THE MAGNETOTAIL AND SUBSTORMS

C. T. RUSSELL and R. L. McPHERRON

Institute of Geophysics and Planetary Physics, University of California,
Los Angeles, Calif., U.S.A.

Originally published in Space Sci. Rev., 15, pp.205-266, 1973.

 

Abstract

The tail plays a very active and important role in substorms. Magnetic flux eroded from the dayside magnetosphere is stored here. As more and more flux is transported to the magnetotail and stored, the boundary of the tail flares more, the field strength in the tail increases, and the currents strengthen and move closer to the Earth. Further, the plasma sheet thins and the magnetic flux crossing the neutral sheet lessens. At the onset of the expansion phase, the stored magnetic flux is returned from the tail and energy is deposited in the magnetosphere and ionosphere. During the expansion phase of isolated substorms, the flaring angle and the lobe field strength decrease, the plasma sheet thickens and more magnetic flux crosses the neutral sheet.

In this review, we discuss the experimental evidence for these processes and present a phenomenological or qualitative model of the substorm sequence. In this model, the flux transport is driven by the merging of the magnetospheric and interplanetary magnetic fields. During the growth phase of substorms the merging rate on the dayside magnetosphere exceeds the reconnection rate in the neutral sheet. In order to remove the oversupply of magnetic flux in the tail, a neutral point forms in the near earth portion of the tail. If the new reconnection rate exceeds the dayside merging rate, then an isolated substorm results. However, a situation can occur in which dayside merging and tail reconnection are in equilibrium. The observed polar cap electric field and its correlation with the interplanetary magnetic field is found to be in accord with open magnetospheric models.

 

1. Introduction

It has long been thought that the energy dissipated in auroral processes and stored in the Van Allen belt particles, including the ring current particles, comes from the solar wind. It has also been long noted that this energy exchange occurs principally in an ordered sequence of events called a magnetospheric substorm [cf. Akasofu, 1968]. The magnetospheric substorm is a phenomenon of the whole magnetosphere, not just of the auroral zone. Historically, however, most of our knowledge of substorms has derived from ground based auroral zone studies. In these studies two phases of the substorm are most evident: the expansion or expansive phase, in which there is a rapid increase in the strength of currents flowing in the auroral oval and a sudden brightening, disruption and poleward motion of auroral arcs; and the recovery phase in which these currents decrease in strength and the auroral forms return essentially to their pre-substorm conditions. Evidence of a third phase preceding the expansion and recovery phases of a substorm has been reported from ground based data (McPherron, 1970). However, the onset of the growth phase is gradual, and its signature is often difficult to observe with ground based observations. Thus the existence of a growth phase has been the subject of much controversy. On the other hand, the growth phase is readily observable in certain magnetospheric data notably in measurements of boundary positions, of tail magnetic field strength and orientation, and of plasma sheet thickness.

In this review we discuss principally four topics: the change in flux content of the tail during substorms; the thinning and expansion of the plasma sheet; the changes in the configuration of the tail and the relative timing of events in the tail. We shall not attempt to provide a complete description of either the magnetotail or substorms but rather shall attempt to describe the role of the magnetotail in substorms and the effect of substorms on the tail. The principal emphasis is on the growth phase of substorms, because the changes in the tail during the growth phase are easily observed and because an understanding of the growth phase, in which the major part of the energy input to the magnetosphere occurs, is essential to the understanding of the behavior of the subsequent expansion phase. We also touch briefly on geomagnetic storms and on the acceleration of electrons and the generation of ELF chorus during the expansion phase of substorms. Finally, we outline a phenomenological model of substorms which is consistent with the magnetospheric observations. While this phenomenological model is not quantitative and provides few answers as to the cause’of certain events, it does serve as a framework with which to order our empirical model and may serve as a guide for future theoretical efforts. Those interested in a recent summary of the history of substorm research and an excellent treatment of ground based magnetometer data should consult the review by Rostoker (1972).

 

2. The Change in Flux Content of the Tail

The number of magnetic field lines, which comprise the tail, is a continually changing function of time. On the ground this is manifested by changes in size of the polar cap or equivalently in the size of the auroral oval. We note, of course, that the polar cap and auroral zone can change shape without changing size. This complicates ground-based studies. In space, the changing flux content of the tail causes magnetospheric boundaries to move, and the currents in the tail to increase and decrease in strength and the location of these currents to move closer to and farther from the Earth.

2.1. THE EROSION OF THE DAYSIDE MAGNETOSPHERE

Fig. 1. 1 min averages of the total magnetic field and the three solar magnetospheric components on an inbound pass of OGO-5 across the magnetopause on March 27, 1968, (Aubry et al., 1970). In solar magnetospheric coordinates, the X-axis points toward the Sun, the X-Z plane contains the Earth's dipole axis and the Y-axis is in the dusk meridian (Ness, 1965).

Although the correlation of geomagnetic activity with the occurrence of southward directed interplanetary field had been known and the dependence of the stability of the tail on its flux content had been predicted for some time, the observation by Aubry et al. (1970) of the erosion of the dayside magnetosphere in the presence of a southward directed interplanetary magnetic field preceding a substorm was a turning point in our understanding of the substorm process. Figure 1 shows the evidence for this erosion of the dayside magnetosphere. This figure shows the three components of the magnetic field in solar magnetospheric coordinates1 and the total magnetic field on an inbound pass of OGO-5 across the magnetopause. OGO-5 first crossed the magnetopause at l700 UT when the interplanetary magnetic field was northward. The interplanetary magnetic field turned southward about 1715 and the magnetopause moved inwards towards the Earth roughly matching the velocity of OGO-5 until 1916 UT when OGO-5 moved ahead of the magnetopause.

During this inward motion, the solar wind velocity and density remained roughly constant, as did the field strength in the outer magnetosphere. Thus, pressure balance was maintained, as expected, across the boundary during this motion.

Such motion of the magnetopause, independent of the solar wind dynamic pressure, but maintaining pressure balance has led to some confusion. Models of the magnetopause such as that of Olson (1969) derive a magnetopause position that is a function only of solar wind dynamic pressure and dipole tilt angle. Such models ignore the viscous interaction of the solar wind on the magnetosphere, field aligned currents, etc., and consequently do not predict the existence or properties of the geomagnetic tail. While pressure balance is maintained locally across the magnetopause in steady state, the magnetic field is the sum of contributions from all current systems, near and distant. This is, in fact, the reason for the iterative procedure used in calculating these magnetopause models. The addition of a tail current system will alter the magnetopause position and shape, and when the tail currents change, the magnetopause position will change. We will discuss this and other possible causes for inward motion of the magnetopause below.

Fig. 2. The OGO-5 trajectory in the plane perpendicular to the Earth-Sun line on March 27, 1968, together with the calculated magnetopause positions (Aubry et al., 1970).

Figure 2 shows the estimated motion of the magnetopause during this period of time. From the first encounter of OGO-5 with the magnetopause at 1700 UT until its last encounter at 1916 UT, the nose of the magnetopause moved inwards over 2 RE. Since there was no compression of the dayside magnetic field this is equivalent to a flux transport of about 1016 Mx to the tail which would increase the total flux content of the tail by about 15%. Figure 3 shows the magnetogram from the Sodankyla auroral zone observatory which at this time was near local midnight. Close to the time of the last encounter with the magnetopause, the expansion phase of a substorm occurred.

This sequence of events studied on a single pass of OGO-5 is supported by statistical studies of both Meng (1970) and Fairfield (1971). Meng examined the position of the magnetopause as a function of the AE index. He found that distant magnetopause encounters invariably correspond to quiet times, whereas abnormally earthward encounters could occur at either quiet or at disturbed times. In the context of magnetospheric erosion, we interpret Meng's observation of quiet inward displacements, as observations during the growth phase of substorms and of disturbed time inward displacement as observations during the expansion phase. Eventually, the flux returned to the magnetosphere from the tail during the expansion phase convects to the dayside returning the magnetopause to its more distant quiet-time position.

Fig. 3. The H, D and Z components of the Sodankyla magnetogram during the inbound pass of OGO-5 on March 27, 1968. The bottom panel shows the Kp and DST indices during this period. The dashed lines E and F mark the times when the plasma sheet respectively thinned and expanded over Imp 4, 30 RE behind the Earth (Aubry et al., 1970).

Fairfield (1971) examined the magnetopause position as a function of the sign of the north-south component of the magnetosheath magnetic field. He found that when the magnetosheath field was southward, the magnetopause was on the average one earth radius closer to the earth than when it was northward.

Fig. 4. The change of the invariant latitude of the polar cusp from its quiet-time position as a function of the duration of southward interplanetary field. The numbers associated with each point give the average southward magnetic field strength during this interval and a merging 'efficiency' (Burch, 1972).

If the dayside magnetosphere shrinks, the polar cusp which lies on the boundary between magnetospheric and polar cap field lines should also move equatorward. Such equatorward motion of the polar cusp in the presence of a southward interplanetary magnetic field and poleward motion in the presence of a northward interplanetary magnetic field has been observed deep in the magnetosphere by Russell et al. (1971a). Observations of the polar cusp at low altitudes with polar orbiting satellites provide a much larger body of data with which statistical and semi-quantitative studies of this erosion process can be performed. Figure 4 is a plot of the equatorward displacement of the polar cusp from its quiet time position as a function of the duration of southward interplanetary magnetic field at the magnetopause (Burch, 1972). In this study Burch used OGO-4 observations of 700 eV electrons to locate the polar cusp. The southward interplanetary magnetic field was obtained from Explorers 33 and 35 Ames Research Center magnetometers. Polar cap magnetograms were used to time the arrival of the southward field at the magnetopause. The polar cusp can move equatorwards about 7 degrees in an hour in the presence of a southward interplanetary magnetic field. The numbers associated with each point on Figure 4 give the average southward magnetic field in solar magnetospheric coordinates and the calculated ratio of eroded magnetic flux to the southward interplanetary flux asymptotically incident on the magnetosphere. Interpreted in terms of simple merging theory, this latter number is equivalent to the ratio of the east-west interplanetary electric field to the electric field in the lobes of the magnetotail. Equivalently this is the ratio of the thickness of the interplanetary medium normal to the plane containing the magnetic field and the solar wind velocity vector which merges with the magnetosphere to the dimensions of the magnetosphere. We note further that the average electric potential across the magnetotail predicted by this result is about 50 kV. Finally, studies of the equatorward motion of midday auroras show that this motion is roughly proportional to the accompanying geomagnetic activity (Akasofu, 1972a, b).

It is obvious from these observations that the magnetopause position is sensitive to factors other than dynamic pressure and dipole tilt. As discussed in the next section, the tail currents strengthen and move closer to the earth as magnetic flux is transported from the dayside magnetosphere to the tail. The effect of these tail currents is to weaken the field in the dayside magnetosphere. This causes the magnetopause to move toward a new equilibrium position inward of its previous position.

This is not the only cause of erosion, however. Merging requires a flow into the boundary from both sides in steady state. If the magnetospheric flow is impeded by the ionosphere, then the boundary must move inward until the magnetic stresses are sufficient to overcome the ionospheric drag or line tying (Coroniti and Kennel, 1973). Such stresses are communicated between the ionosphere and magnetopause by field aligned currents. In the steady state, this field aligned current system, which closes in the ionosphere on the one end and the magnetopause on the other, opposes the earth' s field to provide local pressure balance at a position inward of the usual equilibrium position. Field aligned currents are apparently a common feature of the polar cusp (Zmuda et al., 1967; Fairfield and Ness, 1972; Kivelson et al., 1973a).

In summary, observations of the magnetopause and polar cusp positions show that there is flux transport from the dayside magnetosphere to the magnetotail in the presence of a southward interplanetary magnetic field. This flux transport has important effects on the location and strength of currents in the magnetotail, which we will now examine.

2.2. THE CHANGES IN THE TAIL CURRENT SYSTEM

When magnetic flux is added to the tail, the drag of the solar wind on the tail must increase. In the reconnection theory, this occurs because more field lines now connect the tail to the interplanetary medium; in the viscous drag theory, this occurs because the surface area of the tail increases to encompass the increased flux. This increased stress is measured by the integral of the magnetic pressure over the cross section of the tail (Piddington, 1963). The stress, thus, can be manifested by an increase in the cross section of the tail, an increase in the field strength or a decrease in the thickness of the plasma sheet (Siscoe, 1972a). In practice all three of these effects occur. However, close to the earth the radius of the tail must decrease during the flux transport process because the dayside magnetosphere, to which the tail is attached in an aerodynamic sense, is shrinking.

