Earth and Space Sciences Department and Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California 90024-1567
in Physics of Magnetic Flux Ropes (edited by C.T. Russell, E.R. Priest and L.C. Lee) Pages: 439-453 American Geophysical Union, Washington, D.C., 1990.
While the dipolar magnetic field of the Earth has been known for at least four centuries, the fact that it is bounded on the sunward side by a magnetopause is but a recent concept. The magnetopause was invented to explain the phenomena surrounding geomagnetic storms. Chapman and Ferraro [1931a,b; 1933; 1940] proposed that a plasma, consisting of equal numbers of ions and electrons was emitted by the sun at active times and disturbed the Earth's magnetic field. When this stream hit the Earth's magnetic field it was deflected. Figure 1 shows the situation for a half-space filled with this highly electrically conducting gas. The magnetic field lines are confined to the half-space in which there is a vacuum. Mathematically the field lines in this case are equivalent to those distorted by the presence of an image dipole parallel to the first dipole and an equal distance on the other side of the plasma boundary.
In reality the plasma surface is not planar but curves around the magnetic field as shown in Figure 2. The magnetic cavity is leaky and solar wind plasma enters the interior of the magnetosphere to cause the late or main phase of the storm. The early or compressional phase is caused by the sudden increase in solar wind pressure that pushes the boundary closer to the Earth. Originally, it was thought that the streams were intermittent. However, we now know that the solar wind blows all the time but with varying intensity. Thus there is always a magnetopause. However, as we will see herein the properties of the magnetopause are quite variable.
It was not long before speculation arose about the nature and structure of the magnetopause despite the fact that the evidence of such a boundary was indirect. Figure 3 shows the original simple, perhaps overly simple, paradigm of the structure of the magnetopause [Ferraro, 1952; Willis, 1971]. In this model the flow of cold, unmagnetized plasma comes in from the top and blows against the terrestrial magnetic field. Ions are deflected to the right and electrons to the left. If a charge separation electric field is set up by the differing gyro radii of the ions and electrons then the thickness of the boundary will be the geometric mean of the electron and ion gyro radii. However, if the electric field is neutralized (say by ionospheric electrons) then the thickness will be that of the ions.
The magnetopause is not so simple. As we will see in this review the boundary is several ion gyro radii thick. Nevertheless there is substructure that could be the Ferraro boundary. The reason for this greater than expected thickness is at least in part due to the magnetic field carried by the solar wind. The boundary is not simply a current layer between a cold flowing unmagnetized plasma and a magnetic field. It is the boundary between two hot magnetized plasmas and these two plasmas can interact at the interface.
One way these plasmas can interact is through the process called reconnection. Reconnection affects the plasmas at the magnetopause in many ways. The most important effect is to join magnetic field lines which were originally not joined. This allows the plasmas to mix along the magnetic field lines. The magnetic geometry of the reconnected field lines accelerates plasma initially but later, downstream, decelerates it. This deceleration takes energy out of the flow and stores it in the magnetic field built up in the tail. Thus the magnetopause is a region of both acceleration and deceleration, as well as one of mixing and heating.
The year 1961 was a very important year for the magnetopause both observationally and theoretically. Explorer 10 was launched on March 25 of that year into a very eccentric orbit in the antisunward direction. Only 52 hours of data were obtained on this battery-powered mission which provided measurements out to 43 Earth radii (Re). Part of the orbit skimmed what we know now to be the tail magnetopause, the interface between the geomagnetic tail and the magnetosheath. These first data on the magnetopause are shown in Figure 4 which were obtained at 15 Re by Heppner et al. . While these data provided little resolution on the structure of the magnetopause they did reveal that the magnetopause was constantly in motion. This motion which is much more rapid than the velocity of the spacecraft complicated the study of the magnetopause because it is difficult to convert the temporal profile of a boundary crossing into a spatial profile, and compare the thickness of the boundary with that expected theoretically.
Later this same year, on August 16, Explorer 12 was launched into an elliptical orbit with an apogee of 14 Re initially near noon. As the Earth moved around the sun, apogee which was approximately fixed in inertial space moved around the magnetosphere to dawn. Thus when transmissions ceased on this solar-panel powered spacecraft nearly 4 months later on December 6, Explorer 12 had sampled the entire dawnside near equatorial magnetopause [Cahill and Amazeen, 1963; Cahill and Patel, 1967]. Figure 5 shows the earliest published magneto-pause crossing from this mission. The analysis of the magnetic field data from Explorer 12 provided us with the foundation for our understanding of the magnetopause for the next decade until the launch of the ISEE spacecraft. Fairfield and Cahill  used these data to provide the first real evidence for the reconnecting magnetopause, for example. However, it was data from another spacecraft, OGO-5, which showed that reconnection eroded the magnetic flux from the dayside magnetopause and transported it to the tail [Aubry et al., 1970; Russell et al., 1971].
