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# Magnetospheric convection and magnetic storms

Magnetospheric convection refers to the global flow of plasma in the magnetosphere.

## Electric fields

Even though magnetic field lines severely constrain the motion of individual particles, it is quite possible for a body of plasma—ions and electrons together—to move through a magnetic field with some common bulk velocity, v. All it takes is help from a suitable electric field E, satisfying the Magnetohydrodynamic (MHD) condition.

E = –v×B

If that is satisfied, the magnetic force due to the average motion cancels the one due to E, so that both can be disregarded. If extra energy (e.g. thermal) gives individual particles velocities slightly different from v, then the difference may cause them extra spiraling due to B, but apart from that they still show the bulk flow.

An electric field of this sort, for instance, makes possible "the radial flow of the solar wind", undeflected by the magnetic field filling interplanetary space. The solar wind is accelerated by a powerful thermal process in the solar corona (a process that bears some resemblance to the one accelerating a rocket's jet), and faced by such force, the E required for the motion arises naturally by a slight redistribution of electrons and ions (only a very slight change is needed). In the magnetosphere, wherever a plasma process generates a bulk flow (e.g. the earthward motion of plasma in magnetic storms and substorms), electric fields are similarly employed.

The MHD condition is fundamental to the behavior of space plasmas. Note that only the component v perpendicular to B is involved. Bulk motion parallel to B remains unrestricted, barring effects such as mirroring (which arises from slight variation of the field direction over the circle traced by the particle as it gyrates around its guiding field line).

The equation has many different aspects. If we go to the frame of reverence moving with the bulk velocity v, the electric field sensed by any particle there is

E* = E + v×B

If the MHD condition holds, any particle moving with the bulk speed will experience in that field no electric force. It will also be free from magnetic force, since its velocity relative to the frame is zero (its velocity seen by us is the velocity of the frame, plus velocity relative to the frame). This agrees with the claim that as long as it moves with the frame, E and B have no effect on it.

From the point of view of the charged particles, if any electric field exists, an "electrical drift" u must be added to the motion of the particle, equal to

u = E×B/B2

which again satisfied

E* = E + u×B

Showing that any collection of particles in a magnetic field B, if subjected to an electric field E, will add to its motion a bulk velocity u, which depends on neither the sign of the charge nor on the energy or mass of the particle, a true bulk motion.

This "electric drift" is perpendicular to B (also to E) and resembles in some ways the sideways drift of gyrating particles described in explaining the ring current. There the gyrating motion became tighter as the orbit got closer to Earth, where the field intensity B was (slightly) higher than the average for the whole gyration. Here the particle's velocity fluctuates up and down as E causes it to speed at one end of its circle and slow down at the other; where it slows down, the gyration circle becomes tighter. However, since here both electrons and ions drift with the same velocity (and in the same direction), no electric current is created.

The drift is perpendicular to B (also to E) so that u has no component parallel to B: any motion in that direction depends on other factors. For instance, the solar wind moves radially away from the Sun, while at the Earth's orbit the average IMF makes a 45° angle with the radial direction. Part of the motion of the solar wind is therefore perpendicular to field lines, requiring E, while a comparable part represents unrestrained flow along such lines.

## Field line motion

The MHD equation implies that when a plasma is pushed hard enough to undergo a bulk flow v, an electric field E will arise and make it possible. But what about changes in the magnetic field B? The rate of change ∂B/∂t of the magnetic field with time is involved in Maxwell's 3rd equation, the equation of induction. (It involves differential calculus of vector functions.)

