S. M. Petrinec1, T. Mukai1, A. Nishida1, T. Yamamoto1, T. K. Nakamura1, and S. Kokubun2
1 Institute of Space
and Astronautical Science, 3-1-1 Yoshinodai, Sagamihara, Kanagawa 229,
2Solar-Terrestrial Environment Laboratory, Nagoya University, Toyokawa, Aichi 442, Japan
Observations from the GEOTAIL spacecraft are used to examine the plasma flow and magnetic field within the magnetosheath, at intermediate downtail distances. Simultaneous measurements of the solar wind condition as measured by the WIND spacecraft are also used for this study. Close to the downtail magnetopause, we find that under appropriate solar wind conditions, the plasma flow velocity of the magnetosheath is slowest when the local magnetic field and velocity vectors are aligned, but are largest when the two vectors are perpendicular to one another, though the magnetosheath flow speed remains slower than or equal to the solar wind velocity. A simple model utilizing the magnetic field line tension and Alfvén phase speed is used to explain the observations. Occasionally, close to the magnetopause we find magnetosheath flows which are much greater than the solar wind velocity, but only for certain orientations of the local magnetic field. The source of these fast plasma flows is the low latitude boundary layer (LLBL), and is not the shocked solar wind plasma. Possible reasons for these very fast flows near the magnetotail magnetopause are explored.
Though much has been learned about the interplanetary environment, the physical processes associated with the plasma of the magnetosheath region have not yet been fully understood. The Rankine-Hugoniot relations across planetary bow shocks well describe the sudden change in physical quantities as the solar wind plasma crosses this boundary. In addition, the hydrodynamic relations of Bernoulli's equation and the Newtonian approximation, and the assumption of adiabatic flow enable us to estimate the downstream flow conditions along the surface of the obstacle in the solar wind flow. However, the flow behavior of the plasma in the interior magnetosheath region remains poorly understood. The early numerical gasdynamic model of Spreiter et al. (1966) provided a foundation for understanding the basic variations of density, velocity, and temperature of the plasma flow around the magnetosphere, and an external magnetic field was introduced into later numerical models (Alksne, 1967; Alksne and Webster, 1970; Spreiter and Rizzi, 1974).
In-situ observations of the magnetosheath region can be confusing to analyze, because this region supports a large number of wave modes and plasma instabilities (Song, 1994 and references therein). The behavior of the large scale magnetosheath magnetic field was examined by Fairfield (1967) using OGO 5 observations, while the characteristics of the plasma flow direction were studied by Hundhausen et al. (1969) (Vela 3) and Howe and Binsack (1972) (Explorer 33 and Explorer 35).
Much attention has been paid to the existence of slow mode structures close to the dayside magnetopause. The magnetosheath region along the stagnation streamline is believed to experience a depletion of the plasma density and an enhancement of the magnetic field as particles are squeezed out along the incident magnetic flux tubes (Midgeley and Davis, 1963; Lees, 1964; Sonnerup and Priest, 1975; Zwan and Wolf, 1976). Other studies, however, indicate that the plasma density should be enhanced in association with a decrease in the magnetic field as the plasma approaches the dayside magnetopause (Southwood and Kivelson, 1992). A recently proposed model by Southwood and Kivelson (1995) appears to reconcile these two contradictory models. Slow mode structures adjacent to the dayside magnetopause have been observed in several empirical studies (Crooker et al., 1979; Song et al., 1990, 1992).
Occasionally observations are reported of magnetosheath bulk flow speeds which significantly exceed those of the solar wind. An early examination of Explorer 33 and Explorer 35 plasma data by Howe and Binsack (1972) found occasional magnetosheath speeds adjacent to the magnetopause downstream of the Earth which were 10-20% greater than the solar wind. Two intervals of ISEE spacecraft observations near the magnetopause having magnetosheath plasma speeds 10-20% greater than the solar wind were also reported by Chen et al., (1993), who suggested that these fast flows were caused by plasma which had been accelerated in sling-shot fashion by the magnetic field line tension as the magnetosheath field was dragged around the magnetopause. Other observations of accelerated flows within the flank magnetopause current layer have been attributed to reconection processes (Gosling et al., 1986 (ISEE at low latitude); Kessel et al., 1996 (HAWKEYE at high latitude)).
