ISEE LESSONS FOR CLUSTER
C. T. RUSSELL
Originally published in Proceedings of the Cluster-II Workshop: Multiscale/Multipoint Plasma Measurements, ESA SP-449, edited by R. A. Harris, p. 11-23, European Space Agency, Noordwijk, 2000.
Magnetic field and plasma measurements obtained by the three spacecraft International Sun Earth Explorer mission (ISEE 1, 2 and 3) are examined for possible lessons in the operation of the Cluster mission and the analysis of data therefrom. We examine interplanetary shocks, upstream waves, the bow shock, magnetosheath, magnetopause and magnetotail. No one separation distance is optimum for multi-site measurements in these regions since different phenomena of interest have different scales. Because several of the phenomena to be examined oscillate in position about some average location through which the spacecraft passes, too great a spacing risks significant velocity changes between sightings, or the possibility of some sites not observing the phenomenon. The need for a variety of different separations over the course of the mission adds a new dimension to the study space and requires increased observing time over that of a single spacecraft mission so that the proper combination of plasma conditions and spacecraft configuration are obtained to solve the problem at hand.
The magnetosphere is constantly in motion. Its boundary regions, both inside and outside the magnetopause, are constantly moving. These motions occur because of dynamics internal to the magnetosphere, such as substorms, because of changes in the dynamic pressure of the solar wind and because of changes in the orientation of the interplanetary magnetic field. These boundaries move more rapidly than our spacecraft, often passing over them many times as they traverse the average location of that boundary. Theory gives us scales for these boundaries that can be used to check the theory if we can but measure that scale size in the midst of its motion. Other lengths such as wavelengths, damping lengths and correlation lengths are also of great interest.
ISEE 1 and 2 and their companion upstream monitor, ISEE 3, were launched in 1977 and 1978 in order to address problems of various length scales in the outer magnetosphere, magnetosheath, and near-Earth solar wind [Ogilvie, 1982]. In August 1978 the ISEE-3 spacecraft was launched toward the forward libration point along the trajectory shown in Figure 1 [von Rosenvinge, 1982]. At 237 Re in front of the Earth the libration point data would provide a measure of the solar wind typically 60 minutes prior to its arrival at Earth. However, to minimize fuel usage the orbit was allowed to execute a very large path around the L1 point and as a result was seldom near the streamline intersecting the front of the magnetosphere. The first lesson for Cluster is that the upstream monitor needs to be as close as possible to the solar wind - Earth flow line. A suitably close distance for most purposes is inside 50 Re [Russell et al., 1980; Crooker et al., 1982; Kelly et al., 1986].
|Fig. 1 The trajectory that ISEE 3 took toward its libration point (L1) rendezvous [von Rosenvinge, 1982].|
The ISEE-1 and 2 spacecraft were in identical orbits with variable separations as sketched in Figure 2. In the course of the year as the Earth orbited the sun, the magnetotail maintained its antisunward orientation and crossed the inertially fixed orbit so it appeared that the orbit precessed around the magnetosphere. Gravitational perturbations altered the height of perigee and the orientation of the line of apsides in the course of the mission so that the coverage of the magnetopause and shock varied from year to year. After a very successful launch in October 1977 and 10 years of operation ISEE 1 and 2 entered the atmosphere over Brazil in 1987. The figure of merit of the separation of ISEE 1 and 2 is the time delay between the crossing of the same altitude. This time separation was as large as about 5000 s but was more typically about 300 s. Since there was no
|Fig. 2 The ISEE-1 and 2 orbit illustrating its annual "precession".|
single separation that could achieve all objectives a plan of sweeping the smaller spacecraft ISEE-2 past ISEE-1 with varying rates of motion and maximum separations was adopted. Figure 3 shows the planned and actual temporal separations at apogee for the first two years of the ISEE-1 and 2 mission. One lesson for the ISEE science team when they first saw the actual separation was that a close coupling between the spacecraft operations and the science planners was needed because the plans were not always executed properly and the science team needed to know the separation for planning science operations. Furthermore the science team was very surprised when it learned that the mission began acquiring less simultaneous data from the two spacecraft at large separations because two antennas were needed to acquire data and these were generally not available. When this problem was appreciated plans were changed so that less operation at large separations was requested. The lesson for Cluster is to monitor the actual separations as closely and as frequently as possible, and, when depending on real time transmission as ISEE did, keep the spacecraft as close together as the objectives allow. The ISEE mission reduced its science capability by about one half by not including a tape recorder. Fortunately the lesson was learned by the Cluster mission planners very early.
