CHRISTOPHER T. RUSSELL
Institute of Geophysics and Planetary Physics
University of California, Los Angeles, U.S.A.
Originally Published In: Correlated Interplanetary and Magnetospheric Observations,
(ed. by D.E.Page), P. 3, D. Reidel Publ. Co., Dordrecht, Holland, 1974.
Abstract. Our understanding of the solar wind-magnetosphere interaction has evolved slowly but steadily since the advent of space exploration. The early picture of transient confinement of the geomagnetic field during geomagnetic storms by blast waves of solar plasma was soon replaced by a magnetosphere confined by a continuously flowing solar wind. This magnetosphere was found to be elongated in the antisolar direction forming a region behind the Earth known as the geomagnetic tail. In front of the magnetosphere, a shock front was observed at which the solar wind was decelerated, heated and deflected around the magnetosphere.
While the solar wind dynamic pressure determines the overall size and shape of the magnetosphere, recent measurements show that tangential stresses play an essential role in magnetospheric dynamics particularly in the geomagnetic tail. Much of the tangential stress on the magnetosphere arises due to the merging of the interplanetary field with the magnetospheric field. As the merging rate on the dayside changes and as the reconnection rate in the geomagnetic tail fluctuates, the polar cap expands and shrinks, the field strength in the tail increases and decreases, and the plasma sheet thins and thickens. Magnetospheric: substorms apparently play an important role in this process as expansion phase onsets are correlated with a return to a dipolar configuration of the nightside field lines and with the appearance of southward fields in the plasma sheet, and are followed by a thickening of the plasma sheet. The sequence of events occurring in the tail during a substorm are readily explained by the formation of a neutral point near the Earth at the expansion phase onset followed by the eventual motion of this neutral point away from the Earth.
Finally, the control of the tangential stress on the magnetosphere by the interplanetary field can be used to explain most of the properties of the semiannual variation of geomagnetic activity. In particular, the Dst index, which is used to identify geomagnetic storms, can be quite accurately predicted with a knowledge of only the solar wind number density, velocity, and the north-south component of the interplanetary field.
Before discussing the dynamical processes within the magnetosphere, we present a brief magnetospheric history. This will serve to introduce both the overall configuration of the magnetosphere and the nomenclature used in magnetospheric research. Then, we discuss the evidence for a dynamic magnetosphere and review the nature of the changes in the magnetosphere during a period of enhanced solar wind magnetosphere coupling. Finally, we apply some of our understanding of this interaction to explaining the well-known cycles of geomagnetism, and to predicting geomagnetic activity using solar wind measurements.
2.1. EARLY MAGNETOSPHERIC MODELS
|Fig. 1. Illustration of the dipolar nature of the Earth's magnetic field from Gilbert's De Magnete (Chapman and Bartels, 1940).|
Geomagnetic observations have been made for centuries. An excellent history of these measurements prior to the 20th century can be found in Chapter XXVI of Geomagnetism by Chapman and Bartels (1940). Figure 1 shows the first magnetspheric model published in 1600 by Gilbert. Although the ionosphere was not discovered until 1883 by Balfour Stewart and the distortions in the magnetic field caused by the solar wind until much later, Gilbert wisely avoided extrapolating his field lines far above the surface of the Earth.
The next major step in the understanding of the magnetosphere was also the first major advance in the study of magnetospheric dynamics. Although the idea that solar corpuscular radiation was responsible for geomagnetic storms and aurora was popular in the early 20th century (see the review by Dessler (1967)), it was not until 1930 that a satisfactory theory was proposed.
|Fig. 2. Magnetic field of a dipole in the presence of an infinitely conducting plane. The strength of the magnetic field goes to zero at the points labelled Q. (Chapman and Bartels, 1940)|
In a series of papers, Chapman and Ferraro (1930; 1931; 1932) discussed a mechanism for generating geomagnetic storms. A principal feature of this model was a transient outflow of ionized gas from the Sun consisting of positive ions and electrons but having no net charge. Figure 2 illustrates tile effect of this ionized gas, or plasma in the case of an advancing infinite planar front. The plasma, being highly conducting, excludes field lines from its interior. This is mathematically equivalent to the creation of an equal and parallel dipole moment, at a distance behind the front the same as the distance that the Earth's dipole is ahead of the front. If the front of gas were not planar, as would necessarily occur as the front moved past the Earth, the strength of this image dipole field and its position would both change. We note that, when an approximate description of the magnetospheric field is sufficient, image dipole models are still used today because of their mathematical simplicity.
|Fig. 3. Distortion of the advancing front of solar plasma (ion-clectron gas) by the Earth's magnetic field. This model was proposed by Chapman and Ferraro (1930; 1931; 1932) to explain the sudden compression of the Earth's magnetic field followed by a more gradual depression of the field during a geomagnetic storm.|
Figure 3 illustrates Chapman and Ferraro's method of creating the main phase of a geomagnetic storm, that period when the Earth's magnetic field is reduced. As the front of gas passes the Earth, charged particles leak into the magnetosphere and drift around the Earth, creating a current whose field opposes the Earth's direct main field. While this model is very close to that which we believe today, there was one important change to this picture made 30 yr later. As a result of studies of comet tails (Biermann, 1951; 1953; 1957) and theoretical investigation of the interplanetary gas by Parker (1958a) who also coined the term solar wind (Parker, 1958b), the realization grew that the solar wind was continually flowing. However, short term (~1 day) direct measurements (Gringauz et al., 1960; Gringauz, 1961; Shklovsky et al., 1961; Bonetti et al., 1963a, b) on a variety of spacecraft were not sufficient to convince many. It was not until the continuous Mariner 2 measurements were reported (Neugebauer and Snyder, 1962; Snyder et al., 1963) that the concept of a continuously flowing solar wind became commonly accepted (cf. Dessler, 1967).
While Figure 3 is suggestive of a long geomagnetic tail in the antisolar direction, the geomagnetic field would be confined to a moderately symmetric magnetic bubble by the hot, infinitely conducting solar wind plasma, if there were no viscous interaction between the solar wind and the magnetosphere. For realistic ratios of the static to dynamic pressure, Slutz and Winkelman (1964) obtain a rather short geomagnetic tail, of about 10 to 25 Re, in length. They remark that "the whole shape of the solution reminds one much more of an eyeball than of a teardrop". On the other hand, they did expect a teardrop-shaped wake region, or `wind-tail' in the antisolar direction. Parker (1958b) pointed out that the interaction should be viscous, concluding "It is obvious that the solar wind tends to carry away lines of force of the outer geomagnetic field, just as a high wind blows smoke away from a chimney", This conclusion was not obvious to everyone, and Figure 4 illustrates the two competing models in 1960 as drawn by Piddington (1960) and Johnson (1960).
|Fig. 4. Two magnetospheric models of 1960. The upper panel shows the noon-midnight meridian as drawn by Piddington (1960), and the lower panel shows the noon-midnight meridian as drawn by Johnson (1960).|
Two years later, measurements, made by Explorer 6 and Explorer 10 in the distant midnight magnetosphere, were shown to be consistent with the existence of an extended tail (Smith, 1962). Figure 5 shows these measurements projected to the noon-midnight meridian with the Earth's field removed (Axford et al., 1965). The variation of this residual field along the satellite trajectories is qualitatively as expected for the twin solenoid current system of the magnetotail.
|Fig. 5. Explorer VI and X magnetic field measurements in the distant midnight magnetosphere. The contribution of the Earth's main field has been removed and the residual field has been projected into the noon-midnight meridian. The field in this meridian due solely to a Chapman-Ferraro surface current, HCF, and solely to a twin solenoid tail system, HT, is also shown (Axford et al., 1965).|
2.2. THE OPEN MAGNETOSPHERE
Early models of the solar wind magnetosphere interaction ignored any possible effects of the interplanetary magnetic field. Dungey (1961), however, soon pointed out that the existence of the interplanetary magnetic field had important consequences for this interaction. Figure 6 shows Dungey's two magnetospheric models: the top panel for southward interplanetary fields and the bottom one for northward fields (Dungey, 1963). In the top model, the opposed magnetospheric and interplanetary stream fields merge or reconnect at a neutral point at the front or nose of the magnetosphere. The motion of the solar wind carries the plasma on this interplanetary field line, and hence the field line itself, tailward. As the two halves of the field line move tailward in the interplanetary medium, the magnetospheric part of the lines, each of which has a foot in one polar cap, also move tailward. Eventually, the two halves of the line merge or reconnect in the tail at a neutral point, again forming a magnetospheric field line with two feet on the ground and an interplanetary field line not connected with the Earth. The newly connected field line, then moves earthward to return to the dayside merging region to repeat this process all over again.
|Fig. 6. Schematic illustration of the open magnetosphere, for southward, top panel, and northward, bottom panel, interplanetary fields. These sketches do not attempt to show the correct length of the tail nor the magnitude of the magnetic field normal to the magnetopause. Arrows illustrate plasma flow directions.|
Moving field lines, while a useful concept for some, are totally alien to others and hence the above model is viewed with some suspicion. However, it is entirely equivalent to view the field lines in this model as stationary and talk entirely in terms of plasma motions. The solar wind plasma flows across the interplanetary field lines. When it encounters the magnetosphere, it mixes with an outward flow from the magnetosphere. The magnetopause is not a perfect conductor in this model and part of the interplanetary electric field (determined by the merging rate) penetrates onto the polar field lines and causes a tailward flow in this region. Flow over the north and south polar caps eventually meets in the tail. Then some of the plasma flows earthward and some tailward. We note that the electric field on closed field lines is not due to the penetration of the interplanetary electric field through the magnetopause, but represents the flow of the plasma from the reconnection region in the tail to the merging region on the dayside. Ionospheric drag on this flow will be overcome by the establishment of pressure gradients. Further, the dayside merging rate and the tail reconnection rate can differ significantly for short periods. This results in changing magnetic fields and non-conservative electric fields.
