Magnetic reconnection - Knowledge (XXG)

474:: 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 2714:, 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 451:, 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 1717:

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.

2750:. 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 2260:

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

35:

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.

2259:

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

322:

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

1801:

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

1725:

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

162:

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

129:

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

1716:

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,

1805:

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

350:

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

507:

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

383: 141:

34:

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

179:

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

88:

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

2773:

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

309:

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

370:, 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 1806:

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.

481:

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

2790:

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

1726:

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

978: 515:

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

351:

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.

2766:, 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. 1500: 478:, 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). 259: 111:. 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. 411:

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

1802:

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.

2130:

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,

31: 1188: 1282: 318:. 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 289:

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

2671: 1712: 40: 1937: 1796:

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

1792: 390: 388: 386: 385: 726: 389: 2774:

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.".

1104:

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

885: 788: 4361:

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".

267:(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 345:

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

2396: 876: 3720:

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

1417: 191: 2126: 1053: 387: 1573: 590: 2458: 2043: 333:

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

2191: 2738:) 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 1112: 1380: 2003: 1215: 2156: 301:

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

2249: 45: 44: 41: 2578: 1102: 2758:

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

836: 673: 646: 46: 2681:

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

1639: 287: 175:

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

1869: 1412: 3547:

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

3238:

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

2820:

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

540: 310:

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

180:

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".

3462:

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".

810: 4528: 2844: 2532: 2505: 1311: 1210: 1000: 619: 1959: 1729: 374:

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.

416:(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 384: 2478: 2278: 2063: 1862: 1842: 1635: 1615: 1595: 1525: 1335: 1075: 3513:

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

2583: 327:) 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. 43: 731: 2689:. 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 117:

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

2285: 4150:

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).

4005:

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

678: 2070: 1009: 3057: 4583:, The Magnetospheric Multiscale (MMS) mission, Solving Magnetospheric Acceleration, Reconnection, and Turbulence. Due for launch in 2014. 3370:

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

2677:

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

2796: 2693:, reconnection may proceed more quickly. Two-fluid/collisionless reconnection is particularly important in the Earth's magnetosphere. 1530: 545: 154:" (also called the "frozen-in flux theorem") which applies to large-scale regions of a highly-conducting magnetoplasma, for which the 424:, releasing, in minutes, energy that has been stored in the magnetic field over a period of hours to days. Magnetic reconnection in 4562: 3313: 3288: 2763: 2747: 341:

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

841: 42: 4318:

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

2196:

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

973:{\displaystyle v_{\text{in}}={\frac {E_{y}}{B_{\text{in}}}}\sim {\frac {1}{\mu _{0}\sigma \delta }}={\frac {\eta }{\delta }},} 2715: 675:

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

3304:

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

4520: 2751: 2739: 2686: 103:. Giovanelli proposed in 1946 that solar flares stem from the energy obtained by charged particles influenced by induced 467:, in which four separate magnetic domains exchange magnetic field lines. Domains in a magnetic plasma are separated by 2403: 2008: 1495:{\displaystyle R={\frac {v_{\text{in}}}{v_{\text{out}}}}\sim {\frac {\eta }{v_{A}\delta }}\sim {\frac {\delta }{L}}.} 254:{\displaystyle \nabla \times \mathbf {B} =\mu \mathbf {J} +\mu \epsilon {\frac {\partial \mathbf {E} }{\partial t}}.} 2762:

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

4623: 4414: 2942:"Flattening of the tokamak current profile by a fast magnetic reconnection with implications for the solar corona" 4618: 4457:"Plasmoids Formation During Simulations of Coaxial Helicity Injection in the National Spherical Torus Experiment" 2251:, however, its effect, similar to the anomalous resistivity, is still too small compared with the observations. 4628: 4571: 2807: 2161: 302: 168: 155: 1006:. When the inflow density is comparable to the outflow density, conservation of mass yields the relationship 3141:

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

2782:

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

812:

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

3735: 1597:

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

1340: 4300: 1964: 311: 184: 3635:

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

2134: 413: 291: 176: 151: 3279:

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

2786:

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

2711: 96: 78: 338: 4586: 4138: 2199: 4478: 4429: 4371: 4327: 4256: 4225: 4163: 4081: 4024: 3963: 3908: 3869: 3814: 3771: 3695: 3648: 3601: 3566: 3557:

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

3522: 3471: 3426: 3379: 3342: 3020: 2963: 2898: 2690: 1821: 1003: 441: 408: 95:

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

4566: 2545: 1080: 2865: 2783: 1815: 815: 651: 624: 2810:

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

270: 4502: 4468: 4395: 4282: 4207: 4099: 4071: 4040: 4014: 3987: 3953: 3926: 3838: 3805:

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

3787: 3761: 3749: 3495: 3124: 3038: 3010: 2979: 2953: 2922: 1385: 433: 342: 306: 172: 159: 4598: 4415:"Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas" 3637:"Magnetic reconnection with Sweet-Parker characteristics in two-dimensional laboratory plasmas" 1183:{\displaystyle {\frac {B_{\text{in}}^{2}}{2\mu _{0}}}\sim {\frac {\rho v_{\text{out}}^{2}}{2}}} 838:. By matching the ideal electric field outside of the layer with the resistive electric field 519: 4558: 4494: 4387: 4343: 4274: 4199: 4191: 3979: 3830: 3664: 3617: 3530: 3487: 3444: 3395: 3309: 3284: 3221: 3182: 3116: 3077: 2914: 2799: 2792: 469: 334: 85:

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

66: 4383: 1277:{\displaystyle v_{\text{out}}\sim {\frac {B_{\text{in}}}{\sqrt {\mu _{0}\rho }}}\equiv v_{A}} 795: 133:

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

4486: 4437: 4379: 4335: 4264: 4181: 4171: 4089: 4032: 3971: 3916: 3877: 3822: 3779: 3703: 3656: 3609: 3574: 3526: 3479: 3434: 3387: 3350: 3261: 3213: 3172: 3108: 3069: 3028: 2971: 2906: 2823: 2813: 1505: 1106: 500: 448: 359: 264: 134: 62: 3683: 3636: 2510: 2483: 1289: 1195: 985: 597: 2803: 2743: 2534:

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

1944: 1824:

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

455:

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

1798: 324: 4482: 4433: 4375: 4331: 4260: 4167: 4085: 4028: 3967: 3912: 3873: 3818: 3775: 3699: 3652: 3605: 3570: 3475: 3430: 3383: 3346: 3024: 2967: 2902: 2666:{\displaystyle \omega _{pi}\equiv {\sqrt {\frac {n_{i}Z^{2}e^{2}}{\epsilon _{0}m_{i}}}}} 2463: 2263: 2048: 1847: 1827: 1620: 1600: 1580: 1510: 1320: 1314: 1060: 437: 104: 92: 82: 74: 70: 3033: 2998: 2941: 2754:). These include 'reverse reconnection' that causes sunward convection in the Earth's 4612: 4286: 4211: 4118:"High-Resolution Coronal Imager Photographs the Sun in UV Light at 19.3nm Wavelength" 4036: 3991: 3930: 3842: 3791: 3499: 3042: 2983: 2855: 2727: 1707:{\displaystyle R~\sim {\sqrt {\frac {\eta }{v_{A}L}}}={\frac {1}{S^{\frac {1}{2}}}}.} 504: 429: 319: 315: 298: 164: 138: 122: 4506: 4399: 4103: 3201: 1932:{\displaystyle {d{\mathbf {v} } \over dt}={e \over m}\mathbf {E} -\nu \mathbf {v} ,} 4490: 4339: 4044: 3128: 2926: 2860: 2731: 2158:, which can enhance the reconnection rate in the Sweet–Parker model by a factor of 452: 417: 347: 330: 294:

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

126: 114: 3161:"Magnetic and Electric Phenomena in the Sun's Atmosphere associated with Sunspots" 879: 323:

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

4456: 4117: 3975: 3826: 3707: 2735: 2707: 2678: 1212:

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

367: 358:

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

150:

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

100: 51: 3921: 3896: 3355: 3330: 3249: 89:

connect formerly disconnected magnetic fields, depending on the circumstances.

