Geophys. Res. Lett., 21, 2451, 1994
© Copyright 1994 by the American Geophysical Union
Paper Number 94GL02292
Abstract. Previous surveys of the magnetopause current layer indicated that its thickness ranges from 200 to 1800 km and on average is about 900 km or ~ 10 ion gyroradii [Elphic and Russell, 1979; Berchem and Russell, 1982]. In the present study, we have used ISEE magnetic field data to examine the magnetopause current layer under high beta magnetosheath conditions. Under high beta conditions, we find that the current layer is thinner than observed under typical conditions. The thickness is typically between 200 to 600 km and the peak of the distribution scales to 2-4 ion gyroradii for the high beta magnetopause. However, the velocity of the magnetopause is found to be highly variable similar to the highly variable distribution observed under more typical conditions. A wave-like structure is often observed at the foot of the current layer extending from the current layer into the magnetosheath. The presence of this propagating wave structure at the foot of the magnetopause may lead to some confusion in attempts to determine the thickness of the current layer with a single spacecraft.
The Earth's magnetopause is a complex boundary consisting of both field and plasma transitions. The current sheet flowing at the boundary of the magnetosphere that changes the magnetic field directions and magnitudes characteristic of the magnetosphere to those characteristic of the magnetosheath has been the classical definition of the magnetopause [Chapman and Ferraro, 1931]. However, our present understanding of the magnetopause boundary indicates that the field transition and plasma transition often have different spatial extents and the changes in the plasma occur over a much wider spatial range. In this paper, we attempt to determine the thickness and structure of the magnetopause current layer under the extreme condition of high plasma beta.
Knowledge of the thickness and structure of the magnetopause current layer is crucial to understand physical processes occurring in the interface and has important implications for theoretical models of the magnetopause. It can be used to assess the validity of different theoretical models of microphysical processes at the magnetopause. Prior to the launch of the dual ISEE spacecraft, a considerable effort was made to estimate experimentally the thickness of the magnetopause current layer from single spacecraft measurements [Cahill and Amazeen, 1963; Holzer et al., 1966; Heppner et al., 1967; Cummings and Coleman, 1968; Aubry et al., 1971; Kaufmann and Konradi, 1973; Neugebauer et al., 1974; Sonnerup and Ledley, 1979]. Since the magnetopause is continually in motion, the first step is usually to estimate the speed of the magnetopause in order to separate the temporal and spatial variations. In most of the approaches, this is done by using data from multiple crossings, assuming that the boundary oscillates radially and sinusoidally, or by using plasma measurements. Then the thickness of the magnetopause is obtained from the duration of the current layer crossing. In these early works, the number of cases that could be studied was limited. The speed of the magnetopause was estimated to range from a few km/s to ~60 km/s and a thickness of ~100 - 1000 km was deduced from the magnetic field measurements. A thickness of this scale corresponds to ~1 - 10 gyroradius for 1-keV proton in a 40 nT magnetic field.
The data from the dual ISEE spacecraft made the first major advance in determining the thickness and studying the structure of the magnetopause current layer. The two spacecraft co-orbited in a highly elliptic orbit with separation distance ranging from a few tens km to a few thousand km. The simultaneous measurements can separate temporal and spatial variations under some assumptions and thus reduce some ambiguities in determining the velocity of the magnetopause. Using magnetic field data from the dual ISEE spacecraft, it was found that the velocity of the magnetopause ranges from 4 to 80 km/s and is highly variable even during a single boundary traversal [Russell and Elphic, 1978]. Earlier observations from single spacecraft underestimated this velocity. The thickness of the magnetopause is found to be distributed over a large range between 200 to 1800 km with an average of ~ 900 km or ~ 10 ion gyroradius [Elphic and Russell, 1979; Berchem and Russell, 1982]. This thickness is much greater than the hybrid gyroradius scale expected from the Ferraro model [Ferraro, 1952] and one ion gyroradius in the modified results [Parker, 1967]. The greater thickness may be due to the fact that generally there is a strong magnetic field in the magnetosheath.