In this work we examine the large scale flow behavior of the magnetosheath during two GEOTAIL passes near the magnetopause in the region downstream from the Earth. The simultaneous state of the solar wind was monitored with observations from the WIND spacecraft. The large scale behavior of the magnetosheath is analyzed in terms of previous models and physical understanding.
In this study we employ the magnetic field and plasma parameters obtained from GEOTAIL in the magnetosheath, and from WIND in the solar wind. The GEOTAIL plasma moments examined here are calculated from low energy particle (LEP) measurements of the magnetosheath by the Solar Wind ion analyzer with an energy range of 0.1 to 8 keV/Q (Mukai et al., 1994), and magnetic field values have been determined from the dual fluxgate magnetometers (Kokubun et al., 1994). The time resolution of the GEOTAIL data sets used are of approximately 12 second resolution. The distribution functions measured by the Faraday cups onboard the WIND spacecraft are used to determine the solar wind parameters (Ogilvie et al., 1995), while the interplanetary magnetic field is determined from measurements obtained by the WIND fluxgate magnetometer (Lepping et al., 1995). The temporal resolution of the WIND plasma parameters is between 82 and 94 seconds, and the WIND magnetic field measurements are at 92 second resolution. The temporal resolution of the WIND plasma parameters have been linearly interpolated to match the WIND magnetic field measurements.
Case 1: March 29, 1995
The terrestrial magnetosheath is bounded at the outer edge by a fast mode bow shock and on the inner edge by the magnetopause. Both of these boundaries are current sheets. The magnetopause current system separates and balances the mostly magnetic pressure of the interior magnetosphere from the kinetic, thermal, and magnetic pressures of the magnetosheath. A time series of an inbound pass of the GEOTAIL spacecraft through the equatorial magnetosheath on March 29, 1995 is shown in Figure 1. The magnetopause boundary is also (in the absence of reconnection processes) perfectly conducting. This is exemplified in Figure 2, as we examine the calculated GSE-components of the electric field from a four-hour period (08:55 - 13:25 UT). The spacecraft initially is approximately 4.5 Re from the magnetopause, and crosses the magnetopause at 13:25 UT. Electric field components have been determined from the simultaneous velocity components determined from the Solar Wind ion analyzer and the magnetic field measurements from the magnetometer on board GEOTAIL (E = -vxB). Figure 2a displays Ex-GSE along the horizontal axis and Ey-GSE along the vertical axis. During this four-hour period (with a temporal resolution of 12-seconds), the two components of the calculated electric field are extremely well-correlated (r = +0.996), and demarks the direction normal to the magnetopause. The slope of the regression line reveals a magnetopause normal of angle 20.75 °±0.05 ° to the Sun- Earth line. Figure 2b displays Ey-GSE and Ez- GSE. In this plane there is little correlation, and far greater scatter. There is little connection between the observed behavior in Figure 2b and the GEOTAIL trajectory during this period, nor is there any relation with the dipole tilt angle of the Earth. As we will discuss later, this variation is due to the influence of the magnetosheath magnetic field line tension and the consequential change in magnetosheath speed and direction, which in turn affects the magnetopause shape and position via pressure balance.