81:. Magnetic reconnection involves plasma flows at a substantial fraction of the 3944:

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

3177: 3160: 2755: 371: 118: 4391: 4195: 3857: 3668: 3621: 3534: 3491: 3448: 3399: 3225: 3217: 3186: 3120: 3081: 1787:{\displaystyle {\frac {v_{\text{in}}}{v_{A}}}\approx {\frac {\pi }{8\ln S}}.} 4269: 4244: 4176: 4151: 4094: 4059: 3578: 3331:"On the characterization of magnetic reconnection in global MHD simulations" 3265: 2887:"In situ detection of collisionless reconnection in the Earth's magnetotail" 2787: 721:{\displaystyle \mathbf {J} ={\frac {1}{\mu _{0}}}\nabla \times \mathbf {B} } 499:

The first theoretical framework of magnetic reconnection was established by

17: 4498: 4347: 4278: 4226:"THEMIS Satellites Discover What Triggers Eruptions of the Northern Lights" 4203: 4186: 3983: 3858:"Toward a theory of interstellar turbulence. 2: Strong Alfvenic turbulence" 3834: 3096: 2918: 2886: 125:. The concept was published for the first time in a seminal paper in 1961. 4572:

Discoveries about magnetic reconnection in space could unlock fusion power

30: 3766: 3439: 3414: 2759: 2682: 2005:, then the above equation along with the definition of electric current, 486:, and have been observed in theoretical configurations and solar flares. 2997:

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

1382:

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

420:, may involve the reconnection of large systems of magnetic flux on the 3895:

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

3752:; Vishniac, Ethan (1999). "Reconnection in a Weakly Stochastic Field". 3483: 2817: 355: 108: 3684:"Experimental Test of the Sweet-Parker Model of Magnetic Reconnection" 3413:

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

3391: 3073: 2975: 183:

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

4441: 3660: 3613: 3112: 2910: 2770: 407:

The qualitative description of the reconnection process is such that

4139:

Articles on measurements made from the Cluster II spacecraft mission

4058:

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

3250:"Sweet's mechanism for merging magnetic fields in conducting fluids" 2507:

are turbulence injection length scale and velocity respectively and

463:

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

305:

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

4473: 3958: 3881: 3783: 3015: 2958: 783:{\displaystyle J_{y}\sim {\frac {B_{\text{in}}}{\mu _{0}\delta }},} 337:

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

314:

acting on the reconfigured field lines and ejecting them along the

4521:"How Dr. Fatima Ebrahimi is Geting Humans a Faster Ticket to Mars" 4076: 4060:"Reconnection studies under different types of turbulence driving" 4019: 3682:

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

2999:"Observation of the Evolution of a Current Sheet in a Solar Flare" 425: 29: 1317:. With the above relations, the dimensionless reconnection rate 3592:

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

3308:. Cambridge U.K.: Cambridge University press. pp. 227–285. 4152:"Electron-scale measurements of magnetic reconnection in space" 3283:. Cambridge U.K.: Cambridge University press. pp. 58–90. 2674: 421: 395: 3058:"Magnetic field reconnection: A first-principles perspective" 2391:{\displaystyle v=v_{\text{turb}}\;\operatorname {min} \left,} 1820:

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

871:{\displaystyle \mathbf {E} ={\frac {1}{\sigma }}\mathbf {J} } 4580: 3897:"Stochastic Reconnection for Large Magnetic Prandtl Numbers" 2795:

injection, used to create the initial plasma current in the

61:

is a physical process occurring in electrically conducting

171:

can become small enough to make the diffusion term in the

2121:{\displaystyle \eta =\nu {c^{2} \over \omega _{pi}^{2}}.} 1816:

Spitzer resistivity § Disagreements with observation

1048:{\displaystyle v_{\text{in}}L\sim v_{\text{out}}\delta ,} 2280:, the upper limit for reconnection velocity is given by 1337:

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

4603: 2726:

Magnetic reconnection events that occur in the Earth's

1961:

is the collision frequency. Since in the steady state,

3056:

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

2542:

On length scales shorter than the ion inertial length

3415:"Theory of magnetic connectivity in the solar corona" 3202:"Interplanetary Magnetic Field and the Auroral Zones" 2826: 2586: 2548: 2513: 2486: 2466: 2406: 2288: 2266: 2202: 2164: 2137: 2073: 2051: 2011: 1967: 1947: 1872: 1850: 1830: 1732: 1642: 1623: 1603: 1583: 1533: 1513: 1420: 1388: 1343: 1323: 1292: 1218: 1198: 1115: 1083: 1063: 1012: 988: 888: 844: 818: 798: 734: 681: 654: 627: 600: 548: 522: 273: 194: 158:

