Space Plasma Physics The Study of Solar-System Plasmas (1978) / Chapter Skim
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Magnetic Field Reconnection
Magnetic Field Reconnection
Pages 126-219
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From page 126... ...
Magnetic Field Reconnection Bengt U
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From page 127... ...
Its primary function in the cosmic scheme is to prevent the build up of excessive amounts of magnetic energy in association with intense electric current sheets formed in highly conducting plasmas. The reconnection process is thought to cause a relaxation of such configurations, either partially or completely, and either continuously or sporadically, toward their lowest energy (current-free)
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From page 128... ...
Figure 5 shows the magnetic field configuration expected for a rapidly spinning planetary magnetosphere such as that of Jupiter45'57. All of the above examples, and many possible other ones, such as 70 7R R7 supernova remnants , accretion disks , and galactic dynamos , illustrate cosmic situations in which magnetic field reconnection may occur.
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From page 129... ...
On balance, our best opportunity for learning about reconnection as a viable cosmic energy conversion process is likely to be in the earth's magnetosphere. It is difficult to account for the overall dynamic behavior of the magnetosphere without invoking time-dependent transfer of magnetic flux from closed to open field lines and vice versa.
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From page 130... ...
Section 5 discusses one-fluid and two-fluid approaches to the.plasma dynamics in the diffusion region, which is the site of the field reconnection process itself, and in which plasma microinstabilities are likely to be important. Section 6 discusses possible mechanisms for the generation of finite resistivity in the diffusion region and for the onset of reconnection.
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From page 131... ...
Third, the paper does not deal with applications in tokamaks and other laboratory devices where the physical boundary conditions are such that spatially periodic behavior results. It should be stressed, however, that vigorous interaction between fusion plasma physicists and cosmic physicists on the problem of reconnection is likely to be of substantial benefit to both groups.
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From page 132... ...
In the following subsections we examine several aspects of this physical model: flux transport, external plasma dynamics, nature of the region around the magnetic null point, and electromagnetic energy conversion. The discussion is qualitative.
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From page 133... ...
The use of the concept of moving field lines is then just another way of referring to the electric field E In this model, the use of the term "reconnection" to describe the process is best understood in terms of moving field lines.
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From page 134... ...
Away from that point, the coupling between the B field and the plasma is strong and the plasma dynamics of the process will have dramatic effects in determining the detailed magnetic field configuration and perhaps in limiting the magnitude of the electric field E . We now outline some basic features of the plasma dynamics of the reconnection process.
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From page 135... ...
In particular, Z as will be shown in Section 4.1, the current distribution in the inflow region may influence the reconnection process in a crucial way. An approximate balance of the magnetic shear stress at the shock and the exit momentum flow*
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From page 136... ...
The charge separation effects in that case lead to an electric field E which is a function of the 2 coordinate 2. This limit will not be dealt with in the present paper.
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From page 137... ...
of the diffusion region is expected to adjust itself in such a way that a balance is established between the rate of magnetic flux convected into the diffusion region and the rate of diffusion of that flux through the semistagnant plasma in the diffusion region. The ratio of these two transport rates is measured by the magnetic Reynolds number R = \i0avix*
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From page 138... ...
The resulting plasma turbulence will lead to a reduction in the effective conductivity, as discussed in section 6.2. Whether the plasma dynamics in the diffusion region is described in a continuum fashion, i.e., by use of an effective conductivity, or in terms of individual particle orbits near the magnetic null point, it is easy to see that the net current I in the diffusion region will be along the positive z axis so that E_ • I > 0.
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From page 139... ...
For example, the rate of electromagnetic energy flow into and out of the diffusion region may be estimated as follows:
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From page 140... ...
. It is, however, by no means assured that boundary conditions at large distances or plasma processes in the diffusion region will always permit this upper limit to be reached.
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From page 141... ...
. Henceforth, annihilation will refer to situations where M is sufficiently small so that the diffusion region occupies the entire A l length of the current sheet, i.e., y*
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From page 142... ...
