The sequence of phenomena consisting of solar flares, coronal mass ejections
(CMEs), auroral substorms, and geomagnetic storms is mostly a manifestation
of electromagnetic energy dissipation. Thus, first of all, it is natural to
consider each of them in terms of a sequence of power supply (dynamo), power
transmission (electric currents/circuits), and dissipation (mostly observed
phenomena), i.e., as an input–output process and the electric current line
approach. Secondly, extending this concept, it is attempted in this paper to
consider the whole solar–terrestrial relationship in terms of electric
currents. This approach enables us to follow through not only the sequence in
solar flares, auroral substorms, and geomagnetic storms but also to connect
all phenomena naturally as a continuous flow of magnetic energy
(
In as early as 1967, Alfvén (1967) noted the following: “In some application we can
illustrate essential properties of the electromagnetic state of space
Indeed, the current line approach can follow quantitatively the flow of the
power/energy (physical quantities) as a
In all the phenomena we consider in this paper, the first important subject is the power supply produced by plasma flows in a magnetic field.
The dynamo power
In terms of the current line approach, solar flare processes can be described
by the following terms: photospheric dynamo, the magnetic arcade current system (the
This approach may be contrasted with the present magnetic field line
approach, which involves the following: magnetic reconnection (converting
magnetic energy) and CMEs and downward plasma flows (causing flare phenomena,
like the
In considering solar flares in terms of the current line approach, it is important to recognize that there are two circuits: the magnetic arcade circuit and the loop (prominence) circuit.
The first one is the magnetic arcade current system that is directly driven
by the photospheric dynamo, as described in the following section; its
dissipation is manifested as the
The second one is a loop current system along a filament (prominence) above and along the arcade, in which the magnetic energy is accumulated and then released when the loop current is reduced (Fig. 3). This current is crucial in generating and launching CMEs and eventually causing substorms/storms.
There have been intensive studies on solar flares in the past; some of the recent studies include those by Webb et al. (2000), Fletcher and Hudson (2008), Filippov and Koutchmy (2008), Zao (2009), Wang and Liu (2010), Milligan et al. (2010), Schuck (2010), Steward et al. (2011), Su et al. (2013), Kerr and Fletcher (2014), Aschwanden et al. (2014, 2015), Aschwanden (2015), Fisher et al. (2015), and Kazachenko et al. (2015), in addition to reviews by Zharkova et al. (2011), Hudson (2011), and Shibata and Magara (2011).
Most recent studies of solar flares are based on magnetic reconnection at the outset as the conversion process of magnetic energy or the “merging” of antiparallel magnetic field lines, and they then consider its consequences. They have not considered the power supply, assuming there is enough magnetic energy around sunspots (cf. Shibata and Magara, 2011). Thus, in their approach, the concept of power supply by a dynamo is lacking.
In spite of such a great emphasis and of numerous theoretical and
observational studies on magnetic reconnection, there has been a puzzling
omission of estimating accurately the magnetic field intensity and the amount
of available magnetic energy at the location where magnetic reconnection is
supposed to occur. The only exceptions are an estimate by Priest
(1981, p. 139), who mentioned
the field intensity to be
One of the generally accepted models assumes magnetic reconnection above the
magnetic arcade (Fig. 1a). Unfortunately, there have so far been neither
measurements (not possible at present) of the magnetic field intensity in the
corona nor estimates of it; most coronal magnetic field models assume the
current-free condition, so that there is no expendable magnetic energy under
such a condition. Although the field above the magnetic arcade is not current
free, it may not be very different from the situation similar to the
transition region from the main body of the magnetosphere to the tail region
(the magnetotail). Thus, let us try to roughly estimate the field intensity
where magnetic reconnection is supposed to occur above the arcade. The width
of the arcade is likely to be the distance of two-ribbon flares, namely
The second problem is the absence of the concept of power supply for the historical reason mentioned earlier in the present solar flare study. It can be shown in the following that the power supply is needed not only for the formation of an antiparallel magnetic configuration but also for maintaining flare activities.
Actually, the need for a dynamo in producing an antiparallel configuration
was already
In order to prove the above statement, let us consider first Sweet's
conceptual case on the basis of commonly observed values of these parameters
These numbers are quite common and reasonable in the vicinity of sunspot
groups and can provide power
The purpose of the above estimates is simply to demonstrate the need for a dynamo as the power supply even for magnetic reconnection. Therefore, although in this paper magnetic reconnection is not considered as the process of magnetic energy conversion, it is clear that a photospheric-dynamo process is needed to produce even the desired antiparallel magnetic configuration for magnetic reconnection and to maintain the power supply.
Choe and Lee (1996a, b) developed a photospheric-dynamo model of solar
flares, including active prominences. Its basis is a magnetic arcade which is
formed along the boundary (the neutral line) between two unipolar regions,
where no sunspot pairs or sunspot groups are present. This model was
originally developed by Hirayama (1974) as a magnetic reconnection model
(Fig. 1a), so it did not consider the power supply, namely photospheric
plasma flows in the magnetic arcade; a photospheric dynamo is needed to
produce the antiparallel field to begin with and supplies the power.
