Magnetic reconnection

463:: 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 2703:, 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 440:, 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 1706:

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.

2739:. have made observations of sufficient resolution and in multiple locations to observe the process directly and in-situ. Cluster II is a four-spacecraft mission, with the four spacecraft arranged in a tetrahedron to separate the spatial and temporal changes as the suite flies through space. It has observed numerous reconnection events in which the Earth's magnetic field reconnects with that of the Sun (i.e. the 372: 2249:

is independent of small scale physics such as resistive effects and depends only on turbulent effects. Roughly speaking, in stochastic model, turbulence brings initially distant magnetic field lines to small separations where they can reconnect locally (Sweet-Parker type reconnection) and separate again due to turbulent super-linear diffusion (Richardson diffusion ). For a current sheet of the length

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above and below the separator, reconnect, and spring outward along the current sheet. In-situ spacecraft measurements in the magnetosphere and laboratory plasma experiments mean that this process is increasingly well understood: once started, it proceeds many orders of magnitude faster than predicted by the Parker-Sweet theory.

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In stochastic reconnection, magnetic field has a small scale random component arising because of turbulence. For the turbulent flow in the reconnection region, a model for magnetohydrodynamic turbulence should be used such as the model developed by Goldreich and Sridhar in 1995. This stochastic model

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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

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and in particular rotational discontinuities (RDs). In cases of asymmetric plasma densities on the two sides of the current sheet (as at Earth's dayside magnetopause) the Alfvén wave that propagates into the inflow on higher-density side (in the case of the magnetopause the denser magnetosheath) has

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The fundamental reason that Petschek reconnection is faster than Parker-Sweet is that it broadens the outflow region and thereby removes some of the limitation caused by the build up in plasma pressure. The inflow velocity, and thus the reconnection rate, can only be very small if the outflow region

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dominate in such regions. The frozen-in flux theorem states that in such regions the field moves with the plasma velocity (the mean of the ion and electron velocities, weighted by their mass). The reconnection breakdown of this theorem occurs in regions of large magnetic shear (by Ampére's law these

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coined the term "reconnection" because he envisaged field lines and plasma moving together in an inflow toward a magnetic neutral point (2D) or line (3D), breaking apart and then rejoining again but with different magnetic field lines and plasma, in an outflow away from the magnetic neutral point or

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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,

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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

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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

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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

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Magnetic reconnection: This view is a cross-section through four magnetic domains undergoing separator Parker-Sweet 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

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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 (i.e., along the current sheet) to that of the outflow regions (i.e., threading the

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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

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probes were able to determine 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

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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 (i.e. along the current sheet) and the outflow region (i.e., threading the current sheet). In magnetic

359:, 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 375: 379: 377: 374: 20: 378: 1795:

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.

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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

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system, while experiments on the Magnetic Reconnection Experiment (MRX) at the Princeton Plasma Physics Laboratory (PPPL) have confirmed many aspects of magnetic reconnection, including the Sweet–Parker model in regimes where the model is applicable. Analysis of the physics of

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is narrow. In 1964, Harry Petschek proposed a mechanism where the inflow and outflow regions are separated by stationary slow mode shocks that stand in the inflows. The aspect ratio of the diffusion region is then of order unity and the maximum reconnection rate becomes

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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 initial velocity is simply an

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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.

2755:, launched on 13 March 2015, improved the spatial and temporal resolution of the Cluster II results by having a tighter constellation of spacecraft. This led to a better understanding of the behavior of the electrical currents in the electron diffusion region. 1489: 467:, 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). 248: 376: 100:. 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 (weak or null magnetic field) within structured magnetic fields. 400:

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, called

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a lower propagation speed and so the field rotation increasingly becomes at that RD as the field line propagates away from the reconnection site: hence the magnetopause current sheet becomes increasingly concentrated in the outer, slower, RD.

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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. This is called anomalous resistivity,

1177: 35: 1271: 307:. 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 278:

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

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This expression allows for fast reconnection and is almost independent of the Lundquist number. Theory and numerical simulations show that most of the actions of the shocks that were proposed by Petschek can be carried out by

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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.".

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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

32: 874: 777: 4350:

Gekelman, W; Lawrence, E; Collette, A; Vincena, S; Compernolle, B Van; Pribyl, P; Berger, M; Campbell, J (2010-12-01). "Magnetic field line reconnection in the current systems of flux ropes and Alfvén waves".

256:(ionized gas), 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 334:

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

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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

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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

2180: 2727:) were for many years inferred because they uniquely explained many aspects of the large-scale behaviour of the magnetosphere and its dependence on the orientation of the near-Earth 1101: 1369: 1992: 1204: 2145: 290:

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

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near the polar cusps; 'dayside reconnection', which allows the transmission of particles and energy into the Earth's vicinity and 'tail reconnection', which causes auroral

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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

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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

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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

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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

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plasma core. The Kadomtsev model describes sawtooth oscillations as a consequence of magnetic reconnection due to displacement of the central region with safety factor

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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

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current sheet). 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".

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Mandrini, C. H.; Démoulin, P.; Van Driel-Gesztelyi, L.; Schmieder, B.; Cauzzi, G.; Hofmann, A. (September 1996). "3D magnetic reconnection at an X-ray bright point".

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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.

405:(also called the "frozen-in flux theorem") and can concentrate mechanical or magnetic energy in both space and time. Solar flares, the largest explosions in the 2467: 2267: 2052: 1851: 1831: 1624: 1604: 1584: 1514: 1324: 1064: 3502:

Bagalá, L. G.; Mandrini, C. H.; Rovira, M. G.; Démoulin, P. (November 2000). "Magnetic reconnection: a common origin for flares and AR interconnecting arcs".

2572: 316:) 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. 720: 2678:. 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 106:

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

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Burch, J. L.; Torbert, R. B.; Phan, T. D.; Chen, L.-J.; Moore, T. E.; Ergun, R. E.; Eastwood, J. P.; Gershman, D. J.; Cassak, P. A. (2016-06-03).