|Fig. 3 The initial separation strategy of ISEE 1 and 2. One second separation is equivalent to 2 km at a distance of 15 RE.|
This paper is a complement to an earlier paper written in anticipation of the original Cluster launch (Russell, 1994). We have attempted not to duplicate material in that article but herein have updated our thoughts on some of those earlier topics and added new topics not discussed in the earlier article. Analysis of the ISEE 1 and 2 data continues to this day and still bears fruit and provides lessons for the new generation of multi-spacecraft missions. Other treatments of multipoint measurements can be found in the volume edited by Russell .
2. INTERPLANETARY SHOCKS
The choice of four spacecraft for the Cluster mission was not an arbitrary choice. It represents the minimum number that can determine the orientation and relative speed of a planar discontinuity from measurements of the time of arrival of the plane at the four sites. The four spacecraft themselves cannot lie in a plane but must be
|Fig. 4 Four encounters with the same interplanetary shock on August 18, 1978 as seen in the magnetic fields. Projection of the satellite locations in the GSE XY plane are shown [Russell and Alexander, 1984].|
arranged in a tetrahedron of finite volume. The ratio of the volume of the tetrahedron to its surface area is a figure of merit of the capability of Cluster to make this particular measurement. Figure 4 shows four magnetic profiles observed at ISEE 1, 2, 3 and IMP-8 in August 1978, and the locations of those observations projected on the ecliptic plane. If we denote these locations as 1, 2, 3 and 0, then the shock normal and the speed of the shock along the normal can be determined from the following equation:
where D X10 is the separation vector between spacecraft i and spacecraft 0 and x, y and z are the coordinate axes of the system in which the calculations are performed. V is the speed along the normal and D toi is the time for the planar surface to move from spacecraft 0 to i [Russell et al., 1983]. We assume that the shock speed is constant over the region including the observations and that the shock is plane. A fifth spacecraftís data could easily be added to this solution and the resulting solution would be overdetermined. If one were to have five spacecraft, the equation would be solved by multiplying each side of the equation by the transpose of the leading matrix on the lefthand side that contains the relative locations of the spacecraft. The resulting matrix on the lefthand side is then a square 3x3 matrix. Its inverse can be found, multiplied times the righthand side and the solution for V and N found. This overdetermined solution is analogous to a least squares fit and can be used to estimate the errors in the procedure. These errors may be due to curvature of the front, acceleration of the surface, uncertainties in the measurements etc. Thus it is important to place as many constraints on the determination of the surface orientation as possible. Moreover even with Cluster it is possible that all four discontinuity encounters are not obtained especially if the discontinuity is one that approximately stands in the Earthís frame such as the bow shock and the magnetopause. Fortunately the MHD equations provide us with further constraints. The vectors D B, Bu x Bd, Bu x D V are all perpendicular to the shock normal and can be added to the above equation with zeros in the corresponding element of the D t vector. Here Bu and Bd are the upstream and downstream magnetic fields and D V and D B the changes in the vector velocity and magnetic field across the shock [Russell et al., 1983]. These vector relations can be combined at a single shock crossing to obtain the so-called coplanarity normal [Colburn and Sonett, 1966] and the mixed mode normal [Abraham-Shrauner and Yun, 1976].
The errors in each of these measurements may be quite different so some caution must be used. In general the magnetic field can be measured very precisely but the vector velocity of the solar wind is not so precisely determined in part because it is a multi ion fluid and these multiple ions are not identified separately when moments are taken. A very important caveat is that these formulas require measurements that are basically simultaneous. Thus if the conditions in the solar wind are changing, then one has to be careful to obtain measurements on either side of the discontinuity that correspond to the same upstream conditions. If one can not do this, then the MHD constraints should not be used as the resulting normal will be incorrect and misleading. At interplanetary shocks for magnetic field measurements that are rapid (sub-second cadence) this issue is seldom a problem, except for the waves produced by the shock over which an average should be taken. Solar wind velocity measurements can take an order of magnitude or two longer to be performed than magnetic field measurements but fortunately the solar wind plasma can be steady for a minute or more. However, at the bow shock, where one crosses the shock more slowly, the shock-driven waves upstream and down also extend over a greater distance, and changes in IMF orientation frequently occur on the time scale needed to apply magnetic coplanarity.