Fig. 5. The location of the inner edge of the tail current system, XT, versus the radius of the tail, RT, for several tail field strengths, BT, for an idealized tail (Siscoe and Cummings, 1969).

Since the solar wind is pulling harder on the magnetotail, the tail must then pull harder on the Earth. Siscoe and Cummings (1969) have proposed that in order to achieve the proper balance of forces that tail current system must move towards the Earth as the flux transport progresses. Figure 5 shows the radius of the tail plotted versus the position of the inner edge of the tail current system for different field strengths in the tail as calculated for a simple model by Siscoe and Cummings. The details of this calculation have been criticized by Vasyliunas (personal communication, 1972) but the predicted trends appear to be valid. We note that in a realistic model the change in the angle of attack of the magnetopause to the solar wind, and the thinning of the plasma sheet must be included in order to model the changes in the tail current during the flux transport.

Fig. 6. Typical storm time energetic electron (UM) and magnetic field (UCLA) data at synchronous orbit. Simultaneous change events are labeled S; drifter events are labeled D. Theta is the angle between the geomagnetic vector and the north-pointing vector (Lezniak and Winckler, 1970).

It is very difficult to verify experimentally this proposed inward motion of the current system because the field measured locally at a satellite is also determined by distant currents. However, satellite observations do show the existence of tail-like fields quite close to the Earth in the night hemisphere preceding the onset of the expansion phase of substorms. Figure 6 shows measurements of energetic electrons and the magnetic field at synchronous orbit (Lezniak and Winckler, 1970). The angle measures the angle between the observed magnetic field and geographic north. Preceding a substorm, the field can be tipped at large angles to the nominal dipole field as close to the Earth as 6.6 RE. At the onset of a substorm expansion this field becomes more dipolar. Such changes are greatest near local midnight. These data also illustrate the effect of substorms on the magnetic field strength at synchronous orbit. Before local midnight, 1000 UT at ATS-1, the magnetic field strength usually exhibits a gradual decrease after the onset; after midnight it usually exhibits a rapid increase, accompanied by increases in the flux of energetic electrons.

Fig. 7. 1 min averages of the magnetic field on an inbound pass of OGO-5 near the midnight meridian. The top panel shows the difference between the observed field strength and that of a reference field. The middle two panels show the inclination and declination of the magnetic field. The next panel shows the Z solar magnetospheric component and the bottom panel shows the rms deviations of the field for fluctuations with periods less than 15 s. The vertical dashed lines shows substorm onset times determined from midlatitude magnetograms. The horizontal dashed line shows the inclination of the reference field at the OGO-5 position )McPherron et al., 1973a).

Slightly further out in the magnetosphere, the field can be even more tail-like during the growth phase of a substorm. Figure 7 shows the magnetic field measured on an OGO-5 pass inbound near the midnight meridian (McPherron et al., 1973a). At 0000 UT, OGO-5 was 15 RE behind the Earth and at 0700 UT, it was 8 RE behind the Earth. The inclination of the field, which is the angle between the magnetic field and the local horizontal was virtually unchanged from 15 RE to 8 RE. The thin line on the inclination panel is the inclination of a dipolar field line. After the 0430 and the 0714 substorms the field assumes a dipolar configuration. The 0220 UT substorm was not effective in changing the field orientation at OGO-5 in part because it was a weaker substorm and in part because OGO-5 was much further from the neutral sheet.

As will be discussed in Section 3, the field magnitude plotted in the top trace of Figure 7 shows an increase just before the onset of the 0714 substorm. This field signature together with the behavior of the energetic particles at this time indicates that OGO-5 left the plasma sheet here even though OGO-5 was within 2 RE of the geomagnetic equator. The bottom trace shows the amplitude of fluctuations in the magnetic field with periods less than 15 s. Weak fluctuations are associated with field aligned currents which can cause changes in the declination of the field. The largest occur in the plasma sheet after the substorm onset. ULF, ELF, and VLF fluctuations possibly play an important role in the microscale processes in the tail isotropizing the plasma and causing turbulent resistivity. Noise in the tail has been recently reviewed by Russell (1972a). In this review, we shall discuss mainly the macroscale processes.

We see from the above that quite tail-like fields are observed near midnight as close to the Earth as 6.6 RE but the magnetic field data do not provide information on where these currents are flowing. The increase in the tail-like field can also be due to an increase in the strength of the near-Earth tail current system. This increase in current occurs because, as the flux transport occurs, the magnetosphere shrinks and the tail cross-section grows requiring an increased angle of attack of the surface of the tail to the solar wind. Thus, the dynamic pressure of the solar wind acts to compress the near tail, increasing the flux density and the current strength in this region.

Fig. 8. The cross section of a two dimensional magnetopause for varying amounts of magnetic flux, C' in the tail. As C' increases the dayside magnetosphere shrinks, the polar cusp moves equatorwards, and the tail radius expands and its angle of flaring increases. The inner edge of the tail current system also moves in the solar direction as indicated by the dots on the magnetopause and the vertical lines at the neutral sheet (Unti and Atkinson, 1968).

Figure 8 shows this effect as calculated by Unti and Atkinson (1968) for a two-dimensional magnetosphere with no connection of field across the neutral sheet. The lines show the magnetopause and polar cusp for five cases each with the same solar wind particle density and velocity but each with a different amount of flux in the tail. As the flux in the tail increases, the magnetopause moves towards the Earth, the polar cusp moves equatorwards and the flaring angle of the tail increases. Furthermore, the inner edge of the tail current sheet, indicated by the vertical lines, moves in as the flux in the tail increases. Thus, we expect that the increasing tail-like character of the magnetic field near the Earth during the growth phase of substorms is due to two causes: both an inward motion of the tail current system and an increase in the current strength.

Fig. 9. The magnetic field in the tail as measured by Imp 4 compared with simultaneous Explorer 33 solar wind plasma and magnetic field measurements. The top panel shows the solar wind dynamic and thermal pressure. The next lower panel shows the angle of the magnetic field with the solar equatorial plane. The expected position of Imp 4 from the neutral sheet Z' ranges from -6.3 to -8.9 during this interval. The vertical lines marked SBS indicate substorm expansion phase onsets timed from ground based magnetograms (Aubry and McPherron, 1971).

We can experimentally verify that the tail current increases during the growth phase by examining the tail magnetic field further from the Earth and far from the plasma sheet. Figure 9 shows on the lower panel the magnetic field in the tail as observed by Imp 4 at 25 RE behind the Earth and 8 RE above the expected neutral sheet position (Aubry and McPherron, 1971) (adapted from Fairfield and Ness (1970)). The upper panel shows the solar wind pressure and the angle of the interplanetary field to the ecliptic plane measured by Explorer 33. We see that even though the solar wind dynamic pressure is remaining roughly constant, the field strength in the tail is increasing and decreasing as a function of time. The sudden decrease at 1800 UT is due to an expansion of the plasma sheet. The increases correspond to times when the interplanetary field is southward, the decreases occur after substorm expansion phases begin.

Fig. 10. Substorm signatures in lobes of tail. The top three traces show the horizontal components of ground based magnetograms. The next trace shows the magnetic field strength at Imp 3 at (-23.7, 12.6, -12.9) RE in solar magnetospheric coordinates. The next two traces show the solar ecliptic latitude and longitude of the magnetic field and the lowest trace shows the flux of >40 keV electrons (Meng et al., 1971).

Figure 10 shows Imp 3 magnetometer data taken 24 RE behind the Earth and 13 RE below the expected position of the neutral sheet (Meng et al., 1971). The top three traces show ground magnetograms. Again we see the increase in the tail during the growth phase followed by a decrease at the onset of the substorm expansion phase.

Recent studies have provided many more examples of such tail lobe response. Caan et al. (1973) modeled the tail lobe response to dynamic pressure changes while the interplanetary field was northward and used this to study the tail lobe response to southward interplanetary fields with dynamic pressure effects removed. Their study consistently showed that a southward turning interplanetary field led to an increase in the strength of the lobe field and an expansion phase onset led to a decrease. Nishida and Nagayama (1973) have surveyed the response of the tail during 27 substorms at observation points from 10 to 65 RE behind the Earth. This study did not examine simultaneous interplanetary data. In each of the 27 cases studied the field strength rose before the expansion onset and decreased thereafter. Hruska (1972) has shown statistically the tail field in the lobes increases preceding maxima in the AE index. We note that other authors have studied the magnetic signature of substorms in the tail (Brody et al., 1969; Camidge and Rostoker 1970). However, these studies did not attempt to separate tail lobe response from near plasma sheet response.

Since the magnetic field in the lobes of the tail far behind the Earth and far from the neutral sheet increases and decreases during the growth and expansion phases of a substorm, respectively, we conclude that indeed the distant tail currents are increasing and decreasing in strength during the growth and expansion phases. Thus, the signature of substorms in the neighborhood of the synchronous orbit is at least in part caused by changes in the current strength. Nevertheless, the theoretical studies of Unti and Atkinson and Siscoe and Cummings indicate that this is not the only cause of this signature and the location of the tail current system is also a function of time.

2.3. CONTINUED FLUX TRANSPORT

Fig. 11. The effect of continued southward interplanetary magnetic field. The top two traces show the solar wind number density and bulk velocity as measured by the MIT plasma probe on Explorer 35 in the solar wind. The next trace shows the north-south solar magnetospheric component of the interplanetary magnetic field as measured by the Ames Research Center magnetometer on Explorer 35. The middle trace shows the magnetic pressure in the north lobe of the magnetotail as measured by the UCLA fluxgate magnetometer on OGO-5. The next two traces show auroral zone H component magnetograms from Great Whale River and Fort Churchill. The dashed lines show typical quiet day values. The next trace is the midlatitude H component magnetogram from Fredricksburg. Finally, in the last panel is the H component at 6.6 RE as measured by the ATS-1 fuxgate magnetometer. The inset shows the noon-midnight projections of the positions of Explorer 35 and OGO-5.

Thus far we have examined only isolated substorms. These occur when flux transport takes place for only a limited interval of time. The study of isolated substorms enables us to separate the various phases of a substorm and to separate the effects of one substorm from another. It is possible, however, that the magnetosphere reacts differently if it is subject to a continual large stress or equivalently if flux transport proceeds at a fast rate over an extended period of time. A recent study of OGO-5 data suggests that this in fact is the case (Caan et al., 1973). Figure 11 shows 24 h of interplanetary data as measured by Explorer 35, magnetotail data measured by OGO-5, in the north lobe of the tail, ground station magnetometer records and the magnetic field at ATS-1 in synchronous orbit. The inset shows the projected positions of Explorer 35 and OGO-5 in the noon-midnight meridian. Examining the solar wind velocity and density in the top two traces we see that a sudden increase in the number density occurred beginning about 0330 UT. This was accompanied by a southward turning of the interplanetary magnetic field. This initiated the onset of the growth phase of a substorm in the tail. The middle panel shows the energy density of the magnetic field in the north lobe of the tail about 10 RE behind the Earth. When the combined density increase and southward turning reached the magnetosphere, the field strength in the tail began to increase. Small sudden impulses are seen at ATS-1 and Fredricksburg at this time. Quiet day curves are shown for reference on the bottom panels. About 0535, at the time of the second dashed line, a substorm expansion phase begins. In the tail at OGO-5, the energy density decreases, at mid-latitudes near midnight a positive bay begins, at high latitudes there are sharp negative bays. This is the expansion phase of the substorm. After about 15 min there is a sharp decrease in the field strength at ATS-1. The delay at ATS is normal for this local time.

The interplanetary field stays southward for at least six more hours after this substorm. However, a well defined sequence of substorms with a growth phase and an expansion phase is not seen. Looking at the energy density in the lobe of the tail. We see what appears to be a second growth phase and an expansion but it is only half the size of the first increase and has little effect in ground records. What does occur in the ground data is almost continuous geomagnetic activity. This is confirmed by the ATS-1 magnetic field, which is almost continually depressed below quiet day values. It appears as if once geomagnetic activity got started, the energy input to the tail was transferred directly to the magnetosphere without being stored at all.