The bottom panel shows the situation for northward fields. Here field lines are `laid' on the magnetosphere and merge at two neutral points in the tail. This process effectively adds a dayside field line and removes one from the tail. The flow on closed field lines proceeds from the dayside to the nightside. It seems improbable, though, that this mechanism is effective in removing flux from the tail because it requires that the same interplanetary field line become connected to the magnetosphere at two neutral points (Russell, 1972a).
Some words about the topology of Dungey's model in the presence of a southward interplanetary field are in order here. First, there are three classes of field lines: those with no feet on the ground; those with one foot on the ground; and those with two feet on the ground. These three classes are separated by two surfaces: the one resembling somewhat the surface of an hour glass; and one the surface of a ion doughnut. These two surfaces touch at a line going all the way around from the dayside neutral point to the nightside neutral point. This line is called the separatrix. It is not necessarily neutral because field lines can be parallel to the separatrix without destroying the topology (Stern, 1972). Thus, there are only two neutral points in this model and not necessarily a neutral line, as has been emphasized by Dungey (1963).
It should be noted that Dungey drew his models to emphasize the physical mechanisms and did not attempt to draw the magnetosphere to scale. Unfortunately, this has led to some misinterpretation of Dungey's model. Dungey certainly knew the correct scale. In fact, he used his model to predict the length of the tail to be 500 Re, (Dungey, 1965). This length is close to the length derived from recent studies of energetic solar particle entry into the tail (cf. Scholer, 1974; Vampola, 1974). We note that both studies of solar electrons (Lin and Anderson, 1966; Van Allen, 1970) and solar protons (Van Allen et al., 1971; Morfill and Scholer, 1972; Fennell, 1973) in the magnetotail and over the polar cap leave little doubt that the magnetosphere is open.
2.3. REFINING MAGNETOSPHERIC MODELS
Figure 7 shows two models of the magnetosphere published in 1965. The model in the top panel is an open magnetosphere resembling that of Dungey but more closely approximating the correct scale (Axford et al., 1965). Here the flow in the tail goes into a 'neutral' line. This line, as stated before, is the separatrix and is not necessarily neutral. The merging line would be a more appropriate name. The region labelled neutral sheet is obviously not neutral, in a magnetic sense, since field lines cross this region. We would call this region the plasma sheet today, and reserve the term neutral sheet for the plane separating magnetic field in the tail pointing towards the Earth from that pointing away from the Earth.
|Fig. 7. Two magnetospheric models of 1965. The upper panel shows the open model of the magnetosphere with a finite tail (Axford et al., 1965). The lower panel shows an open model with essentially an infinite length (Dessler and Juday, 1965).|
In the lower panel, Dessler and Juday (1965) have postulated that a true neutral sheet exists with no flux crossing this plane. Similarly, they have postulated that the dayside neutral point is, in fact, a neutral line presumably joining the dimples on the magnetosphere with the neutral sheet.
We note the appearance in this model of the Earth's bow shock. Axford (1962) and Kellogg (1962) had predicted that a bow shock must exist to slow the supersonic solar wind so that it could be diverted around the magnetosphere. Even though measurements of both the magnetosheath and the solar wind had been made by several spacecraft before this time, it was not until October 7, 1962 that a satellite, Explorer 14, crossed the bow shock while transmitting data (Wolfe and Silva, 1965). Early spacecraft with their low sampling rates did little better than identify regions as either being solar wind or magnetosheath, and could not resolve the features of the bow shock itself. However, these measurements did reveal that an apparent shock transition was a permanent feature of the solar wind magnetosphere interaction (Ness et al., 1964; Bridge et al., 1965; Wolfe et al., 1966). It was not until the OGO series of spacecraft with much higher data rates that the shock structure itself could be resolved (Holzer et al., 1966; Heppner et al., 1967). While the shock structure has been under intense study recently, there is yet much to be learned (Formisano, 1974).
|Fig. 8. The steady-state near-Earth neutral point model of Dessler (1968).|
Figure 8 shows an updating by Dessler (1968) of his magnetospheric model. This illustrates the convergence of views to that of an open tail with a neutral point (or line). However, in this model, Dessler has moved the neutral point within 30 Re of the Earth despite the evidence presented by Mihalov et al. (1968) and later by Behannon (1970) that the average neutral point position is beyond the orbit of the Moon. Dessier and Hill (1970) argue the southward component tailward of the neutral point would be small and difficult to observe. Further, Hill and Dessler (1971) present a model for maintaining the plasma sheet on open field lines as this model requires with magnetic turbulence during quiet times. However, this model is not supported by observations of ULF waves in the tail (Russell, 1972b; Garrett, 1973a). Thus, there is little doubt that, at quiet times, the neutral point is beyond the orbit of the Moon. On the other hand, as we will discuss in a later section, the neutral point does move close to the Earth during geomagnetically disturbed times.
While the neutral point in the tail is very important in understanding magnetospheric processes, the so-called neutral points in the dayside magnetosphere, at the dimples in the magnetopause are also of great interest. Even in closed models of the magnetosphere, magnetosheath plasma can gain entry into the magnetosphere, and reach the ionosphere along the flux tube in the noon meridian which separates the field lines which close over the pole from those which close on the dayside. For example, in the image dipole approximation of the magnetopause, shown in Figure 2, the entry occurs at the two neutral points labelled Q.
Despite the myriad of magnetospheric missions during the 1960's, the first probing of this region was not reported until 1971. At this time encounters by four separate spacecraft with this region, called the polar cusp or cleft, were reported. At low altitudes measurements were made by ISIS 1 (Heikkila and Winningham, 1971) and by Injun 5 (Frank and Ackerson, 1971), and at high altitudes by Imp 5 (Frank, 1971) and by OGO 5 (Russell et al., 1971). Most recently, HEOS 2 has probed the polar cusp (Bahnsen et al., 1974; Paschmann et al., 1974; Wenzel, 1974).
|Fig. 9. The dual precipitation zone model of Mishin and Popov (1972). The polar cusp plasma is presumed to precipitate at high latitudes (~78) at all local times as illustrated in the sketch of the polar cap on the lower right. Similarly, there is harder low latitude precipitation from the inner edge of the plasma sheet.|
Figure 9 shows a post-polar cusp magnetospheric model by Mishin and Popov (1972). It illustrates clearly the direct penetration of the polar cusp plasma and that the cusp plasma is topologically connected to the plasma sheet boundary, since the cusp straddles the last closed field lines and first open field lines. However, the magnetopause, in the near Earth tail, is also close to the first open field lines. Thus, polar cusp plasma might be expected in this region also. Such a boundary layer has been observed by HEOS 2 (Paschmann et al., 1974) and Vela satellites (Akasofu et al., 1973). Haerendel (1973) has called this the polar mantle. This model also stresses that different types of precipitation are observed at different latitudes.
While this picture of the polar cusp suggests that the cusp acts mainly as a funnel to channel magnetosheath plasma into the magnetosphere and ionosphere this is far from the case. Strong currents flow in the polar cusp (Fairfield and Ness, 1972; Kivelson et al., 1973; Fredricks et al., 1973), and intense ULF magnetic and VLF electric oscillations are observed there (Russell et al., 1971 ; Scarf et al., 1972; Fredricks and Russell, 1973; Bahnsen et al., 1974). Furthermore, both upstreaming and downstreaming particles are observed (Paschmann et al., 1974).