It is our objective to use the magnetic field data from ISEE 1 and 2 to determine the thickness of the magnetopause current under various solar wind conditions. Ultimately we wish to investigate how the strength and the direction of the magnetic field affect the thickness and the structure of the current layer. We report in this paper a study of one part of parameter space, a study of the thickness and structure of the magnetopause current layer observed when the magnetic field strength is very low in the magnetosheath, or there is a large increase in the magnetic field strength across the current layer. At such times, the plasma beta is very high and the magnetosheath magnetic field is expected to play a less important role in the interaction. Under these conditions, the magnetopause has its closest analogy to the classical simple model of the magnetopause current layer, the interface of unmagnetized plasma on one side and a vacuum magnetic field on the other side.
Selection of Crossings. In the present study, we have used magnetic field data from the dual ISEE spacecraft with full resolution (0.25 s) to determine the thickness of the magnetopause current layer under high beta magnetosheath conditions. By high beta, we mean the magnetic field strength on the sheath side is very small compared to that on the magnetospheric side. Figure 1 shows the magnetic latitudes and longitudes of magnetopause crossings used in this study. The size of the symbols corresponds to the ratio of the magnetic pressures across the local magnetopause, or B2^2/B1^2, where B2 and B1 are the magnetic field strength, averaged over one minute interval, in the magnetospheric side and magnetosheath side, respectively. This ratio roughly represents the plasma beta in the local magnetosheath due to the pressure balance across the magnetopause. This study is concerned with those crossings for which the ratio of magnetic pressures is greater than 10. Twenty-two crossings are selected from 12 orbits, including multiple crossings from the same orbit.
Solar Wind Conditions. We have examined the simultaneous solar wind data observed upstream by either IMP-8 or ISEE 3 and found that several upstream conditions will lead to a high beta condition at the local magnetopause. For majority of the cases in this study, the high beta is associated with high beta and high Mach number in the solar wind due to small interplanetary magnetic field (IMF) strength or large solar wind density or a combination of both. In this case we expect the plasma beta to be high everywhere in the magnetosheath. However, sometimes high beta can be caused locally by some special IMF orientation. For example, when the IMF is nearly flow-aligned, or the IMF cone angle is very small, the magnetic field lines diverge with the solar wind streamlines near the subsolar magnetopause. At such times, the magnetosheath beta near the subsolar magnetopause can be very high regardless of IMF strength and solar wind beta. In one of our cases, the subsolar magnetopause crossing near 1328 UT, October 30, 1980, the IMF strength is very high (8.55 nT) but the cone angle is very small (11 degrees). We also noted that the magnitude of the Bz component was less than 1 nT for all the cases in this study, whether the Bz component was positive or negative.
Structure. We show here the detailed structure of the magnetopause current layer to illustrate how we determine the thickness of the current layer. Figure 2 shows an example of the high-beta magnetopause crossing near 1435 UT, December 11, 1977. The top panel of Figure 2 is the simultaneous magnetic field data (4-s resolution) from ISEE 1 (thick traces) and 2 (thin traces) in GSM coordinates from 1420 to 1450 UT. It is characterized by a very small magnetic field strength in the magnetosheath. Near 1425 UT, there is a short excursion of the magnetosphere/boundary layer. Near 1435 UT, ISEE 2, and then ISEE 1, make a complete crossing of the magnetopause current layer. At this time, the spacecraft are located at (6.94, -5.95, 4.85) RE in GSM coordinates with a separation of 794 km overall and 713 km along the boundary normal direction. After the magnetopause crossing, there are three short excursions of magnetosheath/boundary layer near 1442, 1444 and 1448 UT, respectively, due to the unsteady boundary motion.
The bottom panel of Figure 2 shows details of the current layer crossings in the interval 1433:30 to 1436:30 UT. The magnetic field data with full resolution (0.25 s) are displayed in the boundary normal coordinates, where L is along the magnetic field in the magnetosphere and N is normal to the local magnetopause boundary. The current layer is characterized by a sharp decrease in BL as well as in field strength. The time delay from ISEE 1 to ISEE 2 is nearly constant across the current layer. An average of 12.5 s is measured from the two BL components. From this time delay, the calculated magnetopause velocity is 54.9 km/s relative to the Earth and 57.3 km/s relative to the spacecraft.