∂B/∂t = – ∇×E

where ∇×E ("the curl of E") measures the tendency of E to swirl around, rather than flow directly between electric charges. Applying the curl operation to the MHD condition gives

∇×E = – ∇×(v×B)

and after substitution

∂B/∂t = ∇×(v×B)

an equation involving only B and v, and one expressing the rate of change of the magnetic field. It can be shown to have a very simple intuitive meaning ("field line preservation"): two particles moving with the bulk velocity v which satisfies it, if sharing the same magnetic field line, will always do so. The opposite holds as well: if they do not share the same field line, they will never do so in the future. That was the reason why in an ideal situation (and all these equations are idealized simplification, ignoring factors such as viscosity and turbulence), the plasmas of the solar wind and of the magnetosphere are separated ("closed magnetosphere", above). Each is threaded by field lines of a very different source.

This principle of "field line preservation" is a very powerful help for intuition, for instance in understanding the shape of interplanetary magnetic field lines. The "roots" of such lines are anchored in plasma which rotates with the sun (in about 27 days, as viewed from the rotating Earth, but meanwhile other potions of the line are embedded in plasma which races away radially. The result can be shown to be a spiral (flat in the Sun's equator, wound around a cone far from the equator), becoming closer and closer to circular with growing distance from the Sun.

It is sometimes claimed that "in a plasma, field lines move with the plasma," even while others protest that such lines (like lines of latitude and longitude) are artificial constructs, making their motion meaningless. Indeed, "field line motion" is meaningful only if we identify the field line by means of the particles which share it. Otherwise it should be viewed merely as a visualization aid, providing an intuitive meaning to the interplay of bulk motion and magnetic field, while avoiding the need of deriving the electric field which makes that motion possible.

## Magnetic reconnection

The absolute separation between plasmas containing magnetic fields of different sources has at least one significant loophole. If the fields on opposite sides of the interface have opposing directions, a "neutral point" can form between them, where mutual cancellation of opposing fields reduces the field intensity to zero. There may even exist a "neutral line" of zero intensity, extending in the third dimension.

At an "X-type neutral point" on the boundary (or neutral line), field lines form the shape of a letter X, where (say) field lines on the left of the X point down, on the right they point up, and at the crossing the field is zero. If plasma flows towards such an X-point or X-line, arriving from both left and right, the field lines thy bring embedded in them "lose their identity" at the crossing and are able to "reconnect" or "merge". As the plasma continues its flow and exits from the "X" upwards or downwards, it carries compound field lines - their left half contain plasma from the left source, their right half plasma that has come from the right. In this way, the two magnetic regions become linked.

In the 1950s this idea was applied to solar magnetic fields by Sweet[disambiguation needed], Parker[disambiguation needed] and others, but in 1961 James Dungey in Britain proposed it occurred in the Earth's magnetosphere as well. At noon, where the solar wind first encounters the Earth, the Earth's field lines point northward, on their way from the southern polar cap to the northern one. Suppose, he argued, that the interplanetary magnetic field (about which few observations existed in 1961) pointed southwards then reconnection on the "nose" of the magnetosphere would create compound field lines ("open lines") leading from interplanetary space to the Earth's polar regions.

After reconnection, the solar wind would carry such lines tailwards, deforming them and gradually trapping them along the Earth's tail--lines connected to the north pole pointing northward, lines connected to the southern one pointing away from Earth (just like the tail lobes observed later). Ultimately, he proposed, those opposing fields would reconnect again in the middle, re-uniting terrestrial and interplanetary parts of compound field lines. The interplanetary portions (with the plasma they contain) would rejoin the solar wind, while the terrestrial plasma would have to flow back towards noon, because it could not accumulate indefinitely at midnight.

Dungey's concept became known as the "open magnetosphere", an alternative to the previously proposed "closed magnetosphere" of rigorously separated field lines. Unlike the "closed" configuration, it was expected to be strongly coupled to the solar wind, which could readily supply it with energy and plasma. True, the IMF might not be directed southward, and in fact, that only happens rarely. However, if the field is moderately slanted southwards, points with "anti-parallel" magnetic field lines may still be possible some distance from noon, possible sites for reconnection. The idea of such a process received strong support in 1966, after spacecraft began monitoring the IMF. It then became evident that "storminess" of the magnetosphere ("magnetopheric activity") occurred primarily when the north-south component Bz of the IMF pointed south. Also, while magnetic storms required the arrival of a blast of solar plasma, overtaking the solar wind and preceded by a shock front, big storms and severely compressed boundaries usually required a southward Bz as well.