There is one further refinement necessary in our magnetosphcric model, if we are to understand processes occurring in the inner magnetosphere. That refinement is the addition of the plasmasphere, a region of `cold' (2-10 x 103 K), dense (~102-104 particles cm-3) plasma in the inner magnetosphere, corresponding roughly to the inner cross-hatched region in Figure 9. For a recent review of the plasmasphere, see Chappell (1972). This region is simply the extension of the ionospheric plasma into the magnetosphere. The reason that the ionospheric plasma does not fill all the `closed' flux tubes in the magnetosphere is that the filling time is long compared to the time required for cold plasma in the outer magnetosphere to drift out of the magnetosphere across the magnetopause. In a closed magnetosphere, the cold magnetospheric plasma would be circulated in cells (Axfofd and Hines, 1961)and not leave the system. However, in an open magnetosphere, the convection of plasma intersects the boundary of the magnetosphere except for an inner corotating core. In this inner core the density can build up and form what is called the plasmasphere. While the convection electric field and its time variations have been invoked to explain most of the observed behavior of the plasmasphere, we have only sparse data on the temporal behavior of the conservative and nonconservative electric fields in the magnetosphere (Chappell, 1974; Roederer, 1974).
3.1. THE EVIDENCE FOR A DYNAMIC MAGNETOSPHERE
One of the first suggestions after the discovery of the outer radiation zone was that this zone might be the source of the electrons responsible for auroras (Van Allen et al., 1959). The magnetosphere was viewed as a reservoir occasionally spilling out these electrons into the auroral regions. This was referred to as the leaky bucket model. However, O'Brien (1962) noted that the outer radiation zones would `drain empty' of electrons in a few hours at the observed precipitation rates. He suggested instead that the magnetosphere was a `splash catcher' trapping some of the freshly accelerated particles which caused aurora.
While it is conceivable that auroral activity occurs in a quasi-stationary pattern under which the Earth rotates, there is much evidence that auroral activity is unsteady and hence, the amount of `splash' caught by the magnetosphere varies with time. The classic study of the aurora by Akasofu (1964) showed that there were auroral cycles which could repeat several times during the night. During these cycles, auroral arcs first brightened and then expanded poleward. On the western edge of this poleward expanding bulge, a fold in the arcs develops, called the westward travelling surge, which rapidly moves from midnight towards dusk. This period is called the expansion or break-up phase. Later, the arcs return to their pre-break-up condition during what is called the recovery phase. Chapman suggested that this cycle be called substorm. and this name and the accompanying concept has become generally accepted.
In addition to the auroral substorm, there is a cycle of magnetic activity in which currents flowing in the ionosphere and the magnetosphere change in strength. and in location. This cycle, called the polar magnetic substorm, is intimately related to the auroral substorm. During substorms, there are changes in the ionosphere, in particle precipitation patterns, VLF emissions, and micropulsations. These effects have been comprehensively described by Akasofu (1968), and apparently are all manifestations of one major process, the magnetospheric* substorm.
|Fig. 10. The Expandable Tippy Thundermug model of substorm behavior by Davis (1970). This model continues the earlier concepts of the Van Allen belts as a leaky bucket and a splash catcher, while illustrating many of the phenomena known to occur in the magnetosphere.|
Figure 10 shows a modern splash catcher model of the magnetosphere (Davis, 1970) which summarizes much of what we know about the magnetopsheric processes. Starting with the pipes in the top right-hand corner, this model illustrates that there are two possible sources for magnetospheric particles: solar wind particles and atmospheric particles. The particles then flow into an `expandable tippy thunder mug', with some leakage directly into the polar cap and from the thundermug, or pot, into the auroral zone. In this model, the pot is stable until it fills to a point such that the center of gravity is above the pivots, joining the handle to the mug. Then the pot is in a metastable state, and will tip if perturbed, say, by a southward pointing magnetic field.
When the pot tips, some of the particles are caught in the Van Allen belts and some go directly into the auroral oval. Note that it requires many tippings of the pot to fill the Van Allen belts to capacity in accord with the concept that many substorms are required to cause the main phase depression of a geomagnetic storm. There are many loss processes from the Van Allen belts; the many spigots illustrate this. The fact that the spigots are at different heights illustrates that some of these processes are thought to occur at different levels of geomagnetic activity.
At the level of analogy for which this model was intended, this model is in accord with most of what we know about the magnetosphere, with perhaps one exception. Recent studies show that the sign of the interplanetary magnetic field governs the strength of the solar wind interaction with the magnetosphere. Hence, the hand labelled `sign of interplanetary field' would be more appropriately placed on the tap.
|Fig. 11. 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).|
A recent study by Foster et al. (1971) emphasizes both the cyclic nature of the solar wind-magnetosphere interaction and the control of this interaction by the north-south component of the interplanetary magnetic field. Figure 11 shows their superposed epoch study of the auroral electrojet index and the north-south solar magnetosperic component of interplanetary magnetic field for 54 isolated substorms. T0 was determined in two ways for each event. The first determination was the time of the sharp onset of a negative bay at the auroral-zone station closest to midnight. The second determination was the time of the sharp recovery of the H component at a low latitude premidnight station. When these two determinations agreed within 10 min, as they did in the majority of their chosen isolated events, T0 was taken to be the average of the two determinations: otherwise the event was not used.
The AE index, which measures the strength of currents flowing in the ionosphere over selected auroral zone stations, increases with two distinct rates in this average picture. The slow increase, beginning when the north-south component first becomes southward, lasts about 75 min. We would identify this period with the growth phase of the substorm. (McPherron, 1970). The cause of this pre-onset increase in the AE index could be due to the increase in strength of the magnetospheric convection super-electric field due to enhanced merging on the dayside when the interplanetary field turns southward. It could also be due to the increase in size of the polar cap due to enhanced merging which would move the auroral current systems equatorward of their quiet time positions to a position over the auroral zone stations (Akasofu et al., 1973b).
The second phase, starting at T0 and lasting about 40 min, when the AE index rises most rapidly, we would identify with the expansion phase. While the onset of this phase occurs at the minimum of BZ, we feel this is due to the choice of isolated events for study, since events, in which the field turned northward before a substorm onset, should have a smaller probability of a subsequent onset, and since events, in which the field stayed southward long after the minimum, should be associated with multiple substorm periods and would not be included. We note that the recovery phase, when the AE index is decreasing, begins while the interplanetary field on the average is still southward. The fact that the expansion phase occurs in this average picture during a period of northward turning field suggests that the onset is not due to a strengthening of the interaction and that the increase in current measured by the AE index at this time is associated with changes internal to the magnetosphere, probably controlled by changes in the magnetic field configuration, i.e., with nonconservative electric fields.
While ground-based observations of aurora and magnetic fields have provided our earliest and most complete record of the cyclic nature of the solar wind magnetospheric: interaction, controlled, as we have seen, by the interplanetary magnetic field, there is, of course, much evidence for these cycles, or substorms, in the magnetosphere itself. In the following sections we will examine the magnetospheric response in various regions of space to this time varying interaction.
3.2. THE EROSION OF THE MAGNETOPAUSE
The term 'erosion of the magnetopause' was coined by Aubry et al. (1970) to describe the inward motion of the dayside magnetopause in response to a southward turning of the interplanetary magnetic field even though the dynamic pressure of the solar wind remains constant. This motion can be explained in terms of current systems which arise when the interplanetary field is southward and which oppose the Earth's main field on the dayside of the Earth. Two current systems, both of which probably play a part in the field reduction, are the tail current system, which is observed to strengthen and move towards the Earth when the interplanetary field turns southward and a partial ring current associated with the enhanced convection electric field (Russell and McPherron, 1973a; Russell et al., 1974). To cause the extrapolated subsolar point of the magnetopause to move from 11.7 to 9.5 Re as the observations of Aubry et al. (1970) suggest occurred, requires a reduction of the dayside magnetospheric field of 17 .
In support of this single observation which occurred when the satellite inward motion approximately matched that of the magnetopause, Fairfield (1971) has shown that when the magnetosheath field is southward, the magnetopause is on the average one Earth radius closer to the Earth. Finally, Russell et al. (1971) have shown that the polar cusp moves equatorwards in the presence of a southward interplanetary magnetic field. While this motion implies that the dayside magnetosphere is shrinking, it also implies that the polar cap, at least on the dayside, is getting bigger.
3.3. THE SIZE OF THE POLAR CAP
If merging on the dayside proceeds at a rate faster than reconnection in the tail, the number of open field lines and hence the area of the polar cap will increase. Both the inward motion of the magnetopause and the thinning of the plasma sheet during the growth phase, which we will discuss in a later section, are indications that such is the case. Furthermore, there have been direct measurements of the equatorward motion of the polar cusp. Akasofu (1972a, b) has used all-sky camera data at local noon in winter, when such measurements can be made, to show that the midday aurora move equatorward in proportion to the accompanying geomagnetic activity. More to the point, Burch (1972) has used OGO-4 soft electron (>0.7 keV) data to measure the polar cusp position as a function of time after the southward turning of the interplanetary field, in cases of a quasi-steady southward interplanetary field with no discernible expansion phase onset. He obtains an equatorward cusp velocity of 0.1o invariant latitude per minute. While such measurements do not prove the polar cap increases in size, since it may be simultaneously moving poleward at another local time, they are, on the other hand, consistent with such an increase in size, and, hence, consistent with our interpretation of the erosion of the magnetopause.