is very large: this makes the convective term in the

508:relations for this model during his return travel. 436:, and it is important to the science of controlled 142:relations for this model during his return travel. 2838: 2665: 2572: 2526: 2499: 2472: 2452: 2390: 2272: 2243: 2185: 2150: 2120: 2057: 2037: 1997: 1953: 1931: 1856: 1836: 1786: 1706: 1629: 1609: 1589: 1567: 1519: 1494: 1406: 1374: 1329: 1305: 1276: 1204: 1182: 1096: 1069: 1047: 994: 972: 870: 830: 804: 782: 720: 667: 640: 613: 584: 534: 281: 253: 69:is rearranged and magnetic energy is converted to 3165:Monthly Notices of the Royal Astronomical Society 3143:Monthly Notices of the Royal Astronomical Society 1568:{\displaystyle S\equiv {\frac {Lv_{A}}{\eta }},} 585:{\displaystyle E_{y}=v_{\text{in}}B_{\text{in}}} 50:The evolution of magnetic reconnection during a 2453:{\displaystyle v_{\text{turb}}=v_{l}^{2}/v_{A}} 2038:{\displaystyle {\mathbf {J} }=en{\mathbf {v} }} 3419:Journal of Geophysical Research: Space Physics 3329:Laitinen, T. V.; et al. (November 2006). 4245:"Tail Reconnection Triggering Substorm Onset" 432:is one of the mechanisms responsible for the 167:) which are regions of small width where the 8: 2816:are periodic mixing events occurring in the 2685:are then accelerated to very high speeds by 1077:is the half-length of the current sheet and 297:The resistivity of the current layer allows 2538:Non-MHD process: Collisionless reconnection 648:is the characteristic inflow velocity, and 2305: 4472: 4268: 4185: 4175: 4093: 4075: 4018: 3957: 3920: 3765: 3438: 3354: 3176: 3032: 3014: 2957: 2825: 2653: 2643: 2631: 2621: 2611: 2603: 2591: 2585: 2561: 2552: 2547: 2518: 2512: 2491: 2485: 2465: 2444: 2435: 2429: 2424: 2411: 2405: 2369: 2355: 2336: 2322: 2299: 2287: 2265: 2227: 2212: 2207: 2201: 2186:{\displaystyle \eta _{\text{anom}}/\eta } 2175: 2169: 2163: 2142: 2136: 2107: 2099: 2089: 2083: 2072: 2050: 2029: 2028: 2013: 2012: 2010: 1978: 1972: 1971: 1966: 1946: 1921: 1910: 1900: 1880: 1879: 1873: 1871: 1849: 1829: 1760: 1749: 1739: 1733: 1731: 1688: 1679: 1663: 1652: 1641: 1622: 1602: 1582: 1550: 1540: 1532: 1512: 1479: 1464: 1454: 1443: 1433: 1427: 1419: 1387: 1363: 1342: 1322: 1297: 1291: 1268: 1249: 1238: 1232: 1223: 1217: 1197: 1168: 1163: 1153: 1141: 1127: 1122: 1116: 1114: 1088: 1082: 1062: 1033: 1017: 1011: 987: 957: 939: 929: 918: 908: 902: 893: 887: 863: 853: 845: 843: 817: 797: 765: 754: 748: 739: 733: 713: 699: 690: 682: 680: 659: 653: 632: 626: 605: 599: 576: 566: 553: 547: 521: 274: 272: 232: 226: 212: 201: 193: 2885:Øieroset, M.; et al. (2001-07-26). 1810:Anomalous resistivity and Bohm diffusion 381: 38: 2877: 2065:is the electron number density, yields 440:because it is one mechanism preventing 4604:Magnetic Reconnection Experiment (MRX) 4301:"Secret of Colorful Auroras Revealed" 1375:{\displaystyle (\eta ,\delta ,v_{A})} 495:Slow reconnection: Sweet–Parker model 394:A magnetic reconnection event on the 7: 2706:Magnetic reconnection occurs during 1998:{\displaystyle d{\mathbf {v} }/dt=0} 621:is the out-of-plane electric field, 4557:, Cambridge University Press 2000, 4531:from the original on March 11, 2021 3856:Goldreich, P.; Sridhar, S. (1995). 2742:. Subsequently, spacecraft such as 2151:{\displaystyle \eta _{\text{anom}}} 4587:Cluster spacecraft science results 4567:contents and sample chapter online 4384:10.1088/0031-8949/2010/t142/014032 3097:"A Theory of Chromospheric Flares" 2846:caused by the internal kink mode. 707: 239: 229: 195: 25: 4064:Nonlinear Processes in Geophysics 2764:Magnetospheric Multiscale Mission 2748:Magnetospheric Multiscale Mission 1721:Fast reconnection: Petschek model 1577:the two different expressions of 1414:from the conservation of mass as 4455:Ebrahimi, Fatima (20 May 2015). 4413:Ji, H.; et al. (May 1999). 3159:Giovanelli, R. G. (1947-11-01). 2244:{\displaystyle v_{A}^{2}(mc/eB)} 2030: 2014: 1973: 1922: 1911: 1881: 864: 846: 714: 683: 275: 233: 213: 202: 4120:. AZonano.com. January 24, 2013 3559:Journal of Geophysical Research 3372:Journal of Geophysical Research 3254:Journal of Geophysical Research 3248:Parker, E. N. (December 1957). 3095:Giovanelli, R. G. (July 1946). 2940:Boozer, Allen H. (2020-05-18). 4491:10.1103/PhysRevLett.114.205003 4340:10.1103/PhysRevLett.103.105002 4243:Vassilis Angelopoulos (2008). 2716:High Resolution Coronal Imager 2673:is the ion plasma frequency), 2573:{\displaystyle c/\omega _{pi}} 2238: 2218: 1401: 1389: 1369: 1344: 1097:{\displaystyle v_{\text{out}}} 484:quasi-separatrix layers (QSLs) 447:In an electrically conductive 1: 3306:Introduction to Space Physics 3281:Introduction to Space Physics 2778:Laboratory plasma experiments 2752:Interplanetary Magnetic Field 2740:Interplanetary magnetic field 2721: 831:{\displaystyle \sim 2\delta } 668:{\displaystyle B_{\text{in}}} 641:{\displaystyle v_{\text{in}}} 3200:Dungey, J. W. (1961-01-15). 354:A current problem in plasma 282:{\displaystyle \mathbf {J} } 4553:Eric Priest, Terry Forbes, 3976:10.1103/PhysRevE.100.043205 3827:10.1103/PhysRevE.100.013201 3708:10.1103/PhysRevLett.80.3256 3034:10.3847/2041-8205/821/2/L29 1407:{\displaystyle (\delta ,L)} 4645: 4037:10.1088/0004-637X/700/1/63 3515:Astronomy and Astrophysics 3356:10.5194/angeo-24-3059-2006 2784:Large Plasma Device (LAPD) 1813: 364:fast magnetic reconnection 107:within close proximity of 4007:The Astrophysical Journal 3901:The Astrophysical Journal 3862:The Astrophysical Journal 3754:The Astrophysical Journal 3003:The Astrophysical Journal 1617:and the Lundquist number 535:{\displaystyle E\times B} 27:Process in plasma physics 3922:10.3847/1538-4357/aac517 3732:Cosmical Magnetic Fields 3425:(A8): SSH 3-1–SSH 3-13. 