2.4. THE DEVELOPMENT OF A GEOMAGNETIC STORM

Fig. 12. The development of a gradual commencement geomagnetic storm. The top two traces show the Z solar magnetospheric components of the magnetic field as measured by the Ames Research Center magnetometers in the tail on Explorer 35 at 60 RE and in the solar wind in Explorer 33 at the dusk meridian. The next two traces show the solar wind number density and velocity as measured by the MIT plasma probe on Explorer 33. The bottom two panels show the Dst and AE indices.

Continued strong southward interplanetary magnetic field leads to the development of a geomagnetic storm. This is illustrated in Figure 12. The top two traces are the north-south components of the magnetic field at Explorer 35 and Explorer 33. Explorer 35 is in the center of the tail near the expected position of the neutral sheet. Explorer 33 is in the solar wind near dusk. OGO-5 is in the magnetosphere near perigee at this time and can shed no light on the behavior of the tail magnetic field during this period. The middle two panels show the solar wind number density and velocity. The bottom two panels show the DST index and the AE index.

At the start of the day the interplanetary field is slightly southward and there is some geomagnetic activity as shown by the AE index, but then the field turns northward and geomagnetic activity ceases. Throughout the whole day the solar wind velocity is constant. We note that the solar wind number density was quite variable during the early part of the day. About 1230 UT there was a sudden increase in the field strength (not shown); a drop in the number density and the interplanetary field became quite northward. The density drop caused a negative sudden impulse on the ground. Therefore one could say that this storm started with a negative sudden commencement. The interplanetary conditions then remained remarkably steady with one exception. The field began to rotate about the Earth-Sun line. The field became weakly southward and then strongly southward. DST followed the southward component and auroral zone activity picked up. The Bz component interplanetary field reached about -12 nT and DST had reached -50 nT by midnight and -79 nT on the next day. Geomagnetic activity continued until the interplanetary field turned northward again.

The top trace on the figure is the north-south component of the field in the plasma sheet at the orbit of the Moon near midnight. During the first part of the day the field averaged about 5 nT northward, but after the interplanetary field turned southward, there is much less magnetic flux crossing the neutral sheet. There is even occasionally some southward pointing field. The tail gives the appearance of being stretched by the southward component of the interplanetary field.

Studies of other magnetic storms, both large and small (Russell and McPherron, 1972) confirm this picture. Blast waves are generally associated with storms only because they can generate large interplanetary southward components. Burton (personal communication, 1973), in fact, has shown that Dst during storms can be predicted quite accurately using only the interplanetary electric field.

2.5. SUMMARY

Flux transport from the dayside of the magnetosphere to the tail occurs in the presence of a southward interplanetary magnetic field. This flux transport is accompanied by a shrinking of the dayside magnetosphere, an increase of the tail cross-section and an increase in the flaring angle of the near magnetotail. The currents in the tail increase in strength and move in towards the Earth at this time. Flux is removed from the tail during the expansion phase.

Continued flux transport appears in one case to have led to a steady state in which the flux is removed from the tail at the same rate as it is transported to the tail. In another case, continued flux transport led to the development of a gradual commencement magnetic storm. This storm was not preceded by a blast wave. Rather, a decrease in the solar wind dynamic pressure causing a negative sudden impulse on the ground signaled the arrival of the plasma which eventually would cause the geomagnetic storm.

Finally, we note that none of these observations defines the convective flow over the polar cap or in the lobes of the tail. Various convective flow patterns have their counterparts in the lobes of the tail. These flow patterns are probably controlled by the east-west component of the interplanetary magnetic field (Atkinson, 1972; Friis-Christensen et al., 1972; Russell, 1972b)

 

3. The Thinning and Expansion of the Plasma Sheet

As mentioned in Section 2.2, the stress changes in the tail can be balanced at least in part by the thinning and expansion of the plasma sheet, and such changes in the thickness of the plasma sheet are observed. The role of this motion in the substorm is at best only poorly understood. In fact, even the nature of the static plasma sheet is not well understood at this time (Siscoe, 1972b; Rich et al., 1972). Thus, we will restrict our discussion mainly to the observations of the thinning and expanding boundary of the plasma sheet.

At radial distances of from 15-20 RE the plasma sheet consists of electrons and protons with average energies of about 1 keV and 5 keV respectively and number densities from 0.1 to 1 cm-3 (Bame et al., 1967). The plasma sheet electrons are observed as close as 11 RE at quiet times and 6 RE at disturbed times, and throughout the afternoon hemisphere (Vasyliunas, 1968a, b). The plasma sheet protons merge with the ring current protons (Frank, 1971a). The magnetic field in the plasma sheet is less than that in the lobes, so that the total magnetic pressure in the lobes is approximately equal to the sum of the particle and field pressures in the plasma sheet (Lazarus et al., l968). The plasma sheet is about 6 RE thick in the center of the tail at quiet times at 16 RE, and is generally believed to be thicker near the boundaries of the tail in the center (Bame et al., 1967). However, such a butterfly cross-section would also result from the intersection of a wedge shaped plasma sheet of decreasing thickness as a function of geocentric distance with the Vela orbit sphere. Evidence for a plasma sheet with nearly constant thickness as a function of the solar magnetospheric Y coordinate has been presented by Walker and Farley (1972). Neither the proton nor electron distributions are strictly Maxwellian. Both have significant non-Maxwellian tails (Montgomery, 1968; Buck et al., 1973).

The plasma sheet is best detected with low energy electron and proton detectors, but its presence can also be deduced from its magnetic field signature, and its energetic proton and electron signature. A proper study of the plasma sheet requires a multiple measurement approach using both low energy and high energy electron and proton observations together with magnetic field measurements. However, for a variety of reasons including payload selection and instrument failures such a correlative effort has yet to be achieved. Thus observations of plasma sheet motion have relied on several of the plasma sheet signatures. In the following sections we shall examine these various signatures.

3.1. THE LOW ENERGY PLASMA

Fig. 13. A two satellite study of the position of the plasma sheet. The top panel shows the distance of VELA 3A and VELA 4A from the expected position of the neutral sheet (Russell and Brody, 1967). The bottom two panels show the average electron energy and the electron energy density at the two satellites. The trajectory data ares shown only when the energy density exceeds 4 eV cm-3 ster-1. The vertical dashed lines show the substorm expansion phase onsets determined from midlatitude magnetograms which were associated with these thinning and expansions events (Hones et al., 1971a).

Much of our knowledge of the behavior of the low energy plasma in the plasma sheet comes from the plasma probes carried on the VELA satellites in high inclination circular orbits with semi-major axes of about 18 RE Hones (1972) has recently reviewed the behavior of the low energy plasma during substorms and we will repeat only a few relevant details here. Figure 13 shows data from a two satellite study using two closely spaced VELA satellites 3A and 4A (Hones et al., 1971a). The top panel shows the position of VELA 3A and 4A relative to the expected position of the neutral sheet.2 The positions are shown only when the satellites are within the plasma sheet arbitrarily defined as an electron energy density of 4 electron volts cm-3 ster-1. The fact that the satellite closest to the neutral sheet always sees the thinning last and the expansion first, if at all, indicates the neutral sheet is thinning and expanding rather than flapping. The dashed vertical lines indicate expansion phase onsets as determined from low latitude ground magnetograms. The plasma sheet expansion always follows the onset of the substorm expansion phase. However, not every substorm that occurred during this interval is shown here, only those associated with an event at VELA. As Rostoker and Camidge (1971) have pointed out, substorms can occur which are not seen by satellites in the tail even close to the neutral sheet.

Fig. 14. True and apparent velocities of an expanding boundary. Vn and Vn are the true components of the velocity while Va and Va are the apparent components.

The plasma sheet velocities measured by Hones et al. (1971a), using this and similar data, range from 4 to 20 km s-1 perpendicular to the neutral sheet. However, these are the true velocities of the plasma sheet, only if the plasma sheet is parallel to the neutral sheet. Figure 14 illustrates this. If the boundary of the plasma sheet moves from 1 to 2 at some angle to the neutral sheet with velocity V, two satellites above one another will see an apparent perpendicular velocity and two satellites at different distances down the tail will observe an apparent parallel velocity. However, these velocities are both greater than the perpendicular and parallel components of the true velocity. If we attribute these velocities to an electric field induced drift, then the estimated electric field will also be too large unless the boundary orientation is measured. The boundary normal can be obtained using a cluster of four satellites, or with the magnetic field signature on a single satellite. Finally, we note that the thinning and expansion of the plasma sheet need not be convective motions but in fact may represent the loss and acceleration of the plasma sheet particles.

3.2. PLASMA FLOW MEASUREMENTS

Measurements of flow velocities are important in understanding the source and loss processes of the plasma sheet and in particular the thinning and expansion of the plasma sheet. In this regard we note that flow by itself does not necessarily lead to thinning or expansion of the plasma sheet but that gradients in the flow must exist. For example, flow out of a flexible hose with the tap on does not lead to thinning whereas flow from a toothpaste tube does.

It has been proposed that flow is towards the Earth at distances less than the neutral point and outwards beyond this point in the open model of the magnetosphere (Dungey, 1963). It has also been suggested that the flow might be towards the Earth during the growth phase and away from the Earth during the expansion phase (Hones et al., 1967). The measurement of flow velocities has not been made until recently because the low ratio of convective to thermal velocities of the plasma sheet particles combined with the low counting rates of most instruments has precluded such measurements. However, now such data are available from three separate spacecraft. Hones et al. (1972a) and Prakash (1972) report flows generally towards the Earth. These velocities range from 200 to 1000 km s-1 but an average velocity cannot be assigned because the flow velocities are too low to be measured in general. They also both report some examples of tailward flow consistent with the occasional presence of the neutral point inside the orbit of the Moon (Prakash, 1972) and inside the 18 RE orbit of VELA (Hones et al., 1972a). More recently such flows have been observed (Frank et al., 1972) on Imp-6 with much greater resolution. These measurements reveal a complex perhaps even turbulent pattern of flow velocities which requires much further study. Finally Hones et al. (1972b) have observed plasma sheet protons on the magnetosheath on several occasions. This implies that some of the plasma sheet particles are lost from the sides of the tail. It also emphasizes the fact that the magnetosheath and plasma sheet protons are two quite different populations of particles.

3.3. THE MAGNETIC FIELD

Fig. 15. The signature of the thinning and expanding plasma sheet in the magnetic field. The top three traces show one minute averages of the three solar magnetospheric components of the magnetic field in the tail and the bottom trace shows the field strength (Russell et al., 1971b). On this pass OGO-5 remained near the midnight meridian and only slowly approached the expected position of the neutral as given by Z' (Russell and Brody, 1967).

The motion of the plasma sheet can also be studied profitably using in situ magnetic field measurements. Figure 15 shows the three solar magnetospheric components of the magnetic field and the field strength during an inbound pass of OGO-5 near local midnight from 17 to 7 RE behind the Earth (Russell et al., 1971b). OGO-5 only slowly approached the expected position of the neutral sheet on this pass as indicated by Z' on the top of the figure. The thinning and expansion of the plasma sheet repeatedly caused the plasma sheet to cross OGO-5, causing periodic depressions in the magnetic field. The expanding plasma sheet causes a rather rapid decrease in the field strength; while the thinning of the plasma sheet and the recovery of the field strength proceeds much more slowly. The sequence of changes in the north-south component of the field, Bz, follows essentially the same pattern. The activity in the tail during this interval, while very evident in these records, was not accompanied by strong substorm activity at usual auroral zone stations. Each depression in the magnetic field here was accompanied by increases in the flux of energetic electrons as measured by the UCLA electron spectrometer.

3.4. ENERGETIC PARTICLES

Fig. 16. The signature of the expanding plasma sheet in energetic electron measurements. The same format as Figure 10 (Meng et al., 1971).

The energetic particles observed in the plasma sheet constitute non-Maxwellian tails on the low energy plasma distribution functions. These high energy tails are more variable than the low energy plasma and hence are less reliable indicators of the plasma sheet. Nevertheless, they do provide useful data, especially in the absence of data from low energy plasma experiments. Figure 16 shows Imp 3 data obtained 37 RE behind the Earth and 7 RE below the expected position of the neutral sheet (Meng et al., 1971). The top two traces show ground based auroral zone magnetograms; the middle three traces show the magnetic field at Imp 3; and the bottom trace shows the flux of E>40keV electrons. The gradual increase in the field strength accompanied by a decrease in the flux of greater than 40 keV electrons is interpreted as the thinning of the plasma sheet. The sudden increase in energetic electrons accompanied by a sudden decrease in the magnetic field is interpreted to be due to the expansion of the plasma sheet. Although the first thinning and expansion have very similar signatures in both the magnetic field and the energetic electrons, the second apparent thinning event has a somewhat different signature in the magnetic field and in the particles. It is evident that there are temporal changes in the energetic electrons in addition to the changes caused by the motion of spatial boundaries. Electron events such as those shown in Figure 16, were originally called island events (Anderson, 1965). We know now that the rapid rise in energetic electron flux is associated with the expansion of the plasma sheet and that the slow decay is either due to the slow thinning of the plasma sheet or the temporal decay of these fluxes.