The X type magnetic null point is again located at the origin. The magnetic field is maintained by the currents I in the two metal rods at the center of flux cells fn and \2j, and a return current ZI3flowing in the plasma along an \ outer envelope, which coincides with the outermost field lines in flux cell In the experiments, the current I increases with time so that magnetic flux is generated continually at the two rods, i.e., in cells fn and If we assume for a moment that no plasma is present, the flux in cell increases proportionately so that magnetic flux may be thought of as being t transported from the rods into cells (T)
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From page 143... ...
dz Uo-Z" 2dd E = __ inn + _r-r- -=z 2it \ C* J ZTT 02+d2 • Thus for increasing current J and diameter d, E is positive as required for flux transport into cell In the presence of a .plasma, the field configuration is modified as follows, The electric field now drives plasma currents in the vicinity of the magnetic null line, causing a field deformation of the type shown by the dashed lines in Figure 8.
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From page 144... ...
Impulsive flux transfer events are observed in the double inverse pinch experiments. It appears that,as the magnetic field and associated plasma currents near the null point grow, anomalous resistivity associated with ion sound turbulence sets in abruptly with an associated rapid increase of electric field and decrease of currents at the null point.
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From page 145... ...
Two hyperbolic magnetic null points Xl and X2 are formed in the plane containing the dipole moment vector and the uniform field vector. A basic topological property of such a null point is that many field lines enter it forming a separatrix surface and two single field lines leave it along directions out of that surface, or vice versa.
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From page 146... ...
However, it is believed that the field lines on the separatrix and its immediate vicinity bend to become nearly parallel to the reconnection line extremely close to that line, as shown in Figure 10. Thus parallel electric fields occur only within the diffusion region which surrounds the reconnection line and in which finite resistivity effects permit their presence.
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From page 147... ...
3.4 Definitions On the basis of the preceding discussion we now formalize the definition of several terms, used in the magnetic-field reconnection literature: (i) A separatrix is a surface in space which separates magnetic field lines belonging to different topological families.
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From page 148... ...
In a highly conducting plasma, the diffusion region is imbedded in a much larger convection region, in which magnetized plasma moves toward and away from the separator, in the inflow and outflow regions, respectively, and in which dissipative effects are confined to shocks.
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From page 149... ...
. v 228 Vasyliunas has defined magnetic merging as "the process whereby plasma flows across a surface that separates regions containing topologically different magnetic field lines"; he takes the magnitude of that flow as a measure of the merging rate.
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From page 150... ...
Nonsteady solutions have not been found to date, which describe rapid configuration changes such as might be associated with impulsive flux transfer events in the double inverse pinch experiment (for a circuit model, see Bratenahl and Baum, )
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From page 151... ...
The maximum reconnection rate in this model corresponds to an Alfve"n number M of about one in the inflow just adjacent " 1 to the diffusion region. But because of the increase in flow speed and decrease in magnetic field associated with the fast-mode expansion, the A1fve"n number, M
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From page 152... ...
Far upstream, the fast-mode model is essentially current free and has a nearly uniform flow and magnetic field, while the slow-mode model contains substantial currents which bend the magnetic field lines and cause a deflection of the flow away from the x axis. Vasyliunas has further suggested that the former state of affairs may obtain when a demand for magnetic flux originates at the current sheet itself (the xy plane)
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From page 153... ...
. It might be thought that the reflection of these fans in the x axis, and the subsequent interaction of the reflected waves with the shocks, shown schematically in Figure 16, may be treated exactly by the method of characteristics.
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From page 154... ...
For comparison, the corresponding relationship for the fast-mode model, developed by Soward and Priest , is shown by the dashed curves. It is evident that the different distant boundary conditions for the fast-mode and the slow-mode models may lead to profoundly different inflow conditions into the diffusion region for the two models.
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From page 155... ...
followed by a narrow slow expansion fan. The intermediate wave, which marks the magnetopause, accomplishes the field direction reversal and an associated plasma acceleration parallel to the magnetopause and away from the reconnection line.
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From page 156... ...
This provides a link between the traditional cosmic reconnection models and the problems of reconnection in nearly force-free field configurations, such as the tokamak120^21^22. This procedure has provided the basis of a number of attempts to describe the dependence of the crossmagnetospheric electric potential difference on magnetosheath field direction, assuming the former to be caused by magnetopause reconnection^ 5^55, ^07.
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From page 157... ...