3218:10.1103/PhysRevLett.6.47 1504:Since the dimensionless 878:inside the layer (using 490:Theoretical descriptions 303:Magnetic Reynolds Number 169:Magnetic Reynolds Number 156:Magnetic Reynolds Number 4461:Physical Review Letters 4320:Physical Review Letters 4270:10.1126/science.1160495 4177:10.1126/science.aaf2939 4095:10.5194/npg-19-297-2012 3736:Oxford University Press 3688:Physical Review Letters 3579:10.1029/JZ062i004p00509 3527:2000A&A...363..779B 3266:10.1029/JZ062i004p00509 3206:Physical Review Letters 3178:10.1093/mnras/107.4.338 2255:Stochastic reconnection 805:{\displaystyle \delta } 403:Physical interpretation 4581:Nasa MMS-SMART mission 3730:Parker, E. G. (1979). 2840: 2839:{\displaystyle q<1} 2712:coronal mass ejections 2667: 2574: 2528: 2501: 2474: 2454: 2392: 2274: 2245: 2187: 2152: 2122: 2059: 2039: 1999: 1955: 1933: 1858: 1838: 1788: 1708: 1631: 1611: 1591: 1569: 1521: 1496: 1408: 1376: 1331: 1307: 1278: 1206: 1184: 1098: 1071: 1049: 996: 974: 872: 832: 806: 784: 722: 669: 642: 615: 586: 536: 465:separator reconnection 399: 312:Magnetic tension force 283: 255: 146:Fundamental principles 55: 36: 4555:Magnetic Reconnection 4527:. February 11, 2021. 2841: 2814:Sawtooth oscillations 2769:On 26 February 2008, 2722:Earth's magnetosphere 2668: 2575: 2529: 2527:{\displaystyle v_{A}} 2502: 2500:{\displaystyle v_{l}} 2475: 2455: 2393: 2275: 2246: 2188: 2153: 2123: 2060: 2040: 2000: 1956: 1934: 1859: 1839: 1789: 1709: 1632: 1612: 1592: 1570: 1522: 1497: 1409: 1377: 1332: 1308: 1306:{\displaystyle v_{A}} 1279: 1207: 1205:{\displaystyle \rho } 1185: 1099: 1072: 1050: 997: 995:{\displaystyle \eta } 975: 873: 833: 807: 785: 728:, gives the relation 723: 670: 643: 616: 614:{\displaystyle E_{y}} 587: 537: 459:Types of reconnection 393: 284: 256: 97:particle acceleration 79:particle acceleration 59:Magnetic reconnection 49: 33: 4599:Magnetism on the Sun 3440:10.1029/2001ja000278 2824: 2584: 2546: 2511: 2484: 2464: 2404: 2286: 2264: 2200: 2162: 2135: 2071: 2049: 2009: 1965: 1954:{\displaystyle \nu } 1945: 1870: 1848: 1844:and electric charge 1828: 1822:magnetic diffusivity 1730: 1640: 1621: 1601: 1581: 1531: 1511: 1418: 1386: 1341: 1321: 1290: 1216: 1196: 1113: 1081: 1061: 1010: 1004:magnetic diffusivity 986: 886: 842: 816: 796: 732: 679: 652: 625: 598: 546: 520: 444:of the fusion fuel. 442:magnetic confinement 409:magnetic field lines 271: 192: 4483:2015PhRvL.114t5003E 4434:1999PhPl....6.1743J 4376:2010PhST..142a4032G 4332:2009PhRvL.103j5002L 4261:2008Sci...321..931A 4168:2016Sci...352.2939B 4086:2012NPGeo..19..297K 4029:2009ApJ...700...63K 3968:2019PhRvE.100d3205J 3913:2018ApJ...860...52J 3874:1995ApJ...438..763G 3819:2019PhRvE.100a3201J 3776:1999ApJ...517..700L 3700:1998PhRvL..80.3256J 3653:1999PhPl....6.1743J 3606:1986PhFl...29.1520B 3571:1957JGR....62..509P 3476:1996SoPh..168..115M 3431:2002JGRA..107.1164T 3384:1995JGR...10023443P 3347:2006AnGeo..24.3059L 3335:Annales Geophysicae 3025:2016ApJ...821L..29Z 2968:2020PhPl...27j2305B 2903:2001Natur.412..414O 2866:Magnetic switchback 2434: 2217: 2112: 1173: 1132: 185:Maxwell's equations 4422:Physics of Plasmas 3641:Physics of Plasmas 3484:10.1007/bf00145829 2946:Physics of Plasmas 2836: 2663: 2570: 2524: 2497: 2470: 2450: 2420: 2388: 2270: 2241: 2203: 2183: 2148: 2118: 2095: 2055: 2035: 1995: 1951: 1929: 1854: 1834: 1784: 1704: 1627: 1607: 1587: 1565: 1517: 1492: 1404: 1372: 1327: 1303: 1274: 1202: 1180: 1159: 1118: 1094: 1067: 1045: 992: 970: 868: 828: 802: 780: 718: 665: 638: 611: 582: 532: 513:Sweet–Parker model 400: 343:magnetic monopoles 339:Maxwell's equation 335:magnetic monopoles 307:induction equation 279: 251: 173:induction equation 160:induction equation 56: 37: 4624:Stellar phenomena 4255:(5891): 931–935. 4162:(6290): aaf2939. 3946:Physical Review E 3807:Physical Review E 3694:(15): 3256–3259. 3594:Physics of Fluids 3392:10.1029/95ja02740 3341:(11): 3059–2069. 3074:10.1063/1.3455250 2976:10.1063/5.0014107 2897:(6845): 414–417. 2800:spherical tokamak 2661: 2660: 2473:{\displaystyle l} 2414: 2377: 2363: 2344: 2330: 2302: 2273:{\displaystyle L} 2172: 2145: 2113: 2058:{\displaystyle n} 1908: 1895: 1857:{\displaystyle e} 1837:{\displaystyle m} 1779: 1755: 1742: 1699: 1696: 1674: 1673: 1648: 1630:{\displaystyle S} 1610:{\displaystyle R} 1590:{\displaystyle R} 1560: 1520:{\displaystyle S} 1487: 1474: 1449: 1446: 1436: 1330:{\displaystyle R} 1259: 1258: 1241: 1226: 1178: 1166: 1148: 1125: 1091: 1070:{\displaystyle L} 1036: 1020: 965: 952: 924: 921: 896: 861: 775: 757: 705: 662: 635: 579: 569: 391: 246: 67:magnetic topology 47: 16:(Redirected from 4636: 4619:Plasma phenomena 4541: 4540: 4538: 4536: 4517: 4511: 4510: 4476: 4452: 4446: 4445: 4442:10.1063/1.873432 4428:(5): 1743–1750. 4419: 4410: 4404: 4403: 4358: 4352: 4351: 4315: 4309: 4308: 4297: 4291: 4290: 4272: 4240: 4234: 4233: 4222: 4216: 4215: 4189: 4179: 4147: 4141: 4136: 4130: 4129: 4127: 4125: 4114: 4108: 4107: 4097: 4079: 4055: 4049: 4048: 4022: 4002: 3996: 3995: 3961: 3941: 3935: 3934: 3924: 3892: 3886: 3885: 3853: 3847: 3846: 3802: 3796: 3795: 3769: 3767:astro-ph/9811037 3746: 3740: 3739: 3727: 3721: 3718: 3712: 3711: 3679: 3673: 3672: 3661:10.1063/1.873432 3647:(5): 1743–1750. 