Fig. 17. The thinning of the plasma sheet as observed by a scanning proton spectrometer. The various curves give the spatial distribution of 100 keV protons as determined by measurements at different guiding center locations. The distance is measured perpendicular to the magnetic field in the magnetic meridian and is referenced to the expected position of the neutral sheet. The X marks the position of the satellite for each profile. The Universal Time of each measurement is also given. The top four panels are offset vertically for clarity of presentation. The inset shows the range of guiding centers sampled at four times during the motion of the satellite through a hypothetical stationary profile. In this case, a superposition of the flux measurements at the four separate times would give an overlapping continuous curve (adapted from Buck et al., 1973).

Not only is it possible to detect the plasma sheet by measuring energetic electrons but it can also be done with energetic protons. This is perhaps the most informative means of studying the motion of the plasma sheet from a single satellite because of the large gyro radii of energetic protons. Figure 17 illustrates this technique. The inset on the right shows a spatial distribution of proton flux versus radial distance. A detector which sees particles with a guiding center on one side of a satellite will see particles from a corresponding guiding center on the other side of the satellite when turned 180o. The maximum distance that can be probed is one gyro radius on either side of the satellite. This is done at pitch angles of 90o. For a 100 keV proton in the tail this distance is on the order of 1/2 RE. Measurements at smaller pitch angles provide information between these two limits. Thus, at any one time the satellite sees a finite portion of the spatial distribution and measurements made at different times can be compared to obtain a relative velocity of the satellite and the flux gradient. This is illustrated by the line segments numbered 1, 2, 3, and 4.

The data on the left-hand side of this figure show measurements of 300 keV protons by the Lawrence Livermore Laboratory proton spectrometer on OGO-5 on August 15, 1968 (Buck et al., 1973). As mentioned in Section 2.2 in the discussion of Figure 7, OGO-5 detected a tail-like field at 8 RE at this time and the magnetic field indicated that OGO-5 left the plasma sheet about 0710 UT. The distance plotted along the bottom is the distance in the magnetic meridian perpendicular to the magnetic field. The X marks the position of the satellite. We see that as OGO was moving in towards the Earth, the boundary overtook the satellite and apparently contracted to a thickness of less than 2RE. The velocity of this thinning normal to the plasma sheet ranged from 4 to 10 km s-1. We note that the boundary continued to thin until the substorm began. There is no evidence that the flow stopped or was choked. The substorm expansion is apparently coincident with the time of disappearance of the plasma sheet just tailwards of OGO-5.

3.5. PHENOMENA ASSOCIATED WITH THE PLASMA SHEET EXPANSION

Shortly after the onset of plasma sheet expansion occurs in the near earth magnetotail several associated phenomena occur in the outer midnight magnetosphere near the equator. One of these phenomena, the sudden increase in field strength at (and beyond) synchronous orbit we have mentioned above. Associated with this sudden field compression betatron acceleration of electrons and the generation of ELF chorus have been observed.

3.5.1. The Inward Moving Sudden Field Compression

Fig. 18. Inward moving field compression seen at OGO-5 and then at ATS-1. One second averages of the ATS-1 and OGO-5 magnetic field in solar magnetospheric coordinates on August 7, 1968.

The signature of the expansion phase of substorms at synchronous orbit at and after midnight is a sudden recovery of the magnetic field strength to approximately quiet time values (Coleman and McPherron, 1970). On August 7, 1968, OGO-5 and ATS-1 were approximately lined up on the midnight meridian during a substorm expansion. ATS-1 was at (-5.9, -2.1, 2.2) RE and OGO-5 was at (-8.2, -2.0, 2.1) RE in solar magnetospheric coordinates. Figure 18 shows the magnetic field data in solar magnetospheric coordinates from both spacecraft. The sudden compression of the magnetic field is first seen at OGO-5. Then, 94 s later it is observed at ATS-1. The apparent velocity from OGO-5 to ATS-1 was, thus, 150 km s-1 towards the Earth. Although it is possible that a compressional wave was initiated between ATS and OGO, we feel that the following interpretation is more likely. At the expansion phase onset, the cross-tail currents weaken near the earth, and the field strength increases. The information about this current decrease travels across field lines towards the Earth as a compressional wave. Since the field strength is greater behind the wave, i.e., further from the Earth than in front of it, the compressional wave steepens and forms the observed sudden field increase. We note that although the amplitude of the wave at OGO is much greater than at ATS-1, the change in magnetic pressure across the wave front is comparable at the two locations.

The plasma behind this compressional front must be moving towards the earth. Interpreted in terms of frozen-in flux, the plasma is moving with the field lines which are returning to a more dipole-like configuration. This motion may also be thought of as that required to conserve mass. The density behind the front is greater than that ahead of the front by the ratio of the field strengths behind and ahead. It is easy to show, either from conservation of mass and frozen-in flux arguments, or using the curl of the electric field derived from the magnetic field change, that with planar geometry and velocities perpendicular to the magnetic field, the electric field associated with this flow is the product of the velocity of the front times the field change across the front. Thus, the electric field due to the configurational change in the magnetic field on August 7, 1968 was 2.3 mV m-1 at OGO-5 and 1.3 mV m-1 at ATS-1 if we assume the front was moving at its average velocity at the two locations.

Such plasma motions or equivalently such electric fields must certainly penetrate the plasmapause since they are due to changes in the shape of the field lines. Thus, one would expect that whistler ducts would begin to move inwards near midnight shortly after the onset of the expansion phase. Such motion has been observed by Carpenter and Akasofu (1972). The peak electric field observed for two substorms was 0.8 mV m-1.

3.5.2. Betatron Acceleration of Electrons

Fig. 19. Betatron acceleration event. Top trace shows one second averages of the magnetic field strength as measured by the UCLA OGO-5 fluxgate magnetometer and the bottom two traces show the 'transverse' and 'parallel' fluxes of >50 keV electrons measured by the UCLA OGO-5 electron spectrometer (Kivelson et al., 1973b).

Such a favorable alignment of OGO-5 and ATS-1 during a substorm expansion phase onset is rare, but we have many examples of such compressional waves on either ATS-1 or OGO-5 alone. Near the magnetic equator around midnight these compressional waves produce a significant betatron acceleration of >keV electrons (Walker and Kivelson, 1972). Figure 19 shows the magnetic field strength and the flux of 50-1200 keV electrons at two pitch angles during such an event (Kivelson et al., 1973b). When the magnetic field suddenly increases from 54 nT to 70 nT, the flux of particles with near 90o pitch angles, the ‘transverse’ flux, increases markedly while the ‘parallel’ flux remains relatively constant. This is characteristic of betatron acceleration.

Fig. 20. The comparison of the predicted and observed differential energy spectra for pitch angles of 107o and 158o for the August 15, 1968 betatron acceleration event. The field strengths and fluxes at the two times, indicated by vertical lines in Figure 19, were used for this comparison (Kivelson, et al., 1973b).

Figure 20 shows differential flux spectra at the times of the two solid vertical lines in Figure 19 for pitch angles of 107o and 158o. At 107o, the flux has increased by the same factor irrespective of energy. At 158o, there is very little change in the spectrum. The circles indicate the predicted spectra due solely to betatron acceleration using the measured field strength and particle spectrum at 0733.9 UT and the measured field strength at 0735.2. The measurements and the predictions agree remarkably considering the fluctuating behavior of the particle flux and the field strength during this event.

The observation of this betatron acceleration event is not an isolated occurrence. At least ten other clear examples of betatron acceleration have been observed in the data from the UCLA OGO-5 electron spectrometer. These events have all occurred from about 8 to 12 RE behind the Earth, near midnight and near the magnetic equator (Walker and Kivelson, 1972).

3.5.3. The Generation of ELF and VLF Emissions

During substorms magnetospheric particles are accelerated. This acceleration may be due to gradient and curvature drift of particles across electric potentials, due to betatron acceleration as discussed above, or any one of several other possible mechanisms. Further, the mechanism which is dominant may change during the course of a substorm, and hence changes in the pitch angle distribution are not to be unexpected during a substorm even after the initial acceleration event. Such changes occurred during the event shown in Figures 19 and 20. Figure 21 shows the pitch angle anisotropy at 79, 158 and 266 keV as a function of time together with the power of ELF waves at 216, 467 and 1000 Hz (Kivelson et al., 1972). A positive anisotropy corresponds to a loss cone type distribution.

Fig. 21. Correlation of the occurrence of chorus with the pitch angle anisotropy of energetic electrons near the time of the August 15, 1968 betatron acceleration event. The top three traces show the rms amplitude of the electromagnetic noise in three frequency ranges centered on 216, 467 and 1000 Hz as measured by the UCLA OGO-5 search coil magnetometers. The bottom three traces show the pitch angle anisotropy at 79, 158 and 266 keV electons as measured by the UCLA OGO-5 electron spectrometer (Kivelson et al., 1973b).

At 0725 UT, roughly 10 min after the onset of the expansion phase of the substorm, intense, 100 mV m-1, VLF electric field emissions at 3/2 of the electron gyrofrequency were detected (Scarf et al., 1973). At 0735, these emissions decreased in amplitude, and accompanying the betatron acceleration event, the pitch angle distribution changes from being isotropic at 79 keV and strongly anti-loss cone (i.e., maximum flux at other than perpendicular to the magnetic field) at higher energies to being loss-cone at all energies. Simultaneous with the appearance of a loss-cone pitch angle distribution, ELF chorus was generated at frequencies resonant with the energetic electrons in accord with the theory of Kennel and Petschek (1966). We note that the generation of the electron precipitating chorus emissions occurs after the compression of the field during this and every other substorm expansion phase studied with OGO-5 data in this region. This is in direct contradiction of the model of Parks et al. (1972) in which the chorus caused precipitation causes a subsequent collapse of the magnetic field.

3.6. SUMMARY

The plasma sheet thins and expands during substorms. Near the earth the expansion of the plasma sheet appears to be simultaneous, within minutes, with the onset of the substorm expansion phase as determined from ground based magnetograms. As will be discussed below, the correspondence of substorm onset times and ground events is not as well ordered in the distant tail. The plasma sheet is defined by the presence of low energy plasma, but its presence and hence dynamics can be inferred from both magnetic field, energetic electron and energetic proton data. Energetic proton data allow probing of the plasma sheet to a distance of about 1/2 RE away from the spacecraft. The characteristic rapid expansion and slow thinning of the plasma sheet during substorm events explains the rapid-rise slow-decay island events originally reported in the tail. The plasma sheet expansion is accompanied by an inward moving compressional wave within about 10 RE near midnight. This compressional wave causes betatron acceleration. The consequent change in the pitch angle distribution of energetic electrons to a loss-cone distribution has been observed to be accompanied by the sudden onset of ELF chorus.

 

4. Changes in the Orientation of the Tail Magnetic Field

In addition to changes in the field strength and changes in the thickness of the plasma sheet, changes in the orientation of the tail magnetic field occur during substorms. The field varies from being almost dipolar to being quite tail-like with field lines parallel to the solar wind flow. Increases in the tail-like character of the magnetic field are caused both by increases in the solar-antisolar component of the field and by decreases in the magnetic flux crossing the neutral sheet. The magnetic field normal to the neutral sheet is called the north-south component. Since the neutral is roughly parallel to the solar magnetospheric X-Y plane, the Z solar magnetospheric component of the magnetic field, Bz, is a good approximate measure of the north-south component. The Bz component for a dipolar tail field is northward. However, occasionally the tail field turns southward. Understanding the nature of such occurrences is fundamental in understanding the physical processes in the tail.

4.1. MACROSCOPIC CHANGES

Knowledge of the amount of magnetic flux crossing the geomagnetic equator and the neutral sheet as a function of radial distance can be used to map these field lines onto the surface of the Earth. Thus, invariant latitudes can be assigned to tail field lines as has been done in Figure 22 for pre-substorm or growth phase conditions (Fairfield, 1970). Figure 23 shows the same type of representation of tail-field lines during quiet times after a substorm.