## Magnetospheric convection

What happens inside the magnetosphere is even more significant. Plasma flows back to the dayside, where it may end up on freshly reconnected field lines, after which it may be carried back tailward once more. This circulation of plasma and field lines is known as "magnetospheric convection", since it resembles the convective circulation of a heated fluid, e.g. in a pot of soup on a stove or of air in the atmosphere.

The motion and its associated electric field are shared along the entire length of participating field lines, down to where these lines reach Earth, in the polar ionosphere. Satellites have been measuring those electric fields as voltage differences between the tips of long probes sticking out in opposite directions from low-altitude satellites above the polar caps, like Injun 5 (1971) and OGO-6 (1972). The convection was also related to motions of auroral irregularities by Ian Axford and Colin Hines, who modeled and studied it in 1961. They proposed an alternative mechanism for producing it, by which the magnetosphere is closed but convective flows still exist, driven by viscous-like forces along the boundary. That effect may also exist, but more observations are needed.

Earthward convection of plasma adds energy to its particles. If the magnetosphere has north-south symmetry with a flat equatorial plane in the middle, that is evidently true for charged particles in that plane, with no motion along field lines and hence with magnetic moment μ = W/B, where W is now the total energy. As such particles are convected earthwards, they encounter increasing values of B, and if μ stays the same, W must also grow.

However, convected particles with mirror points far from the equator also gain energy, by the conservation of the second invariant, which approximately reflects the distance along the guiding field line between mirror points. As particles and their field lines are convected closer to Earth, that distance (like the field line itself) gets shorter, and this may be shown to lead to a greater total energy W. The gained energy is provided by the electric field E which drives the convection, which itself (in a roundabout way) comes from the motion of the solar wind.

As convected plasma approaches Earth, it is deflected around the inner magnetosphere by magnetic forces, and an important change takes place. Far from Earth the electric drift u dominates the motion of particles and field lines, imparting exactly the same bulk velocity to positive ions and negative electrons, independent of energy. As Earth is approached, magnetic drifts also become important—such as the one (described earlier) which drives the ring current, caused by B becoming stronger as Earth gets closer. These drifts act differently on ions and electrons and therefore produce a current, a "partial ring current" across the midnight sector.

The circuit is ultimately closed along field lines which continue it to the ionosphere—down on the evening side of Earth (dusk), up on the morning side (dawn), forming "Region 2 of Birkeland currents". Stated differently— positive ions drift from midnight towards dusk, electrons from midnight towards dawn, and region 2 currents drain away those separated charges. The current flow then connects through the ionosphere to the primary Birkeland currents ("Region 1") which is presumably connected to the solar wind through open field lines. Together these currents are believed to form the circuit which powers convection.

## Substorms

Observations suggest one significant modification of this scenario: the process is not continuous but occurs in spurts. Some variation of the reconnection rate is certainly expected because the IMF and its Bz component continuously change. Thus the reconnection rate varies in time, as does its location on the boundary. But a more important reason is that after plasma and its magnetic field lines are swept into the tail, they in general do not immediately reconnect, which delays their flow back earthwards.

Instead, field lines swept into the tail become stretched along the flow of the solar wind, forming the tail lobes. Their plasma, not hindered by any obstacle, flows out with the solar wind and leaves behind a void of very rarefied plasma, density 0.01-2 per cm3 (some low-energy plasma from the polar ionosphere flows into this void, forming the "polar wind"). The magnetic field lines however remain as part of the tail lobes, creating there a stiff and fairly strong (10–20 nT) magnetic field.