The year 1961 also marked the publication of J. W. Dungey's classic model of the reconnecting magnetosphere in which magnetic field lines carried by the solar wind link up with the terrestrial field where the magnetic field lines are antiparallel [Dungey, 1961]. Field lines in the noon-midnight meridian are sketched in Figure 6 for the two cases when the interplanetary magnetic field is antiparallel to the magnetic field near the nose of the magnetosphere (top) and when it is parallel (bottom). In the former case a circulation pattern is set up which can be a steady state pattern but which in practice is quite time varying because the direction of the interplanetary magnetic field varies. In fact, it is the imbalance of the reconnection on the front side of the magnetosphere with the return of magnetic flux from the nightside which causes the erosion of the magnetopause associated with a southward turning of the interplanetary magnetic field. When the interplanetary magnetic field is northward, reconnection still occurs but this time on open magnetic field lines which transports no flux or as sketched here which creates a dayside field line out of a nightside one. While the evidence for this model was strong it did not gain wide acceptance until the 1980's when the results of the ISEE mission became available. The direct observation of the predicted accelerated plasma was the decisive piece of evidence [Paschmann et al., 1979; Sonnerup et al., 1981].
In 1977 the co-orbiting International Sun Earth Explorer 1 and 2 spacecraft were launched into the same highly elliptical orbit extending out to 23 Earth radii. Gas carried on ISEE-2 allowed the separation of ISEE-1 and -2 to be varied so that time delays between boundary crossings could be used to measure the boundary velocities. In order to understand the observed magnetic structure and to measure spacecraft separation, boundary normal coordinates were used [Russell and Elphic, 1978]. These are illustrated in Figure 7. The N direction is chosen to be along the magnetopause normal. The L direction is northward along the magnetospheric field and the M direction is tangential to the boundary toward dawn. The difficulty in using these coordinates is in determining the direction of the normal. Sometimes when the magnetopause is quiet and one may assume that there is no reconnection across the interface one can simply assume that the magnetopause is a tangential discontinuity and take N along the vector cross product of the magnetospheric and magnetosheath magnetic fields. At other times there is sufficient rotational structure that one can find the normal to be along the direction of most constant field or the minimum variance direction [Sonnerup and Cahill, 1968]. At other times one simply has to use the average geometry of the boundary.
The magnetopause is constantly in motion and the velocity of this motion is variable. Figure 8 shows the L-component of the magnetic field in boundary normal components measured by ISEE-1 (heavy line) and ISEE-2 (light line) as the spacecraft made multiple crossings of the magnetopause [Russell and Elphic, 1978]. The L- component increases as the magnetopause is entered. The first entry by ISEE-1 is only partially followed by ISEE-2. After retreating into the magnetosheath again both spacecraft then enter the magnetosphere solidly from about 0742 to 0743 and then return to the magnetosheath. Then after 0751 they again enter the magnetosphere. The horizontal lines joining the magnetic measurements made by the two spacecraft show the time delay between the arrival of the two spacecraft at equivalent locations in the magnetopause. If we divide these time delays into the separation along the normal we obtain the velocities shown on the bottom of the plot. The boundary velocity is quite variable ranging from about 3 to over 40 km/s and typically being about 20 km/s much faster than the velocity of the spacecraft.
Similar analyses have been carried out on a large number of magnetopause crossings by Berchem and Russell [1982a]. The results of these analyses are shown in Figure 9. Velocities over 300 km/s have been recorded. Typically the thickness of the magnetopause as seen in the change in magnetic field strength and direction is between 400 and 900 km, which is equivalent to many thermal ion gyro radii. Since the velocity and thickness measurements are coupled an error in one would affect the other. Figure 10 shows a plot of the measured thickness versus the velocity. They appear to be uncorrelated. Thus we feel these measurements are in fact accurate representations of the velocity and thickness of the magnetopause defined to be the region in which the magnetic field changes from its magnetosheath orientation and strength to those in the magnetosphere.