Fig. 22. Field configuration in the noon-midnight meridian plane drawn to illustrate the thin plasma sheet and small Zsm component associated with the early phases of a geomagnetic substorm (Fairfield and Ness, 1970).

Fig. 23. Field configuration in the noon-midnight meridian plane drawn to illustrate an expanded plasma sheet with enhanced flux crossing the equatorial plane. This configuration exists during quiet conditions or following substorms (Fairfield and Ness, 1970).

These maps illustrate clearly the qualitative changes occurring in the orientation of the tail field at substorm times. During the growth phase, tail field lines tend to parallel the Earth-Sun-line, i.e., the solar wind velocity vector. There is little magnetic flux crossing the neutral sheet. The last closed field line3, the outer boundary of the plasma sheet, is at moderately low invariant latitudes. After the substorm, the field lines are more dipolar and much more flux crosses the neutral sheet near the Earth. Now the last closed field line has moved to higher invariant latitudes.

Unfortunately, maps such as Figures 22 and 23 provide little more than a qualitative picture of the changes in the tail field. They, of necessity, are constructed from statistical data because satellites can only measure the magnetic field at one position at one time, whereas the field is constantly changing during a substorm. Furthermore, the tail is three dimensional, while these maps portray only the noon-midnight meridian. Finally, we note that the invariant latitude of the inner edge of the plasma sheet in these two maps is 66o and 74o. Thus an auroral zone station such as College, Alaska at 64.6o would seldom be on a field line passing through the plasma sheet, if these maps were quantitative. On the other hand there is evidence that the College field line at times reaches the VELA orbit at 18 RE (Hones et al., 1971b).

Obtaining quantitative dynamical models of the change in the magnetic field during substorms is, of course, important in understanding particle injection and acceleration processes. It may be possible to use the measured particle behavior itself to infer the magnetic field configuration. However, this is a difficult inversion problem even under steady state conditions. Another possible method is the use of artificially created particle beams to map field lines. Finally, two satellite studies can be performed to provide a measure of the three dimensional tail behavior end to measure propagation times of events occurring curing the substorm. Until a quantitative dynamical tail model is obtained, it may be impossible to proceed much further in understanding the nature of the particle injection process.

4.2. SOUTHWARD DIRECTED MAGNETIC FIELDS ACROSS THE NEUTRAE SHEET

The magnetic field across the neutral sheet in Figures 22 and 23 is northward everywhere. However, the reconnection model of the geomagnetic tail predicts southward directed fields tailward of a neutral point (Dungey, 1963). This region of southward directed fields may be small (Dessler and Hill, 1970) but nevertheless it must exist. Thus, it is important to examine the tail magnetic field for the occurrence of south- ward directed components.

Fig. 24. Relative occurrence frequency of the Zsm component of the tail field for all geomagnetic conditions and for very quiet conditions; 2.5 min averages were used in this study (Fairfield and Ness, 1970).

Figure 24 shows the percent occurrence of values of the Z solar magnetospheric component BZ of the magnetic field in the tail as measured by Imp 4 at geocentric distances greater than 25 RE (Fairfield and Ness, 1970). Here BZ is negative (southward) 20% of the time. Although the BZ is frequently negative, this should not be considered a proof that reconnection exists since there are two additional mechanisms creating negative Z components in the tail. These are illustrated in Figure 25.

Fig. 25. Three possible sources of southward pointing magnetic fields in the magnetotail. Reconnection at a neutral point causes southward pointing fields above it and tailward of it. Flaring of the tail causes increasingly southward fields as the north and south magnetopause is reached. Tilting of the tail will cause southward components to appear in one or the other of the lobes of the tail.

Reconnection causes a southward component at geocentric distances beyond the neutral point for some distance on either side of the neutral sheet. Flaring of the tail causes BZ to be negative in both lobes of the tail. This is most pronounced near the boundaries. Finally, tilting of the tail can cause a negative Z component to occur. This occurs in only one lobe at a time, but this fact is not helpful in single satellite studies.

Since tilting and flaring as well as reconnection can cause negative BZ components, we should view the results of strictly statistical studies with some caution. Even if the data studied are restricted to a region near the neutral sheet and even if the effect of tilting of the neutral sheet about the Y solar magnetospheric axis is accounted for (cf. Schindler and Ness, 1972), statistical studies can be very misleading. For example, the data used by Schindler and Ness (1972) to support a multiple neutral point structure in the tail, could also be explained by a model involving no reconnection but having a tilt about the Earth-Sun line (Russell, 1973). Thus statistical studies must be accompanied by detailed investigations of individual events including boundary normal determinations, and temporal evolution studies. Studies of the time evolution of structures are best done with two or more satellites to permit measurements of velocities and the direction of motion, but single satellite studies do permit tests of consistency with certain models.

Fig. 26. Observations of the tail field by Imp 4 near the neutral sheet during a period of intense magnetic disturbance. The average spacecraft position during this interval is (-27, -11, 4) RE in solar magnetosphere coordinates. The top trace shows the AE index, the next two traces are the field strength and Z solar magnetospheric component. The bottom two traces are the latitude and longitude of the field (Fairfield and Ness, 1970).

Fig. 27. Observations of the tail field by Imp 4 near the neutral sheet during a period of moderate activity. The spacecraft coordinates are (-29, 11, 0) RE GSM. The same format as Figure 26 is used (Fairfield and Ness, 1970).

Figures 26 and 27 show examples of moderately high resolution data (20 s averages) of the tail magnetic field near the neutral sheet (Fairfield and Ness, 1970). The two traces of interest are the field strength F and the Z solar magnetospheric component of the field plotted in the middle panel. The large decreases and increases in the field strength are caused by expansions and contractions of the plasma sheet across the satellite Imp 4. During the interval of February 11,1968 shown in Figure 26, Imp 4 was at (-27, -11, 4) RE in solar magnetospheric coordinates. During the interval on March 28, 1968 shown in Figure 27, it was at (-29, 11,0) RE. Z' on the figures indicates the expected distance from the neutral sheet.

Figure 26 shows frequent southward directed fields, occasionally exceeding 10 nT negative. We note that these southward directed fields are an order of magnitude greater than those discussed by Schindler and Ness (1972), and are often a significant fraction of the total field strength. Thus, it is very improbable that these southward components are due to a sudden tilting of the neutral sheet. Each of the southward components precedes a plasma sheet expansion, while not every plasma sheet expansion is preceded by a southward component.

This is the pattern produced by dynamic neutral point formation in which the plasma sheet is ‘reformed’ by the neutral point and plasma sheet expansion is associated with the motion of this neutral point. When the neutral point is formed closer to the Earth than the observation point, a southward directed field is observed just before the neutral point passes by the satellite. When the neutral point forms further away from the earth than the satellite, only the expansion is observed.

The data in Figure 27 were obtained during a less disturbed period, and the southward components here are correspondingly smaller (about l to 2 nT negative). However, the same sequence of events is observed, namely, southward component then plasma sheet expansion. One interval of southward field, that at 0330, is not followed immediately by an expansion. It may be that Imp 4 was too far from the neutral sheet at this time to detect the expanding plasma sheet or that the brief expansion at 0410 was associated with the 0330 southward component.

We note that the majority of southward component events in Figures 26 and 27 last less than 2.5 min and would not show up in statistical studies of average data such as that shown in Figure 24. Since early investigations of the tail used 5 min average data such transient behavior was not observed. Finally, we note that if moving tilts of the neutral sheet rather than neutral point formation were the cause of the observed southward field events, as many southward component events preceding plasma sheet contractions as preceding plasma sheet expansions should be observed. There can be little doubt that neutral points form in the tail and that upon formation they tend to move away from the Earth.

4.3. THE LOCATION OF THE NEUTRAL POINT

In the open magnetotail, there is a northward field across the neutral sheet close to the Earth and a southward field far from the Earth. The line separating these two regions, those connected to the Earth and those not connected, is strictly called the separatrix, but is often referred to as the neutral line. However, as Stern (1972) points out, there can exist fields parallel to the separatrix destroying its neutrality. This is also implicit in the work of Dungey (1963). Since the term neutral point has been used historically; since the neutral line intersects the noon-midnight meridian, our most common picture of the tail, at a point; since, as we will discuss in Section 6, we expect merging to occur predominantly in a narrow region of the neutral sheet; and since the neutral line is not necessarily neutral, we will refer to the merging region as the neutral point throughout this review. We note that the separatrix must move when the neutral point or merging region moves and that the separatrix need not be a straight line. In fact, a separatrix may be a closed circle, containing both an X-type and O-type neutral point, if a neutral point forms on closed field lines (Vasyliunas, personal communication, 1973). We note that while such a situation may only be transitory, it may arise during substorms and thus could be of more than academic interest.

The actual radial distance of the neutral point possibly has only small effect on auroral processes, but instead its magnetic location is important. Nevertheless, there has been much debate on its physical position. In any event, knowledge of its location and motion certainly are necessary to understand in situ observations in the outer magnetosphere and tail. Thus, we will discuss this subject at some length.

It has been suggested that the neutral point is at infinity (Dessler, 1964) and also close to the Earth at from 15-30 RE (Dessler, 1968; Dessler and Hill, 1970). Using the occurrence of strong southward components of the magnetic field at current sheet crossings to indicate the existence of a neutral point between the satellite and the Earth, Mihalov et al. (1968) concluded that there was sporadic reconnection within 30 RE of the Earth but that the average tail magnetic field was northward out to at least 75 RE. Behannon (1970) using a larger data set supported these conclusions. However, Behannon’s statistical treatment of the data is subject to the criticisms set forth in the previous section.

Not accepting these data as proof, Dessler and Hill (1970) argued that the neutral point was close to the Earth and the southward component tailward of the neutral point would be weak and confined to a thin region. Therefore, it would be difficult to observe. In this model, the plasma sheet is supported on open field lines by magnetic turbulence during quiet times (Hill and Dessler, 1971). This model is not supported, however, by observations of ULF waves in the tail (Russell, 1972a; Garrett, 1973). Significant turbulence is observed only after substorm expansion. Otherwise the plasma sheet is quiet. Thus, we conclude that as originally suggested by Mihalov et al. (1968), the quiet-time neutral point is well beyond the orbit of the Moon but that occasionally a neutral point forms at radial distances of less than 30 RE. The data discussed in the previous section suggest that such neutral points move outward followed by apparent plasma sheet expansions. The question remaining is where and when do these neutral points form.

The closest report of a southward component of the tail field is at 12 RE (Laird, 1969), although McPherron et al. (1973a) infer a neutral point as close as 9 RE. Nishida and Nagayama (1973b) bracket the location as between 15 and 25 RE. However, the 5 min averaging used in their analysis would not allow the detection of southward turnings such as found by Laird or as shown in Figures 26 and 27. Thus, it is quite probable that the neutral point is on occasion within 10 RE. On the other hand, the large body of magnetic data available at synchronous orbit has never revealed a southward component at 6.6 RE. Thus, it is improbable that reconnection ever occurs within 6.6 RE even during moderately large geomagnetic storms.

The definition of the onset of the expansion phase of substorms is controversial and thus timing of events relative to this onset must be somewhat uncertain. The southward component observed by Laird (1969) occurred during what could be classified as an expansion phase onset but this was during a period of continuing geomagnetic activity. The neutral point formation inferred by McPherron et al. (1973a) was at the onset of the expansion phase as closely as can be determined from midlatitude magnetograms. The southward turning during some 18 events between 25 and 65RE by Nishida and Nagayama (1973b) occurred within 10 min of the expansion onset deter- mined from midnight midlatitude records. Thus, there can be little doubt that the occurrence of a neutral point close to the Earth is an expansion phase phenomenon. Finally, we note that while the duration of intervals of southward magnetic fields at distances of 10 to 25 RE is of the order of seconds to minutes, the duration of southward fields at the orbit of the Moon is of the order of an hour (Nishida and Nagayama, 1973a). This implies an average velocity of the neutral point from the Earth to the Moon of about 1 RE min-1 However, we cannot say whether this velocity is uniform or even whether it is unidirectional with the present data.