3. UPSTREAM WAVES
There are basically four different types of ULF upstream waves in the region where interplanetary magnetic field lines intersect the bowshock. Examples of each of these types of waves are shown in Figure 5. One-Hz waves are whistler mode waves produced at the shock whose group velocity is sufficient to carry the waves upstream along the magnetic field [Orlowski et al., 1995]. Doppler shifting is important for this wave as it can both alter the handedness of the wave and change high frequency cutoffs into low frequency cutoffs etc. These waves are seen independently of the presence of particle beams. At slightly lower frequencies is a rare but spectacular circularly polarized wave that is so intense that it modulates the magnitude of the magnetic field. This wave is produced by backstream anisotropic ion beams [Blanco-Cano et al., 1999]. At still lower frequencies are the 30-second waves that are also driven by backstreaming ions with both resonant and non-resonant instabilities. Finally illustrated in the lower right hand panel are shocklets and discrete wave packets that appear to be non-linear evolutions of the 30-second waves [Russell et al., 1971]. These waves appear to be incipient small shocks that do not have sufficient strength to stand in the flow and are convected backward toward the bow shock. The discrete wave packet on the "trailing" edge is actually a leading "standing" whistler mode wave packet like those seen on the fronts of low-Mach-number shocks. As these waves convect toward the shock they grow and slow
|Fig. 5 Four types of upstream waves [Russell, 1994]|
down as they become fully capable of decelerating the solar wind plasma [Russell, 1988; Thomsen et al., 1988]. These waves were also called SLAMS by a later researcher. This term should be avoided if only because it appears to be plural even though it refers to a single structure so that it can be confusing to use in an English sentence, e.g. "the SLAMS is growing as it approaches the shock". The original shocklet is to be preferred.
The correlation length determines the spacing over which meaningful comparisons of waveforms can be performed in this region. If one wishes to measure wavelengths or wave periods one needs to observe the same wave at multiple locations and not just similar waves. The correlation length of the one-Hertz waves is very short. The 50% level is reached at about 0.02 RE or 120 km on average. Thus the study of these waves will be very difficult for Cluster over the presently planned range of separations. For the three-second waves the correlation length transverse to the flow is about 0.5 RE or 3000 km and for the 30-second waves the correlation length is about 1 RE. Since these lower frequency waves are slowly growing as they are swept toward the bow shock they have longer correlation lengths in the direction of the solar wind flow.
Close separations in the range 100-6000 km are important for studying the plasma physics of upstream waves but they do not tell the whole story as there is a large scale variation in the basic properties of the waves with location in the foreshock. This variation was explored with the AMPTE/UKS and ISEE-1 and 2 spacecraft in late 1984 [Russell et al., 1986]. An example of the behavior is shown in Figure 6 which illustrates the waveform measurements at UKS (top right) and ISEE-2 (bottom right) when both spacecraft are in the upstream region near the bow shock (lower left). The top left panel compares the power of the waves seen as a function of frequency at the two locations. At high frequencies the spectra are identical but the low frequency waves are seen only at UKS. In other regions the spectra are similar but the amplitudes are different. There is great variation in the waves seen as one moves through the foreshock under constant solar wind conditions. We note that one might attempt such a study statistically but since so many parameters in the solar wind vary, such as the Mach number, beta,
|Fig. 6 Upstream waves seen simultaneously by UKS and ISEE-2. Right hand panels show the wave forms. Top left panel shows the power spectrum and the lower left panel shows the geometry of the foreshock and spacecraft in the B-V plane [Russell et al., 1986].|
and magnetic field orientation, that it is difficult to compare one region with another under the same solar wind conditions except using simultaneous multipoint measurements.