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Kowal, G.; Lazarian, A.; Vishniac, E.; Otmianowska-Mazur, K. (2009). "Numerical Tests of Fast Reconnection in Weakly Stochastic Magnetic Fields".

667: 2059: 998: 3046: 4572:, The Magnetospheric Multiscale (MMS) mission, Solving Magnetospheric Acceleration, Reconnection, and Turbulence. Due for launch in 2014. 3359:

Priest, E. R.; Démoulin, P. (1995). "Three-dimensional magnetic reconnection without null points: 1. Basic theory of magnetic flipping".

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decouple from electrons and the magnetic field becomes frozen into the electron fluid rather than the bulk plasma. On these scales, the

2682:, reconnection may proceed more quickly. Two-fluid/collisionless reconnection is particularly important in the Earth's magnetosphere. 1519: 534: 143:" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the 413:, releasing, in minutes, energy that has been stored in the magnetic field over a period of hours to days. Magnetic reconnection in 330:

that the divergence of the field is zero. However, by considering the evolution through the separatrix topology, the need to invoke

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Lawrence, Eric E.; Gekelman, W (2009). "Identification of a Quasiseparatrix Layer in a Reconnecting Laboratory Magnetoplasma".

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Another proposed mechanism is known as the Bohm diffusion across the magnetic field. This replaces the Ohmic resistivity with

962:{\displaystyle v_{\text{in}}={\frac {E_{y}}{B_{\text{in}}}}\sim {\frac {1}{\mu _{0}\sigma \delta }}={\frac {\eta }{\delta }},} 664:

is the characteristic upstream magnetic field strength. By neglecting displacement current, the low-frequency Ampere's law,

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Hughes, J.W. (1995). "The magnetopause, magnetotail, and magnetic reconnection". In Kivelson, M. G.; Russell, C. T. (eds.).

4509: 2785: 92:. Giovanelli proposed in 1946 that solar flares stem from the energy obtained by charged particles influenced by induced 1804: 456:, in which four separate magnetic domains exchange magnetic field lines. Domains in a magnetic plasma are separated by 4551: 3302: 3277: 2752: 2736: 2392: 1997: 1484:{\displaystyle R={\frac {v_{\text{in}}}{v_{\text{out}}}}\sim {\frac {\eta }{v_{A}\delta }}\sim {\frac {\delta }{L}}.} 243:{\displaystyle \nabla \times \mathbf {B} =\mu \mathbf {J} +\mu \epsilon {\frac {\partial \mathbf {E} }{\partial t}}.} 2751:

by injecting particles deep into the magnetosphere and releasing the energy stored in the Earth's magnetotail. The

4403: 2931:"Flattening of the tokamak current profile by a fast magnetic reconnection with implications for the solar corona" 4446:"Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment" 2240:, however, its effect, similar to the anomalous resistivity, is still too small compared with the observations. 4560: 2704: 2150: 995:. When the inflow density is comparable to the outflow density, conservation of mass yields the relationship 3130:

Giovanelli, R.G. (1947). "Magnetic and Electric Phenomena in the Sun's Atmosphere associated with Sunspots".

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Magnetic reconnection has also been observed in numerous laboratory experiments. For example, studies on the

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is the current sheet half-thickness. This relation uses that the magnetic field reverses over a distance of

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are multiplied by each other and then square-rooted, giving a simple relation between the reconnection rate

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Ji, Hantao; Yamada, Masaaki; Hsu, Scott; Kulsrud, Russell; Carter, Troy; Zaharia, Sorin (26 April 1999).

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Priest, E.R. (1995). "The Sun and its magnetohydrodynamics". In Kivelson, M. G.; Russell, C. T. (eds.).

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at UCLA have observed and mapped quasi-separatrix layers near the magnetic reconnection region of a two

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Parker, E. N. (December 1957). "Sweet's mechanism for merging magnetic fields in conducting fluids".

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is credited with the first publication invoking magnetic energy release as a potential mechanism for

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that uses fast magnetic reconnection to accelerate plasma to produce thrust for space propulsion.

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Jafari, Amir; Vishniac, Ethan (2019). "Topology and stochasticity of turbulent magnetic fields".

3724: 1374: 4587: 4404:"Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas" 3626:"Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas" 1172:{\displaystyle {\frac {B_{\text{in}}^{2}}{2\mu _{0}}}\sim {\frac {\rho v_{\text{out}}^{2}}{2}}} 827:. By matching the ideal electric field outside of the layer with the resistive electric field 508: 300: 173: 402: 280: 165: 140: 74:

speed, which is the fundamental speed for mechanical information flow in a magnetized plasma.

4372: 2700: 1266:{\displaystyle v_{\text{out}}\sim {\frac {B_{\text{in}}}{\sqrt {\mu _{0}\rho }}}\equiv v_{A}} 784: 327: 122:

In the meantime, the first theoretical framework of magnetic reconnection was established by

85: 67: 3515: 2812: 4467: 4418: 4360: 4316: 4245: 4152: 4070: 4013: 3952: 3897: 3858: 3803: 3760: 3684: 3672: 3637: 3625: 3590: 3555: 3511: 3460: 3415: 3368: 3331: 3009: 2952: 2887: 2679: 2499: 2472: 1810: 1278: 1184: 992: 974: 586: 430: 397: 2523:

is the Alfvén velocity. This model has been successfully tested by numerical simulations.

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is constant. This can be estimated using the equation of motion for an electron with mass

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in the plasma; the eddy currents have the effect of canceling out the topological change.