The motion of the magnetopause seems to be driven by pressure fluctuations in the solar wind and by reconnection but not by the Kelvin- Helmholtz instability at least over the dayside of the magnetopause. Figure 11 shows the amplitude of motion of the magnetopause as measured by ISEE-1 and -2 from the subsolar point past the terminator when the interplanetary magnetic field (IMF) was strongly southward (top) and strongly northward (bottom) [Song et al., 1988]. For southward IMF the boundary motion increases with distance from the subsolar point. For northward IMF the amplitude remains constant and perhaps decreases. Examination of the amplitude of pressure fluctuations on the magnetopause show that they are large enough to cause the observed boundary motions for northward fields. However, when the IMF is southward the amplitude of motion is much greater than can be explained by solar wind pressure variations. Reconnection must be the cause of these variations. The Kelvin-Helmholtz instability could cause an increase in amplitude with distance from noon but it cannot be operative here because it would also cause such an increase for northward IMF and it does not.
The magnetopause is a complicated plasma boundary even under the best conditions. Figure 12 shows plasma data and magnetic field data across the subsolar magnetopause when the interplanetary magnetic field was strongly northward [Song et al., 1989]. There are five regions of different plasma conditions on this plot. On the left is the magnetosheath where the ion density is high about 40 cm-3 and the temperature relatively cool. The magnetic field and the plasma pressure oscillate out of phase so that the total pressure is fairly constant. These are probably mirror mode waves. As the spacecraft moves closer to the Earth it encounters a region of decreasing density and increasing field strength. Again, the total pressure is fairly constant. This sheath transition layer may be just a boundary layer in the magnetosheath formed as the magnetosheath flows along the magnetopause. Streamlines closest to the magnetopause move the slowest and hence have the oldest plasma. These tubes then have longer time to empty (along the field line) via pitch angle diffusion and thermal motion. Hence the tubes near the magnetopause are less dense. This may correspond to the Zwan-Wolf  depletion layer. We note that this entire region would be included in our previous determination of magnetopause thickness.
The magnetic field and plasma then undergo a small but abrupt change and enter an outer boundary layer. This abrupt change may in fact correspond to the classical Ferraro current layer with a thickness of less than an ion gyro radius. In the outer boundary layer the density drops to a roughly constant level and the temperature rises. As the spacecraft proceeds inwards it enters the inner boundary layer again with a discrete density and temperature. Finally, the spacecraft enters the magnetosphere. The fact that the boundaries between the layers are sharp and the regions between the boundaries moderately uniform indicates that there is little diffusion present at this magnetopause crossing.
The distribution functions of electrons and ions for this magnetopause traversal are shown in Figure 13. The interesting feature of these distributions is that they all cross at a single point and that they are bounded by the magnetosheath and magnetospheric distributions. This means that all interior distributions can be made from the 2 limiting distributions by simple mixing with no acceleration or heating. This raises the question as to how the magnetosheath and magnetospheric plasmas mix without diffusion. Perhaps there is some transitory reconnection, possibly at high latitudes or at all latitudes as proposed by Nishida .
The magnetopause is somewhat different when the IMF is southward. Figure 14 shows the plasma and magnetic field data for such a crossing when ISEE was near the subsolar point [P. Song et al., unpublished manuscript, 1989]. The plasma density is more nearly constant in the transition layer but there is heating and perhaps some acceleration of the bulk motion. As before there is a small but abrupt jump in the magnetic field and plasma at what may be the Ferraro current. In the model of Heyn and Rijnbeek [Heyn et al., 1988; Rijnbeek et al., 1989] the region of depressed field is bounded by two slow shocks one of which is this current layer. However since we do not have full 3D plasma data here we cannot further check this hypothesis. The boundary layers here are quite rarefied and consequently the temperatures are probably in error. The important point to note is that the boundary layers are so rarefied that they are probably open to the magnetosheath or tail and not trapping any plasma. Figure 15 (not available yet) shows the electron and ion distribution functions across the magnetopause. The distributions do not cross at a single point and the magnetosheath and magnetospheric distributions do not bound the other curves. There is acceleration heating and particle loss occurring at this magnetopause.
The acceleration of plasma at the magnetopause depends on more than just direction of the IMF. Figure 16 shows the change in plasma flow velocity seen when the magnetosheath magnetic field was strongly southward as a function of the plasma beta [Paschmann et al., 1986]. It is apparent from this plot that the magnetic field has to be strong relative to the plasma pressure for reconnection to accelerate plasma to high velocities.
Another behavior of the magnetopause that seems to be dependent on the beta of the plasma is the rotation of the magnetic field in the plane of the magnetopause. Berchem and Russell [1982b] showed that the magnetopause usually rotated the magnetic field vector through the shortest rotational path as shown in Figure 17. While generally true this is not universally true. Figure 18 shows the magnetic variation through the Uranian magnetopause which occurred under very high plasma conditions. Here the field does rotate through more than 1800 . This behavior is also seen in some terrestrial magnetopause crossings when is very high [C. T. Russell et al., unpublished manuscript, 1989]. The behavior is similar to that of a slow mode magnetohydrodynamic wave, and appears to be analogous to the whistler standing wave often observed on the leading edge of a fast collisionless shock.