4.4. SUMMARY

The available magnetic field data provide a qualitative picture of the behavior of the tail magnetic field during substorms. During the growth phase the magnetic field becomes more tail-like. This is both because of an increase in the solar-antisolar component of the field (cf. Section 2.2) and a decrease in the magnitude of the north-south component. Substorms return the tail field to a more dipolar configuration. The occurrence of negative Z solar magnetospheric components of the tail field may be due to several causes, but the occasional very large magnitude of these components and their temporal association with the onset of the expansion phase of substorms, in general preceding plasma sheet expansions, is suggestive of a dynamic reconnection model. Although the neutral point must be beyond the orbit of the Moon at quiet times, a neutral point can appear as close to the Earth as 10 RE at the onset of the expansion phase of substorms.

 

5. The Relative Timing of Events

Determining the relative timing of substorm events is perhaps one of the most difficult and controversial tasks in substorm analysis. This difficulty stems in part from having to allow for propagation times to or from the observation point. If an event in the solar wind is detected some tens of earth radii in front of the Earth, we must estimate the time of arrival of this event at the magnetopause. If an intensification of the auroral electrojet is being timed, one must determine whether the apparent intensification at a station was due to motion of the current system or an increase in the current strength. If the apparent intensification is due to motion of the current system then an attempt must be made to determine when this motion started. In the tail the thinning and expanding plasma sheet is usually detected only when the moving boundary crosses the spacecraft. The time of the onset of thinning or the onset of expansion cannot be estimated with any certainty except under certain special conditions.

A second difficulty lies in the definition and identification of the onset of the phases of the substorm. For the growth phase one might define the onset as the time when the interplanetary magnetic field turned southward at the magnetopause or alternatively when the field strength in the lobes of the tail began to increase. However, most often interplanetary and or magnetotail data are unavailable. The signature of the growth phase in ground based data is at best weak and gradual and determining an onset time is extremely difficult.

The onset of the expansion phase can be and has been defined in different ways: with all sky camera data, auroral zone magnetograms and mid and low latitude magnetograms. The brightening of auroral arcs before a poleward expansion and subsequent breakup of aurora is the historical t=0’for the expansive phase auroral substorms. Unfortunately all sky camera pictures or aurora are only available after sunset on clear nights for a limited number of stations. Magnetograms, on the other hand, can be obtained day and night regardless of weather and there are many observatories all around the world. The signature of the intensification and motion of current systems in the auroral zone is very clear, albeit complex, in ground based magnetograms. Unfortunately, the ground signatures are caused mainly by current systems only about 100 km above the ground, a distance much smaller than the usual spacing between observatories. Hence, it is possible to miss changes in the current system at times or not to be able to determine when a change was initiated if such changes occurred between observatories.

The substorm signature of mid and especially of low latitude magnetograms is rather simple and is determined by distant current systems. (This is not necessarily true of equatorial stations however). Thus, given a chain of only about 8 stations evenly distributed in longitude, the onsets of all moderate to large substorms can be determined, quite precisely. The drawback of this technique is in its signal-to-noise ratio. The signature of small substorms is comparable in size to that of moderate sudden impulses and may also be masked by the uncertainties in removing the contribution of the SQ currents to the data. We note, finally, that although all three sets of data are used to define the onset of the expansion phase of substorms, there is no general agreement as to the relative timing of the onsets so determined. In other words, the three techniques have not yet been sufficiently intercalibrated to be used interchangeably.

5.1. TIMING RELATIVE TO THE INTERPLANETARY MAGNETIC FIELD

Many solar wind parameters correlate with geomagnetic activity. However, this should not be taken as evidence that they are all causative agents of geomagnetic activity, since the solar wind parameters are highly intercorrelated (Hirshberg and Colburn, 1969). The first successful attempt at isolating the primary causative agent of geomagnetic activity using correlation techniques was performed by Arnoldy (1971). This attempt was successful in part because of the use of high resolution data, and in part because of the use of the proper coordinate system. The use of high resolution magnetic field data permitted him to compute the amount of southward and northward directed interplanetary field per unit time separately and to cross-correlate them with the AE index. Figure 28 shows the cross correlation of hourly sums of the southward field only, the northward field only, the hourly average field strength, the hourly average number density and the hourly average solar wind velocity with the hourly average AE (auroral electrojet) index. The only significant correlation is with the hourly sum of the southward field only. This correlation is maximum with the AE index one hour later. We note that Arnoldy did not vary his accumulation time for summing the interplanetary field nor the AE index averaging period.

Fig. 28. Linear correlation coefficients of various interplanetary parameters with AE for lead or lag times up to 5 h. Bs (Bn) is computed in solar magnetospheric coordinates by summing only southward (northward) field (Arnoldy, 1971).

To refine this timing, Foster et al. (1971) performed a superimposed epoch study of the interplanetary field and the AE index. They studied only isolated substorms separated by at least 4 h from preceding and subsequent substorms. They also determined substorm onsets from both auroral and low latitude magnetograms, rejecting substorms whose onsets differed by more than 10 min with the two techniques. The results of this study are shown in Figure 29. This average picture shows a field turning southwards 80 min before the substorm onset. Simultaneously the AE index begins to increase. This is the growth phase of the substorm. After the substorm onset, the AE index continues to increase for another 40 m. Finally, the AE index decreases over a period of about 2 h. Thus, for isolated substorms, these data show an average growth phase on 80 min, an average expansion phase of 40 min and an average recovery phase of 2 h, giving a 4 h total duration for the three phases of a substorm.

Fig. 29. Superposed epoch study of 54 isolated substorms showing the average percentage of the maximum value of the AE index and north-south component of the interplanetary magnetic field. The time scale is measured in hours from the onset of the expansion phase (Foster et al., 1971).

5.2. TIMING RELATIVE TO EVENTS IN THE TAIL

The timing of events in the tail relative to onsets determined with ground based data is quite variable because of the unknown propagation velocities to the point of observation. Some events are quite simultaneous. For example, the 0714 UT substorm of Figure 7, discussed in Sections 2.2 and 3.3, caused a plasma sheet expansion simultaneous with the onset of the substorm as determined from mid latitude magnetograms. The simultaneity in this instance was presumably due to the special location of OGO-5, very close to the geomagnetic equator and close to the ‘L shell’ on which the substorm was initiated.

Fig. 30. Simultaneous data from a balloon over College, Alaska from ATS-1 in synchronous orbit and Vela 4A at 18 RE in the magnetotail. The ST detector is sensitive to electrons with 110 keV<E<260 keV. The GMB1 detector is sensitive to electrons with E>40 keV. At the bottom are given the positions of Vela 4A in solar magnetospheric coordinates, its distance from the expected position of the neutral sheet, DZ, and the tilt of the Earth's dipole axis in degrees. Local time at ATS-1 is teh universal time less 10 h (Hones et al., 1971b).

Hones et al. (1971b) have reported simultaneity between the appearance of >40 keV electrons at VELA at 18 RE in the tail and the onset of the expansion phase of a substorm and the appearance of precipitating fluxes of energetic electrons at College, Alaska. Figure 30 shows an example of this. At 0930, there is a small increase in the GMB1 detector sensitive to electrons with E >40 keV, and a much larger increase in the ST detector sensitive to electrons 100 keV <E <260 keV. The decay in the GMB1 flux before this spike indicates that the plasma sheet was probably thinning. The return of the fluxes of energetic electrons signaling the expansion of the plasma sheet past VELA again did not occur until 1016 UT. The top panel shows the measurements of an X-ray detector on a balloon over College, Alaska. The rapid increase is simultaneous to within one minute of the increase in the VELA electron flux. Such spikes of energetic electrons simultaneous with substorm onsets determined from data obtained at College, Alaska are not at all uncommon (Akasofu et al., 1971 ) and are interpreted to mean that the field line through College, Alaska sometimes extends far down the geomagnetic tail.

The detection of thinning and expansion events in the tail bears a much more variable relationship with substorm onsets. Returning to Figure 13, we see that thinning can continue past the time of substorm onsets determined from midlatitude magnetograms and that the observed expansion can vary from being simultaneous to being delayed by about an hour. The most comprehensive study of the relationship of plasma sheet thinning and expansion to substorm events performed to date (Hones et al., 1973), shows that the expansion time at 18 RE is ordered more by the time of recovery of bays on the ground than the onset time of the bays. Their study suggests that the thickening of the plasma sheet begins near the Earth, but this thickening does not proceed uniformly down the tail with time. Instead the plasma sheet at large distances down the tail (Xsm> -15 RE) can remain thin for periods of tens of minutes to hours, until auroral zone negative bays recover. Hones et al. suggest that this recovery coincides with the cessation of dayside merging, i.e., with the cessation of flux transport. Since dayside merging is controlled by the southward component of the interplanetary field, this agrees with the previous suggestion of Aubry and McPherron (1971), that a plasma sheet expansion was triggered by a northward turning of the interplanetary field.

Finally, we note that there are two phenomena in the tail whose timing relative to substorm onsets is not so variable. As discussed in Sections 2 and 4, the lobe field strength begins to decrease and southward magnetic fields appear near the current sheet within minutes of the onset of a substorm expansion. The rapid response of these phenomena is probably due to the fact that the information on the formation of the neutral point and/or enhanced reconnection rate at the expansion phase onset propagates at or near the Alfven velocity which is quite large in the tail.

5.3. FUTURE WORK

The measurement of interplanetary parameters simultaneous with magnetospheric and ground based observations is an essential element for any significant future progress in understanding magnetospheric substorms. The timing of the arrival of events at the magnetopause may be a problem if these interplanetary measurements are made far from the Earth. However, the technique of Burch (1972) of using polar magnetograms to time the arrival appears to provide a solution to this problem.

In the magnetosphere, coordinated multisatellite studies should be conducted. These studies could involve the use of synchronous orbit data as baseline measurements monitoring the state of the magnetosphere, or as one point in a timing study such as the OGO-5 to ATS-1 compressional wave event discussed in Section 3.4.1. Dual satellite missions, such as the proposed, closely-spaced, mother-daughter pair of satellites, can provide essential velocity data near the substorm trigger region in the outer midnight magnetosphere. It is important that the apogee of the orbits of such satellites be at least 20 RE so that the region in which the substorm expansion phase apparently begins is adequately probed.

A serious limitation of many past studies has been the availability and temporal resolution of ground station data (Akasofu and Snyder, 1972). Networks of ground based magnetometers, at mid and low latitudes, at auroral latitudes, and in the polar cap, all play key roles in the study of substorms. The mid and low latitude magnetograms respond to distant current systems monitoring the ring and tail current systems. A chain of 8 stations equispaced in longitude is adequate for this purpose.

It is probably impossible to obtain complete auroral zone coverage because a two dimensional network, rather than a longitudinal chain, is required to measure the ionospheric auroral zone currents associated with substorms. However, much progress can be made with one or more latitudinal chains, such as that set up by G. Rostoker in Canada (Kisabeth and Rostoker, 1971), complementing a longitudinal chain at magnetic latitudes of about 65-70. Such stations should also be equipped with all sky cameras to provide for the inter-calibration of the existing techniques for substorm onset determination.

Polar cap magnetic records should be obtained for timing the arrival of interplanetary events as discussed above. Some day such records may even provide a quantitative measure of the interplanetary field. If so, then measurements in both polar caps will be necessary, since the sunlit polar cap is most responsive to changes in the interplanetary magnetic field (Miller et al., 1972).

All such magnetometers should have digital outputs with a temporal resolution of one minute or better. The availability of digital data facilitates the real time transmission of the measurements, and finally the presentation of the data. The high time resolution is a necessary complement to the satellite data.

Finally, balloon and rocket studies should be coordinated intimately with satellite programs. This can be done in two ways. First, such studies can be scheduled for periods when the relative positions of the operating magnetospheric satellites are especially promising. Such a coordination requires only the advance computation of satellite trajectories and its distribution to the scientific community. Second, payload launches can be delayed until satellite data indicate an upcoming event or that the magnetosphere is in a certain phase of magnetic activity. Such data could be provided by either an interplanetary probe or synchronous satellite in the magnetosphere. Real time transmission of the satellite data to a launch command post would be required for such operations.

 

6. A Qualitative Model

From the phenomenology described in the previous sections we can delineate the sequence of events and the dominant physical processes occurring during substorms. Such a qualitative phenomenological model is useful for ordering past observations and for testing new observations as they are made. The hope, of course, is that the model is accurate enough that new models can evolve by successive perturbations of the old model.