8: 2854: 2772: 4471: 4422: 4364: 4320: 4249: 4156: 4074: 4017: 3956: 3901: 3862: 3807: 3764: 3688: 3641: 3594: 3559: 3464: 3419: 3372: 3335: 3013: 2956: 2891: 2655:{\displaystyle \omega _{pi}\equiv {\sqrt {\frac {n_{i}Z^{2}e^{2}}{\epsilon _{0}m_{i}}}}} 4491: 4457: 4384: 4271: 4196: 4088: 4060: 4029: 4003: 3976: 3942: 3915: 3827: 3776: 3750: 3738: 3484: 3113: 3027: 2999: 2968: 2942: 2911: 2452: 2252: 2037: 1836: 1816: 1609: 1589: 1569: 1499: 1309: 1049: 422: 331: 295: 161: 148: 3022: 2987: 2930: 2743:). These include 'reverse reconnection' that causes sunward convection in the Earth's 4547: 4483: 4376: 4332: 4275: 4263: 4200: 4188: 4180: 4107:"High-Resolution Coronal Imager Photographs the Sun in UV Light at 19.3nm Wavelength" 4025: 3980: 3968: 3919: 3831: 3819: 3780: 3653: 3606: 3519: 3488: 3476: 3433: 3384: 3298: 3273: 3210: 3171: 3105: 3066: 3031: 2972: 2903: 2788: 2781: 1696:{\displaystyle R~\sim {\sqrt {\frac {\eta }{v_{A}L}}}={\frac {1}{S^{\frac {1}{2}}}}.} 458: 323: 55: 4495: 4388: 4092: 3190: 1921:{\displaystyle {d{\mathbf {v} } \over dt}={e \over m}\mathbf {E} -\nu \mathbf {v} ,} 4479: 4475: 4426: 4368: 4328: 4324: 4253: 4170: 4160: 4078: 4033: 4021: 3960: 3905: 3866: 3811: 3768: 3692: 3645: 3598: 3563: 3468: 3423: 3376: 3339: 3250: 3202: 3161: 3117: 3097: 3058: 3017: 2960: 2915: 2895: 2802: 2147:, which can enhance the reconnection rate in the Sweet–Parker model by a factor of 1494: 1095: 489: 437: 348: 283:

which is applied in those theories everywhere outside the small diffusion region.

253: 123: 51: 3150:"Magnetic and Electric Phenomena in the Sun's Atmosphere associated with Sunspots" 312:

the outflow region is much broader, being between shock fronts (now thought to be

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is the mass density of the plasma. Solving for the outflow velocity then gives

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is that observed reconnection happens much faster than predicted by MHD in high

313: 139:

Magnetic reconnection is a breakdown of "ideal-magnetohydrodynamics" and so of "

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connect formerly disconnected magnetic fields, depending on the circumstances.

70:. Magnetic reconnection involves plasma flows at a substantial fraction of the 63: 59: 3933:

Jafari, Amir; Vishniac, Ethan (2019). "Magnetic stochasticity and diffusion".

3166: 3149: 1303: 71: 4601: 4380: 4184: 3846: 3657: 3610: 3523: 3480: 3437: 3388: 3214: 3206: 3175: 3109: 3070: 2844: 2716: 1776:{\displaystyle {\frac {v_{\text{in}}}{v_{A}}}\approx {\frac {\pi }{8\ln S}}.} 493: 418: 308: 304: 287: 153: 127: 111: 4258: 4233: 4165: 4140: 4083: 4048: 3567: 3450: 3320:"On the characterization of magnetic reconnection in global MHD simulations" 3254: 2876:"In situ detection of collisionless reconnection in the Earth's magnetotail" 710:{\displaystyle \mathbf {J} ={\frac {1}{\mu _{0}}}\nabla \times \mathbf {B} } 488:

The first theoretical framework of magnetic reconnection was established by

4487: 4336: 4267: 4215:"THEMIS Satellites Discover What Triggers Eruptions of the Northern Lights" 4192: 4175: 3972: 3847:"Toward a theory of interstellar turbulence. 2: Strong Alfvenic turbulence" 3823: 3085: 2907: 2875: 2849: 2720: 868: 441: 406: 336: 319: 115: 114:. The concept was published for the first time in a seminal paper in 1961. 103: 4561:

Discoveries about magnetic reconnection in space could unlock fusion power

3755: 3428: 3403: 2724: 2696: 2667: 1994:, then the above equation along with the definition of electric current, 475:, and have been observed in theoretical configurations and solar flares. 356: 89: 40: 2986:

Zhu, Chunming; Liu, Rui; Alexander, David; McAteer, R. T. James (2016).

1371:

using the result earlier derived from Ohm's law, the second in terms of

409:, may involve the reconnection of large systems of magnetic flux on the 3884:

Jafari, Amir; Vishniac, Ethan; Kowal, Grzegorz; Lazarian, Alex (2018).

3741:; Vishniac, Ethan (1999). "Reconnection in a Weakly Stochastic Field". 3472: 2744: 360: 107: 4046: 3993: 3673:"Experimental Test of the Sweet-Parker Model of Magnetic Reconnection" 3402:

Titov, Vyacheslav S.; Hornig, Gunnar; Démoulin, Pascal (August 2002).

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The equivalence of magnetic shear and current can be seen from one of

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The qualitative description of the reconnection process is such that

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Articles on measurements made from the Cluster II spacecraft mission

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Kowal, G; Lazarian, A.; Vishniac, E.; Otmianowska-Mazur, K. (2012).

3239:"Sweet's mechanism for merging magnetic fields in conducting fluids" 2496:

are turbulence injection length scale and velocity respectively and

452:

In two dimensions, the most common type of magnetic reconnection is

294:

small and so this alone can make the diffusion term dominate in the

4462: 3947: 3870: 3772: 3004: 2947: 2748: 2671: 772:{\displaystyle J_{y}\sim {\frac {B_{\text{in}}}{\mu _{0}\delta }},} 326:

would exist, albeit for a very limited period, which would violate

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acting on the reconfigured field lines and ejecting them along the

4510:"How Dr. Fatima Ebrahimi is Geting Humans a Faster Ticket to Mars" 4065: 4049:"Reconnection studies under different types of turbulence driving" 4008: 3671:

Ji, Hantao; Yamada, Masaaki; Hsu, Scott; Kulsrud, Russell (1998).

2988:"Observation of the Evolution of a Current Sheet in a Solar Flare" 2806: 1306:. With the above relations, the dimensionless reconnection rate 344: 97: 3581:

Biskamp, D. (1986). "Magnetic reconnection via current sheets".

