Magnetic Reconnection: This view is a cross-section through four
magnetic domains undergoing separator reconnection. Two separatrices
(see text) divide space into four magnetic domains with a separator at
the center of the figure. Field lines (and associated plasma) flow
inward from above and below the separator, reconnect, and spring outward
horizontally. A current sheet (as shown) may be present but is not
required for reconnection to occur. This process is not well understood:
once started, it proceeds many orders of magnitude faster than
predicted by standard models.
A magnetic reconnection event on the
sun.
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
(defined by the field line connectivity) 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 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.
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 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.
Theoretical descriptions of magnetic reconnection
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.
[1] Eugene Parker was in attendance at this conference and developed scaling relations for this model during his return travel.
[2]
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
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.
[3]
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.
[4]
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.
[5] 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),
ions
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
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. Two-fluid/collisionless
reconnection is particularly important in the Earth's magnetosphere.
Observations of magnetic reconnection in nature and the laboratory
The Solar Atmosphere
Magnetic reconnection occurs during
solar flares,
coronal mass ejections,
and many other events in the solar atmosphere. The observational
evidence for solar flares includes observations of inflows/outflows,
downflowing loops, and changes in the magnetic topology. In the past
observations of the solar atmosphere were done using remote imaging;
consequently, the magnetic fields were inferred or extrapolated rather
than observed directly. However, the first direct observations of solar
magnetic reconnection were gathered in 2012 (and released in 2013) by
the
High Resolution Coronal Imager.
[6]
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
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.
[7]
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.
[8]
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.".
[9]
Laboratory Plasma Experiments
The process of magnetic reconnection has been studied in detail by
dedicated laboratory experiments, such as the Magnetic Reconnection
Experiment (MRX) at Princeton Plasma Physics Laboratory (PPPL).
Experiments such as these have confirmed many aspects of magnetic
reconnection, including the Sweet-Parker model in regimes where this
model is applicable.
[10]
The confinement of plasma in devices such as
tokamaks,
spheromaks, and
reversed field pinches
requires the presence of closed magnetic flux surfaces. By changing the
magnetic topology, magnetic reconnection degrades confinement by
disrupting these closed flux surfaces, allowing the hot central plasma
to mix with cooler plasma closer to the wall.
[citation needed]
See also
References
- Eric Priest, Terry Forbes, Magnetic Reconnection, Cambridge University Press 2000, ISBN 0-521-48179-1, contents and sample chapter online
- Discoveries about magnetic reconnection in space could unlock fusion power, Space.com, 6 February 2008
- Nasa MMS-SMART mission,
The Magnetospheric Multiscale (MMS) mission, Solving Magnetospheric
Acceleration, Reconnection, and Turbulence. Due for launch in 2014.
- Cluster spacecraft science results
- ^ Sweet,
P. A., The Neutral Point Theory of Solar Flares, in IAU Symposium 6,
Electromagnetic Phenomena in Cosmical Physics, ed. B. Lehnert
(Dordrecht: Kluwer), 123, 1958
- ^ Parker, E. N., Sweet's Mechanism for Merging Magnetic Fields in Conducting Fluids, J. Geophys. Res., 62, 509, 1957
- ^ Biskamp, D., Magnetic reconnection via current sheets, Physics of Fluids, 29, 1520, 1986
- ^ Ji,
H., M. Yamada, S. Hsu, R. Kulsrud, T. Carter, & S. Zaharia,
Magnetic reconnection with Sweet-Parker characteristics in
two-dimensional laboratory plasmas, Physics of Plasmas, 6, 1743, 1999
- ^ Petschek,
H. E., Magnetic Field Annihilation, in The Physics of Solar Flares,
Proceedings of the AAS-NASA Symposium held 28–30 October 1963 at the
Goddard Space Flight Center, Greenbelt, MD, p. 425, 1964
- ^ "High-Resolution Coronal Imager Photographs the Sun in UV Light at 19.3nm Wavelength". AZonano.com. January 24, 2013. Retrieved February 9, 2013.
- ^ NASA - THEMIS Satellites Discover What Triggers Eruptions of the Northern Lights
- ^ Tail Reconnection Triggering Substorm Onset
- ^ Secret of Colorful Auroras Revealed | Space.com
- ^ Ji, H.; et al. (May 1999). "Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas". Physics of Plasmas 6 (5): 1743. Bibcode:1999PhPl....6.1743J. doi:10.1063/1.873432.
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