As the process continues, more and still more magnetic field lines with plasma are transferred into the tail lobes. The field intensity in the distant lobe cannot rise (its value is determined by pressure balance with of the solar wind) and instead the lobes become wider, with a widening front which presents a greater obstacle to the solar wind. The force of the solar wind pressing on that front increases, trying to tear off the magnetotail. That force is transmitted to the plasma sheet, the layer separating the lobes and their opposing magnetic fields, and it presses the lobes together in that front part of the tail.

Ultimately, the lobes squeeze out the plasma sheet and reconnect, at a distance estimated at 20-25 RE. When that happens, a rapid and violent process begins, known as a magnetic (or magnetospheric) substorm'. Unfortunately, most of our data come from isolated satellites, unable to resolve details of the process, which are still widely debated.

Plasma nightwards of the reconnection site is pushed tailwards, with its field lines, to form a blob surrounded by oval field lines ("plasmoid") which is carried away with the solar wind. Plasma on the sunward side is hurled earthwards, gaining energy and triggering increased Birkeland currents and polar aurora (see article on the polar aurora for details). Ultimately the earthward rush ends about 6 Earth radii, with most of the flow diverted away from the inner magnetosphere. That is where "Region 2" Birkeland currents originate, as well as many of the "discrete arcs" of the polar aurora. Field lines from that region lead to the auroral zone, while field lines of the polar caps, around the magnetic pole, mostly lead to the tail lobes.

The footprints Birkeland currents in the polar ionosphere are traced by the famous "snake diagram" of Tom Potemra and Takesi Iijima (1976), with "Region 1" forming the inner strip and "Region 2". By some odd property of the magnetic field, however, the magnetic effects of these current systems almost cancel out at ground level. What does not cancel is the signature of a secondary Hall current, possibly confined to the ionosphere, flowing towards midnight perpendicular to currents which bridge the gap between the regions (it is also possible their ends connect to distant regions). That is the "auroral electrojet" whose magnetic signature on the ground can exceed 1000 nT, in a relatively narrow area of the auroral zone (big magnetic storms very rarely exceed 400 nT, though rgwie effect is world-wide). An "auroral electrojet" (AE) index derived from that disturbance, as recorded by a network of observatories, is often used to gauge the level of substorm disturbances, which typically last 30-60 minutes.

## Magnetic storms

### Solar activity

The sun generates a variety of magnetic fields, most conspicuously in sunspots, concentrated areas of relatively intense magnetic fields (0.15 tesla or 1500 gauss). As found by Heinrich Schwabe around 1847, the number and extent of sunspots rises and falls in an irregular cycle of about 11 years. In addition, the sun also has a global magnetic field, with two opposing magnetic poles. Its strength is about 0.5 millitesla (5 gauss), reversing its polarity in every sunspot cycle.

Presumably, the sun's magnetism is due to some dynamo action inside it, probably associated with the observed uneven ("differential") rotation observed on the surface, fastest at the equator. It is hard to tell much more, because most of the process occurs below the visible surface. However, it is widely believed that the heating of the corona—source of the solar wind and hence of magnetospheric phenomena—comes from the release of small-scale magnetic energy near the surface.

Large and rapid releases of magnetic energy certainly occur, in active sunspot regions often associated with complex groups of sunspots. Solar flares (first observed in 1859) produce a rapid brightening in the chromosphere, conspicuous in the red hydrogen-α line generated there, also bursts of X-rays, radio emissions, occasional bursts of high energy ions and often a rapid outflow of solar plasma, piling up a shock front ahead of themselves.

Coronal mass ejections (CMEs) are giant bubbles of plasma emitted from active regions, observed since the Skylab mission in 1973. They too seem to be associated with rapid plasma outflows and shock fronts, although their relation to flares, and the causing mechanism of both phenomena, are still poorly understood.

When such a shock front arrives at Earth, especially if the IMF has a southward Bz component, a magnetic storm may follow.