3297:. Cambridge U.K.: Cambridge University press. pp. 227–285. 4349: 4141:"Electron-scale measurements of magnetic reconnection in space" 2759: 19: 3272:. Cambridge U.K.: Cambridge University press. pp. 58–90. 2526: 3047:"Magnetic field reconnection: A first-principles perspective" 2380:{\displaystyle v=v_{\text{turb}}\;\operatorname {min} \left,} 1809:

In the Sweet–Parker model, the common assumption is that the

860:{\displaystyle \mathbf {E} ={\frac {1}{\sigma }}\mathbf {J} } 414: 4569: 3886:"Stochastic Reconnection for Large Magnetic Prandtl Numbers" 3501: 2784:

injection, used to create the initial plasma current in the

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is a physical process occurring in electrically conducting

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can become small enough to make the diffusion term in the

2663: 2110:{\displaystyle \eta =\nu {c^{2} \over \omega _{pi}^{2}}.} 1805:

Spitzer resistivity § Disagreements with observation

1037:{\displaystyle v_{\text{in}}L\sim v_{\text{out}}\delta ,} 410: 384: 2269:, the upper limit for reconnection velocity is given by 1326:

can then be written in two forms, the first in terms of

483: 4592: 2715:

Magnetic reconnection events that occur in the Earth's

1950:

is the collision frequency. Since in the steady state,

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Mozer, Forrest S.; Pritchett, Philip L. (2010-06-01).

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On length scales shorter than the ion inertial length

4231: 3404:"Theory of magnetic connectivity in the solar corona" 3191:"Interplanetary Magnetic Field and the Auroral Zones" 2815: 2575: 2537: 2502: 2475: 2455: 2395: 2277: 2255: 2191: 2153: 2126: 2062: 2040: 2000: 1956: 1936: 1861: 1839: 1819: 1721: 1631: 1612: 1592: 1572: 1522: 1502: 1409: 1377: 1332: 1312: 1281: 1207: 1187: 1104: 1072: 1052: 1001: 977: 877: 833: 807: 787: 723: 670: 643: 616: 589: 537: 511: 262: 183: 147:

is very large: this makes the convective term in the

4138: 1709: 3401: 497:relations for this model during his return travel. 425:, and it is important to the science of controlled 131:relations for this model during his return travel. 3670: 3623: 2827: 2654: 2561: 2515: 2488: 2461: 2441: 2379: 2261: 2232: 2174: 2139: 2109: 2046: 2026: 1986: 1942: 1920: 1845: 1825: 1775: 1695: 1618: 1598: 1578: 1556: 1508: 1483: 1395: 1363: 1318: 1294: 1265: 1193: 1171: 1085: 1058: 1036: 983: 961: 859: 819: 793: 771: 709: 656: 629: 602: 573: 523: 270: 242: 58:is rearranged and magnetic energy is converted to 3154:Monthly Notices of the Royal Astronomical Society 3132:Monthly Notices of the Royal Astronomical Society 4599: 4306: 3844: 3737: 2766: 1557:{\displaystyle S\equiv {\frac {Lv_{A}}{\eta }},} 574:{\displaystyle E_{y}=v_{\text{in}}B_{\text{in}}} 39:The evolution of magnetic reconnection during a 2442:{\displaystyle v_{\text{turb}}=v_{l}^{2}/v_{A}} 2027:{\displaystyle {\mathbf {J} }=en{\mathbf {v} }} 3932: 3793: 3408:Journal of Geophysical Research: Space Physics 3358: 3318:Laitinen, T. V.; et al. (November 2006). 3044: 4234:"Tail Reconnection Triggering Substorm Onset" 421:is one of the mechanisms responsible for the 156:) which are regions of small width where the 2805:are periodic mixing events occurring in the 2674:are then accelerated to very high speeds by 1066:is the half-length of the current sheet and 286:The resistivity of the current layer allows 2527:Non-MHD process: Collisionless reconnection 637:is the characteristic inflow velocity, and 478: 3147: 3083: 2294: 2243: 391: 4461: 4257: 4174: 4164: 4082: 4064: 4007: 3946: 3909: 3754: 3427: 3343: 3165: 3021: 3003: 2946: 2175:{\displaystyle \eta _{\text{anom}}/\eta } 134: 4443: 3317: 2874:Øieroset, M.; et al. (2001-07-26). 2873: 2710: 1799:Anomalous resistivity and Bohm diffusion 447: 370: 27: 18: 3580: 2054:is the electron number density, yields 429:because it is one mechanism preventing 4600: 4593:Magnetic Reconnection Experiment (MRX) 3718: 3545: 3292: 3267: 3236: 3188: 2928: 4290:"Secret of Colorful Auroras Revealed" 1364:{\displaystyle (\eta ,\delta ,v_{A})} 484:Slow reconnection: Sweet–Parker model 383:A magnetic reconnection event on the 2695:Magnetic reconnection occurs during 1987:{\displaystyle d{\mathbf {v} }/dt=0} 610:is the out-of-plane electric field, 4546:, Cambridge University Press 2000, 4520:from the original on March 11, 2021 3845:Goldreich, P.; Sridhar, S. (1995). 2731:. Subsequently, spacecraft such as 2690: 2140:{\displaystyle \eta _{\text{anom}}} 13: 4576:Cluster spacecraft science results 4556:contents and sample chapter online 4536: 4401: 4373:10.1088/0031-8949/2010/t142/014032 3311: 3086:"A Theory of Chromospheric Flares" 2835:caused by the internal kink mode. 696: 228: 218: 184: 14: 4629: 4581: 4053:Nonlinear Processes in Geophysics 2922: 2867: 2753:Magnetospheric Multiscale Mission 2737:Magnetospheric Multiscale Mission 1710:Fast reconnection: Petschek model 1566:the two different expressions of 1403:from the conservation of mass as 4444:Ebrahimi, Fatima (20 May 2015). 4402:Ji, H.; et al. (May 1999). 3148:Giovanelli, R. G. (1947-11-01). 2233:{\displaystyle v_{A}^{2}(mc/eB)} 2019: 2003: 1962: 1911: 1900: 1870: 853: 835: 703: 672: 264: 222: 202: 191: 4502: 4437: 4395: 4343: 4300: 4282: 4225: 4207: 4132: 4121: 4109:. AZonano.com. January 24, 2013 4099: 4040: 3987: 3926: 3877: 3838: 3787: 3731: 3712: 3703: 3664: 3617: 3574: 3548:Journal of Geophysical Research 3539: 3530: 3495: 3444: 3395: 3361:Journal of Geophysical Research 3352: 3286: 3261: 3243:Journal of Geophysical Research 3237:Parker, E. N. (December 1957). 3230: 3084:Giovanelli, R. G. (July 1946). 2929:Boozer, Allen H. (2020-05-18). 2685: 4480:10.1103/PhysRevLett.114.205003 4329:10.1103/PhysRevLett.103.105002 4232:Vassilis Angelopoulos (2008). 3221: 3182: 3141: 3124: 3077: 3038: 2979: 2705:High Resolution Coronal Imager 2662:is the ion plasma frequency), 2562:{\displaystyle c/\omega _{pi}} 2227: 2207: 1390: 1378: 1358: 1333: 1086:{\displaystyle v_{\text{out}}} 473:quasi-separatrix layers (QSLs) 436:In an electrically conductive 1: 3295:Introduction to Space Physics 3270:Introduction to Space Physics 2860: 2767:Laboratory plasma experiments 2741:Interplanetary Magnetic Field 2729:Interplanetary magnetic field 820:{\displaystyle \sim 2\delta } 657:{\displaystyle B_{\text{in}}} 630:{\displaystyle v_{\text{in}}} 366: 3189:Dungey, J. W. (1961-01-15). 