Although the model presented here is qualitative and phenomenological, this is not to imply that excellent quantitative theoretical work on substorms does not exist. On the contrary, for example, Coroniti and Kennel (1972a, b; 1973) have treated quantitatively several of the key processes in this model. We refer the interested reader directly to these papers. Unfortunately, finding mathematical justification for what we see nature do, is often a time consuming task. This work continues.

6.1. FLUX TRANSPORT

In our model flux transport from the dayside magnetosphere to the tail occurs via the merging of the closed dayside magnetospheric field lines with the interplanetary field lines to form open field lines. The magnetospheric lines are then swept back by the solar wind to form the magnetotail. The rate of this merging process is strongly dependent on the southward component of the interplanetary field. Nothing in the observations of flux transport discussed in Section 2 demands that the transport take place via merging. However, both studies of solar electrons (cf. Lin and Anderson, 1966; Van Allen, 1970) and solar protons (cf. Van Allen et al., 1971; Morfill and Scholer, 1972; Fennell, 1973) show that the polar cap and magnetotail field lines are open and directly connected to the interplanetary medium. Since we know that the polar cap is growing larger during the growth phase (cf. Burch, 1972), the flux transfer must occur by merging. The merging process has also been called field cutting and reconnection. When used for the dayside field cutting process, the term reconnection is a misnomer since the magnetospheric and interplanetary fields are being connected for the first time. Later in the tail the magnetospheric field lines are reconnected. Figure 31 shows a cartoon of the field cutting process on the dayside magnetosphere with newly cut magnetic flux being pulled over the polar caps into the tail. We know that the rate of merging is controlled by the east-west solar magnetospheric component of the solar wind electric field (i.e., the electric field associated with the southward component of the interplanetary magnetic field). However, we do not know the relationship between the electric field and the rate of flux transport and how other parameters in the solar wind might modify this relationship.

Fig. 31. Field cutting or merging on the dayside magnetopause.

The importance of merging in magnetospheric physics was first emphasized by Dungey (1958). Figure 32 shows Dungey's sketches of the magnetosphere for the two extreme cases of southward (top) and northward (bottom) interplanetary fields (Dungey, 1963). These diagrams were not intended to be to scale, and show only essential field lines. Dungey obviously realized the proper length of the tail (Dungey, 1965) and therefore the size of the normal component to the magnetopause in the tail. The top model shows merging on the dayside carrying field to the tail where it is reconnected at a neutral point, N, and carried back into the magnetosphere. In this model the tail field lines are open. The bottom model, for northward fields, shows connection at two points in the tail. This model, as sketched, removes flux from the tail which would be replaced by convection of closed field lines from the dayside. In this model the tail field lines are closed.

Fig. 32. Magnetic field configuration of the magnetosphere in the presence of a southward interplanetary field (top panel) and in the presence of a northward interplanetary field (bottom panel) (Dungey, 1963).

Studies of the entry of energetic solar particles into the magnetotail appear to indicate that the tail is always open regardless of whether the interplanetary magnetic field is northward or southward (cf. West and Vampola, 1971; Fennell, 1973). A simple modification of Dungey's model shown in the bottom panel of Figure 32 is consistent with this observation (Russell, 1972b). The modification is to note that it is improbable for the same field line to become connected to both the north and south neutral points on the tail boundary. The interplanetary field lines merge with the tail lines and cause a reshuffling of the tail field but cause no transfer of flux from the dayside to the nightside of the magnetosphere. It is important to note that the north lobe of the tail becomes connected to the solar wind south of the magnetosphere and the south lobe to the north solar wind. This process is sketched for one lobe of the tail in Figure 33. Other field lines are connecting with the south tail neutral point (not shown). Field line B b is convected to the magnetopause, and merges at a neutral point N with an open tail line E ' to form two lines E b' and B' '. The first line convected to the Earth forms a new tail line E b". The dashed portion indicates that the line is out of the page. The other line B" " is removed from the tail. We note that the tail cannot remain open indefinitely without flux transfer from the dayside, since there is probably always at least a little reconnection at the neutral point internal to the tail, and since the closure of open flux by merging of the same field line at both surface neutral points is possible.

Fig. 33. Modification of Dungey's model of the magnetosphere for northward interplanetary magnetic fields noting that the connection of the same field line to both north and south neutral points is improbable (Russell, 1972b).

Since this process does not involve flux transfer it does not play a role in substorms. However, its effects must be separated from substorm effects so we will mention a few of these and contrast these effects with those involving flux transfer. First, since the north lobe becomes connected to the south solar wind and vice versa for the south lobe, there is a tangential stress on the tail field lines pulling towards the neutral sheet. Secondly, if the field is not exactly northward more field connected to the north neutral point will skip around the magnetosphere on one side of the magnetosheath than the other. The flow will have the opposite asymmetry for the other lobe. This turns the tangential stress into a torque and could cause a twisting of the plane of the neutral sheet. Further, it leads to asymmetries in the polar cap electric fields or alternatively in polar convection patterns. These have been observed. Finally, this effect brings some features of a recent magnetospheric model (Frank, 1971) into accord with Dungey's original model.

6.2. MAGNETIC MERGING THEORY

Since magnetic merging plays such a fundamental role in our model, we will briefly discuss the state of merging theory. Theoretical treatments of merging are generally two dimensional and can be divided into two classes according to the dimensions which they treat. The first class considers the plane containing the two oppositely directed magnetic fields and the normal to the current sheet. In the Earth's magnetotail this would be roughly the solar magnetospheric X-Z plane. Such models have been discussed by Petschek (1964), Sonnerup (1970) and Yeh and Axford (1970). These models have a normal component of the magnetic field across the current sheet except for a small region near the neutral point itself. The other class of merging models considers the plane perpendicular to the magnetic field. In the Earth's magnetotail this would be roughly the solar magnetospheric Y-Z plane. A model of this type was first discussed by Alfven (1968) and has since been extended by Cowley (1971, 1973) to preserve charge neutrality and by Hill (1972) to apply to fields at arbitrary angles. It has no component of the magnetic field normal to the current sheet, and thus most nearly approximates the conditions in the plane normal to that of the first class near or at the neutral point. A further distinction between the two types of models is that the former models are fluid treatments while in the latter models particle orbits are important.

Neither of these classes of models can adequately describe the merging process in the Earth's magnetotail. We would hope, however, that such treatments could provide some general guides as to the behavior of the neutral point in a realistic model. Unfortunately, the predictions of the theories are sufficiently diverse as to make this very difficult. For example, Yeh and Axford state that in their model flow goes from the larger to the smaller wedge. Therefore, one would expect that there would be no flow for equal size wedges. Unfortunately, Sonnerup obtains maximum flow for equal sized wedges. While some of these differences may be more apparent than real (Coroniti, personal communication 1973), it is beyond the scope of this review to attempt to explain why such similar models lead to apparently contradictory results. The lesson to be learned here is that much work remains to be done on the merging problem, both experimental and theoretical, and that predictions from these models should be viewed with some caution at the present time. Fortunately, magnetic merging can be and has been produced in a laboratory plasma (Bratenahl and Yeates, 1970). While the experimental configuration did not reproduce the geometry of the magnetopause nor the tail, and while the plasma here was collisional rather than collisionless, many of the predictions of the Petschek theory were confirmed, raising the hope that laboratory experiments may provide adequate proving grounds for refining present merging theory.

6.3. THE ELECTRIC FIELD IN THE TAIL

In the absence of reconnection, there would be two adjacent interplanetary field lines which would be diverted around the magnetopause on opposite sides of the magnetosheath. There is only an infinitesimal electric potential difference between these field lines in the solar wind. If there is infinite conductivity along field lines, then there is no electric field applied to magnetosphere by the solar wind.

Fig. 34. A cross section of the distant tail and solar wind parallel to the dawn-dusk meridian as viewed from the Earth and at a time when the magnetotail is connected to a southward interplanetary magnetic field. The radius of the tail is R and the thickness of the interplanetary medium connected to the tail is D.

If there is connection, then as sketched in Figure 34 the lines flowing on opposite sides of the magnetosphere are separated by a thickness, D, of interplanetary plasma across which there is a change in electric potential. This electrical potential difference is applied to the magnetotail. We note that we must specify another boundary condition if we are to determine the electric field inside the tail. Processes at the neutral sheet also affect the flow. For example, all the flow might move towards a narrow region on the dusk side of the neutral sheet (Cowley, 1971; 1973).

Fig. 35. A noon-midnight meridian cut of the distant tail under the same conditions as Figure 34. The velocity of the magnetotail plasma V is controlled in part by boundary conditions internal to the tail.

Figure 35 shows a noon-midnight meridian cross-section of the tail. During flux transfer from the dayside field lines are laid on the tail by the solar wind like a paint roller applying coats of paint. If reconnection is occurring at the neutral sheet, these field lines sink into the tail. If it is not, then the newly transported flux piles up.

Flows in the tail have their counterparts in the polar cap. Roughly, the sinking of field lines into the center of the tail is the counterpart of flow across the center of the polar cap, and flow around the edges of the tail corresponds to flow parallel to the auroral oval. Unfortunately, we cannot simply map the observable polar flows into the tail or map expected tail electric fields into the polar cap, because of the possible presence of electric fields parallel to field lines, and the frequent existence of electric fields due to time varying magnetic fields in the tail. Nevertheless if these warnings are kept in mind, it is instructive to examine hypothetical polar cap flow patterns expected to occur for the different merging situations. These are illustrated in Figure 36.

Fig. 36. Qualitative polar cap convection pattern due to merging of the interplanetary field with the dayside magnetospheric field lines and with tail field lines, and due to merging of open tail field lines across the neutral sheet. Plus signs indicate the area enclosed by the last closed field lines (LCF) is increasing; minus signs indicate it is decreasing. Dawn dusk asymmetries in the flow may arise when there is a non-zero east-west component of the interplanetary magnetic field. The asymmetry sketched in the middle pair of diagrams is that expected for a negative solar magnetospheric component of the interplanetary magnetic field (Russell, 1972b).

The top two pictures illustrate the effect of dayside merging and neutral sheet reconnection. In the former case, the polar cap, the area enclosed by the last closed field line (LCF) is increasing and the latter case decreasing in area. When the interplanetary field is southward, the flow should be essentially across the center of the polar cap, although the existence of an east-west component should introduce an asymmetry in the flow pattern.

The middle two pictures show the effect of the merging of a northward interplanetary field with the boundary of the tail. The polar caps do not change in size in this case. However, the fact that the north polar cap is connected to the south solar wind causes the flow to move parallel to the auroral oval. Again asymmetries are expected in this flow, controlled by the east-west component of the interplanetary magnetic field. The asymmetries are, of course, opposite in the north and south polar caps. When there is a positive Y solar magnetospheric component, i.e., opposite planetary motion, of the interplanetary magnetic field, the flow should be strongest at dawn in the northern polar cap and at dusk in the southern polar cap. For a negative east-west component, in the direction of planetary motion, the asymmetry in the flow is reversed. This latter case is shown here. We note that the direction of the asymmetry is independent of whether the field is north or south, and that the observations of Heppner (1972) are in accord with this picture.

It is theoretically expected that merging can occur even between fields at angles of less than 90o (Petschek, 1964). Thus, one might expect merging on the dayside for northward fields. While observations of the flux transport process show that the dayside magnetosphere is very insensitive to northward fields, observations of sunward flows over the polar cap have not been reported. Thus dayside merging for northward interplanetary magnetic field probably takes place. If so, then the pattern shown in the bottom left pictures should arise. If reconnection at the neutral sheet occurred, the bottom right pattern should arise.

Before discussing how the expansion phase of substorms is initiated, we will mention briefly how the energy input to an open tail occurs. Whenever there is a normal component across the magnetopause, there is momentum flow across the boundary. The stress exerted by the solar wind on the tail or the drag of the normal component on the solar wind is (BT BN/4 ) per unit area where BT is the tail field, and BN is the normal component. The total stress is this quantity integrated over the whole magnetopause. We note that BN is difficult to measure experimentally because it is very small in the tail. Through reconnection in the current sheet, the magnetic energy is converted to particle energy. If the rate of energy input at the magnetopause exceeds the rate of conversion of magnetic to particle energization at the current sheet, then storage of the energy in the magnetic field occurs. Increases in the lobe field strength and decreases in the plasma sheet thickness are both manifestations of this storage. In our model, the growth phase is the period during which the storage of energy in the magnetic field occurs. Energy input to the tail may continue into the expansion phase and, in fact, the magnetotail may reach a state in which the energy input is large but it is converted to particle energy immediately causing sustained auroral activity. In this model, the expansion phase represents only a change in the rate of conversion of magnetic to particle energy.