In Figure 3, we display the bulk plasma speed of the solar wind as determined by the WIND spacecraft, and the speed of the magnetosheath plasma as determined from the GEOTAIL plasma instrument. We have plotted each of these quantities as a function of their respective angle between the local velocity vector and the local magnetic field vector . The WIND observation period (at xGSE = 218, yGSE = 49, zGSE = 17 Re) has been advanced in time by the solar wind convection speed, to match the time period of GEOTAIL. The solar wind speed during this interval is very steady, and no dependence on the speed of the solar wind with the direction of the interplanetary magnetic field (IMF) is observed. However, the speed of the shocked solar wind plasma of the magnetosheath near the magnetopause is modified by the local magnetic field direction. We find that the magnetosheath plasma speed is slowest when the magnetosheath velocity and magnetic field vectors are aligned, and is fastest when these vectors are perpendicular to one another. The fastest magnetosheath speeds during this interval are approximately 12% slower than the solar wind speed. This behavior has been observed in other passes through the magnetosheath tailward of the Earth by the GEOTAIL spacecraft, though often the dependence is not very clear, due to the necessity of having an extended period of constant solar wind speed while the IMF changes direction. This enhancement of the magnetosheath bulk plasma speed is not due to the sign of the zGSM-component of the IMF; rather it is related to the magnetic field line tension of the shocked solar wind plasma as it is slowed and diverted around the magnetosphere, catching up to the unshocked solar wind plasma which shares the same magnetic field line.
Fig. 1. Time series for the GEOTAIL inbound pass through the magnetosheath and into the magnetosphere (shaded region) on March 29, 1995. The horizontal bar in the velocity panel is the average simultaneous speed of the solar wind, as determined from the WIND spacecraft. Parameters are plotted in GSE coordinates.
Fig. 2. Electric field components of the magnetosheath near the magnetopause as calculated from simultaneous measurements of GEOTAIL velocity moments and magnetic field measurements (-vxB), in GSE coordinates.
Fig. 3. The total velocity of the solar wind, as determined from the plasma observations from WIND, and the total velocity values obtained from GEOTAIL in the magnetosheath. Each quantity is plotted as a function of the angle between the local velocity and magnetic field vectors ().
The enhancement of the speed of the magnetosheath plasma close to the magnetopause as a function of can be best understood by treating the observed plasma velocity as two components; a base level velocity (vo) which is approximately equal to that determined by gasdynamics (with no magnetic field), and an additional component due to magnetic field line tension (v1). The acceleration of the plasma as determined from the Navier-Stokes equation varies with , such that the perturbation velocity (v1) is perpendicular to the ambient magnetic field and is parallel to the unit vector of the magnetic field line radius of curvature (we assume here that centrifugal forces are negligible, so that and v1 are parallel). In Figure 4, the velocity vo is in the equatorial magnetosheath (x-y GSE plane), and the magnetic field lies within a plane (x-z GSE plane) perpendicular to the equatorial plane. The entire magnetosheath region can be thought of as a perturbation of the IMF (in the solar wind rest frame) which initiates an Alfvén wave. The direction of propagation of this large scale Alfvén wave is determined by the angle between the solar wind velocity and the IMF. The magnetic field and velocity change caused by the bow shock and obstacle causes magnetic field line tension, which results in an increase in the bulk velocity (v1) as the shocked plasma struggles to catch up to the unshocked plasma of the solar wind which shares the same magnetic field line. This increase in bulk velocity is conjugate to the direction of propagation of the large scale Alfvén wave. The perturbation velocity components of the shocked plasma are then v1x=vAsin2 , and v1z=vAcossin, where vo is the local Alfvén speed (, where Bo and are the magnetosheath magnetic field intensity and mass density respectively) and is the angle between the magnetosheath magnetic field and the 'gasdynamic' velocity vo (these are the two parameters which define the coordinate system). This formulation gives v1 = 0 when the magnetic field and velocity vectors are aligned, and a maximum value of v1 = vA when the magnetic field is perpendicular to the velocity vo. We also put forth the conjecture that smaller amplitude Alfvén waves within the magnetosheath exist, but are constrained in amplitude according to the available energy. Specifically, given the magnetic field energy , for which the enhancement of bulk plasma kinetic energy is , then the maximum amplitude of the smaller scale Alfvén waves within the magnetosheath is . For such conditions, we can place a wave vector k along the ambient magnetosheath velocity vo, as displayed in Figure 4. Thus, the magnetic energy of the magnetosheath is expressed as Alfvén wave energy within the magnetosheath and an enhancement of the kinetic energy of the magnetosheath plasma flow. The distribution of magnetic energy between these two components is determined by the local direction of the magnetic field with respect to the local direction of the gasdynamic flow velocity (vo). The angle is closely related to but not exactly equal to (Figure 4). Assuming that the parameters at a given position do not vary with time, we are able to produce the following simple two-dimensional set of equations:
Fig. 4. Schematic of the gasdynamic velocity (vo), the perturbation velocity due to field line tension (v1), the magnetic field and polar diagram of the Alfvén phase speed.