3.4. MAGNETOTAIL FLARE AND ENERGY DENSITY
Given that the size of the polar cap, i.e., the region of open field lines, increases in area, then the magnetic flux in the tail must increase. Far down the tail where the normal stresses on the boundary are due essentially to the thermal and magnetic pressures of the solar wind, this flux increase will result in an increase in the diameter of the tail and no change in flux density. However, closer to the Earth this is not necessarily true. The erosion of the magnetopause decreases the cross section of the magnetosphere, and hence the diameter of the near tail region, at the same time the distant tail diameter is increasing. In other words, the flaring angle of the tail boundary in the near Earth region must increase. Using the simple pressure balance model of the magnetopause (Willis and Pratt, 1972) we expect the field strength in this region to increase as the number of open field lines grow. The first observational evidence that this process was occurring came from a joint study of Pioneer 7 magnetic field and plasma data by Lazarus et al. (1968). While plasma sheet thinning and expansion across an observation point can lead to local increases and decreases in the field strength, this joint study separated variations in the relative energy density of particles and fields from the overall changes of energy density. Lazarus et al. (1968) showed that this build-up in energy density preceded a substorm, beginning about 2 h before the subsequent decrease in energy density. They also showed that one such energy density decrease was coincident with the onset of a substorm. They did not, however, have simultaneous solar wind data and could not unambiguously determine the source of the energy density increase. It could have, for instance, been due to a change in the solar wind velocity or number density.
Camidge and Rostoker (1970) and Fairfield and Ness (1970) also confirmed this sequence with many more examples. However, neither of these studies used data to separate plasma sheet effects from strictly tail lobe changes. Aubry and McPherron (1971) showed that increases in the energy density of the tail lobes were associated with a southward turning of the interplanetary magnetic field, and not with changes in the solar wind pressure, and that the decreases were not associated with any interplanetary effect, but rather followed the onset of substorm expansion phases.
While these data are in accord with our expectations as outlined above and apprently leave no room for any interpretation except that the energy density in the near tail increases when the interplanetary field turns southward and decreases at substorm onsets, much work continues on this phenomenon. Figure 12 shows ground-based H-component magnetograms from the auroral zone near local midnight (top three traces) during an increase and subsequent decrease in the tail field strength (middle trace) at Imp 3, 24 Re behind the Earth and 13 Re, below the expected position of the neutral sheet (Meng et al., 1971). The constancy of the > 40 keV electron flux (bottom trace) shows that such changes are not associated with plasma sheet effects.
|Fig. 12. Substorm signature in lobes of the tail. The top three traces show horizontal components of ground based magnetograms. The next trace shows the magnetic field strength at Imp 3 (-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).|
Some of the disagreement in the interpretation of data such as these arises because there is auroral zone activity while the tail field is increasing. This, however, may occur during the substorm growth phase because, when the merging rate on the dayside increases, the convection electric field throughout much of the magnetosphere should increase, and thus auroral zone currents should increase. Furthermore, the changing electric and magnetic fields during the growth phase should certainly lead to increased electron precipitation, and hence to increased auroral zone conductivity, which would also lead to stronger currents.
To avoid the difficult task of interpreting auroral zone magnetograms, and since all-sky camera data are not generally available, several authors have used the sharp onset of positive bays in H-component magnetograms in the records of midlatitude observatories in the midnight sector. These studies have been quite successful. Figure 13 shows data in the lobes of the tail at a distance of from 35 to 55 Re behind the Earth using midlatitude records in this way (Nishida and Nagayama, 1973). In every case, the midlatitude onset of magnetic activity is followed by a decrease in the lobe field strength, as measured by Bx. While this study adds six more clear examples of lobe decreases associated with onsets of magnetic activity it does not examine the simultaneous behavior of the solar wind as Aubry and McPherron (1971) have done.
|Fig. 13. Behavior or the magnetic field in the distant tail lobes (- 35> x -55 Re) around the onset time of positive H-component bays at midlatitudes near midnight (Nishida and Nagayama, 1973).|
To clarify further and to quantify the lobe magnetic variations, Caan et al. (1973a) have examined in detail the solar wind, the interplanetary magnetic field, midlatitude magnetograms, and ATS-1 magnetograms in synchronous orbit together with OGO-5 data in the lobes of the geomagnetic tail. In accord with Aubry and McPherron they find that tail lobe energy density increases are associated with southward interplanetary fields and decreases with magnetospheric-wide substorms. However, they also find that localized, off-center or multiple-onset substorm expansion phases have little effect on the lobe magnetic field.
In an extension of this work, Caan et al. (1973b) have performed a superposed epoch study of the tail lobe field change using the time of the midlatitude onset of magnetic activity to order the data in the manner of the study of Foster et al. (1971) discussed in Section 3.1. Figure 14 shows the result of a superposition of responses in 24 cases. The rise time is about 90 min, the decay time 45 min, and the decay begins coincident with the midlatitude onset. The slight difference between presubstorm field strength and post-substorm lobe field strength is an orbit effect. OGO 5 is typically outbound when it is high in the lobes of the tail and field strength decreases with increasing radial distance become decreases with time.
|Fig. 14. Average behavior of tail lobe magnetic energy density during 24 isolated substorms. The magnitude of the lobe energy density for each trace has been normalized to a value of unity at the onset of the midlatitude positive H-component bay near midnight (Caan et al., 1973b).|
In summary, the studies of the tail lobe magnetic field leave little doubt that southward turning of the interplanetary field leads to an increase in the energy density and magnetospheric-wide substorms cause the energy density in this region to decrease. Unfortunately, controversy still surrounds this latter point, not because of a lack of clarity in the reported correlations, but possibly because of a lack of understanding of the meaning of the all-sky camera and the auroral magnetogram records from which the concept of the substorm first arose. In other words, it may well be that some poleward motions of aurora do not signal expansion onsets of the magnetospheric-wide substorms and that not all auroral zone magnetic bays signal substorms. A further possibility is that auroral zone phenomena and midlatitude bays are caused by different mechanisms, both substorm related, whose onsets are often, but not necessarily, coincident.
The increases and decreases of energy density in the tail lobes must be associated with changes in the angle of flaring of the magnetotail boundary near the Earth as the amount of magnetic flux in the tail increases and decreases. Increases in the tail flux are, of course, the result of an increase in the dayside merging rate. Similarly, as we will discuss in the next section, decreases in the magnetic flux in the tail are caused by an increase in the reconnection rate.
3.5. NEUTRAL POINT FORMATION
As mentioned in the discussion of the open magnetosphere in Section 2.2, there must be a neutral point in the tail, and a separatrix, or merging line, passing through the neutral point. Even at quiet times we would expect some reconnection here, causing conversion of field to particle energy and contributing to the maintenance of the quiet time plasma sheet. There would be flow towards the Earth and a northward magnetic field at the so called neutral sheet on the Earthward side of the neutral point, and a tailward flow and southward field on the tailward side. The existence of a southward or northward pointing magnetic field near the neutral sheet is usually an accurate indicator of whether an observation point is Earthward or tailward of the neutral point. Using this technique, quiet time observations place the neutral point beyond the orbit of the Moon (Mihalov et al, 1968).
In order to decrease the energy density in the tail lobes, flux must reconnect in the tail faster than it merges on the dayside. Since expansion phase onsets of magnetospheric-wide substorms are correlated with decreases in the energy density, substorm onsets must be associated with the onset of an enhanced reconnection rate. This is not a new idea. Two of its earliest advocates were Atkinson (1966) and Rostoker (1968a). However, now tail data are available which demand this explanation.