Thus the assumption underlying 2 Equation 4-1 , of one and the same value of B on the magnetospheric and the 2 magnetosheath side of a typical magnetopause reconnection model, may be invalid. It is noted that this assumption corresponds to a situation where the net current in the magnetopause (and in the diffusion region)
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From page 158... ...
Hill does not treat the flow and field configurations in the inflow or in these weak shocks. Rather he assumes that, away from the magnetic null point at the origin, the field lines form an angle x with the current sheet.
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From page 159... ...
2 He obtains the formula 4-1 for the angular dependence of the reconnection potential . The particle energization in a model of Hill's type is seen to be the direct result of inertia and gradient drifts in the current sheet, moving positive ions in the direction of the reconnection electric field, electrons in the opposite direction.
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From page 160... ...
The two-fluid description of the diffusion region is dealt with in sections 5.2 and 5.3. The former discusses the importance of the electron inertial length in determining the width 2x*
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From page 161... ...
2 The first lumped analysis of the diffusion region was performed by fifi 77^ Parker with application to Sweet's resistive current-sheet model 'l of a solar flare. The analysis yielded the following expression for the reconnection rate in incompressible flow )
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From page 162... ...
The basic point made by Petschek is that equation 5-1 determines, not the reconnection rate, but the height y* of the diffusion region.
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From page 163... ...
The field lines are straight and parallel to the current sheet. Thus, purely resistive magnetic field annihilation without reconnection occurs, as illustrated in Figure 21.
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From page 164... ...
1? ion inertial length.
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From page 165... ...
" pioneered the study of electron inertial effects in the diffusion region. In an approximate lumped analysis which neglected compresoo sibility (later included by Coroniti and Eviatar )
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From page 166... ...
. 5.3 Two-Fluid Effects; Ion Scale Lengths It is not clear how a diffusion region of the small physical dimensions implied by equation 5-5 can be joined to an external solution with slow 20 shocks of thickness comparable to, or greater than, the ion inertial length.
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From page 167... ...
~~" Z & in the stagnation-point flow discussed in the previous section (and indeed along the x axis of any configuration) , it cannot vanish throughout the diffusion region.
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From page 168... ...
The expected current flow and field pattern is shown schematically in Figure 24. The behavior of the B and B components indicated in y z the figure should be easy to identify in magnetic-field vector measurements from a satellite which crosses the diffusion region.
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From page 169... ...
But from the preceding discussion it appears possible that the ion length scales may determine the overall width 2x* of the diffusion region while the electron length scales give the size of the detailed structures of j 3 j 3 and j near x = 0.
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From page 170... ...
In reading the present section, it will be useful to refer to the typical values of several physical parameters given in Table 1. 6.1 Inertial Resistivity The concept of inertial resistivity was first discussed, in the 1 08 context of magnetic field reconnection, by Speiser • The basic idea is that a particle spends only a finite amount of time in the diffusion region and thus can pick up only a finite amount of energy from the electric field E0z_.
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From page 172... ...
The average displacement, AF, along the electric field £0, of a particle in the diffusion region may be obtained from a simple mass balance over a box of dimensions 2x*
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From page 173... ...
so that the size of the diffusion region decreases toward zero as the reconnection rate approaches its maximum value. Thus, for large reconnection rates, the required width of the diffusion region may be substantially less than the relevant plasma scale (the inertial length or gyroradius, depending on Bi)
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From page 174... ...
6.2 Plasma Turbulence A variety of plasma instabilities may serve to generate plasma turbulence in the diffusion region and an associated turbulent conductivity at L We now discuss such effects in an assumed quasi-steady state of reconnection.
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From page 175... ...
In the geomagnetic tail, the instability would be driven, not in the diffusion region itself, but rather by the pressure gradient and field curvature in the near-earth section of the tail plasma sheet (see figure 4)
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From page 176... ...
For a current-driven instability such as the ion-acoustic one to occur, the current density in the diffusion region must exceed a certain minimum value, corresponding to a critical current velocity v , i.e., j > nev . If G G Hall currents are present, as discussed in section 5.3, the total current must be considered.
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From page 177... ...
, e i e i ^i and for B of order unity or less, the critical diffusion region width is of ^ the order of the electron inertial length.
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From page 178... ...