A comparison of the model prediction with the observations of the magnetosheath velocity components is presented below. The following values have been used for the March 29, 1995 interval: <ni> = 9 cm-3, Bo = 14 nT, and vo = 375 km/s (to account for the expected presence of He++ ions, the mass density was increased by 16%). These values result in an Alfvén speed of 95 km/s, which is equivalent to the average Alfvén speed for this interval. Magnetic field and velocity components and values are calculated from the above equations for , and the velocity components are displayed as a function of in Figure 5. The observed magnetosheath velocity has been reduced to 2 dimensions by rotating about the zGSE axis to eliminate the yGSE-component. The calculated velocity components (and ) are compared with the observations. We find in Figure 5 very strong agreement between the calculated and observed components for this interval, confirming that the variation in magnetosheath flow near the magnetopause is ordered by the Alfvén phase speed. The variations in the z-component of the magnetosheath velocity also affect the balance of pressure at the magnetopause, and are the cause of the scatter in the z-component of the calculated electric field in Figure 2b. The differences and scatter of the GEOTAIL observations about the model prediction in Figure 5 are attributed to small changes in the solar wind properties, the continually changing distance of the spacecraft from the magnetopause (which is rarely exactly within the equatorial plane), and smaller scale turbulence and wave activity within the magnetosheath. The dependence of the plasma bulk flow of the magnetosheath with the local magnetic field direction is consistent with observations in the magnetosheath near the dayside magnetopause when the magnetic shear across the magnetopause is small, as reported by Phan et al. .
Unfortunately, it is difficult to directly examine the Alfvén wave activity within the magnetosheath region. One reason for this difficulty is the uncertainty of the Alfvén frequency. Unlike the closed magnetic field lines of the Earth's magnetosphere (which have a specific length and a well defined frequency), the magnetic field lines of the magnetosheath are open. Even if the Alfvén frequency is determined by the length of the magnetic field line through the magnetosheath (either from the bow shock to the magnetopause or from one side of the bow shock to the other), this length changes dramatically with the magnetic field orientation. In addition, the magnetosheath region supports a large number of wave modes at many frequencies (Song, 1994, and references therein), and many have both compressional and transverse components.
Fig. 5. The components of the bulk plasma speed of the magnetosheath as determined from observations from the GEOTAIL LEP instrument, as a function of (rotated into two- dimensions). Also plotted is the model based upon the Alfvén speed.
CASE 2: DECEMBER 5-6, 1994
On December 5, 1994, the GEOTAIL spacecraft was on an outbound pass from the magnetotail into the magnetosheath on the dawn side of the Earth. The spacecraft was located approximately 40 Re downstream from the Earth, and crossed the magnetopause several times, as the boundary swept across the GEOTAIL trajectory. In Figure 6, the shaded regions denote the magnetosphere. When the spacecraft was within the magnetotail, it appeared to be close to the neutral sheet, since there were several changes in the sign of the x-component of the magnetic field. However, the spacecraft was more often in the southern lobe (<zGSM> = -7.7 Re and the average dipole tilt angle was -20 °). Because of the motions of the magnetotail and variations of the magnetic field within, it is difficult to determine the shear angle of the magnetic field across the magnetopause.
We have plotted the bulk plasma speed of the magnetosheath (unshaded regions of Figure 6) as a function of in Figure 7a for the interval of 19:45 - 21:20 UT on December 5, 1994. Also shown in this figure are the speed of the solar wind as a function of the upstream , and the model curve, using the vo = 260 km/s, <ni> = 8.5 cm-3, and a magnetic field strength of 7.5 nT. The IMF during this time remained nearly perpendicular to the solar wind velocity, but had rotated about the solar wind velocity vector. Because of this rotation, the angle between the magnetosheath magnetic field and the magnetosheath velocity spans almost the entire range between 0 and 180 °, causing GEOTAIL in the magnetosheath to sample a large range of magnetic field draping configurations.