From the magnetopause velocity, time can be transformed to distance. We can also calculate the density of the current that causes the change of the magnetic field, assuming that BL and BM only vary along the boundary normal direction: JL=(dBM/dt)/VMP and JM=-(dBL/dt)/VMP, where VMP is the velocity of the magnetopause. Figure 3 shows the magnetic field versus the distance from the foot of the current layer. In this figure, the current layer observed by ISEE 1 and 2 is aligned. The thickness of the current layer (from CS to CE in Figure 3) is 487 km. This thickness is defined from the profile of the azimuthal current density JM (not shown). It is smaller than the separation of ISEE 1 and 2 (713 km). This is consistent with the observation in Figure 2, where ISEE 2 leaves the current layer about 5 seconds before ISEE 1 enters the current layer. It is apparent that the structure of BL is very different at the foot of the current layer at ISEE 1 and 2. A propagating wave-like structure extends from the current layer to the magnetosheath. The wave extends for half a cycle and ISEE 1 and 2 see the wave structure at different phases. The wave seems to be associated with the current layer, since it does not appear to be the same as the waves observed in the magnetosheath immediately upstream from the current layer. Similar types of structure have been observed in 10 out of 21 crossings. We also note that the wave-like structure at ISEE 2 is very similar to the precursor wave at the foot of Uranian magnetopause current layer observed by Voyager 2 [Russell et al., 1989], where the plasma beta is very high due to the solar wind conditions at large heliospheric distance.
It has been reported that the thickness of the magnetopause current layer determined by the change of field direction is sometimes greater than that determined by the change of the field strength [Kaufmann and Konradi, 1973; Ogilvie et al., 1971; Neugebauer et al., 1974]. Our observations demonstrate that even the thickness defined by the change of field direction is sometimes not reliable when only single spacecraft data are available due to the wave attached to the current layer. The observation from a single spacecraft can not resolve this wave structure. Observations from two spacecraft with high time resolution can remove this ambiguity. From Figure 3, it is apparent that the main current layer occurs from point CS to point CE. This is in general agreement with the current layer defined by the field strength only when the sheath field is very small. If we used the BL component from ISEE 2, we would have obtained a much thicker current layer.
The magnetopause velocity can vary very quickly, resulting in apparently different magnetic field structures at ISEE 1 and 2. Figure 4 shows a high beta magnetopause crossing in September 27, 1980 and is in the same format as Figure 2. At this crossing, the spacecraft is located near (8.31, -1.91, 3.89) RE in GSM coordinates. ISEE 1 and 2 are separated by 839 km overall and 714 km along the boundary normal coordinates. The ISEE 1 and 2 magnetopause crossings are nearly two minutes apart. However, the time duration of the current layer crossing at ISEE 1 is 63.2 s, much greater than the duration of 17.3 s at ISEE 2. This may be caused by the very different magnetopause velocity at the two times. ISEE 1 crosses nearly stationary current layer at the spacecraft velocity. Later the magnetopause passes ISEE 2 with a large velocity. Using the velocity of ISEE 1 along the magnetopause normal (2.4 km/s), the thickness of the current layer is estimated as 151 km. If we assume this thickness stays the same at ISEE 2 crossing, the velocity of the magnetopause during the ISEE 2 crossing is 8.8 km/s relative to the spacecraft and 6.2 km/s relative to the Earth. Using the time delay technique, the magnetopause velocity averaged over the entire current is 2.1 km/s relative to the Earth. This gives a thickness of 171 km. Both estimates are in general agreement.
Using the estimated magnetopause velocities at ISEE 1 and 2, we transform the time into the distance from the foot of the current layer, as shown in Figure 5. This figure is obtained by assuming that the thickness of the current layer stays the same at ISEE 1 and ISEE 2. After the current layer is aligned, it is clear that a wave-like structure at the foot of the current layer is seen by both ISEE 1 and 2. Similar to the previous crossing in Figure 2, the BL component has different phase at ISEE 1 and 2. The bi-polar signature in the BN component associated with the wave and not seen in the previous crossing has the appearance of a flux transfer event (FTE). The phase of the bi-polar signature is opposite at ISEE 1 and 2. This is contrary to the strong positional control of the bi-polar signature seen in true FTEs [Rijnbeek et al., 1984; Berchem and Russell, 1984]. We believe this structure is associated with the current layer but is not a flux transfer event, since they are not seen simultaneously at ISEE 1 and 2 as would true FTEs. Rather they are seen two minutes apart in time at the same spatial location, the foot of the current layer. The spacecraft separation is much less than the typical scale length of a flux transfer event ( ~ 1 RE). We note that even in single satellite studies of the magnetopause, this event would not be classified as an FTE because of its duration (< 20 s) and because it occurred on the boundary where surface waves may mimic FTE signatures.