The cause of the increase in the reconnection rate is not obvious, however. The duration of the growth phase, i.e., the delay between the enhanced dayside merging and the enhanced tail reconnection should be a clue, but it has several possible interpretations. On the one hand, Rostoker (1968b) and Coroniti and Kennel (1973) have suggested that the duration of the growth phase is the time required to propagate information to the tail neutral point to start reconnection. On the other hand, the duration of the growth phase may be the length of time for the plasma sheet to thin to near zero thickness near the Earth (McPherron, 1972; Russell, 1972a; Kennel et al., 1973). Such an interpretation is also implicit in the model of Hill and Dessler (1971) who propose that the neutral point is located within the plasma sheet near the Earth at all times, but during substorms the plasma sheet disappears and merging proceeds at a more rapid rate, in a process termed vacuum merging (Dessler, 1968). However, as stated earlier this model is inconsistent with present data. More recently Hill (1973) has proposed that variations in the rate of particle entry through the magnetopause control the thickness of the plasma sheet. A more likely cause of the thinning is that during the growth phase the dayside merging rate exceeds the tail reconnection rate, causing a gradient in the flow velocity down the tail, so that near the Earth there is relatively rapid convection but far down the tail there is little or no convection (Holzer, 1971 ; Kennel et al., 1973). To see how this causes thinning, consider a cross-sectional slab of the plasma sheet perpendicular to the Earth-Sun line. More plasma leaves this slab than enters it in the presence of such a gradient. However, the pressure in the slab is roughly constant or slightly increasing at this time, so to accommodate the net loss of plasma the slab thickness must decrease.
Plasma sheet thinning and its subsequent expansion are well established phenomena in the tail (Hones et al., 1971). The thinning and expansion also affects the magnetic field observations, controls the appearance of energetic electrons and protons in tail measurements and is in fact responsible for the occurrence of islands (Russell and McPherron, 1973a). The thinning velocity is of the order of 5 to 10 km s-1 (Hones et al., 1971; Buck et al., 1973). The reported expansion velocity varies from about 20 km s-1 (Vasyliunas et al., 1973) to about 100 km s-1 (Buck et al., 1973). We note that one should exercise caution in interpreting what these values mean. Especially, they should not be used to calculate electric fields directly (Russell and McPherron, 1973a).
If we assume that the plasma sheet is parallel to the neutral sheet and 3 Re, in half thickness and is thinning at a rate of 5 km s-1 then the plasma sheet will reach zero thickness in slightly over one hour, a time not unlike the duration of the growth phase. Furthermore, Buck et al. (1973) observed the plasma sheet to thin to almost zero thickness and then expand within minutes of the onset of a magnetosphericwide substorm. Thus, the concept of a plasma sheet that thins during the growth phase until the plasma sheet reaches some critical thickness or actually disappears somewhere, thus permitting rapid merging, is in accord with observations, and forms a key part of a recent model of the growth phase (McPherron, 1972; Russell, 1972; Russell and McPherron, 1973a).
Several explanations of the thinning and thickening of the plasma sheet have been proposed in addition to convective loss and then acceleration of new plasma. The thinning and expansion could represent compression and expansion of the same volume of gas. Hones et al. (1971) have shown that there is little change in energy density during the thinning process ruling out the latter explanation as a significant factor. Some compression must occur as the energy density in the lobes increases but this compression is only about 25% (Caan et al.,1973b) and cannot nearly account for the observed thinning.
Loss of plasma sheet particles could also occur by diffusion perpendicular to the neutral sheet onto open field lines, or by cross-tail motion into the magnetosheath. During thinning the tail is magnetically quiet, so that the former process does not appear to be important (Russell, 1972b; Garrett, 1973). On occasion plasma sheet particles have been detected in the magnetosheath (Hones et al., 1972) suggesting that cross-tail flows are important in the thinning process. However, the Vela orbit lies on a spherical shell intersecting the magnetosheath near dawn and dusk. Thus, these particles could have travelled a more or less Earthward flow path before being lost to the magnetosheath.
If a new neutral point forms closer to the Earth during this thinning process, it could form when the plasma sheet thinned to zero thickness in some limited local time sector. It might also form on closed lines eventually merging more and more closed lines until it reached open field lines. How this might occur is shown schematically in Figure 15. The top panel shows the noon-midnight meridian. The stipled region shows field lines which close on themselves. The cross hatched region is the plasma sheet whose field lines have two feet on the ground. The middle panel shows the intersection of this bubble of field lines which close on themselves with the plane of the current sheet. As in our earlier examples, the neutral lines are not necessarily neutral. The bottom panel shows the tail cross section. This size of the bubble might increase or decrease with time depending on the external boundary conditions. We emphasize that the magnetic field lines sketched are not drawn to illustrate the Maxwell stresses expected in a near equilibrium situation.
|Fig. 15. Sketch of formation of X-0 neutral point pair on closed field lines as seen in three orthogonal planes.|
3.6. THE LOCATION AND MOTION OF THE NEUTRAL POINT
While the data leave no doubt that enhanced reconnection does occur marking the end of the growth phase, and while it is possible to explain at least qualitatively why and how a new neutral point might form, it is not obvious where this neutral point should first form. Fortunately, the magnetic field data in the tail provide us with some limits. McPherron et al. (1973) infer a location within about 9 Re, for one particular substorm. Laird (1969) reports a southward component near the neutral sheet at 12 Re. On the other hand, two years of ATS 1 2.5 min average magnetic field data near midnight reveal no southward fields. Furthermore, the sample tail data of Fairfield and Ness (1970) show many examples of transient southward fields within 34 Re. Finally, Figure 16 shows the results of a study by Nishida and Nagayama (1973) of the tail field behavior in the plasma sheet at the onset of positive midlatitude bays near midnight. In every case for |Y| Rethe north-south component Bz becomes negative or southward immediately after the onset of the positive bay. Thus, we conclude that neutral point formation inside of 25 Re is common for moderately large substorms, and, at least occasionally, may occur as close as 10 Re, but it seldom, if ever occurs within synchronous orbit at 6.6 Re.
|Fig. 16. Behavior of the magnetic field in the plasma sheet for - 25 < x < - 35 Re around the onset time of positive H-component bays at midlatitude near midnight (Nishida and Nagayama, 1973.).|
The average southward component duration in the region -25 x -35 Re is about 1 h, according to Figure 16. The obvious reason for its disappearance after one hour is that the neutral point moved away from the Earth. This is supported by laboratory work. Merging experiments using a collisional plasma device have been performed (Bratenahl and Yeates, 1970). In an extension of this work to test the effect of boundary conditions on the merging rate, a conducting rod was placed in one of the two plasma jets coming out of the merging region. The merging region responded by moving the other way (Bratenahl, 1973). Similarly, we expect that if the tail reconnection rate significantly exceeds the dayside merging rate, pressure gradients will develop which cause the neutral point to move tailward.
In this picture, the plasma sheet is recreated on closed field lines in the merging process. Thus, as the neutral point moves away from the Earth, a satellite will observe a plasma sheet expansion. Furthermore, as convection is slowed near the Earth, the field compresses creating a stronger and more dipolar field. Alternatively, one may view the reconnection process as disrupting the tail currents. Observationally, this return to a more dipolar state is well documented and we will discuss it further in the next section.
Finally, we note that Schindler and Ness (1972) have proposed a steady state configuration of the tail field consisting of many loops similar to the loop sketched in Figure 15, which is a snapshot of a time evolving structure. While the model proposed by Schindler and Ness cannot be ruled out, there are several alternate explanations of these data. In particular, they may be observing `quiet time' transient phenomena. For, in the one example of high resolution `neutral point' data they show, there was a small negative bay at Narssarssuaq, Greenland near local midnight (Russell, 1973).
3.7. THE INWARD MOVING FIELD COMPRESSION
Fairfield and Ness (1970) have shown that one of the major effects of a substorm is to return the nightside magnetosphere to a more dipolar state. How this return occurs is both interesting and important for several magnetospheric processes. On August 7, 1968 OGO 5 and ATS 1 were approximately lined up near the midnight meridian at the onset of a midlatitude positive bay, in excellent position to observe the near tail effects of the substorm (Russell et al., 1973a). 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 17 shows one second averages in solar magnetospheric coordinates of the field at both spacecraft. The onset of the midlatitude bay was about 1120 UT; a compression of the field was seen at OGO 5 at 1129:03 and then 93 s later at ATS 1. The most obvious interpretation of this event is the return of magnetic flux from the tail. The average velocity of the front from OGO 5 to ATS 1 was 160 km s-1 which corresponds to a change in the non-conservative electric field at OGO 5 of 2.3 mV m-1 and at ATS 1 of 1.3 mV m-1.
|Fig. 17. One second averages of the vector magnetic field at ATS 1 and OGO 5 in solar magnetospheric coordinates and the total field strength at the two spacecraft during an isolated substorm on August 7, 1968. At this time OGO and ATS were both close to the midnight meridian. The inward moving compression reached OGO 5 about 9 min after the substorm onset as determined from midlatitude magnetograms and then reached ATS 1 94 s later (Russell et al., 1973b).|
Such compressions of the field are not rare in this region, but such an alignment of ATS and OGO during one is. Walker and Kivelson (1972) have reported more than 10 occurrences of such events near midnight in the OGO-5 data, many of them associated with betatron acceleration of electrons and the subsequent generation of ELF chorus emissions. Further, we note that the non-conservative electric field associated with the inward moving compression is large enough to explain the sudden inward motion of whistler ducts in the outer plasmasphere at substorm onsets as reported by Carpenter and Akasofu (1972).