The magnetosheath speed is slowest when the magnetosheath velocity and magnetic field vectors are antiparallel. The plasma speed of the magnetosheath increases as decreases from 180 to 90 °. This behavior agrees with that observed in the previous example, and with the model. When the magnetosheath magnetic field and velocity vectors are parallel (both directed antisunward), however, the bulk speed is significantly faster than when these vectors are perpendicular to one another, and considerably exceeds the speed of the unshocked solar wind plasma. The convected solar wind IMF (in GSM coordinates) in Figure 7a is northward, while intervals of both northward and southward magnetic fields are observed in the magnetosheath. The magnetosheath magnetic field is always northward for < 90 °, and is both northward and southward for > 90 °.
The WIND spacecraft (at xGSE = 80, yGSE = -8, zGSE = 4 Re) recorded a sudden solar wind speed increase from ~330 km/s to ~380 km/s at 21:02 UT on December 5, 1994 (21:20 UT at the position of GEOTAIL). The model curve for the magnetosheath flow is now calculated for vo = 275 km/s, <ni> = 18.5 cm-3, and a magnetic field strength of 22 nT. Though the speeds of the solar wind and magnetosheath have increased as compared to the previous interval, the general behavior of the magnetosheath bulk speed as a function of local remains unchanged. When the magnetic field vector is most aligned with the flow velocity, the bulk plasma speed is more than 20% faster than that of the solar wind. In Figure 7b, the z-component of the magnetosheath magnetic field is both northward and southward in equal percentages across the entire range of , while the IMF remained northward throughout this interval. This indicates the presence of strong turbulence and/or wave activity in this region.
Fig. 6. Time series of magnetospheric and magnetosheath parameters as determined from GEOTAIL observations, on an outbound pass on December 5- 6, 1994. The solid horizontal lines in the velocity panel denote the average speed of the solar wind, as determined from the WIND spacecraft. Parameters are in GSE coordinates.
The behavior observed in Figures 7a and 7b for < 90 ° gradually disappears as the GEOTAIL spacecraft continues on its outbound pass. The bulk plasma speed of the magnetosheath in Figure 7c for < 90 ° after 00:40 UT on December 6, 1994 decreases as decreases from 90 to 0 °. This behavior is similar to that observed in Figure 3, and agrees well with the model prediction (using <ni> = 25 cm-3 and a magnetic field value of 25 nT). No significant change in the solar wind has been found to coincide with the change in behavior in the magnetosheath speed; thus, we conclude that the change in flow speed behavior for < 90 ° is simply related to the increased distance of the spacecraft from the magnetopause. After 06:00 UT on December 6, 1994 the solar wind speed again increases, and becomes unsteady.
Fig. 7. a-c) Plasma speed of the solar wind and magnetosheath, as a function of for three consecutive intervals. d-f) Plasma speed of the magnetosheath as a function of the ion number density. g-i) Magnetosheath ion temperature as a function of ion number density.
Although some of the high bulk plasma speeds lie adjacent to the magnetopause, some of the fastest flow intervals are found tens of minutes from the nearest clear magnetopause crossing, and we cannot conclude with certainty where the spacecraft is with respect to the magnetopause when these accelerated flows are observed.