4. BOW SHOCK
The bow shock is very important because it produces the first and largest alteration of the solar wind plasma as it approaches the Earthís magnetopause. The bow shock is a highly non-linear wave that slows, compresses, heats and deflects the flow around the magnetic obstacle. It is of much theoretical interest to determine how this is achieved. At one time wave processes were deemed to be responsible for the dissipation, but Scudder et al. [1986a, b] demonstrated that the process was a steady state process. Waves, of course, arise in this non-equilibrium plasma as it returns to a maxwellian state but the main processes involve pressure gradients and electric potential drops. The scale size over which the transition occurs is of much interest and that can be determined with two spacecraft only if the shock orientation is known. This is not as difficult to determine as that of an interplanetary shock because the geometry of the interaction provides a good first order estimate of the shock orientation. The goal of such studies is to produce results such as those in Figure 7 that shows the magnetic field change across the shock front for increasing shock strength from subcritical to slightly supercritical. Displayed this way, as a fraction of the distance along the shock normal normalized by the ion initial length, the shocks appear to be quite similar in thickness, even though they were crossed in varying lengths of time because of the different velocities of the shocks. However, the high frequency waves do look different. This may be an artifact if the waves in the original time series are affected by the anti-aliasing filters in the magnetometer. The waves on the shocks that are moving quickly can be Doppler shifted to higher frequencies and attenuated. Thus it is important to have a wide bandwidth in performing this study.
|Fig. 7 Magnetic field strength at five terrestrial bow shock crossings as the Mach number varies from subcritical to supercritical plotted versus ion inertial length.|
As mentioned earlier the bow shock oscillates about its average location and if the multiple spacecraft are separated too much then the bow shock will turn around and move backward before it crosses all the spacecraft. At the other extreme, if the spacecraft are too close, then there are uncertainties in timing the arrival of the shock that are comparable to the transit time between spacecraft so that the speed of the shock becomes uncertain. A range of separations of 50 to 500 km was found to be suitable for the ISEE study of shocks.
The shocks in Figure 7 are all quasi-perpendicular shocks with the orientation of the interplanetary magnetic field greater than 45o from the shock surface. In the quasi-parallel regime when the field is less than 45o from the shock surface the structure can become much more turbulent. Greenstadt et al.  showed that the correlation length in this region is short, less than 1000 km. It is perhaps surprising that the correlation length is so short here because the upstream waves that are convecting backward toward the shock have a correlation length of 1 RE. However, something very spectacular happens when these waves arrive at the quasi-parallel shock. Figure 8 shows an example of ISEE-1 and 2 data obtained very close to a high Mach number quasi-parallel shock [Russell, 1988]. The ISEE-1 data have been shifted by 1.5 sec to account for the solar wind travel time. The steepened was being convected by the solar wind toward the shock and ISEE-2, 600 km upstream from ISEE-1, sees the upstream waves structures first as expected. Near the shock where ISEE-1 is located, the waves slow down and the field becomes compressed. The difference in field strength over 600 km is very striking but the wave structures at ISEE-1 are clearly the same as those that convected over ISEE-2 seconds earlier, only amplified. Understanding what triggers the sudden slow down and amplification of the field and how the upstream waves affect the quasi-parallel shock is an important area in which Cluster can contribute.
|Fig. 8 ISEE 1 and 2 measurements of upstream waves immediately in front of the quasi-parallel bow shock on Sept. 1, 1979. The ISEE-2 spacecraft is 600 km in front of the ISEE-1 spacecraft at this time. ISEE 1 data have been shifted by 1.5 see to compensate for the solar wind convection time. ISEE 2 always sees the upstream waves first but the ISEE 2 signatures nearer to the quasi-parallel shock can be much larger [Russell, 1988].|
The magnetosheath is the region of shocked plasma that has been deflected to flow around the magnetosphere. The compressibility of this plasma determines the standoff distance of the shock front. When the Mach number of the shock drops, the magnetosheath is not much compressed and the shock moves outward away from the magnetopause. If the solar wind velocity drops below that of the fast magnetosonic mode, then the shock will move to infinity. In general three different waves are needed to make an arbitrary change in the flow of a plasma. The fast magnetosonic wave is just one of these three. There are two more, the Alfven or intermediate mode and the slow magnetosonic mode. The Alfven wave, that travels at an intermediate speed, should stand off from the magnetopause further than the slow mode that will match the flow speed closer to the magnetopause. The plasma and the field must both be carried around the magnetosphere but obey different laws. Flow of the plasma along the magnetic field can remove plasma from a region but the parallel flow of that plasma does not affect the field. The field lines must be transported by the motion perpendicular to the magnetic field. The Alfven wave rotates both the magnetic field and the flow. If the plasma needs to be turned in such a way that the field and flow can be twisted together, an Alfven wave can do the job. However, if the plasma and field have to be essentially separated, this is the role of the slow wave. In the slow wave the magnetic pressure and thermal pressure are in anti-phase so that the magnetic field increases when the plasma is depleted. The slow wave is also very much guided by the magnetic field so that it should be geometrically restricted and move with changes in the direction of the IMF.