3.8. THE CAUSE OF MIDLATITUDE POSITIVE BAYS
While it is possible to describe ground observations of magnetic perturbations with a variety of different current systems, the addition of satellite data restricts the choice of possible circuits. In particular, the fact that ATS-1 magnetic field fluctuations at synchronous orbit during substorms often closely follow the ground station measurements at midlatitude directly beneath the satellite indicates that much of the current is flowing beyond ATS 1 (Cummings and Coleman, 1968). Figure 18 shows a model current system consistent with both the ground and ATS-1 signatures (McPherron et al., 1973a). Currents originally flowing across the tail flow down the field lines into the auroral ionosphere and then back up the field lines bypassing the region of recently merged field. These currents may be thought of as being driven by the induction of the tail and provide a mechanism for directly converting the stored energy in the tail into ionospheric heating.
|Fig. 18. Field-aligned current system, corresponding to diversion of tail current through ionosphere, which is in accord with positive H-component bays observed at midlatitudes in the midnight sector during the expansion phase of substorms (McPherron et al., 1973b).|
The observations discussed above reveal a dynamic and constantly changing magnetosphere. Isolated substorms, those in which the end of one cycle is clearly distinguishable from the start of the next, and which are therefore easiest to study, have two clearly defined phases in space: the growth phase and the expansion phase. The neutral point motion away from the Earth may constitute a third phase, the recovery phase. In ground records, there are also two well-defined phases: the expansion phase and the recovery phase. While the growth phase has been reported in ground based data, its identification has been the subject of controversy.
Figure 19 summarizes the magnetospheric changes during the growth phase. The dayside magnetopause is eroded, the polar cusp moves equatorward, and the polar cap increases in area. The increase of magnetic flux in the polar cap, and hence in the lobes of the tail, causes an enlargement of the cross-section of the tail far away from the Earth, but erosion reduces the near-Earth cross section. The result is increased flaring of the tail boundaries and an increase in the energy density in the tail lobes near the Earth. At the same time the plasma sheet thins because merging is occurring on the dayside faster than reconnection is proceeding at night. As the convection velocity increases, we expect the plasma sheet particles to drift closer to the Earth before precipitation losses dominate (Kennel, 1969). The duration of the growth phase is probably the length of time from the onset of enhanced merging on the dayside, until the plasma sheet has become thin enough to allow the formation of a new near-Earth neutral point.
|Fig. 19. Summary of the magnetospheric changes during the growth phase.|
Figure 20 summarizes the sequence of tail events. Satellites such as OGO 5 whose August 15, 1968 position is shown with an X and Vela, denoted by an asterisk, see evidence for thinning. When the neutral point is formed (second panel), OGO 5 may leave the plasma sheet temporarily only to re-enter it rapidly. However, Vela may continue to observe thinning. Sometime later the neutral point moves tailward past Vela, enveloping Vela in an expanding plasma sheet. When the neutral point forms, the current in the neutral sheet is disrupted, and the tail currents are diverted via a field aligned current system through the ionosphere. Finally, the return to a more dipolar field configuration in the midnight outer magnetosphere is accomplished by an inward moving compressional front.
|Fig. 20. Model of the expansion phase in the tail. Dotted area represents plasma sheet and length of arrows roughly proportional to convective velocity. The X marks position of OGO 5 during a substorm on August 15, 1968 studied by many authors. The asterisk marks the position of the Vela satellite during a typical event. In the upper panel flow is fastest in the near-earth plasma sheet and it thins. In the next panel it neutral point forms near the Earth, but flow towards the Earth is impeded somewhat so that the neutral point moves as shown in panel C. In the last panel the neutral point has moved past the Vela orbit, thus causing the plasma sheet to expand across Vela (after Russell, 1972a).|
Finally, we note that several different authors have recently proposed models which are essentially identical to this one (Nishida and Nagayama, 1973; Hones, 1974). In a field which is often characterized with almost diametrically opposed theories and many heated controversies, such convergence of opinion is indeed reassuring.
Geomagnetic records have been kept continuously for about a century. One of the reasons for continuing to record these data, was the hope that a determination of the statistical behavior of geomagnetic activity would lead to better insight into its causes. Unfortunately, this expectation was not realized despite the discovery of well-defined diurnal, semiannual, annual, 11-yr and 22-yr cycles. On the other hand, if our understanding of the solar wind-magnetosphere interaction, and the properties of the solar wind and the Sun are correct, these cycles should be a natural consequence of our models. Thus, it is of some interest to attempt to explain these periodic variations in terms of our present knowledge. In the following section, we will briefly discuss how to explain some of these variations in terms of the control of the solar wind-magnetosphere interaction by the north-south component of the interplanetary field.
Another application we can make of our knowledge is to predict geomagnetic activity. If there is a spacecraft in the near-earth interplanetary medium, we might obtain an advanced warning of the order of an hour before the observed solar wind plasma reaches the Earth. The storage time and reaction times of the magnetosphere probably vary significantly with the strength of the interaction, but on the average these delay times might add an hour more. Thus, with real time telemetry of interplanetary data to Earth, we could possibly predict moderately accurately the conditions within the magnetosphere during the next two hours.
If we wish to extend this prediction further into the future we have to know the properties of the Earth-intersecting solar wind while it is closer to the Sun, and be able to predict how these properties will be modified in transit to the Earth. If, for example, we could infer the properties of the solar wind from solar data, from which area on the Sun the Earth-intersecting plasma came, and how these properties would change in transit, we could obtain a 2 to 5 day warning. For an even longer warning or prediction, we would have to understand how solar activity evolved, i.e., we would have to predict solar activity too.
At the present time, we are in a position to predict geomagnetic activity up to two hours in advance by using in situ interplanetary measurements. We will discuss this in Sections 4.5 and 4.6. On the other hand, it appears that any attempt to predict geomagnetic activity for longer periods in other than the most general terms is premature at the present time.
4. 1. THE SEMIANNUAL VARIATION
The semiannual variation of geomagnetic activity has been known for over half a century (Cortie, 1912). It can be seen in all indices of geomagnetic activity from storm counts to Kp. It also is a very significant modulation, clearly evident in most data even from only a few years data. Figure 21 shows the semiannual variation as determined from storm counts from data of Chapman and Bartels (1940) and by using the Dst index (Russell and McPherron, 1973b). While the phase of these variations exhibits some variation, possibly because of counting statistics, the semiannual nature and the 2 to 1 enhancement of equinoctial to solstitial storm occurrence is clearly evident. Russell and McPherron (1973b) show that such an enhancement in storm counts can be produced by a modulation of the strength of the interaction such that only 40% more energy was being extracted from the solar wind during the equinoxes than at the solstices.
|Fig. 21. The semiannual variation of the
occurrence of geomagnetic storms. Left: occurrence of great storms and smaller
storms from 1875 to 1927 given by Chapman and Bartels (1940). Right: occurrence of storms with
Dst minimums less than -40, -80, and |
-160 during the years 1958 and 1961 through 1969 (Russell and McPherron, 1973b).
Russell and McPherron pointed out that since the interplanetary field was ordered in a solar coordinate system and the interaction of the solar wind with the magnetosphere in a geomagnetic system, the varying relative orientation of these two systems could give a semiannual variation in geomagnetic activity if the magnetosphere acted as a rectifier. Since, as is well known, the magnetosphere interacts more strongly with southward fields than northward fields, the magnetosphere does act as a rectifier. Unfortunately, we do not know quantitatively the rectification laws, nor even which is the optimum coordinate system. (We do know though that the solar magnetospheric coordinate system is better than the solar ecliptic system (Hirshberg and Colburn, 1969).)
While only a limited number of rather simplistic models were tested by Russell and McPherron they did produce one which reproduced the correct phase of the semiannual variation and which could account for its amplitude. This model assumed that the solar magnetospheric system ordered the interaction, that the interaction was proportional to the strength of the southward component and that there was no interaction for northward fields.
This model, and any similar model, predicts that the semiannual variation can be separated into two annual variations, one maximizing in spring and one in fall, using the sector polarity of the interplanetary magnetic field. In particular, the activity should maximize in spring for fields in towards the Sun as measured along the Parker spiral, and in fall for fields outwards from the Sun. This prediction is confirmed by studies of the Kp index (Otaola, 1971), of the AE index (Burch, 1973) and of the C9 index (Russell and McPherron, 1973b). Thus, there can be little doubt that the semiannual variation is but another manifestation of the control of magnetospheric dynamics by the southward component of the interplanetary field.
