Basic requirement
Now, since the magnetic field configuration in the main body (within 10 Re) of the magnetosphere is far from antiparallel, it is unlikely that magnetic reconnection can occur there; indeed, satellite observations show that magnetic reconnection is rare within a distance of 10 Re (Ge and Russell, 2006). Thus, unless proven otherwise, it is necessary to find processes other than magnetic reconnection in converting the magnetic energy for the energy of the expansion phase. In fact, as Fig. 11c shows, the magnetic field is absent in the middle of the intensified current sheet.
It was concluded in The expansion phase (UL) dynamo power that the expansion phase requires a dynamo of the power 3.5 × 1018 erg/s in generating Bostrom’s current. The conversion process must be able to generate the currents in Bostrom’s 3-D current. Thus, the search for the cause of the expansion phase may begin by identifying the nature of the dynamo for the expansion phase, which causes the unloading process of the accumulated magnetic energy.
The UL current (the auroral electrojet, directed westward) is the ionospheric part of the 3‑D current system, which can be driven by a southward electric field of more than 100 mV/m (100 V/km) and perhaps about 250 mV/m in the ionosphere during the peak of the expansion phase. As mentioned earlier and shown in Fig. 6, in Bostrom’s circuit, the only place where E⋄ J < 0 is located in the equatorial part of the circuit (actually, a thin magnetic shell near the earthward end of the current sheet, The UL current system for the expansion phase) in the meridional component [Akasofu, 2003a], not in the ionosphere where E⋄ J > 0, indicating that the expansion phase dynamo must be located in the magnetosphere.
Synthesis
Synthesizing what we have learned in the above, we attempt to consider a possible process for the expansion phase. It is emphasized here this section describes only an exercise. First of all, in order to produce electric currents for a discharge, it is necessary to separate electrons from protons (either chemically [a battery] or by force [a dynamo]). Further, in generating the UL current, the electric field thus produced must be directed earthward, as mentioned in The UL current system for the expansion phase. One possibility is as follows (Figs. 14 and 15).
When the power ε is increased, the current in the plasma sheet is increased during the growth phase, inflating the magnetosphere (accumulating magnetic energy. When the accumulated energy W = [(1/2)J
2
L] reaches 2 × 1022—or at most 1023—ergs, the magnetosphere becomes unstable and unload the energy in order to stabilize itself). It is this very process which causes the spectacular expansion phase.
The magnetic energy, which inflates the inner magnetosphere, is caused by the sheet current in the plasma sheet. Thus, the fact that the magnetosphere becomes unstable (because of the accumulated energy) means that the current in the current sheet becomes unstable. The limit of stability (breakpoint) of the current in the plasma sheet may be equivalent to that of the strength of the spring attached to the tippy bucket (Fig. 4). In fact, such an instability was observed at the time of expansion onset (Fig. 16).
Thus, in the process of stabilizing itself, the magnetosphere must reduce the accumulated magnetic energy W = [(1/2)J
2
L] by reducing the current J in the plasma sheet. As a result, the magnetosphere deflates itself. The reduced magnetic energy W must be consumed for the expansion phase. In other words, the accumulated magnetic energy must be consumed to generate the expansion phase dynamo. Thus, the deflation process must generate the expansion phase dynamo, namely the separation of electrons from protons (Fig. 14).
The deflation of the magnetosphere increases B inside the current sheet; there is little magnetic energy inside the current sheet (see Fig. 11c). Thus, it is expected that ∂Bz/∂t > 0 there during the expansion phase, when W is reduced. The resulting electric field can be very roughly estimated to be about ([−∂B/∂t)∫ ∂y] = 150 mV/m (=50 nT/20 min × 20 Re = 1.26 × 1010 emu). This value of the electric field is larger than what is observed by a satellite (Fig. 16). The deflation will end in about 1 h by spending the accumulated magnetic energy, explaining the short life of the expansion phase. Bostrom (1974) estimated the time constant of the UL circuit to be 8 min (=50H/0.1Ω), so that the dissipation rate δ can reach the peak value in a rather short time. This may also explain a sharp increase of the UL current at the beginning and the explosive nature of the expansion phase.
As mentioned earlier, the reduction of the current may be caused by developing plasma instabilities. If plasma instabilities can occur in reducing the current in the current sheet, the frozen-in magnetic field lines condition is expected to break down at the critical moment of expansion onset. Microscopically, the deflating magnetosphere brings electrons (gyrating tightly around the magnetic field lines) toward the earth, but not protons and thus separating both electrons and protons in the plasma sheet, and thus also generating an earthward electric field in a thin shell near the earthward end of the current (plasma) sheet. This process does not require the whole plasma motion (v × B). As shown earlier, a simple estimate of the electric field is about 150 mV/m.
This process of charge separation was suggested by Lui and Kamide (2003), as shown schematically in Fig. 14. The separated electrons in a thin magnetic shell thus produced will be discharged along the magnetic field lines toward the ionosphere, producing the field-aligned current sheet and brightening an auroral arc as an initial indication of expansion onset. The reason why the separation occurs near the earthward end of the plasma sheet is related to the fact that a typical onset arc lies near the equatorward boundary of the auroral oval.
