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Use the link below to share a full-text version of this article with your friends and colleagues. Learn more. Whistler wave generation near the magnetospheric separatrix during reconnection at the dayside magnetopause is studied with data from the Magnetospheric Multiscale mission.

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The dispersion relation of the whistler mode is measured for the first time near the reconnection region in space, which shows that whistler waves propagate nearly parallel to the magnetic field line. A linear analysis indicates that the whistler waves are generated by temperature anisotropy in the electron tail population. This is caused by loss of electrons with a high velocity parallel to the magnetic field to the exhaust region. There is a positive correlation between activities of whistler waves and the lower hybrid drift instability both in laboratory and space, indicating the enhanced transport by lower hybrid drift instability may be responsible for the loss of electrons with a high parallel velocity.

Magnetic reconnection is a fundamental process in magnetized plasma, during which magnetic energy is converted to particle energy. Due to this nature of magnetic reconnection, there are many free energy sources that can excite plasma waves such as lower hybrid and whistler waves. Whistler waves near the boundary between the magnetosphere and the exhaust region of magnetic reconnection have been observed over many decades. However, the propagation characteristic and the exact excitation mechanism associated with magnetic reconnection have not been well understood.

Here the dispersion relation of the whistler wave is clearly measured for the first time by using correlations between four satellites of the Magnetospheric Multiscale mission. The measured dispersion shows that the whistler wave propagates mostly parallel to the background magnetic field toward the central reconnection region, which agrees well with a linear theory. A linear calculation with the measured electron distribution function verifies that the whistler wave is excited by temperature anisotropy in energetic electrons whose energy is much larger than that of bulk electrons.

Volume 45 , Issue Flux Transfer in Time-Dependent and Three Dimensional Configurations The two-dimensional steadyreconnection model outlined in Section 2 is useful as a vehicle for introducing certain basic aspects of reconnection. But it appears likely that in any real cosmic applications of the process, three-dimensional and temporal effects are important, perhaps even dominant.

For this reason it is useful to consider briefly a few reconnection configu- rations which incorporate these effects. To date, the plasma dynamics asso- ciated with such geometries has not been dealt with in a substantial way, so that the discussion is confined mainly to the electromagnetic field topology and flux transfer aspects of the process. In the following subsections we describe the two-dimensional but time-dependent double inverse pinch configu- ration, a simplified steady-state three-dimensional magnetopause topology and a possible three-dimensional time-dependent magnetotail configuration.

Finally, in Section 3. The X type magnetic null point is again located at the origin. It is of interest to calculate the electric field responsible for this flux transport. The vector potential for the vacuum configuration is given by where the rod separation is 2c, the minor diameter of the return-current en- velope is 2d, and the radii ri and r2 are measured from the two rods as shown in Figure 8. In the experiment, the current I and the envelope diameter both increase with time; in a more general case, the rod separation might be imagined to depend upon time also.

But for our purposes it suffices to consider the time variation of the current I and the diameter d. In particular, on the separatrix it has the value yo-Z" 0 ,. The separatrix intersection angle a falls below its vacuum value.

These effects imply an excess of magnetic flux in cells 7 and? Thus, a certain amount of free magnetic energy is stored in the system. However, at the same time a considerable amount of flux trans- port into cell 5 takes place. The principal difference between the present case and the steady-state model in Section 2 is the spatial nonuniformity of the instantaneous electric field. This effect occurs because in the nonsteady case some of the flux transported in the xy plane is being deposited locally,causing a field magnitude increase at each point.

Associated with this flux accumulation, a plasma compression must also occur. But this would appear to be a relatively minor effect so that the steady model in Section 2 may provide an adequate instantaneous des- cription of the flow away from the rods and the return envelope. Thus the essential qualitative features of the reconnection flow may be obtained by examination of a sequence of steady-state configurations. Impulsive flux transfer events are observed in the double inverse pinch experiments. It appears that,as the magnetic field and associated plasma cur- rents near the null point grow, anomalous resistivity associated with ion sound turbulence sets in abruptly with an associated rapid increase of elec- tric field and decrease of currents at the null point.

Evidently the stored free magnetic energy described in the previous paragraph is being rapidly con- verted into plasma energy. These events occur on a time scale much shorter. But the conditions for onset of such an event may perhaps be identified by examination of such a sequence. This topology, shown in one cross section in Figure 9, has been discussed extensively in the litera- ture 24j32j. 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. The separatrix surfaces associated with ATX and X2 intersect along a circular ring located in a plane through the two points and perpendicular to the plane of Figure 9. This ring is referred to alternatively as a singular line, a reconnection or merging line, a critical line, an X line, or a separator line.