6.3 Onset of Rapid Reconnection There is ample observational evidence relating to solar flares, to the earth's magnetotail, and to the double inverse pinch experiment, to int dicate that occasionally rapid reconnection is switched on in an abrupt, almost explosive manner. At the earth's magnetopause, if reconnection actually occurs there, the switch-on appears more gentle and may be a direct consequence of the interplanetary field turning southward so that the angle between the reconnecting fields exceeds some critical value (compare section 4.4)
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From page 179... ...
In the geomagnetic tail, an abrupt decrease in B1 value occurs if the plasma sheet in which the tail current sheet is imbedded shrinks to a thickness equal to the current sheet thickness. On the other hand, at the subsolar magnetopause, Lees and Zwan and Wolf have described a magnetosheath plasma depletion mechanism (by escape along the magnetic field lines)
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From page 180... ...
This 2 electric field, which is initially confined to the current sheet, is subsequently spread by fast-mode expansion waves propagating outward from the sheet as the configuration converts itself to one of steady or quasi-steady reconnection. If the conductivity is reduced to the level given by equation 6-12, E 2 may be one or two orders of magnitude larger than typical steady-state values.
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From page 181... ...
iS^abiVij|y_._ An abrupt onset of interchange turbulence in the geomagnetic tail^SS may occur if the ionosphere becomes decoupled from the tail plasma sheet by the development of electric fields parallel to the magnetic lines of force. 6.4 Particle Acceleration One of the most important, and at the same time most poorly understood, aspects of magnetic-field reconnection is its presumed ability to accelerate particles to high energies.
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From page 182... ...
Particle acceleration may occur either in turbulent small-scale electric fields or in the large-scale reconnection electric field E . Both types of 2 acceleration are expected to be operative principally in high-current regions: the diffusion region and the shocks.
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From page 183... ...
The lack of nonsteady reconnection models prevents a detailed analysis of particle acceleration. But the simple model given below may serve as an illustration of how electron energization might occur in the diffusion region.
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From page 184... ...
They may then return from B to A by gradient drift in the vicinity of the 0 type neutral line BOA where the electric field vanishes. Subsequently they reenter the acceleration region at A
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From page 185... ...
Section 7.2 contains a brief discussion of direct measurements of magnetic field and plasma in the vicinity of what may have been reconnection sites. 7.1 Flux Transfer Evidence The case for the occurrence of flux transfer in the magnetosphere from closed to open field lines is based on four sets of observations, discussed below: (i)
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From page 186... ...
Either this flux is transferred to open field lines in the polar cap by dayside magnetopause reconnection or it is moved into the tail while remaining on closed field lines. In the latter case, the flux might be added to the lobe of closed field lines in the tail or it might possibly be placed on open field lines by reconnection at the tail magnetopause.
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From page 187... ...
A substantial body of evidence indicates that the magnetic field intensity in the tail starts to increase shortly after the onset of a southward component of the interplanetary magnetic field while at the same time the asymptotic tail cross section increases5^. The observed concurrent gradual thinning of the tail plasma sheet (which is believed to contain the closed tail field lines)
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From page 188... ...
. 7.2 Measurements Near Reconnection Sites In a strict sense, direct evidence for reconnection consists of insitu observations of the hyperbolic magnetic field configuration associated with a separator and an electric field along that line.
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From page 189... ...
Observations of proton jetting in the tail ' of energetic particle bursts5J68J98, and of lunar shadow 73 patterns of electron fluxes , while generally compatible with tail reconnection, nevertheless cannot be claimed to provide unambiguous proof of the occurrence of the process. At the dayside magnetopause, magnetic field components perpendicular to 2 08 the magnetopause have been observed 3 although not as a permanent feature not even when the magnetosheath field opposes the terrestrial one.
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From page 190... ...
943 difficult to reconcile with the presence of magnetic field components perpendicular to the magnetopause, unless one is willing to accept potential differences of the order of 50 kvolt along field lines extending from the magnetopause into the solar wind; or unless one argues that such perpendicular components are never present over any substantial part of the dayside magnetopause.
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From page 191... ...
The picture that emerges is of a process, simple in concept but extremely complicated and multifaceted in detail. Nonlinear magnetohydrodynamic processes in the external flow region, governed by distant boundary conditions, are coupled to non-linear microscopic plasma processes in the diffusion region in a manner not clearly understood.
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From page 192... ...
(ii) Plasma processes in the diffusion region.