Following the lead of Hapgood and Bryant (1992) and Sibeck and Gosling (1996), we examine the total velocity and ion temperature as a function of the ion number density for the three intervals of Figure 7a-c. Sibeck and Gosling (1996) have shown that this procedure can discriminate between the plasma populations of the dayside magnetosphere, magnetosheath, and intervening boundary layers. In Figure 7d-f we display the total bulk velocity versus the ion number density, and in Figure 7g-i the ion temperature versus ion number density, for the same intervals used in Figure 7a-c. During the first two intervals, the lowest ion densities coincide with the highest velocities and temperatures. Small ion densities suggest that the spacecraft is very close to the magnetopause (the ion density of the flank magnetosheath decreases with decreasing distance from the magnetopause in numerical models (e.g., Spreiter and Rizzi, 1974)), and may actually be sampling the outermost edge of the low latitude boundary layer. In any case, the implication is that plasma speeds near the magnetopause which are substantially (10-20%) greater than the solar wind plasma flow speed are not directly due to the shocked solar wind, but arise from the LLBL, and is indicative of dynamic processes occurring along the magnetopause. The most likely sources include magnetic reconnection, boundary waves such as the Kelvin-Helmholtz instability which cause the outer LLBL to pass over the spacecraft, or energetic plasma beams from the LLBL which are able to escape along the draped magnetosheath magnetic field, but remain close to the magnetopause. These features are not present during the third interval, as the GEOTAIL spacecraft travels further from the magnetopause.
Interestingly, magnetic reconnection along the magnetopause flanks appears to be the least likely cause of these flows. Since the GEOTAIL spacecraft often crossed through the southern lobe of the magnetotail, the fastest flows should have been observed when the magnetosheath magnetic field and velocity vectors are anti-parallel, rather than parallel to one another. It could be argued that perhaps reconnection is occurring along the northern lobe of the magnetotail (but near the equatorial plane) earthward of the spacecraft, and that the accelerated flows are observed by GEOTAIL while it is south of the equatorial plane. This does not explain, however, why accelerated flows are not also observed when approaches 180 °. Thus, other explanations for the existence of accelerated flows near the equatorial magnetopause downstream of the Earth are explored.
The second possibility is that the magnetopause is not a smooth surface, possibly due to the convection of foreshock waves through the bow shock and/or the generation of Kelvin-Helmholtz waves along the magnetopause. The suggestion that the magnetopause is not a smooth surface is supported by the correlation between the x- and y-components of the calculated electric field (r = -0.199, -0.880, and -0.775 for the three respective intervals). Though we have separated the magnetosheath observations from those of the magnetosphere, the spacecraft may still occasionally graze the outermost edge of the magnetotail, since the highest plasma speeds are associated with a low density, high temperature plasma. The dependence of boundary wave amplitude on the magnetic field orientation must be further studied.
The third possibility is that the draping of the magnetosheath magnetic field parallel to the magnetic field of the magnetotail allows higher energy particles of the low latitude boundary layer to easily escape the magnetotail along the draped magnetic field lines. The plasma of the LLBL is typically of greater flux at higher energies than the magnetosheath plasma, and are field aligned (Traver et al., 1991). Such higher energy particle fluxes are observed in the summary color spectrograms from the EPIC instrument during these intervals. If this is the case, then two distinct peaks should be present in the plasma distribution functions; a higher speed peak of LLBL particles, and a smaller, lower speed peak of shocked solar wind plasma. Unfortunately, because of the higher temperatures of the fastest flows, this feature could not be discerned.
The magnetopause is, in the absence of reconnection, a very highly conducting bundary, as evidenced by the extremely high correlation between the components of the calculated electric field, which is directed normal to the magnetopause boundary. We have found that magnetosheath flow near the magnetopause is controlled by the direction of the local magnetic field with respect to the local velocity vector, and this behavior is not reflected in the solar wind. In the absence of dynamic processes at the magnetopause, the flow speed of the magnetosheath plasm is slowest when the velocity and magnetic field vectors are aligned and is fastest when the two vectors are parallel to one another, though the magnetoheath flow is slower than the corresponding speed of the solar wind plasma. The enhancement in flow speed is a consequence of magnetic field line tension, and is governed by the Alfvén speed. A simple model has been developed which explains the partitioning of the magnetic energy of the plasma flow into wave energy and increased kinetic energy of the bulk plasma flow. The model predictions agree very well with the magneosheath velocity characteristics as determined from GEOTAIL observations. However, some questions remain. For example, the local curvature of the magnetic field line is an important parameter (Chen et al., 1993) in the determination of the plasma bulk speed, yet it has not been formally included in the above model.