Thickness and Velocity. We have estimated the thickness and velocity for all 21 high beta magnetopause crossings. The time delay technique was used to determine the velocity and thickness of the magnetopause current layer. Whenever the spacecraft separation is a few times smaller than the thickness, we also use the staircase technique to determine the thickness [Russell and Elphic, 1978] and compare with that from time delay technique. We have found that the results agree with each other within 100 km. Especially when the field variation in the current layer is smooth, the results are almost identical. Figure 6 shows the distribution of the velocity and thickness of the magnetopause current layer. The top two panels are reproduced from Berchem and Russell  containing magnetopause under various conditions. The bottom two panels are from this study. The velocity of the magnetopause is highly variable and the distribution of the velocity is similar to that in Berchem and Russell . However, under high beta conditions, the magnetopause current layer is thinner than under typical conditions. The smallest thickness in this study is 149 km and 80% of the currents layers in this study have a thickness less than 600 km. The peak of the distribution occurs in the range between 200 to 400 km, about half of the thickness for typical magnetopause in Berchem and Russell . The thickness of this scales to ~ 2 to 4 gyroradii of magnetosheath thermal ions of ~ 107 oK in a 40 nT magnetic field. Due to a limited number of cases, we did not obtain any dependence of the thickness upon the location of the magnetopause crossing, such as on latitude, longitude or solar zenith angle.
We have studied the magnetopause current layer under the extreme condition of very low magnetosheath field strength, or high plasma beta. Under this condition, the magnetopause should be most similar to the interface separating an unmagnetized plasma from a magnetic field. However, the magnetopause current layer structure is far from simple. A wave-like structure is sometimes observed at the magnetosheath edge of the current layer. Two spacecraft observations reveal that the wave appears to be propagating rather than standing. The wave is similar to the precursor wave observed at Uranian magnetopause where the plasma beta is very high [Russell et al., 1989], suggesting that plasma beta is an important parameter in determining the structure of the magnetopause current layer. The presence of this propagating wave structure at the foot of the magnetopause may lead to some confusion in attempts to determine the thickness of the current layer with a single spacecraft.
The velocity of the magnetopause is found to be highly variable under high beta conditions. It ranges from 0 to 200 km/s and the distribution is similar to that observed during typical conditions in Berchem and Russell . However, the thickness of the high beta magnetopause is found to be thinner than that under typical conditions. It scales to 2-4 ion gyroradii for the high beta magnetopause compared to ~ 10 ion gyroradius under typical conditions.
In earlier theoretical models, the magnetopause current layer has been considered as an interface separating an unmagnetized plasma from the magnetic field [e.g., Ferraro, 1952; Parker, 1967; Su and Sonnerup, 1971]. The thickness of the current ranges from the electron skin depth to one ion gyroradii, or ~ 2 to 100 km, from the predictions of these models. Our observations are taken from cases closest to these models, but the observed thickness is still much greater. We hope that this result can help in assessing the validity of the different theoretical models of microphysical processes at the magnetopause.
Acknowledgments. This work was supported by the National Science Foundation under research grant ATM91-11913.
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(Received April 11, 1994; revised July 25, 1994; accepted August 16, 1994)
Figure 1. Magnetic latitudes and longitudes of the magnetopause crossings in this study. The size of the symbols represents the ratio of magnetic pressures across the magnetopause.
Figure 2. Simultaneous magnetic field observations from ISEE 1 (thick) and ISEE 2 around the magnetopause crossing on December 11, 1977.
Figure 3. The magnetic field versus the distance from the foot of the current layer near the December 11, 1977 magnetopause crossing. The distance is deduced from the magnetopause velocity.
Figure 4. Simultaneous magnetic field observations from ISEE 1 (thick) and ISEE 2 around the magnetopause crossing on September 27, 1980.
Figure 5. The magnetic field versus the distance from the foot of the current layer near the September 27, 1980 magnetopause crossing. The distance is deduced from the magnetopause velocity.
Figure 6. Histograms of the velocity (left panels) and thickness (right) of the magnetopause. The top panels are reproduced from Berchem and Russell  for magnetopause under various conditions. The bottom panels are from this study containing only high beta magnetopause.