6.4. THE EXPANSION PHASE

The onset of the expansion phase may be triggered by the solar wind, an ionospheric event or by a magnetospheric event. The OGO-5 observation of a very thin plasma sheet at 8 RE with no choking of the flow, which was discussed in Section 3.3, leads us to postulate that the onset occurs when the plasma sheet somewhere thins to zero thickness. However, there is a theoretical basis for expecting the onset to occur when the magnetosphere becomes uncoupled from the ionosphere by electric potential drops along field lines, caused by anomalous resistivity in field aligned currents flowing into the auroral zone (Coroniti and Kennel, 1972b). A sudden increase in the merging rate in the tail might very shortly force this ionospheric instability to occur. Alternatively, the sudden cessation of line-tying associated with the onset of the instability might very shortly trigger a thinning of the plasma sheet and produce a new reconnection point close to the Earth. This model for the expansion onset bears some resemblance to that proposed by Hill and Dessler (1971). However, in their model, the neutral point was close to the Earth at all times and the plasma sheet existed on open field lines. In this model, the neutral point is usually beyond the moon but appears near the Earth at the expansion onset. Also, the plasma sheet is on closed field lines.

Although OGO-5 was only once in the proper position to observe the extremely thin near earth plasma sheet at the expansion phase, we have additional evidence that this is not a special event or a coincidence. First, there is the fact that substorms can be centered at local times far from midnight, anywhere from 2100 LT to 0300 LT (cf. McPherron et al., 1972; Clauer et al., 1972). For this to occur the substorm must be initiated within 15 RE if effects propagate radially. Second, we have the observation that southward components precede plasma sheet enhancements at Xsm < -25 RE. This indicates that a neutral point forms within 25 RE and moves away from the Earth. Third, we have the observation of near simultaneity of events at synchronous orbit, and at OGO-5 at about 10 RE with onsets determined from ground data, while greater and greater delays are observed with distance from the Earth.

Fig. 37. A model for the onset of the expansion phase of a magnetospheric substorm. The X marks the position of the OGO-5 satellite during a well documented substorm on August 15, 1968. The asterisk marks a typical location of a VELA satellite during a substorm. At time A, the plasma sheet is thinning but thins faster near the earth. At time B, an X type neutral point has formed near OGO-5, enveloped in the expanding plasma sheet. Finally, at D, the neutral point has moved far down the tail enveloping VELA in the plasma sheet also (Russell, 1972b).

Figure 37 shows schematically the sequence of events we presume to occur around substorm expansion phase onset. In panel A, the plasma sheet is thinning. The two most exterior field lines are the boundaries of the plasma sheet. OGO-5 on August 15, 1968 was at the position marked by the X. A typical VELA position at 18 RE is marked with an asterisk. The plasma sheet is presumed to thin down faster near the Earth. The reason for this is a matter for speculation.

Soon, as shown in panel B, a neutral point forms. This could be within the plasma sheet on closed lines or it could be on open lines. In the latter case, the three dimensional nature of the tail has to be invoked allowing a zero thickness plasma sheet at one local time. On August 15,1968, OGO-5 left the plasma sheet at this time. At the VELA orbit, there might be no noticeable effect at this time with the plasma sheet continuing to thin. It is also possible that sometimes VELA is located at or near the last closed field line at this epoch of the expansion phase. At such a location, a burst of energetic electrons simultaneous with the formation of the neutral point would be least surprising. For example, it could represent a loss of Van Allen outer zone electrons onto open field lines. A measurement of the spectrum and the complete pitch angle distribution of these electrons would shed light on this point.

In panel C, the expansion of the plasma sheet has begun. This expansion occurs as the neutral point moves away from the Earth. One would expect the neutral point to move away because the pressure on the near Earth side is greater than the tailward side. However, this is not necessarily the case because the dayside magnetosphere could be flux deficient because of the erosion process and in fact could be pulling’flux to the dayside. Alternatively, the reconnection rate at the neutral point may be a function of position of the neutral point. Then, the neutral point would move to a location at which flux was merged as rapidly as demanded by external forces. In such a case, the interplanetary magnetic field could control the time of plasma sheet expansion at large radial distances, just as it controls the onset of thinning during the growth phase as suggested by Aubry and McPherron (1971).

In panel D, the plasma sheet expansion has reached VELA after some time delay. We note that all during the substorm process field lines have been convecting towards the Earth. In these sketches we have allowed them to pile up on the night side. In reality, they would convect out of, or into the page and around to the day side. During the expansion phase, the current strength in the tail decreases. At this time, the field becomes more dipolar and throughout most of the magnetosphere becomes stronger. It is the compressional wave propagating into the midnight magnetosphere from the tail signaling this decrease in current strength which causes the effects discussed in Section 3.4.

Cowley (personal communication, 1972) has pointed out that many of the effects observed on the ground do not require an increase in the overall merging rate. He proposes that instead of enhanced merging causing enhanced convection at an expansion onset, there is merely a localization of the electric field and hence of convection. This is a natural result of the decrease in the normal component of the magnetic field across the current sheet during the growth phase. In Cowley's model, when this normal component becomes small enough in the near Earth region, the earthward convection is channeled into a small corridor. Thus, locally there would be an enhanced flow. Although this might occur in the absence of the formation of a neutral point, we feel the observations that the tail lobe field decreases at the onset of the expansion phase indicate that the merging rate, indeed, increases at the onset of the expansion phase. Furthermore, the appearance of southward tail fields near the Earth at the onset of the expansion phase indicates there is a neutral point in this region.

Hill (1972, 1973) has proposed that the plasma sheet is maintained by magnetosheath particles which enter through the dayside magnetopause. In this model, the entry rate is large for northward fields and small for southward fields. Thus, when the interplanetary field turns from northward to southward the source of the plasma sheet particles diminishes and the plasma sheet shrinks. This model is at present very preliminary and qualitative and it is perhaps premature to comment. Nevertheless we note that in the model we have presented, the quiet time neutral point, which controls the formation of the plasma sheet, is beyond the orbit of the Moon, and the flow in the plasma sheet is towards the Earth between the neutral point and the Earth. Thus, the plasma sheet is relatively insensitive to particle entry rates across the dayside magnetopause. Thinning occurs in our model when the convection velocity increases near the Earth while remaining unchanged far down the tail.

Finally, we would like to point out that a hypothesis of Cowley may provide an explanation of the westward surge. Cowley's work (1971, 1973), shows that the steady state tail should have a localization or channeling in the flow near dusk. However, we note that there is no requirement that the neutral point form in this region initially. Thus, if a neutral point formed near midnight, charge neutrality requirements would soon cause this region to move towards dusk. We do not know, however, how fast this motion would be and thus whether this motion is consistent with observed westward surge motions.

Cowley has also pointed out (personal communication, 1972) that when all the current is carried by plasma coming in from the sides, there is no reconnection and when it is all provided by plasma `coming in from the sides' there is maximum reconnection. For intermediate cases with some current carrying plasma provided by the lobes and some by the magnetosheath, the reconnection rate is appropriately modified. Dessler (1968) has suggested that magnetosheath plasma has little access to the plasma sheet within 30 RE but can provide the particles necessary for the current sheet beyond 30 RE. Thus, if the neutral point were far down the tail in a 'selfconsistent'’tail region (Beard et al., 1970; Bird and Beard, 1972), we might expect little merging. However, if Dessler's hypothesis were true and if the neutral point were close to the Earth, current carrying particles would have to be supplied by lobe plasma and hence the reconnection rate could be large. Unfortunately, this problem requires a calculation of self-consistent currents and fields in a three dimensional geometry and is not soluble with such a simple superposition of idealized models. Nevertheless, it is tempting to speculate that the position of the neutral point is associated with the rate of reconnection, and that distant neutral points occur during periods of little or no reconnection.

 

7. Summary

The tail plays a very active and important role in substorms. It is in this region that the growth phase is best defined. Here the flux eroded from the dayside magnetosphere is stored. During this phase, the tail flares more; the field strength in the near tail increases; and the currents strengthen and move closer to the Earth. Further, the plasma sheet thins and the flux crossing the neutral sheet lessens.

The onset of the expansion phase appears to be signaled with the formation of a neutral point in the near tail. Eventually this moves away from the Earth causing an expanding plasma sheet. In the near midnight region in the vicinity of synchronous orbit and beyond an inward moving compressional wave causes betatron acceleration of electrons. The resulting pitch angle distributions are unstable to the generation of ELF electromagnetic emissions. It is at this point during the substorm that strong ELF emissions are generated.

The growth phase starts with the southward turning of the interplanetary field. However, the trigger for the start of the expansion phase is not as clear. It could be an ionospheric event, a magnetospheric event, or a solar wind induced change. Whatever the cause, its primary effect seems to be the formation of a near Earth neutral point which eventually propagates down the tail.

Although we feel this qualitative model is a useful approximation of the time sequence of substorm events, we by no means feel this is a complete model. For example, we have made no attempt to model multiple onset substorms nor the detailed behavior of aurora. Further we are aware of the tremendous variability of substorm phenomena as observed on the ground. We feel that substorm research, both experimental and theoretical is as important and necessary today as ever in the past. Now, however, the problems to be solved are much better defined. Further, most of the studies necessary to solve these problems, if not already underway or approved, are being proposed to the appropriate agencies. We look forward to the day when these projects are completed and we have defined quantitatively the laws governing the various stages of the substorm sequence.


1. Although most studies show that the interaction of the solar wind with the magnetosphere is best ordered in solar magnetospheric coordinates, much of the data necessary for such studies is given in other coordinate systems. A description of these various coordinate systems and how to transform from one to another has been given by Russell (1971).

2. The terms neutral sheet and current sheet will be used in this paper to refer to the plane which separates field lines pointing towards the Earth from those pointing away from the Earth. These are merely names like John and Mary. No sheet of zero field strength has been observed in the tail, nor are the currents which reverse the field from the north lobe to the south confined to a thin sheet.

3. As discussed in Section 6.1, the evidence in favor of an open magnetosphere in which polar cap and tail lobe field lines connect directly with the interplanetary medium is overwhelming. In most open models, a plasma sheet like region on closed field lines is a natural consequence of reconnection. Regardless of source, plasma sheet particle density should decrease abruptly in going from closed to open field lines, because on open field lines particles can execute at most one bounce before leaving the tail. Alternatively one can consider 'last closed field fine' just a name for the outer boundary of the plasma sheet.

 

Acknowledgments

We would first like to thank our co-workers on OGO-5 who have lent us their data, advice, and encouragement throughout our substorm studies. These include M. P. Aubry, R. Buck, C. R. Chappell, P. J. Coleman, Jr., T. A. Farley, R. W. Fredericks, R. E. Holzer, M. G. Kivelson, M. Neugebauer, F. L. Scarf, E. J. Smith, and H. I. West, Jr. The value of the OGO-5 data was at least doubled by the contribution of correlative data from other satellites and ground based data by J. H. Binsack, D. L. Carpenter, D. S. Colburn, D. H. Fairfield, G. K. Parks, and C. P. Sonett. The resources of both the National Space Science Data Center and World Data Center A were also often called upon. We would also like to acknowledge many fruitful discussions of this work with F. V. Coroniti, S. W. J. Cowley, T. E. Holzer, and C. F. Kennel. The National Aeronautics and Space Administration provided support for analysis of OGO-5 magnetic field data reported herein under NASA contract NAS 5-9098, for the analysis of the OGO-5 energetic electron data under NASA contract NAS 5-9097, for the analysis of ATS-1 magnetic field data under NASA grant NGR 05-007-004, and for the correlation of Explorer 33 and 35 data with the OGO-5 magnetic field data under NASA grant NGR 05-007-305. The National Science Foundation provided support for the study of geomagnetic storms under NSF grant GA 34148-X. Finally, we would like to thank D. B. Beard, J. W. Dungey, H. B. Garrett, T. W. Hill, A. Hruska, L. J. Lanzerotti, W. F. Libby, M. D. Montgomery, G. E. Morfill, G. Rostoker, C. P. Sonett, R. J. Walker, H. I. West, Jr., and D. J. Williams for their many useful comments on an earlier version of this paper.

 

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