
where
is the AlfvénAlfvén wave
An Alfvén wave, named after Hannes Alfvén, is a type of magnetohydrodynamic wave.-Definition:An Alfvén wave in a plasma is a low-frequency travelling oscillation of the ions and the magnetic field...
velocity. The dimensionless reconnection rate can then be written as
where the dimensionless Lundquist number
Lundquist number
In plasma physics, the Lundquist number is the dimensionless ratio of an Alfvén wave crossing timescale to a resistive diffusion timescale...
is given by
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. Results from the Magnetic Reconnection Experiment (MRX) of collisional reconnection show agreement with a generalized Sweet-Parker model which incorporates compressibility, downstream pressure, and anomalous resistivity.
Petschek reconnection
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 1964, Harry Petschek proposed a mechanism where the inflow and outflow regions are separated by stationary slow mode shocks. The aspect ratio of the diffusion region is then of order unity and the maximum reconnection rate becomes
This expression allows fast reconnection almost independent of the Lundquist number.
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.
Collisionless reconnection
On length scales shorter than the ion inertial length (where is the ion plasma frequency), ionIon
An ion is an atom or molecule in which the total number of electrons is not equal to the total number of protons, giving it a net positive or negative electrical charge. The name was given by physicist Michael Faraday for the substances that allow a current to pass between electrodes in a...
s decouple from electrons and the magnetic field becomes frozen into the electron fluid rather than the bulk plasma. On these scales the Hall effect
Hall effect
The Hall effect is the production of a voltage difference across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current...
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 electron
Electron
The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...
s are then accelerated to very high speeds by Whistler waves
Electromagnetic electron wave
An electromagnetic electron wave is a wave in a plasma which has a magnetic field component and in which primarily the electrons oscillate.In an unmagnetized plasma, an electromagnetic electron wave is simply a light wave modified by the plasma...
. 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
Magnetohydrodynamics
Magnetohydrodynamics is an academic discipline which studies the dynamics of electrically conducting fluids. Examples of such fluids include plasmas, liquid metals, and salt water or electrolytes...
, reconnection may proceed more quickly. Two-fluid/collisionless reconnection is particularly important in the Earth's magnetosphere.
The Earth's magnetosphere
New measurements from the Cluster mission for the first time now can determine unambiguously the scale sizes of magnetic reconnection in the Earth's magnetosphereMagnetosphere
A magnetosphere is formed when a stream of charged particles, such as the solar wind, interacts with and is deflected by the intrinsic magnetic field of a planet or similar body. Earth is surrounded by a magnetosphere, as are the other planets with intrinsic magnetic fields: Mercury, Jupiter,...
, both on the dayside magnetopause
Magnetopause
The magnetopause is the abrupt boundary between a magnetosphere and the surrounding plasma. For planetary science, the magnetopause is the boundary between the planet’s magnetic field and the solar wind. The location of the magnetopause is determined by the balance between the pressure of the...
and in the magnetotail. Cluster
Cluster mission
Cluster II is a space mission of the European Space Agency, with NASA participation, to study the Earth's magnetosphere over the course of an entire solar cycle. The mission is composed of four identical spacecraft flying in a tetrahedral formation...
is a four-spacecraft mission, with the four spacecraft in a tetrahedron arrangement, to separate spatial from temporal changes as the suite flies through space. Cluster has now also unambiguously discovered 'reverse reconnection' near the polar cusps. 'Dayside reconnection' allows interconnection of the Earth's magnetic field with that of the Sun (the Interplanetary Magnetic Field
Interplanetary Magnetic Field
The interplanetary magnetic field is the term for the solar magnetic field carried by the solar wind among the planets of the Solar System....
), allowing particle and energy entry into the Earth's vicinity. Tail reconnection allows release of energy stored in the Earth's magnetic tail, injecting particles deep into the magnetosphere, causing auroral substorms. 'Reverse reconnection' is reconnection of Earth's tail magnetic fields with northward Interplanetary Magnetic Fields, causing sunward convection in the Earth's ionosphere
Ionosphere
The ionosphere is a part of the upper atmosphere, comprising portions of the mesosphere, thermosphere and exosphere, distinguished because it is ionized by solar radiation. It plays an important part in atmospheric electricity and forms the inner edge of the magnetosphere...
. The upcoming Magnetospheric Multiscale Mission
Magnetospheric Multiscale Mission
The Magnetospheric Multiscale Mission is a NASA unmanned space mission, to study the Earth's magnetosphere using four identical spacecraft flying in a tetrahedral formation...
will improve on Cluster results by having a tighter constellation of spacecraft, allowing finer spatial measurements and finer time detail. In this way the behavior of the electrical currents in the electron diffusion region will be better understood.
On 26 February 2008, THEMIS
Themis
Themis is an ancient Greek Titaness. She is described as "of good counsel", and is the embodiment of divine order, law, and custom. Themis means "divine law" rather than human ordinance, literally "that which is put in place", from the verb τίθημι, títhēmi, "to put"...
probes were able to determine, for the first time, the triggering event for the onset of magnetospheric substorms. Two of the five probes, positioned approximately one third the distance to the Moon, measured events suggesting a magnetic reconnection event 96 seconds prior to Auroral intensification. Dr. Vassilis Angelopoulos of the University of California, Los Angeles, who is the principal investigator for the THEMIS mission, claimed, "Our data show clearly and for the first time that magnetic reconnection is the trigger.".