3632: 3626: 3625: 3614:10.1063/1.865670 3600:(5): 1520–1531. 3589: 3583: 3582: 3554: 3548: 3545: 3539: 3538: 3510: 3504: 3503: 3459: 3453: 3452: 3442: 3410: 3404: 3403: 3367: 3361: 3360: 3358: 3326: 3320: 3319: 3301: 3295: 3294: 3276: 3270: 3269: 3245: 3239: 3236: 3230: 3229: 3197: 3191: 3190: 3180: 3156: 3150: 3139: 3133: 3132: 3113:10.1038/158081a0 3092: 3086: 3085: 3053: 3047: 3046: 3036: 3018: 2994: 2988: 2987: 2961: 2937: 2931: 2930: 2911:10.1038/35086520 2882: 2845: 2843: 2842: 2837: 2730:(in the dayside 2702:Solar atmosphere 2672: 2670: 2669: 2664: 2662: 2659: 2658: 2657: 2648: 2647: 2637: 2636: 2635: 2626: 2625: 2616: 2615: 2605: 2604: 2599: 2598: 2579: 2577: 2576: 2571: 2569: 2568: 2556: 2533: 2531: 2530: 2525: 2523: 2522: 2506: 2504: 2503: 2498: 2496: 2495: 2479: 2477: 2476: 2471: 2459: 2457: 2456: 2451: 2449: 2448: 2439: 2433: 2428: 2416: 2415: 2412: 2397: 2395: 2394: 2389: 2384: 2380: 2379: 2378: 2370: 2368: 2364: 2356: 2346: 2345: 2337: 2335: 2331: 2323: 2304: 2303: 2300: 2279: 2277: 2276: 2271: 2250: 2248: 2247: 2242: 2231: 2216: 2211: 2192: 2190: 2189: 2184: 2179: 2174: 2173: 2170: 2157: 2155: 2154: 2149: 2147: 2146: 2143: 2127: 2125: 2124: 2119: 2114: 2111: 2106: 2094: 2093: 2084: 2064: 2062: 2061: 2056: 2044: 2042: 2041: 2036: 2034: 2033: 2018: 2017: 2004: 2002: 2001: 1996: 1982: 1977: 1976: 1960: 1958: 1957: 1952: 1938: 1936: 1935: 1930: 1925: 1914: 1909: 1901: 1896: 1894: 1886: 1885: 1884: 1874: 1863: 1861: 1860: 1855: 1843: 1841: 1840: 1835: 1793: 1791: 1790: 1785: 1780: 1778: 1761: 1756: 1754: 1753: 1744: 1743: 1740: 1734: 1713: 1711: 1710: 1705: 1700: 1698: 1697: 1689: 1680: 1675: 1672: 1668: 1667: 1654: 1653: 1646: 1636: 1634: 1633: 1628: 1616: 1614: 1613: 1608: 1596: 1594: 1593: 1588: 1574: 1572: 1571: 1566: 1561: 1556: 1555: 1554: 1541: 1526: 1524: 1523: 1518: 1506:Lundquist number 1501: 1499: 1498: 1493: 1488: 1480: 1475: 1473: 1469: 1468: 1455: 1450: 1448: 1447: 1444: 1438: 1437: 1434: 1428: 1413: 1411: 1410: 1405: 1381: 1379: 1378: 1373: 1368: 1367: 1336: 1334: 1333: 1328: 1312: 1310: 1309: 1304: 1302: 1301: 1283: 1281: 1280: 1275: 1273: 1272: 1260: 1254: 1253: 1244: 1243: 1242: 1239: 1233: 1228: 1227: 1224: 1211: 1209: 1208: 1203: 1189: 1187: 1186: 1181: 1179: 1174: 1172: 1167: 1164: 1154: 1149: 1147: 1146: 1145: 1131: 1126: 1123: 1117: 1107:dynamic pressure 1103: 1101: 1100: 1095: 1093: 1092: 1089: 1076: 1074: 1073: 1068: 1054: 1052: 1051: 1046: 1038: 1037: 1034: 1022: 1021: 1018: 1001: 999: 998: 993: 979: 977: 976: 971: 966: 958: 953: 951: 944: 943: 930: 925: 923: 922: 919: 913: 912: 903: 898: 897: 894: 882:), we find that 877: 875: 874: 869: 867: 862: 854: 849: 837: 835: 834: 829: 811: 809: 808: 803: 789: 787: 786: 781: 776: 774: 770: 769: 759: 758: 755: 749: 744: 743: 727: 725: 724: 719: 717: 706: 704: 703: 691: 686: 674: 672: 671: 666: 664: 663: 660: 647: 645: 644: 639: 637: 636: 633: 620: 618: 617: 612: 610: 609: 591: 589: 588: 583: 581: 580: 577: 571: 570: 567: 558: 557: 541: 539: 538: 533: 414:Alfvén's theorem 392: 360:Lundquist number 292:Alfvén's theorem 288: 286: 285: 280: 278: 260: 258: 257: 252: 247: 245: 237: 236: 227: 216: 205: 177:Alfvén's theorem 152:Alfvén's theorem 48: 21: 4644: 4643: 4639: 4638: 4637: 4635: 4634: 4633: 4629:Solar phenomena 4609: 4608: 4595: 4576:6 February 2008 4550: 4548:Further reading 4545: 4544: 4534: 4532: 4519: 4518: 4514: 4454: 4453: 4449: 4417: 4412: 4411: 4407: 4364:Physica Scripta 4360: 4359: 4355: 4317: 4316: 4312: 4307:. 24 July 2008. 4299: 4298: 4294: 4242: 4241: 4237: 4224: 4223: 4219: 4149: 4148: 4144: 4137: 4133: 4123: 4121: 4116: 4115: 4111: 4057: 4056: 4052: 4004: 4003: 3999: 3943: 3942: 3938: 3894: 3893: 3889: 3855: 3854: 3850: 3804: 3803: 3799: 3748: 3747: 3743: 3729: 3728: 3724: 3719: 3715: 3681: 3680: 3676: 3634: 3633: 3629: 3591: 3590: 3586: 3556: 3555: 3551: 3546: 3542: 3512: 3511: 3507: 3461: 3460: 3456: 3412: 3411: 3407: 3369: 3368: 3364: 3328: 3327: 3323: 3316: 3303: 3302: 3298: 3291: 3278: 3277: 3273: 3247: 3246: 3242: 3237: 3233: 3199: 3198: 3194: 3158: 3157: 3153: 3140: 3136: 3107:(4003): 81–82. 3094: 3093: 3089: 3055: 3054: 3050: 2996: 2995: 2991: 2939: 2938: 2934: 2884: 2883: 2879: 2874: 2852: 2822: 2821: 2808:plasma thruster 2804:Fatima Ebrahimi 2780: 2724: 2704: 2699: 2649: 2639: 2638: 2627: 2617: 2607: 2606: 2587: 2582: 2581: 2557: 2544: 2543: 2540: 2514: 2509: 2508: 2487: 2482: 2481: 2462: 2461: 2440: 2407: 2402: 2401: 2351: 2350: 2318: 2317: 2316: 2312: 2295: 2284: 2283: 2262: 2261: 2257: 2198: 2197: 2165: 2160: 2159: 2138: 2133: 2132: 2085: 2069: 2068: 2047: 2046: 2007: 2006: 1963: 1962: 1943: 1942: 1887: 1875: 1868: 1867: 1846: 1845: 1826: 1825: 1818: 1812: 1765: 1745: 1735: 1728: 1727: 1723: 1684: 1659: 1658: 1638: 1637: 1619: 1618: 1599: 1598: 1579: 1578: 1546: 1542: 1529: 1528: 1509: 1508: 1460: 1459: 1439: 1429: 1416: 1415: 1384: 1383: 1359: 1339: 1338: 1319: 1318: 1315:Alfvén velocity 1293: 1288: 1287: 1264: 1245: 1234: 1219: 1214: 1213: 1194: 1193: 1155: 1137: 1133: 1111: 1110: 1084: 1079: 1078: 1059: 1058: 1029: 1013: 1008: 1007: 984: 983: 935: 934: 914: 904: 889: 884: 883: 840: 839: 814: 813: 794: 793: 761: 760: 750: 735: 730: 729: 695: 677: 676: 655: 650: 649: 628: 623: 622: 601: 596: 595: 572: 562: 549: 544: 543: 518: 517: 497: 492: 461: 405: 382: 380: 269: 268: 238: 228: 190: 189: 148: 105:electric fields 65:, in which the 39: 28: 23: 22: 15: 12: 11: 5: 4642: 4640: 4632: 4631: 4626: 4621: 4611: 4610: 4607: 4606: 4601: 4594: 4593:External links 4591: 4590: 4589: 4584: 4578: 4569: 4549: 4546: 4543: 4542: 4512: 4467:(20): 205003. 