343:A current problem in plasma 271:{\displaystyle \mathbf {J} } 7: 4542:Eric Priest, Terry Forbes, 3965:10.1103/PhysRevE.100.043205 3816:10.1103/PhysRevE.100.013201 3697:10.1103/PhysRevLett.80.3256 3023:10.3847/2041-8205/821/2/L29 2838: 1396:{\displaystyle (\delta ,L)} 10: 4634: 4026:10.1088/0004-637X/700/1/63 3504:Astronomy and Astrophysics 3345:10.5194/angeo-24-3059-2006 2773:Large Plasma Device (LAPD) 1802: 353:fast magnetic reconnection 96:within close proximity of 3996:The Astrophysical Journal 3890:The Astrophysical Journal 3851:The Astrophysical Journal 3743:The Astrophysical Journal 2992:The Astrophysical Journal 1606:and the Lundquist number 524:{\displaystyle E\times B} 16:Process in plasma physics 3911:10.3847/1538-4357/aac517 3721:Cosmical Magnetic Fields 3414:(A8): SSH 3-1–SSH 3-13. 3207:10.1103/PhysRevLett.6.47 1493:Since the dimensionless 867:inside the layer (using 479:Theoretical descriptions 292:Magnetic Reynolds Number 158:Magnetic Reynolds Number 145:Magnetic Reynolds Number 4450:Physical Review Letters 4309:Physical Review Letters 4259:10.1126/science.1160495 4166:10.1126/science.aaf2939 4084:10.5194/npg-19-297-2012 3725:Oxford University Press 3677:Physical Review Letters 3568:10.1029/JZ062i004p00509 3516:2000A&A...363..779B 3255:10.1029/JZ062i004p00509 3195:Physical Review Letters 3167:10.1093/mnras/107.4.338 2244:Stochastic reconnection 794:{\displaystyle \delta } 392:Physical interpretation 4570:Nasa MMS-SMART mission 3719:Parker, E. G. (1979). 2829: 2828:{\displaystyle q<1} 2701:coronal mass ejections 2656: 2563: 2517: 2490: 2463: 2443: 2381: 2263: 2234: 2176: 2141: 2111: 2048: 2028: 1988: 1944: 1922: 1847: 1827: 1777: 1697: 1620: 1600: 1580: 1558: 1510: 1485: 1397: 1365: 1320: 1296: 1267: 1195: 1173: 1087: 1060: 1038: 985: 963: 861: 821: 795: 773: 711: 658: 631: 604: 575: 525: 454:separator reconnection 388: 301:Magnetic tension force 272: 244: 135:Fundamental principles 44: 25: 4544:Magnetic Reconnection 4516:. February 11, 2021. 2830: 2803:Sawtooth oscillations 2758:On 26 February 2008, 2711:Earth's magnetosphere 2657: 2564: 2518: 2516:{\displaystyle v_{A}} 2491: 2489:{\displaystyle v_{l}} 2464: 2444: 2382: 2264: 2235: 2177: 2142: 2112: 2049: 2029: 1989: 1945: 1923: 1848: 1828: 1778: 1698: 1621: 1601: 1581: 1559: 1511: 1486: 1398: 1366: 1321: 1297: 1295:{\displaystyle v_{A}} 1268: 1196: 1194:{\displaystyle \rho } 1174: 1088: 1061: 1039: 986: 984:{\displaystyle \eta } 964: 862: 822: 796: 774: 717:, gives the relation 712: 659: 632: 605: 603:{\displaystyle E_{y}} 576: 526: 448:Types of reconnection 382: 273: 245: 86:particle acceleration 68:particle acceleration 48:Magnetic reconnection 38: 22: 4588:Magnetism on the Sun 3429:10.1029/2001ja000278 2813: 2573: 2535: 2500: 2473: 2453: 2393: 2275: 2253: 2189: 2151: 2124: 2060: 2038: 1998: 1954: 1943:{\displaystyle \nu } 1934: 1859: 1837: 1833:and electric charge 1817: 1811:magnetic diffusivity 1719: 1629: 1610: 1590: 1570: 1520: 1500: 1407: 1375: 1330: 1310: 1279: 1205: 1185: 1102: 1070: 1050: 999: 993:magnetic diffusivity 975: 875: 831: 805: 785: 721: 668: 641: 614: 587: 535: 509: 433:of the fusion fuel. 431:magnetic confinement 398:magnetic field lines 260: 181: 4472:2015PhRvL.114t5003E 4423:1999PhPl....6.1743J 4365:2010PhST..142a4032G 4321:2009PhRvL.103j5002L 4250:2008Sci...321..931A 4157:2016Sci...352.2939B 4075:2012NPGeo..19..297K 4018:2009ApJ...700...63K 3957:2019PhRvE.100d3205J 3902:2018ApJ...860...52J 3863:1995ApJ...438..763G 3808:2019PhRvE.100a3201J 3765:1999ApJ...517..700L 3689:1998PhRvL..80.3256J 3642:1999PhPl....6.1743J 3595:1986PhFl...29.1520B 3560:1957JGR....62..509P 3465:1996SoPh..168..115M 3420:2002JGRA..107.1164T 3373:1995JGR...10023443P 3336:2006AnGeo..24.3059L 3324:Annales Geophysicae 3014:2016ApJ...821L..29Z 2957:2020PhPl...27j2305B 2892:2001Natur.412..414O 2855:Magnetic switchback 2423: 2206: 2101: 1162: 1121: 174:Maxwell's equations 4411:Physics of Plasmas 3630:Physics of Plasmas 3473:10.1007/bf00145829 2935:Physics of Plasmas 2825: 2652: 2559: 2513: 2486: 2459: 2439: 2409: 2377: 2259: 2230: 2192: 2172: 2137: 2107: 2084: 2044: 2024: 1984: 1940: 1918: 1843: 1823: 1773: 1693: 1616: 1596: 1576: 1554: 1506: 1481: 1393: 1361: 1316: 1292: 1263: 1191: 1169: 1148: 1107: 1083: 1056: 1034: 981: 959: 857: 817: 791: 769: 707: 654: 627: 600: 571: 521: 502:Sweet–Parker model 389: 332:magnetic monopoles 328:Maxwell's equation 324:magnetic monopoles 296:induction equation 268: 240: 162:induction equation 149:induction equation 45: 26: 4613:Stellar phenomena 4244:(5891): 931–935. 4151:(6290): aaf2939. 3935:Physical Review E 3796:Physical Review E 3683:(15): 3256–3259. 3583:Physics of Fluids 3381:10.1029/95ja02740 3330:(11): 3059–2069. 3063:10.1063/1.3455250 2965:10.1063/5.0014107 2886:(6845): 414–417. 2789:spherical tokamak 2650: 2649: 2462:{\displaystyle l} 2403: 2366: 2352: 2333: 2319: 2291: 2262:{\displaystyle L} 2161: 2134: 2102: 2047:{\displaystyle n} 1897: 1884: 1846:{\displaystyle e} 1826:{\displaystyle m} 1768: 1744: 1731: 1688: 1685: 1663: 1662: 1637: 1619:{\displaystyle S} 1599:{\displaystyle R} 1579:{\displaystyle R} 1549: 1509:{\displaystyle S} 1476: 1463: 1438: 1435: 1425: 1319:{\displaystyle R} 1248: 1247: 1230: 1215: 1167: 1155: 1137: 1114: 1080: 1059:{\displaystyle L} 1025: 1009: 954: 941: 913: 910: 885: 850: 764: 746: 694: 651: 624: 568: 558: 380: 235: 56:magnetic topology 36: 4625: 4608:Plasma phenomena 4530: 4529: 4527: 4525: 4506: 4500: 4499: 4465: 4441: 4435: 4434: 4431:10.1063/1.873432 4417:(5): 1743–1750. 