Evidence for the slow mode has been reported by Song et al. . Figure 9 shows such evidence in the form of an enhanced density where the magnetic field is depressed. We note that downstream from this region just the opposite happens. The density drops and the
|Fig. 9 ISEE-2 plasma and magnetic field data on a pass through the magnetosheath. The region of slow mode density enhancement is indicated by dashed vertical lines and shading [Song et al., 1992].|
magnetic field builds up. This behavior is that of a slow mode expansion wave.
The slow mode wave is a propagating wave. A similar but non-propagating wave is the mirror mode wave illustrated in Figure 10 [Huddleston et al., 1999]. Such waves have been found in cometary comas, in the wake of Io, in the interplanetary medium, and in the magnetosheath. The magnetosheath is the only place where such waves have been studied with multiple spacecraft. In Figure 11 we show a set of such oscillations seen by ISEE-1 and 2 on December 21, 1977 when the spacecraft are only 54 km apart in the direction along the magnetopause normal and 500 km apart parallel to the magnetopause surface. There is almost no correlation between these structures at the two locations. Studies on other days show that the spacecraft need to be within about 100 km of each other to become significantly correlated and even then there are occasioned large differences. Thus studying mirror mode waves with Cluster may be very difficult despite the great theoretical interest these waves have engendered because of their enigmatic origin.
|Fig. 10 Schematic illustration of the structure of mirror mode waves. Top panel shows the trapping of charged particles in magnetic bottles. The bottom shows the time series of magnetic field and density as the spacecraft traverses these structures [Huddleston et al., 1999].|
|Fig. 11 Mirror mode oscillations seen at ISEE-1 and 2 on December 21, 1977 when the spacecraft were 54 km apart along the magnetopause normal and 500 km apart parallel to the magnetopause surface [Russell, 1994].|
Some of the most significant results of the ISEE mission were obtained at the subsolar magnetopause. Here was the first compelling in situ evidence for reconnection, the acceleration of plasma away from the subsolar region by the action of the magnetic field stress [Paschmann et al., 1979]. Figure 12 shows the field and plasma measured at a multiple crossing of the magnetopause [Sonnerup et al., 1981]. This event shows the acceleration of the plasma induced by the reconnection of antiparallel fields at the subsolar magnetopause. It demonstrates by its steadiness across the multiple crossings at the two spacecraft that reconnection can take place as a steady-state process. It is not just explosive or transient.
|Fig. 12 Plasma and magnetic field measurements across multiple crossings of the magnetopause when reconnection was taking place almost continually [Sonnerup et al., 1981].|
One of the longest running controversies in the study of the magnetopause is the relative roles of diffusion, the Kelvin-Helmholtz instability and reconnection. Since boundaries between various magnetopause plasma layers are quite sharp even for northward IMF [Song et al., 1990] it is clear that diffusion does not play an important role at the magnetopause. While Kelvin-Helmoltz waves seem to be present, it is not clear that they provide much momentum transfer across the boundary. Again reconnection seems to be the process that creates the sharp plasma boundaries, makes them oscillate and transfers momentum. This is true whether the IMF is northward or southward.
Figure 13 shows a subsolar magnetopause for southward IMF. This figure emphasizes how turbulent is the current sheet in the presence of strong reconnection. This also is a good example to illustrate another misconception about the magnetopause. The magnetopause is a thick boundary several tens of ion gyro-radii thick [Berchem and Russell, 1982]. However, as is evident here within that transition from magnetosphere to magnetosheath there can be sharp ion gyro-radius-sized transitions within that layer.
|Fig. 13 Plasma and magnetic field measurements across the subsolar magnetopause for southward IMF.|
The temporal resolution at which the magnetopause is probed is also important. Figure 14 shows a hodogram of the magnetic field as ISEE crossed the magnetopause on August 9, 1978. The top panels shows the measurements as 12-second averages. The bottom panels show the same data at full quarter-second resolution. The difference is striking. A strong 27 nT normal component occurs temporarily right in the middle of the crossing [Russell, 1995].