4.2. THE ANNUAL VARIATION
While the semiannual variation is well defined in all geomagnetic indices, the annual variation is less well defined. In fact, it is so poorly defined that some authors ignore its existence by referring to the 6 month variation as the annual variation. However, by annual variation we mean here a 12 month cycle. Another source of confusion is the fact that, at any one station, there will be an annual variation due to the annual variation in the properties of the ionosphere. Furthermore, the planetary annual variation might be either of two types: an annual variation independent of the semiannual variation or an amplitude modulation of the semiannual variation. Fourier analysis of geomagnetic indices would yield an annual peak, in the former case and peaks at 0.5 and 1.5 yr in the latter case. When Fourier analysis of long continuous series of geomagnetic indices is performed there is no annual line nor is there a line at 1.5 yr (Fraser-Smith, 1972). There is, of course, a strong line at 0.5 yr corresponding to the semiannual variation.
Despite this fact, there has been a recent resurgence of interest in the annual variation in geomagnetic activity. Some of these papers seem to propose that there is an annual variation independent of the semiannual variation (Wulf, 1971 ; Mayaud, 1972), while others propose a modulation mechanism (Meyer, 1972; Münch, 1972). In addition, both Meyer and Münch provide a plausible explanation of why the annual variation is not usually found in harmonic dial analyses or in Fourier analyses. This is due to the variable phase of the annual modulation. It can be strongest in spring or strongest in fall, and one phase only persists a few years. This explains why the annual variation has been occasionally detected, for example, as sidebands on the 27 day peak (Coleman and Smith, 1966), or as the occasional appearance of the 1.5 yr peak (Fraser-Smith, 1972).
While the explanation of the semiannual variation proposed by Russell and McPherron does not in itself contain an annual variation, it is easy to see how such a modulation might arise. Since the spring maximum is caused by fields predominantly towards the Sun and the fall maximum by fields away from the Sun, a situation in which one of the equinoxes is more active than the other will occur when fields of one polarity are more `active' than those of the other polarity. Since there is such a strong variation in the magnetic sector structure with latitude (Rosenberg and Coleman, 1969) it is reasonable to presume that the sector boundaries are more nearly parallel to the ecliptic than perpendicular to it. A similar picture has been proposed by Schulz (1972) on slightly different grounds. Thus, these variations in the activity of sectors with different polarities simply represent north-south asymmetries in activity on the Sun. We note that Münch (1972) reaches the same conclusion about north-south asymmetries causing the annual modulation using a nonmagnetic, axial model for the interaction. Finally, we note that the reason for the reversal in the phase of this effect, i.e., which equinox has the strongest activity, is due both to the reversal of the solar magnetic field every 22 yr and to reversals in the north-south asymmetry.
4.3. THE 11-AND 22-YR CYCLES
Since solar activity follows an 11-yr cycle in which the number of active centers, i.e., sunspots, changes, as well as the positions of these active centers on the solar disk, it is not surprising that geomagnetic activity also follows an 11-yr cycle. Almost any model of the interaction predicts this. There is also a 22-yr solar cycle in overall solar magnetic polarity. This cycle is not obvious in sunspot number or position, but it does show up in the relative magnetic polarity of the leading and following spots in sunspot groups.
A corresponding 22-yr cycle in geomagnetic activity was first found by Chernosky (1966) in which a 22-yr cycle consists of 11 active years followed by 11 quiet years, with the switch between active and quiet years occurring about 2 yr after solar maximum.
The existence of this effect is in accord with our present knowledge of the solar wind-magnetosphere interaction. Furthermore, the phase of the effect and the phase of observed variations in the sector structure over the course of the 22-yr cycle are in accord with the model of Russell and McPherron (1973b), since the switching point (~2 yr after solar maximum) is when the heliographic latitude dependence of the dominant polarity of the interplanetary magnetic field switches sign (Rosenberg and Coleman, 1969; Wilcox and Scherrer, 1972). This heliographic latitude dependence either increases the amount of southward field at the equinoxes, by modulating the amount of away and towards polarity, or decreases it, according to the polarity of the solar field.
4.4. THE DIURNAL VARIATION
Many authors have found diurnal variations of geomagnetic activity (Nicholson and Wolf, 1955; McIntosh, 1959; Mayaud, 1967). The question at hand is whether these variations are due to ionospheric effects or whether they are controlled by the solar wind-magnetosphere interaction. In order to check whether such diurnal variations exist in so called `planetary' indices, the diurnal variation of Kp and Dst (Russell and McPherron, 1973c) and AE (Allen, 1973) has been studied as a function of time of year. In each case, there was a diurnal variation, but this variation was constant throughout the year while all reasonable theories of the interaction predict a changing diurnal variation. While it is possible that in designing these planetary indices the originators were able to remove the annual cycle in the diurnal variation yet permit a constant diurnal variation to exist, it indicates that these indices and their cousins have severe limitations for short time scale variations.
Finally, we note that when treating ground station records, extreme caution must be exercised in interpreting the results of diurnal variation studies. Ground stations are very sensitive to nearby current systems in the ionosphere. Further, the interplanetary magnetic field is not the only agent producing semiannual variations on the Earth. Thus, if a semiannual variation of the diurnal pattern is found, it is not necessarily associated with the solar wind-magnetosphere interaction. The semiannual variation in the density of the upper atmosphere is well established (Cook, 1968; 1970) and can be explained in terms of EUV heating, taking care to include properly the effects of oblique incidence of the solar flux, sphericity of the atmosphere and ellipticity of the neutral density is accompanied by corresponding changes in the ionosphere (Bhatnagar, 1971). Thus, there is good reason to suspect that the semiannual variations of the diurnal pattern of geomagnetic activity may not be a magnetospheric effect. To settle this question ground station records should be analyzed to determine how these records respond to specific interplanetary events as a function of time of day, time of year, and geomagnetic latitude.
4.5. THE CAUSE OF GEOMAGNETIC STORMS
A geomagnetic storm is defined by the existence of a `main phase' during which the magnetic field at the Earth's surface is depressed. This depression is caused by a ring current within the magnetosphere. While we have examined magnetospheric substorms in detail, and have made the analogy of the Van Allen belts acting as a bucket catching the splash from substorms, we have not actually discussed what conditions are required to build up the ring current, and thus `cause' a geomagnetic storm.
In one of the first studies of the cause of geomagnetic storms, using interplanetary data, Hirshberg and Colburn (1969) examined the response of the magnetosphere to four `interplanetary' storms using three hour averages of the interplanetary magnetic field. The one interplanetary storm with only northward field produced the smallest amount of geomagnetic activity. One of these storms was examined with high resolution data, and it was found that the main phase began coincident with the arrival of the southward field. However, later they showed that the arrival of the southward field was coincident, within the resolution of their data, with the arrival of the helium-enriched driver gas (Hirshberg et al., 1969; Hundhausen, 1970). We note that the solar wind dynamic pressure data were only available sporadically during the course of the storm.
Kokubun (1972) has studied several SSC storms in 1967 using hourly averages of the solar wind velocity, density and interplanetary magnetic field. His study showed that only shock waves followed by southward fields caused geomagnetic storms. He was unable to determine the functional relationship between the size of the storm and the parameters of the solar wind, possibly because of his use of low temporal resolution data.
More recently Russell et al. (1973a) have pursued this topic using high time resolution data. Figure 22 shows the solar wind number density and velocity, the interplanetary magnetic field strength and solar magnetospheric north-south component measured on Explorer 33 in the solar wind on March 3, 1968. In the bottom two panels are the Dst and AE indices for the same time period. The apparent cause of the strengthening of the ring current, by almost 30 after 1600 UT, was the strong southward component of the interplanetary magnetic field at 1500 UT. No change is seen in the solar wind number density, velocity or the magnetic field strength. On the other hand, the magnetic field is predominantly southward on this day.
|Fig. 22. Solar wind and geomagnetic activity data for March 3, 1968. From top to bottom: the solar wind number density, Nsw, and the solar wind velocity, Vsw, measured by the MIT plasma probe on Explorer 33, the interplanetary field strength, |B|, and its solar magnetospheric Z-component, Bz, as measured by the Ames Research Center fluxgate magnetometer on Explorer 33; 2.5 min evaluations of the Dst and AE indices (Russell et al., 1973a).|
This and several similar examples led Russell et al. (1973a) to postulate that there was a threshold, i.e., that the southward component had to exceed a certain value, depending on solar wind velocity and pre-existing ring current strength, before lay further injection would occur. They postulated that this occurred because the rate of energy input to the ring current was proportional to the product of the solar wind velocity and the north-south component of the interplanetary magnetic field (i.e., the interplanetary east-west electric field) and that the rate of loss of energy from the ring current was proportional to the strength of the ring current. Thus, net injection would occur only when the southward component exceeded a threshold value, and would proceed until a new ring current strength was reached at which dissipation balanced injection.