4408: 4399: 4393: 4392: 4347: 4341: 4340: 4304: 4298: 4297: 4286: 4280: 4279: 4261: 4229: 4223: 4222: 4211: 4205: 4204: 4178: 4168: 4136: 4130: 4125: 4119: 4118: 4116: 4114: 4103: 4097: 4096: 4086: 4068: 4044: 4038: 4037: 4011: 3991: 3985: 3984: 3950: 3930: 3924: 3923: 3913: 3881: 3875: 3874: 3842: 3836: 3835: 3791: 3785: 3784: 3758: 3756:astro-ph/9811037 3735: 3729: 3728: 3716: 3710: 3707: 3701: 3700: 3668: 3662: 3661: 3650:10.1063/1.873432 3636:(5): 1743–1750. 3621: 3615: 3614: 3603:10.1063/1.865670 3589:(5): 1520–1531. 3578: 3572: 3571: 3543: 3537: 3534: 3528: 3527: 3499: 3493: 3492: 3448: 3442: 3441: 3431: 3399: 3393: 3392: 3356: 3350: 3349: 3347: 3315: 3309: 3308: 3290: 3284: 3283: 3265: 3259: 3258: 3234: 3228: 3225: 3219: 3218: 3186: 3180: 3179: 3169: 3145: 3139: 3128: 3122: 3121: 3102:10.1038/158081a0 3081: 3075: 3074: 3042: 3036: 3035: 3025: 3007: 2983: 2977: 2976: 2950: 2926: 2920: 2919: 2900:10.1038/35086520 2871: 2834: 2832: 2831: 2826: 2719:(in the dayside 2691:Solar atmosphere 2661: 2659: 2658: 2653: 2651: 2648: 2647: 2646: 2637: 2636: 2626: 2625: 2624: 2615: 2614: 2605: 2604: 2594: 2593: 2588: 2587: 2568: 2566: 2565: 2560: 2558: 2557: 2545: 2522: 2520: 2519: 2514: 2512: 2511: 2495: 2493: 2492: 2487: 2485: 2484: 2468: 2466: 2465: 2460: 2448: 2446: 2445: 2440: 2438: 2437: 2428: 2422: 2417: 2405: 2404: 2401: 2386: 2384: 2383: 2378: 2373: 2369: 2368: 2367: 2359: 2357: 2353: 2345: 2335: 2334: 2326: 2324: 2320: 2312: 2293: 2292: 2289: 2268: 2266: 2265: 2260: 2239: 2237: 2236: 2231: 2220: 2205: 2200: 2181: 2179: 2178: 2173: 2168: 2163: 2162: 2159: 2146: 2144: 2143: 2138: 2136: 2135: 2132: 2116: 2114: 2113: 2108: 2103: 2100: 2095: 2083: 2082: 2073: 2053: 2051: 2050: 2045: 2033: 2031: 2030: 2025: 2023: 2022: 2007: 2006: 1993: 1991: 1990: 1985: 1971: 1966: 1965: 1949: 1947: 1946: 1941: 1927: 1925: 1924: 1919: 1914: 1903: 1898: 1890: 1885: 1883: 1875: 1874: 1873: 1863: 1852: 1850: 1849: 1844: 1832: 1830: 1829: 1824: 1782: 1780: 1779: 1774: 1769: 1767: 1750: 1745: 1743: 1742: 1733: 1732: 1729: 1723: 1702: 1700: 1699: 1694: 1689: 1687: 1686: 1678: 1669: 1664: 1661: 1657: 1656: 1643: 1642: 1635: 1625: 1623: 1622: 1617: 1605: 1603: 1602: 1597: 1585: 1583: 1582: 1577: 1563: 1561: 1560: 1555: 1550: 1545: 1544: 1543: 1530: 1515: 1513: 1512: 1507: 1495:Lundquist number 1490: 1488: 1487: 1482: 1477: 1469: 1464: 1462: 1458: 1457: 1444: 1439: 1437: 1436: 1433: 1427: 1426: 1423: 1417: 1402: 1400: 1399: 1394: 1370: 1368: 1367: 1362: 1357: 1356: 1325: 1323: 1322: 1317: 1301: 1299: 1298: 1293: 1291: 1290: 1272: 1270: 1269: 1264: 1262: 1261: 1249: 1243: 1242: 1233: 1232: 1231: 1228: 1222: 1217: 1216: 1213: 1200: 1198: 1197: 1192: 1178: 1176: 1175: 1170: 1168: 1163: 1161: 1156: 1153: 1143: 1138: 1136: 1135: 1134: 1120: 1115: 1112: 1106: 1096:dynamic pressure 1092: 1090: 1089: 1084: 1082: 1081: 1078: 1065: 1063: 1062: 1057: 1043: 1041: 1040: 1035: 1027: 1026: 1023: 1011: 1010: 1007: 990: 988: 987: 982: 968: 966: 965: 960: 955: 947: 942: 940: 933: 932: 919: 914: 912: 911: 908: 902: 901: 892: 887: 886: 883: 871:), we find that 866: 864: 863: 858: 856: 851: 843: 838: 826: 824: 823: 818: 800: 798: 797: 792: 778: 776: 775: 770: 765: 763: 759: 758: 748: 747: 744: 738: 733: 732: 716: 714: 713: 708: 706: 695: 693: 692: 680: 675: 663: 661: 660: 655: 653: 652: 649: 636: 634: 633: 628: 626: 625: 622: 609: 607: 606: 601: 599: 598: 580: 578: 577: 572: 570: 569: 566: 560: 559: 556: 547: 546: 530: 528: 527: 522: 403:Alfvén's theorem 381: 349:Lundquist number 281:Alfvén's theorem 277: 275: 274: 269: 267: 249: 247: 246: 241: 236: 234: 226: 225: 216: 205: 194: 166:Alfvén's theorem 141:Alfvén's theorem 37: 4633: 4632: 4628: 4627: 4626: 4624: 4623: 4622: 4618:Solar phenomena 4598: 4597: 4584: 4565:6 February 2008 4539: 4537:Further reading 4534: 4533: 4523: 4521: 4508: 4507: 4503: 4442: 4438: 4406: 4400: 4396: 4353:Physica Scripta 4348: 4344: 4305: 4301: 4296:. 24 July 2008. 4288: 4287: 4283: 4230: 4226: 4213: 4212: 4208: 4137: 4133: 4126: 4122: 4112: 4110: 4105: 4104: 4100: 4045: 4041: 3992: 3988: 3931: 3927: 3882: 3878: 3843: 3839: 3792: 3788: 3736: 3732: 3717: 3713: 3708: 3704: 3669: 3665: 3622: 3618: 3579: 3575: 3544: 3540: 3535: 3531: 3500: 3496: 3449: 3445: 3400: 3396: 3357: 3353: 3316: 3312: 3305: 3291: 3287: 3280: 3266: 3262: 3235: 3231: 3226: 3222: 3187: 3183: 3146: 3142: 3129: 3125: 3096:(4003): 81–82. 