At a chosen point on the ring the magnetic field does not vanish in general, but it is directed along the ring. Only at Xl and X2 is the field intensity zero. If the uni- form field is exactly antiparallel to the dipole field a degenerate situation arises in which the magnetic field vanishes at each point on the ring.

A schematic picture of the two separatrix surfaces is shown in Figure 10, in a configuration that may be appropriate for magnetopause reconnection. The upper part of the figure shows a view in the antisolar direction of field lines on the separatrix surface associated with the null point X2; the lower part shows the same view of the Xl separatrix. The total picture is an overlay. Part of the solar-wind electric field E is impressed across the configuration and must be sustained along the reconnection line. Thus, in the vicinity of that line a strong electric field component is present along the magnetic field.

Unless special circumstances exist, such parallel electric fields do not arise in highly conducting plasmas. 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 Thus parallel electric fields occur only within the diffusion region which surrounds the reconnection line and in which finite resistivity effects permit their presence.

Figure 10 suggests that it may be possible to study reconnection in this geometry by use of a locally two-dimensional model which is then applied to each short segment of the reconnection line.

Such a model will be similar to that discussed in Section 2, but with an added magnetic field component B x,y. Thus the reconnection of fields that are 2 not antiparallel is obtained. Further discussion of such geometries is given in Section 4. The dynamics of the motion near the points Xl and X2 has not been studied to date.

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It may well be that these points mark the end points of a reconnection line segment on the front lobe of the magnetopause surface. Referring to Figure 5, which represents a cut through the earth's magneto- sphere in the noon midnight meridional plane, it is seen that reconnection at the magnetopause, as described above, serves to transport magnetic flux from the interplanetary cell T and from the front-lobe magnetospheric cell into the polar cap cells 5 and 7.

The evolution of the field geom- etry in the noon-midnight meridional plane is shown in Figure Note the formation of an X type and an 0 type neutral point. The bubble originally has a very small longitudinal dimension. As it grows in size in the noon- midnight plane, it also occupies an increasing longitude sector. The actual three-dimensional magnetic field topology of such a bubble is not known, but it may be represented schematically by an X type and an 0 type null line as in Figure The points A, X, B and 0 in that figure all emerge at the same place at the time of onset of reconnection.

Subsequently they move apart as the reconnection process continues and the bubble grows. This field presumably has an inductive and an electrostatic part which tend to cancel along AOB while adding along AXB. By necessity the separatrix is everywhere tangential to the magnetic field. The field lines constituting the surface originate at a hyperbolic neutral point in the field, ii A separator is the line of intersection between two separatrices or the line of intersection of one separatrix with itself. The separator is also called reconnection line, merging line, or X line.

The terms neutral line, singular line, or critical line should be avoided, since they may refer to the 0-type topology as well.

In a highly conducting plasma, the dif- fusion 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. The term magnetic-field merging may be taken to encompass both reconnection and annihilation.


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It is desirable to express this rate in a nondimensional form by dividing the electric field by the product of a characteristic velocity and a characteristic magnetic field. In nonsteady flow, the electric field at the refer- o Af ence point, E , in general differs from E , and M? How- ever, the one adopted here, in terms of an electric field component along the separator works also for flows at arbitrary R. Note also that for the degenerate case of magnetic field annihilation there is no plasma flow across a separatrix.

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There is, however, an electric field and a corresponding magnetic flux transport. The Convection Region The plasma dynamics in the regions away from the immediate neighborhood of the reconnection line usually is described by use of continuum equations. Nonsteady solutions have not been found to date, which describe rapid con- figuration 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,. Three-dimensional solutions also have not been obtained. Hence the discussion in the present section is confined to steady- state plane reconnection.

While this limit is invalid in most cosmic applications, it has the advantage of yielding simple analysis. Thus it provides an opportunity to study certain basic features of the reconnection flow without undue mathematical complications. We first des- cribe two incompressible reconnection flows with fundamentally different be- havior.

Certain compressibility effects are considered in the second subsection. The third subsection discusses asymmetric reconnection configurations, perhaps applicable to the magnetopause. The fourth subsection deals with the recon- nection of magnetic fields that are not antiparallel, a common situation at the magnetopause. Finally, a partial single-particle model is discussed briefly.

The model contains a set of four Alfve"n discontinuities which in compressible flow may be identified. As pointed out by Vasyliunas, this behavior is charac- teristic of fast-mode expansion of the plasma as it approaches the reconnection line.

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Because the fast-mode propagation speed is infinite in the incompressible limit, such expansion is by necessity an elliptic effect, that is, no standing expansion wavelets are possible. 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.