|Fig. 14 Hodograms of the magnetic field across the magnetopause at 2009 UT on August 9, 1978 for 12s average (top) data and full resolution (0.25s) (bottom) data [Russell, 1995]. Coordinate system is the boundary normal system with N along the normal.|
If one is interested in determining the current structure of the magnetopause one would like to use Cluster to measure the curl of the magnetic field. It is worth emphasizing how close the spacecraft need to be to do this. Figure 15 shows magnetic field measurements when ISEE 1 and 2 were separated in space by only 15 km [Elphic, 1988]. In the bottom panel are the differences between the two spacecraft. We see that the difference in the field strength is less than about 10 nT everywhere while the total current flowing in the magnetopause causes a field change of about 100 nT. Thus the two spacecraft appear to be both in the current sheet at the same time and separated by a small fraction of the thickness of the sheet. Since magnetometers can easily resolve differences even smaller than this, smaller separations would be possible and would enable even thinner current sheets to be resolved. However, to exploit this technique at the magnetopause with Cluster requires separations that are much smaller than presently planned.
|Fig. 15 The magnetic field (top) the difference magnetic field (bottom) when ISEE-1 and 2 were within 15 km on Nov. 12, 1997 [Elphic, 1988].|
A final lesson about the magnetopause for Cluster regards its size and shape. It is quite clear that the solar wind dynamic pressure controls the overall size of the magnetosphere but it has not been as clear what controls the relative balance of magnetic flux in the dayside magnetosphere and in the tail. The studies of Petrinec and Russell [1996a, b, c] have shown that it is the southward component of the IMF that controls the shape of the magnetosphere and the flux in the tail. When the IMF is northward the shape of the magnetopause and flux in the tail is quite constant.
7. FLUX TRANSFER EVENTS
In the neighborhood of the magnetopause the magnetic field component along the normal to the magnetopause often points outward for some tens of seconds and then inward or vice versa. At the magnetopause itself magnetosheath plasma often is seen mixed with magnetospheric plasma in tubes of magnetic flux in which these fluctuations in the normal magnetic field occur. Furthermore, these tubes of plasma and magnetic flux are moving, possibly at a speed greater than that of
the magnetosheath plasma. These events were termed flux transfer events, or FTEs, by Russell and Elphic , because these events represented transient transport of magnetic flux and appeared to be associated with subsolar reconnection. Much work has been done on these events in the interim, some of it challenging the initial hypothesis, other work adding to the original hypothesis, but none of it altering the basic picture, first proposed.
Figure 16 shows over one hour of ISEE 1 and 2 measurements at the magnetopause on November 29, 1977 [Elphic and Russell, 1979]. The magnetic field in the magnetosheath is southward and in the magnetosphere (on the right) is northward. The magnetic field in the magnetosheath is very weak on this day so that the FTEs are quite noticeable in the field magnitude. The normal component is quite consistent from event to event: first outward and then inward. The BL and BM components parallel to the magnetopause surface do change. At the first encounter the FTE field is southward, at the next encounter it is mainly westward and in the third encounter it is strongly westward with no BL component. As is obvious from this figure none of these directions is similar to that of the field in the magnetosphere or the magnetosheath. The field of the FTE is quite distinct.
|Fig. 16 The magnetic field in boundary normal coordinates across the magnetopause in the presence of FTEs on November 29, 1977 [Elphic and Russell, 1979].|
Our interpretation of FTEs is shown in Figure 17. The FTE is formed by the interconnection of a magnetosheath flux tube with a magnetospheric flux tube. The interconnection process has an onset and a termination so that a structure of finite (about 1 RE) extent is formed. This structure then convects across
|Fig. 17 Artistís conception of the connection of the FTE to the magnetosphere. Right panel shows the expected draping of the magnetic field over this tube.|
the magnetopause surface and straighten as much as it can. As shown on the right of Figure 17, the resulting bulge pushes the magnetospheric field lines inward and magnetosheath field lines outward causing the normal component signature that we discussed above as the structure moves away from the subsolar point. This layered structure of draped and interconnected flux tubes has been confirmed by Le et al. [1999a] with plasma observations. A critical observation would be of the field orientation where the magnetic field lines enter the magnetosphere. One such possible observation has been reported by Zhu et al.  in which the magnetic field is oriented almost along the normal to the magnetopause. Since FTEs are fairly large structures they are ideal for study by the Cluster spacecraft. Nevertheless we still recommend that the separation used in this study be kept to a fraction of the typical FTE dimension so that the entire constellation fits inside the FTE at the time of encounter. A size of 1000-2000 km should be appropriate.