Though the above model explains well the observations of the magnetosheath flow, some questions remain. Very far downstream, the magnetosheath velocity (vo+v1) will slightly exceed (by a few percent at most) the solar wind speed. At this point, the shocked plasma velocity is expected to slowly decrease until it has caught up to the unshocked solar wind and the speed of the shocked plasma is equivalent to that of the unshocked solar wind plasma, so that the magnetic tension is eliminated. However, the process by which the shocked plasma speed decreases is not known. The curvature of the magnetic field line is an important parameter (Chen et al., 1993) in the determination of the plasma speed, yet it has not been formally included in the above model.
Occasionally, close to the magnetopause the plasma flow is considerably faster (10-20%) than that of the solar wind. The fast flow speeds are well ordered by the local magnetic field, such that the fastest plasma speeds are observed when the magnetic field is most parallel to the bulk velocity direction. Examination of the plasma moments indicates that these very fast plasma flows are from the low latitude boundary layer, though it is unclear whether they are observed within the outer LLBL or in the magnetosheath. These fast flows are not due to acceleration of the shocked solar wind plasma by magnetic field line tension. Three potential sources have been proposed to explain the observation of these fast flows, though the exact mechanism remains uncertain.
ACKNOWLEDGMENTS. We cordially thank K. W. Ogilvie, A. J. Lazarus, R. P. Lepping and the WIND teams for the use of solar wind magnetic field measurements and plasma parameters. In addition, we thank the D. Williams and S. Nylund for placing the EPIC summary plots on the World Wide Web for public use. One author (S. M. P.) was supported by a Center of Excellence fellowship at the Institute of Space and Astronautical Science.
Alksne, A. Y., The steady-state magnetic field in the transition region between the magnetosphere and the bow shock, Planet. Space Sci., 15, 239-245, (1967).
Alksne, A. Y. and D. L. Webster, Magnetic and electric fields in the magnetosheath, Planet. Space Sci., 18, 1203-1212, (1970).
Chen, S.-H., M. G. Kivelson, J. T. Gosling, R. J. Walker, and A. J. Lazarus, Anomalous aspects of magnetosheath flow and of the shape and oscillations of the magnetopause during an interval of strongly northward interplanetary magnetic field, J. Geophys. Res., 98, 5727-5742, (1993).
Crooker, N. U., T. E. Eastman, and G. S. Stiles, Observations of plasma depletion in the magnetosheath at the dayside magnetopause, J. Geophys. Res., 84, 869-874, (1979).
Fairfield, D. H., The ordered magnetic field of the magnetosheath, J. Geophys. Res., 72, 5865-5877, (1967).
Gosling, J. T., M. F. Thomsen, S. J. Bame, and C. T. Russell, Accelerated plasma flows at the near-tail magnetopause, J. Geophys. Res., 91, 3029-3041, (1986).
Hapgood, M. A. and D. A. Bryant, Exploring the magnetospheric boundary layer, Planet. Space Sci., 40, 1431-1459, (1992).
Howe, H. C. Jr. and J. H. Binsack, Explorer 33 and 35 plasma observations of magnetosheath flow, J. Geophys. Res., 77, 3334-3344, (1972).
Hundhausen, A. J., S. J. Bame, and J. R. Asbridge, Plasma flow pattern in the Earth's magnetosheath, J. Geophys. Res., 74, 2799-2806, (1969).
Kessel, R. L., S.-H. Chen, J. L. Green, S. F. Fung, S. A. Boardsen, L. C. Tan, T. E. Eastman, J. D. Craven, and L. A. Frank, Evidence of high-latitude reconnection during northward IMF: Hawkeye observations, Geophys. Res. Letts., 23, 583-586, (1996).
Kokubun, S., T. Yamamoto, M. H. Acuña, K. Hayashi, K. Shiokawa, and H. Kawano, The GEOTAIL magnetic field experiment, J. Geomag. Geoelectr., 46, 7-21, (1994).
Lees, L., Interaction between the solar plasma wind and the geomagnetic cavity, AIAA J., 2, 2065, (1964).