3082: 3078: 3043: 3039: 2984: 2980: 2927: 2923: 2872: 2868: 2863: 2841: 2814: 2811: 2810: 2797:plasma thruster 2793:Fatima Ebrahimi 2769: 2713: 2693: 2688: 2642: 2638: 2632: 2628: 2627: 2620: 2616: 2610: 2606: 2600: 2596: 2595: 2592: 2580: 2576: 2574: 2571: 2570: 2550: 2546: 2541: 2536: 2533: 2532: 2529: 2507: 2503: 2501: 2498: 2497: 2480: 2476: 2474: 2471: 2470: 2454: 2451: 2450: 2433: 2429: 2424: 2418: 2413: 2400: 2396: 2394: 2391: 2390: 2358: 2344: 2340: 2339: 2325: 2311: 2307: 2306: 2305: 2301: 2288: 2284: 2276: 2273: 2272: 2254: 2251: 2250: 2246: 2216: 2201: 2196: 2190: 2187: 2186: 2164: 2158: 2154: 2152: 2149: 2148: 2131: 2127: 2125: 2122: 2121: 2096: 2088: 2078: 2074: 2072: 2061: 2058: 2057: 2039: 2036: 2035: 2018: 2017: 2002: 2001: 1999: 1996: 1995: 1967: 1961: 1960: 1955: 1952: 1951: 1935: 1932: 1931: 1910: 1899: 1889: 1876: 1869: 1868: 1864: 1862: 1860: 1857: 1856: 1838: 1835: 1834: 1818: 1815: 1814: 1807: 1801: 1754: 1749: 1738: 1734: 1728: 1724: 1722: 1720: 1717: 1716: 1712: 1677: 1673: 1668: 1652: 1648: 1647: 1641: 1630: 1627: 1626: 1611: 1608: 1607: 1591: 1588: 1587: 1571: 1568: 1567: 1539: 1535: 1531: 1529: 1521: 1518: 1517: 1501: 1498: 1497: 1468: 1453: 1449: 1448: 1443: 1432: 1428: 1422: 1418: 1416: 1408: 1405: 1404: 1376: 1373: 1372: 1352: 1348: 1331: 1328: 1327: 1311: 1308: 1307: 1304:Alfvén velocity 1286: 1282: 1280: 1277: 1276: 1257: 1253: 1238: 1234: 1227: 1223: 1221: 1212: 1208: 1206: 1203: 1202: 1186: 1183: 1182: 1157: 1152: 1144: 1142: 1130: 1126: 1122: 1116: 1111: 1105: 1103: 1100: 1099: 1077: 1073: 1071: 1068: 1067: 1051: 1048: 1047: 1022: 1018: 1006: 1002: 1000: 997: 996: 976: 973: 972: 946: 928: 924: 923: 918: 907: 903: 897: 893: 891: 882: 878: 876: 873: 872: 852: 842: 834: 832: 829: 828: 806: 803: 802: 786: 783: 782: 754: 750: 749: 743: 739: 737: 728: 724: 722: 719: 718: 702: 688: 684: 679: 671: 669: 666: 665: 648: 644: 642: 639: 638: 621: 617: 615: 612: 611: 594: 590: 588: 585: 584: 565: 561: 555: 551: 542: 538: 536: 533: 532: 510: 507: 506: 486: 481: 450: 394: 371: 369: 263: 261: 258: 257: 227: 221: 217: 215: 201: 190: 182: 179: 178: 137: 94:electric fields 54:, in which the 28: 17: 12: 11: 5: 4631: 4621: 4620: 4615: 4610: 4596: 4595: 4590: 4583: 4582:External links 4580: 4579: 4578: 4573: 4567: 4558: 4538: 4535: 4532: 4531: 4501: 4456:(20): 205003. 4436: 4394: 4342: 4315:(10): 105002. 4299: 4281: 4224: 4221:. 7 June 2013. 4206: 4131: 4120: 4098: 4059:(2): 297–314. 4039: 3986: 3925: 3876: 3871:10.1086/175121 3837: 3786: 3773:10.1086/307233 3749:(2): 700–718. 3739:Lazarian, Alex 3730: 3711: 3702: 3663: 3616: 3573: 3554:(4): 509–520. 3538: 3529: 3494: 3459:(1): 115–133. 3443: 3394: 3367:(A12): 23443. 3351: 3310: 3303: 3285: 3278: 3260: 3249:(4): 509–520. 3229: 3220: 3181: 3160:(4): 338–355. 3140: 3138:(4): 338–355. 3123: 3076: 3037: 2978: 2941:(10): 102305. 2921: 2865: 2864: 2862: 2859: 2858: 2857: 2852: 2847: 2840: 2837: 2824: 2821: 2818: 2768: 2765: 2712: 2709: 2692: 2689: 2687: 2684: 2676:Whistler waves 2645: 2641: 2635: 2631: 2623: 2619: 2613: 2609: 2603: 2599: 2591: 2586: 2583: 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Oxford: 3005:1603.07062 2998:(2): L29. 2948:2005.02285 2861:References 2791:, led Dr. 2745:ionosphere 2733:Cluster II 1803:See also: 459:separatrix 367:Properties 361:turbulence 108:solar wind 4381:0031-8949 4294:Space.com 4276:206514133 4201:206647580 4185:0036-8075 4066:1203.2971 4009:0903.2052 3981:201070540 3920:126072383 3896:(2): 52. 3832:199120046 3781:119349364 3658:1070-664X 3611:0031-9171 3524:0004-6361 3489:120072450 3481:0038-0938 3438:0148-0227 3389:0148-0227 3215:0031-9007 3176:0035-8711 3110:0028-0836 3071:0031-9228 3032:119188103 2973:218502561 2777:flux rope 2749:substorms 2672:electrons 2630:ϵ 2590:≡ 2578:ω 2548:ω 2299:⁡ 2170:η 2156:η 2129:η 2086:ω 2070:ν 2064:η 1938:ν 1908:ν 1905:− 1762:⁡ 1752:π 1747:≈ 1645:η 1639:∼ 1547:η 1527:≡ 1471:δ 1466:∼ 1460:δ 1446:η 1441:∼ 1382:δ 1343:δ 1337:η 1251:≡ 1245:ρ 1236:μ 1219:∼ 1189:ρ 1146:ρ 1140:∼ 1128:μ 1029:δ 1016:∼ 979:η 952:δ 949:η 938:δ 935:σ 926:μ 916:∼ 869:Ohm's law 848:σ 815:δ 809:∼ 789:δ 761:δ 752:μ 735:∼ 700:× 697:∇ 686:μ 516:× 465:separator 229:∂ 219:∂ 213:ϵ 210:μ 199:μ 188:× 185:∇ 4524:April 7, 4518:Archived 4496:24545773 4488:26047235 4389:29910900 4337:19792321 4268:18653845 4193:27174677 4093:53390559 3973:31770890 3824:31499931 2908:11473310 2839:See also 2782:helicity 2735:and the 2034:, where 461:surfaces 337:Dungey's 98:sunspots 4468:Bibcode 4419:Bibcode 4361:Bibcode 4317:Bibcode 4246:Bibcode 4238:Science 4153:Bibcode 4145:Science 4071:Bibcode 4034:4671422 4014:Bibcode 3953:Bibcode 3898:Bibcode 3859:Bibcode 3857:: 763. 3804:Bibcode 3761:Bibcode 3685:Bibcode 3638:Bibcode 3591:Bibcode 3556:Bibcode 3512:Bibcode 3510:: 779. 3461:Bibcode 3416:Bibcode 3369:Bibcode 3332:Bibcode 3118:4139384 3010:Bibcode 2953:Bibcode 2916:4412119 2888:Bibcode 2807:tokamak 2569:(where 2449:. 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