4447: 4405: 4353: 4326:(10): 105002. 4310: 4292: 4235: 4232:. 7 June 2013. 4217: 4142: 4131: 4109: 4070:(2): 297–314. 4050: 3997: 3936: 3887: 3882:10.1086/175121 3848: 3797: 3784:10.1086/307233 3760:(2): 700–718. 3750:Lazarian, Alex 3741: 3722: 3713: 3674: 3627: 3584: 3565:(4): 509–520. 3549: 3540: 3505: 3470:(1): 115–133. 3454: 3405: 3378:(A12): 23443. 3362: 3321: 3314: 3296: 3289: 3271: 3260:(4): 509–520. 3240: 3231: 3192: 3171:(4): 338–355. 3151: 3149:(4): 338–355. 3134: 3087: 3048: 2989: 2952:(10): 102305. 2932: 2876: 2875: 2873: 2870: 2869: 2868: 2863: 2858: 2851: 2848: 2835: 2832: 2829: 2779: 2776: 2723: 2720: 2703: 2700: 2698: 2695: 2687:Whistler waves 2656: 2652: 2646: 2642: 2634: 2630: 2624: 2620: 2614: 2610: 2602: 2597: 2594: 2590: 2567: 2564: 2560: 2555: 2551: 2539: 2536: 2521: 2517: 2494: 2490: 2469: 2447: 2443: 2438: 2432: 2427: 2423: 2419: 2410: 2387: 2383: 2376: 2373: 2367: 2362: 2359: 2354: 2349: 2343: 2340: 2334: 2329: 2326: 2321: 2315: 2311: 2308: 2298: 2294: 2291: 2269: 2256: 2253: 2240: 2237: 2234: 2230: 2226: 2223: 2220: 2215: 2210: 2206: 2182: 2178: 2168: 2141: 2117: 2110: 2105: 2102: 2098: 2092: 2088: 2082: 2079: 2076: 2054: 2032: 2027: 2024: 2021: 2016: 1994: 1991: 1988: 1985: 1981: 1975: 1970: 1950: 1928: 1924: 1920: 1917: 1913: 1907: 1904: 1899: 1893: 1890: 1883: 1878: 1853: 1833: 1811: 1808: 1783: 1777: 1774: 1771: 1768: 1764: 1759: 1752: 1748: 1738: 1722: 1719: 1703: 1695: 1692: 1687: 1683: 1678: 1671: 1666: 1662: 1657: 1651: 1645: 1626: 1606: 1586: 1564: 1559: 1553: 1549: 1545: 1539: 1536: 1516: 1491: 1486: 1483: 1478: 1472: 1467: 1463: 1458: 1453: 1442: 1432: 1426: 1423: 1403: 1400: 1397: 1394: 1391: 1371: 1366: 1362: 1358: 1355: 1352: 1349: 1346: 1326: 1300: 1296: 1271: 1267: 1263: 1257: 1252: 1248: 1237: 1231: 1222: 1201: 1177: 1171: 1162: 1158: 1152: 1144: 1140: 1136: 1130: 1121: 1087: 1066: 1044: 1041: 1032: 1028: 1025: 1016: 991: 969: 964: 961: 956: 950: 947: 942: 938: 933: 928: 917: 911: 907: 901: 892: 866: 860: 857: 852: 848: 827: 824: 821: 801: 779: 773: 768: 764: 753: 747: 742: 738: 716: 712: 709: 702: 698: 694: 689: 685: 658: 631: 608: 604: 575: 565: 561: 556: 552: 531: 528: 525: 496: 493: 491: 488: 460: 457: 438:nuclear fusion 404: 401: 379: 376: 362:plasmas (i.e. 277: 250: 244: 241: 235: 231: 225: 222: 219: 215: 211: 208: 204: 200: 197: 165:current sheets 147: 144: 93:Ron Giovanelli 75:thermal energy 71:kinetic energy 26: 24: 14: 13: 10: 9: 6: 4: 3: 2: 4641: 4630: 4627: 4625: 4622: 4620: 4617: 4616: 4614: 4605: 4602: 4600: 4597: 4596: 4592: 4588: 4585: 4582: 4579: 4577: 4574:, Space.com, 4573: 4570: 4568: 4564: 4563:0-521-48179-1 4560: 4556: 4552: 4551: 4547: 4530: 4526: 4522: 4516: 4513: 4508: 4504: 4500: 4496: 4492: 4488: 4484: 4480: 4475: 4470: 4466: 4462: 4458: 4451: 4448: 4443: 4439: 4435: 4431: 4427: 4423: 4416: 4409: 4406: 4401: 4397: 4393: 4389: 4385: 4381: 4377: 4373: 4369: 4365: 4357: 4354: 4349: 4345: 4341: 4337: 4333: 4329: 4325: 4321: 4314: 4311: 4306: 4302: 4296: 4293: 4288: 4284: 4280: 4276: 4271: 4266: 4262: 4258: 4254: 4250: 4246: 4239: 4236: 4231: 4227: 4221: 4218: 4213: 4209: 4205: 4201: 4197: 4193: 4188: 4187:10044/1/32763 4183: 4178: 4173: 4169: 4165: 4161: 4157: 4153: 4146: 4143: 4140: 4135: 4132: 4119: 4113: 4110: 4105: 4101: 4096: 4091: 4087: 4083: 4078: 4073: 4069: 4065: 4061: 4054: 4051: 4046: 4042: 4038: 4034: 4030: 4026: 4021: 4016: 4012: 4008: 4001: 3998: 3993: 3989: 3985: 3981: 3977: 3973: 3969: 3965: 3960: 3955: 3952:(4): 043205. 3951: 3947: 3940: 3937: 3932: 3928: 3923: 3918: 3914: 3910: 3906: 3902: 3898: 3891: 3888: 3883: 3879: 3875: 3871: 3867: 3863: 3859: 3852: 3849: 3844: 3840: 3836: 3832: 3828: 3824: 3820: 3816: 3813:(1): 013201. 3812: 3808: 3801: 3798: 3793: 3789: 3785: 3781: 3777: 3773: 3768: 3763: 3759: 3755: 3751: 3745: 3742: 3737: 3733: 3726: 3723: 3717: 3714: 3709: 3705: 3701: 3697: 3693: 3689: 3685: 3678: 3675: 3670: 3666: 3662: 3658: 3654: 3650: 3646: 3642: 3638: 3631: 3628: 3623: 3619: 3615: 3611: 3607: 3603: 3599: 3595: 3588: 3585: 3580: 3576: 3572: 3568: 3564: 3560: 3553: 3550: 3544: 3541: 3536: 3532: 3528: 3524: 3520: 3516: 3509: 3506: 3501: 3497: 3493: 3489: 3485: 3481: 3477: 3473: 3469: 3465: 3464:Solar Physics 3458: 3455: 3450: 3446: 3441: 3436: 3432: 3428: 3424: 3420: 3416: 3409: 3406: 3401: 3397: 3393: 3389: 3385: 3381: 3377: 3373: 3366: 3363: 3357: 3352: 3348: 3344: 3340: 3336: 3332: 3325: 3322: 3317: 3315:0-521-45104-3 3311: 3307: 3300: 3297: 3292: 3290:0-521-45104-3 3286: 3282: 3275: 3272: 3267: 3263: 3259: 3255: 3251: 3244: 3241: 3235: 3232: 3227: 3223: 3219: 3215: 3211: 3207: 3203: 3196: 3193: 3188: 3184: 3179: 3174: 3170: 3166: 3162: 3155: 3152: 3148: 3144: 3138: 3135: 3130: 3126: 3122: 3118: 3114: 3110: 3106: 3102: 3098: 3091: 3088: 3083: 3079: 3075: 3071: 3067: 3063: 3062:Physics Today 3059: 3052: 3049: 3044: 3040: 3035: 3030: 3026: 3022: 3017: 3012: 3008: 3004: 3000: 2993: 2990: 2985: 2981: 2977: 2973: 2969: 2965: 2960: 2955: 2951: 2947: 2943: 2936: 2933: 2928: 2924: 2920: 2916: 