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From page 193... ...
It is through vigorous activities in the aforementioned areas, and effective interaction between scientists involved in them, that our understanding of the reconnection process may be most rapidly advanced. To bring about such a state of affairs, two proposals are made: (A)
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From page 194... ...
A current sheet A-B develops during time lKKro. Rapid reconnection sets in at t = t0 and relaxes the configuration toward a potential field in the short time et0.
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From page 195... ...
DEC. 2I00 FIGURE 3 Sector structure of the interplanetary magnetic field in the ecliptic plane as observed by IMP-1 in 1963.
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From page 196... ...
Solid lines are magnetic field lines; dashed lines are streamlines. The shaded region at the center is the diffusion region.
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From page 197... ...
. FIGURE 8 Field configuration in double inverse pinch experiment (after Bratenahl and Baum1')
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From page 198... ...
FIGURE 10 Schematic of separatrix surfaces for magnetopause reconnection. Lower figure shows separatrix of the null point ,V,; upper figure that of X2.
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From page 199... ...
FIGURE 12 Three-dimensional sketch of reconnection bubble with the reconnection line along AXB and an 0-type magnetic null line along AOB.
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From page 200... ...
FIGURE 14 Slow-mode reconnection model with MA )
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From page 201... ...
. = 5 FIGURE 16 Schematic showing "reflection" of slow mode expansion fan in the x axis (Yang and Sonnerupi25)
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From page 202... ...
Solid curves refer to slow-mode expansion model,125 dashed curves to the Soward-Priest110 analysis of the fast-mode expansion model. FIGURE 18 Upper half of compressible slowmode model of magnetopause reconnection for MAI = .2 and/3]
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From page 203... ...
Left hand figure shows the field components BI andfij tangential to the magnetopause during an OGO-5 crossing; right hand figure shows the nearly constant magnetic-field component 83 normal to the magnetopause. The field is given in units of y (ly = Int)
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From page 204... ...
957 B ^ B ••.V FIGURE 21 Magnetic field lines and streamlines for stagnation point flow,^ = (-k^x,kiy,k3z) , at a current sheet.
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From page 205... ...
958 «=0 10 0-25 05 -> -I FIGURE 22 Nondimensional magnetic-field profiles /£ = By(E0 \fi! 0a/k> for the configuration in Figure 21 in the resistive limit (a = ki/ki ;k3=ki -Ar2 )
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From page 206... ...
= (kTt/me) Vl/vc where vc is the critical current velocity for onset of ion-acoustic instability (after Fredricks40)
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From page 207... ...
P Lin, Observations of interplanetary field lines in the magnetotail, J
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From page 208... ...
T Russell, The terrestrial magnetosphere: a half-wave rectifier of the interplanetary electric field, Science, 189, 717, 1975.
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From page 209... ...
W H., Magnetic field-line reconnexion in a highly conducting incompressible fluid: Properties of the diffusion region, J
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From page 210... ...
W., Consistency of fields and particle motion in the Speiser model of the current sheet, Planet. Space Sci., 2£, 1555, 1972.
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From page 211... ...
Res., 79_, 4186, 1974. 50 Haerendel, G., Microscopic plasma processes related to reconnection, J
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From page 212... ...
P., High latitude electric fields and the modulations related to interplanetary magnetic field parameters, Radio Sci., 8., 933, 1973. 56 Heyvaerts, J., and E
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From page 213... ...
P Armstrong, Possible evidence for large transient electric fields in the magnetotail from oppositely directed anisotropies of energetic protons and electrons, Geophys.
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From page 214... ...
Meng, and S.-I. Akasofu, Search for the magnetic neutral line in the near earth plasma sheet, 2., Systematic study of IMP 6 magnetic field observations, J
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From page 215... ...
E., The mechanism for reconnection of geomagnetic and interplanetary field lines, in The Solar Wind, R
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From page 216... ...
F., Current instability in reconnecting current sheets, J Geophys.
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From page 217... ...
R Priest, Resistive MHD stagnation point flows at a current sheet, J
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From page 218... ...
J., 207, 837, 1976a. 129 Yeh, T., Reconnection of magnetic field lines in viscous conducting fluids, J
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From page 219... ...
I Axford, On the re-connexion of magnetic field lines in conducting fluids, J
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