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.
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.
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 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.
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.
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.
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
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
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)
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
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.
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
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
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.
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
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
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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.
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
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.
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).
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.
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 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.
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 enhan
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).
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).
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).
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).
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).
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).
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.
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.
3. The Thinning and Expansion of the Plasma Sheet
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).
Fig. 14.
True and apparent velocities of an expanding boundary.
V 
n and
V
n are
the true components of the velocity while Va and
Va are
the apparent components.
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).
Fig. 16.
The signature of the expanding plasma sheet in energetic
electron measurements. The same format as Figure 10 (Meng et al., 1971).
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).
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.
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).
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).
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).
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).
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).
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.
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).
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).
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).
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).
Fig. 31.
Field cutting or merging on the dayside magnetopause.
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).
' 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).
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.
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.
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).
) 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.
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).