These results indicate that the occurrence of a sufficiently strong southward interplanetary magnetic field, (say, Bz<-5 ), for a sufficiently long time, (several hours), will produce a moderate size geomagnetic storm, (Dst ~ -50 to -75 ). The stronger is the southward component and the longer the injection persists, at least until saturation is reached, the more intense the main phase minimum will be. In this model, the frequent appearance of shocks or sudden pressure increases, several hours before the main phase begins, occurs because these discontinuities are effective producers of strong magnetic fields normal to the solar equatorial plane. When these strong normal fields are southward a main phase begins to develop.
4.6. PREDICTING GEOMAGNETIC ACTIVITY
As stated in the introduction to Section 4, the most we can hope to do at the present time, is to issue detailed predictions of geomagnetic activity two hours in advance using in situ measurements and real time telemetry. Accurate and moderately detailed predictions 2 to 5 days in advance may be possible in the future, but much more research has to be performed into how structures are modified in their passage from the sun to the Earth and how the characteristics of the solar corona and the near-Sun solar wind can be predicted from solar observations.
Arnoldy (1971) has studied the relationship of the interplanetary parameters to the AE index. The principal contribution to the AE index was the integrated southward magnetic field over the previous hour. In this integral northward fields are set equal to zero. Garrett (1973b) has performed a similar study and found two populations of substorms: one set which responds as Arnoldy predicted and one set which responded roughly twice as strongly to an equivalent southward magnetic field, but which was associated with a large variance in the interplanetary magnetic field. One solution to this apparent dichotomy of magnetospheric behavior is that the product of solar wind velocity times the interplanetary southward component, i.e., the east-west electric field, integrated over the previous hour controls, the AE index, and the apparent correlation with the variance is due to an association of large variances with high speed streams.
Burton et al. (1973), on the other hand, have concerned themselves with predicting the Dst index using in situ measurements of the solar wind velocity and number density and the interplanetary field strength. Figure 23 shows the result of this prediction for March 3, 4 and 5, 1968, a moderately disturbed period. The philosophy of this calculation is to take an initial Dst value, calculate the energy lost and the energy injected during an interval, calculate a change in Dst, add this to the initial value, and then repeat for the next interval. Since Dst is also responsive to the solar wind dynamic pressure, an attempt is also made to remove dynamic pressure contribution and calculate ring current losses using a `true' ring current strength, Dst'.
|Fig. 23. Prediction of Dst using solar wind dynamic pressure and interplanetary electric field. Top panel: square root of the dynamic pressure. Middle panel: square of the westward solar magnetosphereic component of the interplanetary electric field times its sign. Bottom panel: actual (solid line) and predicted (dashed line) Dst (Burton et al., 1973).|
The calculation proceeds as follows:
where m is the proton mass, n the number density and V the velocity of the solar wind. Ew is the east-west component of the interplanetary (V x B) electric field, set equal to zero if Ew is negative or eastward, and is a time lag for magnetospheric response. In these expressions, Dst is in , P in eV cm -3 and E in mV m-1. The constants used in constructing Figure 23 from Equations (1) to (3) are: a equals 0.18 - (eV cm-3)-1/2; b equals 16 ; d equals 3.5 x 10-5 s-1; and c equals 4.4 x 10-4 - (mV m-1)-2s-1. The response time , of the magnetosphere to the interplanetary electric field has been held constant at 30 min in this study. While these constants work equally well on quiet days as well as disturbed, optimization of these constants is continuing using data obtained during a variety of geomagnetic conditions during several different years.
It is indeed reassuring that, with our present knowledge of the solar wind interaction with the magnetosphere and some of the properties of the solar wind and the Sun, we can provide plausible mechanisms to explain the various cycles of geomagnetic activity. It is surprising though that an explanation for the diurnal variation is not as simply derived, in view of the success of the model in explaining the semiannual, annual and 22-yr cycles. This is probably due to the fact that the diurnal variation is associated with ionospheric effects rather than due to some deficiency in our understanding of the magnetosphere.
It is also reassuring that we are now in a position to predict geomagnetic activity on the basis of interplanetary measurements. While this does not demonstrate the accuracy of our understanding of the details of magnetospheric processes, the quantitative, empirical relationships that have been derived, place well defined boundary conditions on these processes.
The history of the magnetosphere demonstrates the difficulty of achieving progress in magnetospheric research without in situ observations. This is not simply because remote sensing equipment, such as a ground based magnetometer, or an all-sky camera is insensitive to major magnetospheric processes, nor is it always because the correct theory cannot be deduced from the available data. For example, the concept of a magnetospheric cavity, a continually flowing solar wind, a geomagnetic tail, and a bow shock preceded their direct observation. However, these concepts did not gain popular acceptance until in situ measurements were available, in part because of the existence of alternate models, which were also apparently consistent with the data.
On the other hand, there are certain processes occurring in and around the magnetosphere for which remote sensing is no help. For example, the structure and nature of the bow shock and the magnetopause leave no signature in ground based data. A knowledge of the structure and the nature of the processes occurring therein is necessary, if we are to be able to extend our magnetospheric experience to astrophysical and plasma physical environments. Otherwise, the magnetospheric physicist will be just a weatherman, with a detailed knowledge of what has happened in the past and therefore what should happen in the future, but little other than this empirical knowledge.
Fortunately, the decade of the 1960's provided magnetospheric physicists with a wealth of in situ data, and our models of the magnetosphere evolved very rapidly, to a point today where there is very little controversy about the observational magnetosphere. Controversy now focuses on mechanisms and temporal behavior. For example, there are no longer any serious questions about whether the magnetosphere is open or closed. However, many arguments as to the relative timing of auroral zone phenomena, midlatitude events and magnetospheric changes still persist. Many of these arguments appear capable of resolution from presently acquired but incompletely analyzed data. However, some future data remains to be gathered to settle some timing questions, such as on the relative timing of the equatorward motion of aurora near local noon and the southward turning of the interplanetary magnetic field.
Further, there is still a need for properly conceived correlative observations, which do not involve timing so much as relative magnitudes and locations, such as comparing the magnitude of changes in the tail energy density with the strength of the plasma injection at synchronous orbit, and comparing ionospheric current systems deduced from ground station chains with currents measured in space. Finally, there are measurements that have never been made such as of the velocity,thickness and current density of magnetospheric boundaries, which require coordinated measurements from a closely spaced pair of satellites.
The experimental task is made easier though, by the fact that we know roughly what we are looking for. We know the range of parameters to be measured and we have phenomenological models for the behavior of the magnetosphere, which while they may not provide the reasons for magnetospheric behavior, they outline what this behavior is.
As the term phenomenological model implies, we have not achieved much progess in magnetospheric theory in the past few years, especially in the area of magnetospheric dynamics. For example, a successful theory might involve modelling all the stresses in the magnetosphere and showing how a perturbation of this stress balance would cause growth of some macroscopic instability of the night time magnetosphere. However, such modelling is still in its infancy. On the other hand, for many purposes, we do not need to know the explicit details of these mechanisms. For example, we can now explain many of the patterns of geomagnetic activity, and can predict the state of the magnetosphere as measured by geomagnetic indices from interplanetary measurements. Thus, while we have not solved all problems of magnetospheric dynamics, we can draw some satisfaction from the fact that we now have knowledge which can be put to use.
The work on substorms at UCLA much of which is incorporated in this manuscript is the culmination of the ideas and work of many individuals. These include M. P. Aubry, R. K. Burton, M. N. Caan, P. J. Coleman, Jr., F. V. Coroniti, T. A. Farley, R. E. Holzer, C. F. Kennel, M. G. Kivelson, R. L. McPherron and R. J. Walker. Equally important to this effort were the contributions of advice and data from our collaborators, both those associated with OGO 5: R. M. Buck, C. R. Chappell, R. W. Fredricks, M. Neugebauer, F. L. Scarf, E. J. Smith and H. I. West, Jr.; and those associated with other satellites and ground based observations: J. H. Binsack, D. L. Carpenter, D. S. Colburn, D. H. Fairfield, G. K. Parks and C. P. Sonett. Both the resources of the National Space Science Data Center and the World Data Center A were invaluable in our studies. The National Aeronautics and Space Administration provided support for the analysis of OGO-5 magnetic field data reported herein under NASA contract NAS 5-9098 and under NGR 05-007-004. The National Science Foundation provided support for the study of geomagnetic storms under NSF grant GA 34148-X.
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*While, in retrospect. the magnetospheric nature of substorms is obvious, it was not until 1967 that the term magnetospheric substorm was suggested(McPherron et al., 1967) or the magnetospheric consequences of the substorm discussed (Brice, 1967: Jelly and Brice, 1967; McPherron et al., 1967). (Back to text)