2912: 2908: 2904: 2900: 2896: 2892: 2888: 2881: 2878: 2871: 2867: 2864: 2862: 2859: 2857: 2856:Current sheet 2854: 2853: 2849: 2847: 2833: 2830: 2827: 2819: 2815: 2811: 2809: 2806:to propose a 2805: 2801: 2798: 2794: 2789: 2785: 2777: 2775: 2772: 2767: 2765: 2761: 2757: 2753: 2749: 2745: 2741: 2737: 2733: 2729: 2728:magnetosphere 2719: 2717: 2713: 2709: 2701: 2696: 2694: 2692: 2688: 2684: 2680: 2676: 2654: 2650: 2644: 2640: 2632: 2628: 2622: 2618: 2612: 2608: 2600: 2595: 2592: 2588: 2565: 2562: 2558: 2553: 2549: 2537: 2535: 2519: 2515: 2492: 2488: 2467: 2445: 2441: 2436: 2430: 2425: 2421: 2417: 2408: 2398: 2385: 2381: 2374: 2371: 2365: 2360: 2357: 2352: 2347: 2341: 2338: 2332: 2327: 2324: 2319: 2313: 2309: 2306: 2296: 2292: 2289: 2281: 2267: 2254: 2252: 2235: 2232: 2228: 2224: 2221: 2213: 2208: 2204: 2194: 2180: 2176: 2166: 2139: 2128: 2115: 2108: 2103: 2100: 2096: 2090: 2086: 2080: 2077: 2074: 2066: 2052: 2025: 2022: 2019: 1992: 1989: 1986: 1983: 1979: 1968: 1948: 1939: 1926: 1918: 1915: 1905: 1902: 1897: 1891: 1888: 1876: 1865: 1851: 1831: 1823: 1817: 1809: 1807: 1803: 1800: 1794: 1781: 1775: 1772: 1769: 1766: 1762: 1757: 1750: 1746: 1736: 1720: 1718: 1714: 1701: 1693: 1690: 1685: 1681: 1676: 1669: 1664: 1660: 1655: 1649: 1643: 1624: 1604: 1584: 1575: 1562: 1557: 1551: 1547: 1543: 1537: 1534: 1514: 1507: 1502: 1489: 1484: 1481: 1476: 1470: 1465: 1461: 1456: 1451: 1440: 1430: 1424: 1421: 1398: 1395: 1392: 1364: 1360: 1356: 1353: 1350: 1347: 1324: 1316: 1298: 1294: 1284: 1269: 1265: 1261: 1255: 1250: 1246: 1235: 1229: 1220: 1199: 1190: 1175: 1169: 1160: 1156: 1150: 1142: 1138: 1134: 1128: 1119: 1108: 1085: 1064: 1055: 1042: 1039: 1030: 1026: 1023: 1014: 1005: 989: 980: 967: 962: 959: 954: 948: 945: 940: 936: 931: 926: 915: 909: 905: 899: 890: 881: 858: 855: 850: 825: 822: 819: 799: 790: 777: 771: 766: 762: 751: 745: 740: 736: 710: 700: 696: 692: 687: 656: 629: 606: 602: 592: 573: 563: 559: 554: 550: 542:velocity, so 529: 526: 523: 514: 509: 506: 505:Eugene Parker 502: 494: 489: 487: 485: 479: 477: 473: 471: 466: 458: 456: 454: 453:eddy currents 450: 445: 443: 439: 435: 431: 430:magnetosphere 427: 423: 419: 415: 410: 402: 397: 377: 375: 373: 369: 365: 361: 357: 352: 349: 344: 340: 336: 332: 328: 326: 321: 320:current sheet 317: 316:current sheet 313: 308: 304: 300: 299:magnetic flux 295: 293: 266: 261: 248: 242: 223: 220: 217: 209: 206: 198: 187: 186: 181: 178: 174: 170: 166: 161: 157: 153: 145: 143: 140: 139:Eugene Parker 136: 131: 128: 124: 123:magnetosphere 121:into Earth's 120: 116: 112: 110: 106: 102: 98: 94: 90: 86: 84: 80: 76: 72: 68: 64: 60: 53: 32: 19: 4575: 4554: 4533:. Retrieved 4524: 4515: 4464: 4460: 4450: 4425: 4421: 4408: 4367: 4363: 4356: 4323: 4319: 4313: 4304: 4295: 4252: 4248: 4238: 4229: 4220: 4159: 4155: 4145: 4134: 4122:. Retrieved 4112: 4067: 4063: 4053: 4013:(1): 63–85. 4010: 4006: 4000: 3949: 3945: 3939: 3904: 3900: 3890: 3865: 3861: 3851: 3810: 3806: 3800: 3757: 3753: 3744: 3731: 3725: 3716: 3691: 3687: 3677: 3644: 3640: 3630: 3597: 3593: 3587: 3562: 3558: 3552: 3543: 3518: 3514: 3508: 3467: 3463: 3457: 3422: 3418: 3408: 3375: 3371: 3365: 3338: 3334: 3324: 3305: 3299: 3280: 3274: 3257: 3253: 3243: 3234: 3212:(2): 47–48. 3209: 3205: 3195: 3168: 3164: 3154: 3146: 3142: 3137: 3104: 3100: 3090: 3068:(6): 34–39. 3065: 3061: 3051: 3006: 3002: 2992: 2949: 2945: 2935: 2894: 2890: 2880: 2861:Solar corona 2812: 2781: 2768: 2732:magnetopause 2725: 2708:solar flares 2705: 2697:Observations 2691:standard MHD 2541: 2399: 2282: 2258: 2195: 2129: 2067: 1940: 1866: 1819: 1804: 1799:Alfvén waves 1795: 1724: 1715: 1576: 1527:is given by 1503: 1285: 1191: 1056: 981: 791: 593: 512: 510: 498: 483: 480: 475: 468: 464: 462: 446: 418:Solar System 406: 368:Solar flares 363: 353: 329: 325:Alfvén waves 296: 262: 188: 182: 149: 132: 115:James Dungey 113: 101:solar flares 91: 87: 58: 57: 18:Reconnection 4124:February 9, 2736:magnetotail 2734:and in the 2679:Hall effect 501:Peter Sweet 135:Peter Sweet 83:Alfvén wave 52:solar flare 4613:Categories 4525:Energy.gov 4474:2203.16018 4370:: 014032. 3959:1908.06474 3734:. Oxford: 3016:1603.07062 3009:(2): L29. 2959:2005.02285 2872:References 2802:, led Dr. 2756:ionosphere 2744:Cluster II 1814:See also: 470:separatrix 378:Properties 372:turbulence 119:solar wind 4392:0031-8949 4305:Space.com 4287:206514133 4212:206647580 4196:0036-8075 4077:1203.2971 4020:0903.2052 3992:201070540 3931:126072383 3907:(2): 52. 3843:199120046 3792:119349364 3669:1070-664X 3622:0031-9171 3535:0004-6361 3500:120072450 3492:0038-0938 3449:0148-0227 3400:0148-0227 3226:0031-9007 3187:0035-8711 3121:0028-0836 3082:0031-9228 3043:119188103 2984:218502561 2788:flux rope 2760:substorms 2683:electrons 2641:ϵ 2601:≡ 2589:ω 2559:ω 2310:⁡ 2181:η 2167:η 2140:η 2097:ω 2081:ν 2075:η 1949:ν 1919:ν 1916:− 1773:⁡ 1763:π 1758:≈ 1656:η 1650:∼ 1558:η 1538:≡ 1482:δ 1477:∼ 1471:δ 1457:η 1452:∼ 1393:δ 1354:δ 1348:η 1262:≡ 1256:ρ 1247:μ 1230:∼ 1200:ρ 1157:ρ 1151:∼ 1139:μ 1040:δ 1027:∼ 990:η 963:δ 960:η 949:δ 946:σ 937:μ 927:∼ 880:Ohm's law 859:σ 826:δ 820:∼ 800:δ 772:δ 763:μ 746:∼ 711:× 708:∇ 697:μ 527:× 476:separator 240:∂ 230:∂ 224:ϵ 221:μ 210:μ 199:× 196:∇ 4535:April 7, 4529:Archived 4507:24545773 4499:26047235 4400:29910900 4348:19792321 4279:18653845 4204:27174677 4104:53390559 3984:31770890 3835:31499931 2919:11473310 2850:See also 2793:helicity 2746:and the 2045:, where 472:surfaces 348:Dungey's 109:sunspots 4479:Bibcode 4430:Bibcode 4372:Bibcode 4328:Bibcode 4257:Bibcode 4249:Science 4164:Bibcode 4156:Science 4082:Bibcode 4045:4671422 4025:Bibcode 3964:Bibcode 3909:Bibcode 3870:Bibcode 3868:: 763. 