It is difficult to determine the geometry of such 3-dimensional structures with two spacecraft. Thus there is still some ambiguity. Simulations both in the laboratory and in the computer can provide some guidance here, even though the exact relative scale lengths cannot be maintained in the laboratory and the resistivity of computer simulations may be artificial. Terrella experiments in which a magnetized plasma is fired down a tube at a magnetic dipole have shown that when the Alfven Mach number is low the reconnection pattern at the magnetopause strongly resembles the Dungey picture sketched in Figure 6. However at high Mach numbers when the IMF is strongly southward reconnection appears to take place at high latitudes in the south and north forming a visor or curl over the front of the magnetosphere [Dubinin et al., 1977; 1980]. The visor itself is subject to the tearing mode and then forms small tearing islands as shown in Figure 20. We note that FTE's do not look like tearing islands because they usually are well isolated from each other and they do not represent the passage of x-points because the field is strong when normal component of the field reverses, not weak.
When there is an east-west component of the IMF in addition to the southward component, rather than tearing islands, a rope appears [Dubinin et al., 1980]. The formation of this structure is shown in Figure 21. The rope is not connected by field lines to the magnetosphere. This rope cannot build up indefinitely. Eventually it must slide off to the north or to the south. Such a structure has many attractive properties. It is twisted so that it remains a discrete entity. Moreover, not only do FTE's appear to be twisted in directions different from the magnetosphere or magnetosheath but they also appear to require a twisted field configuration to balance their internal pressure [Paschmann et al., 1982]. It also provides connection to the magnetospheric plasma but since field lines are open to the solar wind on both ends the plasma can escape rapidly. Moreover, this configuration provides only a single rope across the magnetosphere that can only flow or roll one way north or south at a time while Elphic and Southwood  feel that the data requires that there be simultaneous perturbations in the north and the south.
This rope formation mechanism does seem to be consistent with the dependence of FTE occurrence on the southward component of the IMF shown in Figure 22 [Berchem and Russell, 1981]. When the IMF is more than slightly northward FTE's do not occur. In the Dubinin et al. model reconnection switches from field lines connected to the high latitude dayside magnetosphere to those connected to the polar cap thus shutting off rope formation. Another constraint is where FTE's are observed as a function of the IMF direction. This is shown in Figure 23 (not available yet) [Russell et al., 1985]. When the IMF is horizontal, FTE's are seen in a horizontal band along the equator. When the IMF is at 450 to the horizontal, the FTE occurrence band swings around the subsolar point following the magnetic field. When the IMF is southward, there seems to be no clearly defined band of occurrence. This behavior at first glance is consistent with the Dubinin et al. picture, because the band where the ropes are formed should follow the IMF direction. However, since in this model the rope has to roll or slip around the magnetosphere it has to be detected everywhere on the boundary, not just in a band.
The only model that limits the FTE occurrence to a band is the transient, patchy reconnection model originally proposed by Russell and Elphic [1978, 1979] and shown in Figure 24. In this model magnetic field lines in the magnetosheath become connected to the magnetospheric field in the subsolar region and then create 2 connected tubes one convecting over the north and one the south. Simultaneous observations above and below the equator by ISEE and AMPTE seem to require two simultaneously oppositely moving tubes [Elphic and Southwood, 1987].
Many computer models have produced flux ropes in two dimensions and in three. Some of these result from subsolar multiple x-line reconnection [cf. Lee and Fu, 1985] and others are the result of high latitude reconnection [cf. Ogino et al., 1989]. However, the relevance of these structures to the observed properties of FTE's is still not clear. The exact geometrical structure of FTE's is still somewhat of a mystery.
Finally we note that Flux Transfer Events occur on the magnetopause of both Mercury [Russell and Walker, 1985] and Jupiter [Walker and Russell, 1985]. Figure 25 shows an example of a Mercury FTE. At Mercury the FTE's are brief, lasting only a second or two and more frequent than on Earth. At Jupiter the FTE's are similar in size and frequency to their terrestrial counterparts. This has led to a suggestion that both the magnetopause thickness and the dimensions of the system play a role in determining the size of FTE's [Kuznetsova and Zeleny, 1986].
Acknowledgments. The author thanks, R. C. Elphic and P. Song with whom most of the work described here was performed. This work was supported by the National Aeronautics and Space Administration under research grant NAG5-1067.