Further, when the earthward electric field is communicated to the ionosphere by the streaming electrons, it becomes a southward electric field that can drive the UL current (the auroral electrojet). This process continues until the deflation is complete. Figure 15 schematically shows an overall possible chain of processes which could lead to substorm onset. Thus, this suggested chain of processes requires breakdown of the condition of the frozen-in field line during the expansion phase. The generation of the earthward electric field requires new theoretical and observational studies without using the concept of frozen-in field lines condition.
In summary, the proposed chain of processes described here is
-
(1)
The magnetosphere accumulates magnetic energy in the main body (its inductive circuit) during the growth phase (1 h) because the ionoshere cannnot dissipate the power. Thus, the magnetosphere is inflated.
-
(2)
When the accumulated energy reaches 2 × 1022 ergs or at most 1023 ergs, the current in the current sheet develops plasma instabilities and becomes unstable.
-
(3)
Thus, the current is reduced, and the magnetosphere is deflated and the accumulated magnetic energy is unloaded.
-
(4)
During the deflation (unloading) process (1 h), a charge separation occurs, separating electrons from protons.
-
(5)
The separation of the charges causes an earthward electric field near the earthward end of the current sheet. Thus, the unloaded magnetic energy is consumed in producing the earthward electric field (and thus the expansion phase dynamo).
-
(6)
The electric current thus produced causes a great variety of auroral activities during the expansion phase as an electrical discharge process.
Supporting satellite observation
There is an important set of satellite observations which are consistent with the above chain of processes at 8.1 Re (Lui, 2011); Fig. 16. One of the THEMIS satellites observed: (i) plasma instabilities, (ii) a electric current reduction, (iii) break down of the frozen-in field line condition, (iv) an earthward electric field of 20 ∼ 30 mV/m, (v) simultaneously with onset of an auroral substorms. The intensity of this observed electric field is less than that drives the UL current in the ionosphere. These observational facts are consistent with the synthesis described in the above. However, other cause–effect relationships even for the same set (or other set) of the facts should be explored.
Triggering?
When the magnetosphere accumulates about or more than it can hold, the magnetosphere is likely to be ready to unload the accumulated energy. The reduction of the current in the current sheet could be induced by a stimulation, namely by triggering. Busty bulk flows (BBFs) could trigger some substorms, although they do not have enough energy causing substorms. This subject will be discussed further in Auroral displays.
On the other hand, it is known that a significant number of substorms occur at about the time of ‘northward turning’ of the IMF some time after a southward turning [after ε becomes above 1018 erg/s] (Lyons et al. 2001). In these cases, it is expected that a northward turning (external cause) can trigger the expansion onset by the reduction of ε because ε and the current in the current sheet are reduced at the time of ‘northward turning.’ It is known that interplanetary shock waves can also trigger substorms, if they are accompanied by a southward IMF.
Other studies
Since the cause of the expansion phase is such an important subject, a large number of observational and theoretical efforts have been made. A few recent examples are satellite observations, such as GEOTAIL, THEMIS, IMAGE, and others (cf. Machida et al. 1994; Ohtani et al. 2002; Perraut et al. 2003; Shiokawa et al. 2005; Coumans et al. 2007; Angelopoulos et al., 2008), theoretical studies (cf. Cheng, 2004; Haerendel 2007, Harendel 2008, Haerendel 2009; Israelevich et al. 2008), and numerical simulation studies (cf. Birn et al., 2012); there have been many simultaneous observations between satellite and ground-based observations (cf. Nishimura et al. 2010) in addition to ground-based optical observations (cf. Henderson, 2009) and superDARN radar observations (cf. Lyons et al. 2010). However, it is regrettably not the intent of this paper to review these works and many others since it is beyond the capability of the present author.
On magnetic reconnection
Magnetic reconnection has been mentioned earlier a few times. It may be worthwhile to summarize them here. This theory is based on the premise that the magnetotail (where the field is nearly antiparallel) has sufficient magnetic energy to be converted into the energy of substorms by magnetic reconnection. However, it was shown in (Where is the magnetic energy accumulated during the growth phase?) that the magnetotail does not have sufficient energy.
Further, magnetic reconnection is supposed to generate a tail-wide plasma flow so that it is supposed to produce the DD current (not the UL current), but the DD current is not mainly responsible for the expansion phase. The expansion phase requires an electrical discharge along Bostrom’s circuit. Further, even if the expected flows by magnetic reconnection are narrow and short-lived, such as those observed BBFs, they do not have enough energy (1021 ergs or less). At most, they might only trigger some substorms (but not all) by inducing the abovementioned instability (Triggering).
Above all, however, the theory, in particular simulation studies, has to rely on fictitious resistivity called “effective resistivity” because the theory is based on the “frozen-in field lines” concept, in spite of the fact that Alfven warned in as early as 1967 that it should not be applied to magnetospheric physics.
So far, the “magnetic field lines” approach has not provided quantities which can be compared and discussed with those given in this paper. In fact, for example, there is no way to discuss quantitatively our observed result of the impulsiveness of the expansion phase with simulation results so long as they rely on effective resistivity which is supposed to determine how fast magnetic reconnection is supposed to occur and has so far not demonstrated as a physical quantity.