Lepping, R. P., M. H. Acuña, L. F. Burlaga, W. M. Farrell, J. A. Slavin, K. H. Schatten, F. Mariani, N. F. Ness, F. M. Neubauer, Y. C. Whang, J. B. Byrnes, R. S. Kennon, P. V. Panetta, J. Scheifele, and E. M. Worley, The WIND magnetic field investigation, in: The Global Geospace Mission, ed. by C. T. Russell, 207-229, Kluwer Academic Publishers, Belgium, (1995).
Midgeley, J. E. and L. Davis, Calculation by a moment technique of the perturbation of the geomagnetic field by the solar wind, J. Geophys. Res., 68, 5111-5123, (1963).
Mukai, T., S. Machida, Y. Saito, M. Hirahara, T. Terasawa, N. Kaya, T. Obara, M. Ejiri, and A. Nishida, The low energy particle (LEP) experiment onboard the GEOTAIL satellite, J. Geomag. Geoelectr., 46, 669-692, (1994).
Ogilvie, K. W., D. J. Chornay, R. J. Fitzenreiter, F. Hunsaker, J. Keller, J. Lobell, G. Miller, J. D. Scudder, E. C. Sittler, Jr., R. B. Torbert, D. Bodet, G. Needell, A. J. Lazarus, J. T. Steinberg, J. H. Tappan, A. Mavretic, and E. Gergin, SWE, a comprehensive plasma instrument for the WIND spacecraft, in: The Global Geospace Mission, ed. by C. T. Russell, 55-77, Kluwer Academic Publishers, Belgium, (1995).
Phan, T.-D., G. Paschmann, W. Baumjohann, N. Sckopke, and H. Lühr, The magnetosheath region adjacent to the dayside magnetopause: AMPTE/IRM observations, J. Geophys. Res., 99, 121- 141, (1994).
Sibeck, D. G. and J. T. Gosling, Magnetosheath density fluctuations and magnetopause motion, J. Geophys. Res., 101, 31-40, (1996).
Song, P., C. T. Russell, J. T. Gosling, M. F. Thomsen, and R. C. Elphic, Observations of the density profile in the magnetosheath near the stagnation streamline, Geophys. Res. Letts., 17, 2035-2038, (1990).
Song, P., C. T. Russell, and M. F. Thomsen, Slow mode transition in the frontside magnetosheath, J. Geophys. Res., 97, 8295-8305, (1992).
Song, P., Observations of waves at the dayside magnetopause, in Solar Wind Sources of Magnetospheric Ultra-Low- Frequency Waves, Geophys. Monogr. 81, ed. by Engebretson, Takahashi, and Scholer, 159-171, (1994).
Sonnerup, B. U. Ö. and E. R. Priest, Resistive MHD stagnation-point flows at a current sheet, J. Plasma Phys., 14, 283-294, (1975).
Southwood, D. J. and M. G. Kivelson, On the form of the flow in the magnetosheath, J. Geophys. Res., 97, 2873-2879, (1992).
Southwood, D. J. and M. G. Kivelson, Magnetosheath flow near the subsolar magnetopause: Zwan-Wolf and Southwood-Kivelson theories reconciled, Geophys. Res. Letts., 22, 3275-3278, (1995).
Spreiter, J. R., A. L. Summers, and A. Y. Alksne, Hydromagnetic flow around the magnetosphere, Planet. Space Sci., 14, 223-253, (1966).
Spreiter, J. R. and A. W. Rizzi, Aligned magnetohydrodynamic solution for solar wind flow past the earth's magnetosphere, Acta Astro., 1, 15-35, (1974).
Traver, D. P., D. G. Mitchell, D. J. Williams, L. A. Frank, and C. Y. Huang, Two encounters with the low-latitude boundary layer: Further evidence for closed field topology and investigation of the internal structure, J. Geophys. Res., 96, 21025-21035, (1991).
Zwan, B. J. and R. A. Wolf, Depletion of solar wind near a planetary boundary, J. Geophys. Res., 81, 1636-1648, (1976).