|Fig. 18 Location of UKS and ISEE during the period of on 19 September 1984 when they both observed the effects of FTEs [Elphic and Southwood, 1987].|
Periods of larger separation could also be profitably used as well. Figure 18 shows the location of ISEE 1 and 2 and AMPTE/UKS on Sept. 19, 1984 when the three spacecraft (and AMPTE/IRM) passed through the magnetopause 8 RE apart nearly simultaneously. As shown in Figure 19 correlated disturbances were seen at the two sites indicating the global nature of the magnetopause disturbance [Elphic and Southwood, 1987].
|Fig. 19 The normal component of the field at UKS and the total field at ISEE-1 and ISEE-2 as the three spacecraft crossed the magnetopause on 19 September 1989 when both were sensing FTEs.|
8. THE MAGNETOTAIL
The current sheet in the tail lies almost parallel to the ISEE-1 and 2 orbit. Thus the spacecraft only slowly crossed the current sheet. This had some advantages and some disadvantages. Fortunately Cluster crosses the current sheet principally along its normal and will complement the results from the ISEE mission. In order to determine the electric current density in the plasma sheet we needed first to find the normal to the current sheet and we needed to find times when the sheet moved swiftly and completely past the spacecraft. Times when the solar wind direction changed rapidly proved to be good times to probe the current sheet [McComas et al., 1986]. These authors find a current density of about 50 na/m2 and a current layer of about 10,000 km in thickness with a sharp maximum in the center.
Another phenomenon in the tail that would benefit from the Cluster configuration is the bursty, bulk flow [Angelopoulos et al., 1994]. These events, that are associated with rapid plasma flows, >400 km/s, but 10ís of minutes and involve an unknown cross-section of the tail. These events must be quite wide in extent because it is easy to find such flow bursts associated with auroral zone activity.
Another lesson to be learned from ISEE is the dependence of the thickness of the current layer on magnetic activity. In this study the long term residence of the ISEE spacecraft near the current sheet is an advantage. Figure 20 shows the location of ISEE-1, 2 and IMP-8 on April 22, 1979 when all three spacecraft were in the tail and near the current sheet [Zhou et al., 1997a; 1997b]. We can use the difference in the field measurements at the two spacecraft as modeled with a Harris current sheet to model the distance of ISEE from the current sheet and the thickness of the current.
|Fig. 20 Location of IMP-8, and ISEE when tail study period commenced at 0840 UT on April 22, 1979 [Zhou et al., 1997a].|
Figure 21 shows the thickness of the current sheet as a function of time on April 22, 1979 and the position of the center of the current sheet in GSM coordinates. The increase in the calculated thickness at the time of the current sheet crossings reflects the simplifying assumptions used such as that the current sheet moves simply up and down as a unit and there are no surface waves traveling along the sheet. Cluster could avoid these assumptions. The important observation here is the variation with time of the current sheet thickness. The (half) thickness of the current sheet is initially about 2 RE thick but after 10 UT when the IMF turns southward the current sheet thins significantly to less than 0.5 RE thick. This observation is ideally suited for follow-up by Cluster using its snapshots of current sheet density in a statistical study ordered by the IMF conditions and substorm phase.
|Fig. 21 (Top) Magnetic field in the X-component at ISEE-1 and 2 during a disturbed period on 22 April, 1979. (Middle) The inferred location of the center of the current sheet using a Harris current sheet model. (Bottom) the inferred thickness of the sheet [Zhou et al., 1997b].|
9. SUMMARY AND CONCLUSIONS
The ISEE mission has paved the way for later more sophisticated missions. It has enabled the refinement of techniques for using multiple spacecraft and it has provided lessons on how to conduct such missions. In particular it has shown that a good solar wind monitor is essential for all studies of the dynamic magnetosphere and that this monitor needs to be closer than 50 RE to the solar wind flow line that intersects the nose of the magnetosphere. Most importantly that monitor must be continuous. IMP-8 was not a suitable substitute for ISEE-3 measurements when it was hijacked to study the tail and later the comet Giacobini-Zinner studies that were performed better later with, spacecraft properly instrumented for tail and comet studies.