3815:Bibcode 3772:Bibcode 3696:Bibcode 3649:Bibcode 3602:Bibcode 3567:Bibcode 3523:Bibcode 3521:: 779. 3472:Bibcode 3427:Bibcode 3380:Bibcode 3343:Bibcode 3129:4139384 3021:Bibcode 2964:Bibcode 2927:4412119 2899:Bibcode 2818:tokamak 2580:(where 2460:. Here 1313:is the 1002:is the 356:physics 130:line. 63:plasmas 4561: 4505: 4497: 4398: 4390: 4346: 4285: 4277: 4210: 4202: 4194: 4102: 4043: 3990: 3982: 3929: 3841: 3833: 3790: 3667: 3620: 3533: 3498: 3490: 3447: 3398: 3312: 3287: 3224: 3185: 3127: 3119: 3101:Nature 3080: 3041: 2982: 2925: 2917: 2891:Nature 2771:THEMIS 2480:, and 2400:where 1941:where 1647: 1286:where 1192:where 1109:gives 1057:where 982:where 792:where 594:where 449:plasma 434:aurora 331:Dungey 265:plasma 127:Dungey 77:, and 4503:S2CID 4469:arXiv 4418:(PDF) 4396:S2CID 4283:S2CID 4208:S2CID 4100:S2CID 4072:arXiv 4041:S2CID 4015:arXiv 3988:S2CID 3954:arXiv 3927:S2CID 3839:S2CID 3788:S2CID 3762:arXiv 3496:S2CID 3125:S2CID 3039:S2CID 3011:arXiv 2980:S2CID 2954:arXiv 2923:S2CID 426:Earth 263:In a 4559:ISBN 4537:2022 4495:PMID 4388:ISSN 4368:T142 4344:PMID 4275:PMID 4230:NASA 4200:PMID 4192:ISSN 4126:2013 3980:PMID 3831:PMID 3665:ISSN 3618:ISSN 3531:ISSN 3488:ISSN 3445:ISSN 3396:ISSN 3310:ISBN 3285:ISBN 3222:ISSN 3183:ISSN 3117:ISSN 3078:ISSN 2915:PMID 2831:< 2797:NSTX 2675:ions 2413:turb 2301:turb 2171:anom 2144:anom 511:The 503:and 163:are 137:and 4487:doi 4465:114 4438:doi 4380:doi 4336:doi 4324:103 4265:doi 4253:321 4182:hdl 4172:doi 4160:352 4090:doi 4033:doi 4011:700 3972:doi 3950:100 3917:doi 3905:860 3878:doi 3866:438 3823:doi 3811:100 3780:doi 3758:517 3704:doi 3657:doi 3610:doi 3575:doi 3519:363 3480:doi 3468:168 3435:doi 3423:107 3388:doi 3376:100 3351:doi 3262:doi 3214:doi 3173:doi 3169:107 3147:107 3109:doi 3105:158 3070:doi 3029:doi 3007:821 2972:doi 2907:doi 2895:412 2307:min 1445:out 1225:out 1165:out 1090:out 1035:out 428:'s 422:Sun 396:sun 366:). 99:in 4615:: 4565:, 4523:. 4501:. 4493:. 4485:. 4477:. 4463:. 4459:. 4436:. 4424:. 4420:. 4394:. 4386:. 4378:. 4366:. 4342:. 4334:. 4322:. 4303:. 4281:. 4273:. 4263:. 4251:. 4247:. 4228:. 4206:. 4198:. 4190:. 4180:. 4170:. 4158:. 4154:. 4098:. 4088:. 4080:. 4068:19 4066:. 4062:. 4039:. 4031:. 4023:. 4009:. 3986:. 3978:. 3970:. 3962:. 3948:. 3925:. 3915:. 3903:. 3899:. 3876:. 3864:. 3860:. 3837:. 3829:. 3821:. 3809:. 3786:. 3778:. 3770:. 3756:. 3702:. 3692:80 3690:. 3686:. 3663:. 3655:. 3643:. 3639:. 3616:. 3608:. 3598:29 3596:. 3573:. 3563:62 3561:. 3529:. 3517:. 3494:. 3486:. 3478:. 3466:. 3443:. 3433:. 3421:. 3417:. 3394:. 3386:. 3374:. 3349:. 3339:24 3337:. 3333:. 3258:62 3256:. 3252:. 3220:. 3208:. 3204:. 3181:. 3167:. 3163:. 3145:. 3123:. 3115:. 3103:. 3099:. 3076:. 3066:63 3064:. 3060:. 3037:. 3027:. 3019:. 3005:. 3001:. 2978:. 2970:. 2962:. 2950:27 2948:. 2944:. 2921:. 2913:. 2905:. 2893:. 2889:. 2718:. 2710:, 2193:. 1864:: 1770:ln 1741:in 1435:in 1240:in 1124:in 1019:in 920:in 895:in 756:in 661:in 634:in 578:in 568:in 73:, 4539:. 4509:. 4489:: 4481:: 4471:: 4444:. 4440:: 4432:: 4426:6 4402:. 4382:: 4374:: 4350:. 4338:: 4330:: 4289:. 4267:: 4259:: 4214:. 4184:: 4174:: 4166:: 4128:. 4106:. 4092:: 4084:: 4074:: 4047:. 4035:: 4027:: 4017:: 3994:. 3974:: 3966:: 3956:: 3933:. 3919:: 3911:: 3884:. 3880:: 3872:: 3845:. 3825:: 3817:: 3794:. 3782:: 3774:: 3764:: 3738:. 3710:. 3706:: 3698:: 3671:. 3659:: 3651:: 3645:6 3624:. 3612:: 3604:: 3581:. 3577:: 3569:: 3537:. 3525:: 3502:. 3482:: 3474:: 3451:. 3437:: 3429:: 3402:. 3390:: 3382:: 3359:. 3353:: 3345:: 3318:. 3293:. 3268:. 3264:: 3228:. 3216:: 3210:6 3189:. 3175:: 3131:. 3111:: 3084:. 3072:: 3045:. 3031:: 3023:: 3013:: 2986:. 2974:: 2966:: 2956:: 2929:. 2909:: 2901:: 2834:1 2828:q 2655:i 2651:m 2645:0 2633:2 2629:e 2623:2 2619:Z 2613:i 2609:n 2596:i 2593:p 2566:i 2563:p 2554:/ 2550:c 2520:A 2516:v 2493:l 2489:v 2468:l 2446:A 2442:v 2437:/ 2431:2 2426:l 2422:v 2418:= 2409:v 2386:, 2382:] 2375:2 2372:1 2366:) 2361:L 2358:l 2353:( 2348:, 2342:2 2339:1 2333:) 2328:l 2325:L 2320:( 2314:[ 2297:v 2293:= 2290:v 2268:L 2239:) 2236:B 2233:e 2229:/ 2225:c 2222:m 2219:( 2214:2 2209:A 2205:v 2177:/ 2116:. 2109:2 2104:i 2101:p 2091:2 2087:c 2078:= 2053:n 2031:v 2026:n 2023:e 2020:= 2015:J 1993:0 1990:= 1987:t 1984:d 1980:/ 1974:v 1969:d 1927:, 1923:v 1912:E 1906:m 1903:e 1898:= 1892:t 1889:d 1882:v 1877:d 1852:e 1832:m 1782:. 1776:S 1767:8 1751:A 1747:v 1737:v 1702:. 1694:2 1691:1 1686:S 1682:1 1677:= 1670:L 1665:A 1661:v 1644:R 1625:S 1605:R 1585:R 1563:, 1552:A 1548:v 1544:L 1535:S 1515:S 1490:. 1485:L 1466:A 1462:v 1441:v 1431:v 1425:= 1422:R 1402:) 1399:L 1396:, 1390:( 1370:) 1365:A 1361:v 1357:, 1351:, 1345:( 1325:R 1299:A 1295:v 1270:A 1266:v 1251:0 1236:B 1221:v 1176:2 1170:2 1161:v 1143:0 1135:2 1129:2 1120:B 1086:v 1065:L 1043:, 1031:v 1024:L 1015:v 968:, 955:= 941:0 932:1 916:B 910:y 906:E 900:= 891:v 865:J 856:1 851:= 847:E 823:2 778:, 767:0 752:B 741:y 737:J 715:B 701:0 693:1 688:= 684:J 657:B 630:v 607:y 603:E 574:B 564:v 560:= 555:y 551:E 530:B 524:E 398:. 276:J 249:. 243:t 234:E 218:+ 214:J 207:= 203:B 54:. 20:)

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Index