### Phases of magnetic storms

In magnetic storms, as in substorms, magnetic plasma is injected earthward from the tail, but with much greater intensity and deeper earthward penetration. The ring current grows significantly, adding a world-wide southward magnetic field Bz. (Note: This Bz is completely different with the similarly denoted component in the IMF.) This allows the strength of the magnetic storm to be gauged by the so-called Dst index.

The Dst index is defined as the average change in the southward component Bz observed at the Earth's equator. Its negative sign shows a reduction—the internal Earth field has a northward Bz at the equator—and it is derived using a number of observatories (usually 3–4) evenly distributed around the equator. The initial estimate of Dst is reduced by an opposing effect, by the extra compression of the magnetosphere from the added pressure of the plasma front causing the storm. Afterwards, using observations of the solar wind in space, a corrected Dst* is calculated, representing only the effect of the added ring current. It was shown by Dessler and Parker (1959) and later expanded by Sckopke (1966) that Dst* is approximately proportional to the extra energy given to the ring current.

Typical values may be Dst=−30 to −50 nT for a small storm (perhaps once a month), Dst=−50 nT for a moderate one and Dst=−100 nT for intense storms, which may reach −400 nT. Very intense storms may occur only a few times per solar cycle.

The storm begins with a sharp but small northward jump (sudden commencement) in Bz observed on Earth, due to the compression of the magnetopause by the abrupt arrival of a shock front. That feature was correctly explained by Chapman and Ferraro in 1930. If the IMF slants northward, such a "sudden impulse" may be all that happens.

If however a storm develops, the observed Bz keeps dropping, reaching minimum within 6–12 hours ("main phase") after which the field may slowly recover over the next 1-3 days. During the main phase, because of the increased ring current, the auroral oval is greatly expanded and the auroras produced by the storm are seen much closer to the equator than ordinary aurora. They are often colored red, color of the 630 nm oxygen line, suggesting the auroral electrons are of lower energy and are stopped at higher altitudes.

The gradual recovery coincides with a loss of injected ring-current ions, and an initial rapid recovery has been credited to ions which are not actually trapped but keep drifting out of the front of the magnetosphere. Most losses however seem to come from charge-exchange collisions with atoms of the geocorona. In such events, the incoming energetic ion just grabs an electron from the atom, resulting in a nearly stationary ion and an "energetic neutral atom" (ENA). ENAs are of interest in studying the magnetosphere since they move in straight lines (ions are deflected by magnetic forces) and therefore their direction of arrival points towards their origin. The IMAGE satellite launched in 2000 was designed to collect ENA information, but unfortunately the rate of such ions is very low, yielding sparse data.

Magnetic stroms are poorly understood, mainly because they are relatively rare, also quite variables. A storm in 1991, for instance, not an exceptionally intense one, unexpectedly created an additional inner radiation belt centered around 2.1 RE, with ions and electrons of typically 10–20 MeV; it probably lasted at least one year.

Large magnetic storms are generally associated with sunspot activity, but Edward Maunder noted in 1905 that moderate storms often occurred when few or no sunspots are seen. They tended to recur at 27-day intervals, suggested that their invisible sources (named "M-regions" for magnetic) rotated with the sun. They turned out to be "coronal holes", regions free of magnetic activity where the sun's magnetic field lines pointed more or less straight out. That allowed an unhampered acceleration of the solar wind to speeds 50% or more above the average, producing "co-rotating fast streams" first observed from space by Mariner 2 in 1962. The Ulysses space probe confirmed that similar fast streams exist almost all the time above the poles of the sun, where (as suggested by eclipse photographs) field lines also stick straight out.

## Effects associated with northward IMF

When the interplanetary Bz component points northwards, the magnetosphere is generally quiet and the auroral zone becomes very small. Certain interesting features may however occur including auroral arcs stretching sunwards across the polar cap ("poleward arcs" and "theta aurora"). No good explanation exists, though it has been proposed that magnetic reconnection with the IMF may then occur tailwards of the cusps, where the Earth field near the boundary points southwards.