Four spacecraft can determine the normal to a discontinuity if they are appropriately in a tetrahedron of finite volume and not coplanar, but this alone may not be sufficient to characterize the discontinuity. The discontinuity might be accelerating; it might be curved; and there might be noise or other sources of errors in the measurements. Thus it is necessary to use other constraints such as those provided by Maxwellís laws to find the best normal determination.
The phenomena encountered in geospace have a variety of scale sizes and correlation lengths. The upstream wave correlation lengths vary from 100 km to 6000 km. Thus a strategy of variable separations is needed. The science team should oversee this strategy closely to ensure that it is carried out. Moreover, they should ensure that the necessary overlapping data from all four vehicles are acquired. Missing data and data gaps were very detrimental to the science return from the ISEE mission.
There are also important objectives that can be addressed with large multi-RE separations. The advantage of these studies over statistical studies using individual satellites is that the observations are obtained under identical solar wind conditions facilitating comparisons.
Temporal resolution is an important consideration since varying Doppler shift is caused by the varying velocity of structures past the satellite. Anti-aliasing filters are essential in preserving the integrity of the data but they can affect the apparent frequency content of the observations due to the motion of the boundary. The rapid changes near the quasi-parallel shock requires much further study and all bow shock studies require separations of 500 km or less because of the variable motion of the shock.
The magnetosheath is an understudied region. Techniques have now been developed for comparing quantitatively with numerical models [Song et al., 1999a,b] by properly scaling and normalizing the data. Studies also show that the fast mode shock is only one of several important waves that can significantly affect the flow. The multipoint measurements of Cluster will be able to identify these structures more clearly than has been done thus far. Cluster will not be able to address the structure of some very small scale phenomena such as mirror mode waves or the current density of the magnetopause from the curl of B without careful attention to the accurate determination of spacecraft location and a strategy that brings the spacecraft very close together.
The magnetopause is a very dynamic plasma environment that is suited for Cluster multipoint measurements. However, the data rate needs to be high to resolve the small scale features and the spacecraft need to be within about 500 km of each other to resolve the motion of the boundary. Flux transfer events have been extensively studied but the process that initiates them is not well defined. It may be possible to find structures similar to FTEs near the cusp under northward IMF conditions [Le et al., 1999b]. Again widely spaced measurements can be used to study large-scale transport and large-scale variation in properties at the magnetopause, just as they can in the upstream wave region.
The orbit of cluster is particularly well suited for probing the current sheet in the tail as it moves rapidly perpendicular to the current sheet. While this will not provide long term monitoring of tail properties as the state of the tail responds to the IMF direction and substorm phase, it will give accurate snapshots of the tail current. Cluster is also better suited than ISEE for studying bursty, bulk flows if periods can be found where Cluster lingers longer near the current sheet.
In summary ISEE has served as an excellent pathfinder for the Cluster mission. It has tested many analysis techniques that will prove useful for Cluster. It has sharpened the scientific focus on a number of significant outstanding questions and it has defined the range of separations and temporal resolutions needed to solve these outstanding questions. All that remains now is to get the Cluster spacecraft safely into orbit and to operate them for a sufficiently long time for the data to be acquired to solve the problems at hand. We emphasize in closing that the solar wind plasma conditions are quite variable and the right combination of plasma condition, Cluster location, and separation configuration to address any particular question may be rare. Thus acquiring as much data as possible and extending the mission as long as the budgets allow is extremely important, yea critical to the success of the Cluster mission.
I am extremely grateful to the many collaborators and students who worked with me on the analysis of the data from the ISEE mission. In particular I thank UCLA students, C. J. Alexander, V. Angelopoulos, R. C. Elphic, M. H. Farris, T. J. Kelly, G. Le, D. J. McComas, D. S. Orlowski, S. M. Petrinec, L. Scurry, P. Song and X.M. Zhu, who all made important contributions to the study of the ISEE data, and also my colleagues, C. A Cattell, R. J. Fitzenreiter, J. T. Gosling, E. W. Greenstadt, C. C. Harvey, M. M. Hoppe (Mellott), D C. Hubert, C. Lacombe, J. G. Luhmann, F. S. Mozer, K. W. Ogilvie, S. Ohtani, G. Paschmann, N. Sckopke, J. D. Scudder, B. U. O. Sonnerup, M. F. Thomsen and X-Y. Zhou. This review was supported by the National Aeronautics and Space Administration under research grant NAG5-7721.
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