## Plasma Waves

A variety of plasma waves has been observed in the magnetosphere, many of which may be viewed as modifications of electromagnetic waves, affected by the presence of plasma. Two basic types of resonance exist in a plasma--due to oscillation of charge density (giving resonance at the "plasma frequency") and due to the gyration frequencies of electrons and ions in the magnetic field. The propagation of such a modified wave depends on the position of its frequency relative to the various resonances, as well as on the angle between its propagation and the magnetic field direction, and also on its polarization. Many wave modes exist, but two are of particular interest:

(a) Whistler modes, first noted as whistling sounds descending in tone, heard in the background on telephone lines and on field telephones in World War I. They were recognized to be radio waves whose (very low) frequency overlapped that of audible sound waves. Owen Storey identified their source in 1953 as lightning. In a typical event, the stroke of lightning occurred in the opposite hemisphere, and the wave, in a form modified by plasma surrounding Earth, is guided along magnetic field lines to the opposite hemisphere (because of the ionosphere, it may be reflected, and bounce back and forth more than once). Because of the modified wave mode, propagation velocity depends on frequency - higher frequency travels faster - spreading out the signal into a descending whistle.

(b) Low frequency radio waves (around 150 kHz) are generates on field lines along which the aurora precipitates, and are known (from their wavelength) as "auroral kilometric radiation" (AKR). Though they are quite intense, they are effectively blocked by the ionosphere and were only discovered from space.

## Instruments

A wide range of ground based magnetospheric observations exist. Magnetometers monitor the auroral zone (also providing the AE index; see substorms, above) as well as the equatorial region (leading to the Dst index; see magnetic storms, above). Two types of radar - coherent scatter and incoherent scatter - are used to probe the auroral ionosphere. By bouncing signals off ionospheric irregularities (which convect with their field lines) one can trace their motion and infer magnetospheric convection.

Spacecraft instruments include

(a) Magnetometers, usually of the fluxgate type. Usually these are at the end of booms, to keep them away from magnetic interference by the spacecraft and its electric circuits.Magnetometers

(b) Electric sensors at the ends of opposing booms are used to measure potential differences between separated points, to derive electric field associated with convection. The methodworks best at high plasma densities in low Earth orbit; far from Earth long booms are needed, to avoid shielding-out of electric forces.

(c) Radio sounders from the ground can bounce radio waves of varying frequency off the ionosphere, and by timing their return get the profile of electron density in the ionosphere - up to its peak, past which radio waves no longer return. Radio sounders in low Earth orbit aboard the Canadian Alouette (1962) and Alouette 2 (1965), beamed radio waves easrthward and observed the electron density profile of the "topside ionosphere." Other radio sounding methods were also tried in the ionosphere (e.g. on IMAGE).

(d) A great variety of "particle detectors" has operated in orbit. The original observations of the radiation belt used a Geiger counter, a crude detector unable to tell particle charge or energy. Later scintillator detectors were used, and still later "channeltron" electron multipliers have found particularly wide use. To derive charge and mass composition, as well as energies, a variety of mass spectrograph designs were used. For energies up to about 50 keV (which constitute most of the magnetospheric plasma) time-of-flight spectrometers (e.g. "top-hat" design) are widely used.

(e) Computers are not usually viewed as scientific instruments, but they have been indispensable in magnetospheric research, and not just by pre-processing complex satellite data for more economical transmission of data to the ground. Computers have also made it possible to bring together decades of isolated magnetic observations and extract average patterns of electrical currents and average responses to interplanetary variations.

A different application are simulations of the global magnetosphere and its responses, by solving the equations of magnetohydrodynamics (MHD) on a numerical grid. Appropriate extensions must be added to cover the inner magnetosphere, where magnetic drifts and ionospheric conduction also need to be taken into account. So far the results are interesting, but their interpretation is not easy, and certain assumptions are still needed to cover small-scale phenomena.