Figure 2a shows the geometry associated with the dynamo considered by Choe
and Lee (1996a, b). Their model assumes an antiparallel
plasma flow (
Choe and Lee's (1996a, b) computer simulation is extended
here. An additional calculation shows that the
The intensity of the field-aligned current is about 10
Therefore, the study by Choe and Lee (1996a, b) suggests
that the photospheric dynamo alone can directly produce the two-ribbon
Intense flares tend to occur among an active sunspot group. In particular,
the two-ribbon emission tends to occur along a neutral line in an active
sunspot group. It is expected that both
One of the most interesting features of flare phenomena is active
prominences, which require processes other than the
A sudden reduction in the loop current is expected to release its magnetic energy (Alfvén and Carlqvist, 1967). Let us assume that the magnetic energy is accumulated when the loop current is building up.
The magnetic energy
The conversion of magnetic energy
The released magnetic energy is expected to cause CMEs. Chen and Krall (2003) showed that the Lorentz force (
This is an example to show that the current line approach suggests that there are two current circuits and can also suggest a requirement of the initial condition in launching CMEs, when CMEs have a helical magnetic structure (Sect. 3), which is crucial in predicting the intensity of auroral substorms/geomagnetic storms. Thus, when CMEs have a clear helical magnetic structure, one of the initial conditions should specifically include the expanding loop current rather than a thermal expansion or magnetic reconnection alone.
Some CMEs have a helical magnetic structure (cf. Burlaga et al., 1981).
Furthermore, Gosling et al. (1986) showed that some of magnetic loops have
their feet on the photosphere. Thus, at least some CMEs have
Thus, by assuming currents of 10
It is suggested that both methods should work together, instead of considering the MHD simulation approach alone. In the previous section, we emphasized that the initial condition in launching CMEs of a helical structure should have a current loop associated with active prominences (Chen and Krall, 2003).
As will be shown in the next section, the magnetic structure of CMEs is
crucial in predicting the intensity and its time variations in geomagnetic
storms, which are a vital part of space weather science. The polar angle
In terms of the current line approach, magnetospheric processes associated with auroral substorms can be described as a combination of the following: the Chapman–Ferraro current (see Sect. 5.1), the solar wind–magnetosphere dynamo, the directly driven (DD) current system, the unloading component (UL) current, and the ring current as a result of loading/unloading of magnetic energy in the main body of the magnetosphere.
This approach may be contrasted with the magnetic field line approach, which involves the following: dayside reconnection, flux transfer, magnetic reconnection in the magnetotail, and the resulting plasma flows and their consequences (in producing the substorm current system and the ring current).
The solar wind–magnetosphere dynamo power has been empirically expressed by
Perrault and Akasofu (1978):
There are two important implications in the above expression of the power.
From the point of view of the energy flow from the sun, the above expression
of the power indicates that the magnetic energy (
The second implication is that the magnetic energy carried by the solar wind (which is identical to the power of the solar wind–magnetosphere dynamo, the Poynting flux) flows across the magnetopause and flows in the direction perpendicular to the magnetic field lines, so that a significant amount of the power thus generated flows across the magnetopause toward a dipole-like field of the main body of the magnetosphere. This point is very important in considering where the magnetic energy is accumulated for the expansion phase
The substorm current has two components: the DD component and the UL;
Akasofu (2013). The DD component is directly driven by the solar
wind–magnetosphere dynamo of power
The DD current:
Figure 6 shows how the DD and UL components vary during substorms, together
with
Time variations in the power
The major dissipation associated with auroral substorms is the Joule heat
production in the ionosphere. The amount of the Joule dissipation can tell us
how much energy a single substorm consumes and thus also how much energy the
magnetosphere can accumulate. The current line approach is so far the only
way to provide this crucial quantity observationally. The Joule heat
production is proportional to the intensity of the current in the ionosphere
because it is proportional to
When the magnetic energy is accumulated in the main body of the
magnetosphere, the magnetosphere is loaded and thus “inflated”. Figure 8
shows a second-order calculation of the inflation centered at 6
There is uncertainty about the limiting amount of magnetic energy that makes
the magnetosphere unstable. Since
For these reasons, it is expected that the magnetosphere tries to stabilize itself, resulting in the unloading of the accumulated magnetic energy. It is suggested that the expansion phase of auroral substorms is a consequence of this process.
In order to illustrate the two roles of the magnetosphere, a tippy bucket has
been considered to represent the UL component. The development of individual
substorms is very complicated, because the input function
The magnetosphere is capable of accumulating more magnetic energy at closer
distances (where
Joule heat production. The distribution of the Joule heat production in the ionosphere during a substorm, including a quiet period and the growth phase (prior to the expansion onset) (Akasofu, 2017).
Changes in the earth's magnetic configuration when magnetic energy
is accumulated centered around 6
The conversion or unloading process of the accumulated magnetic energy is
likely to be different in the magnetotail and in the main body of the
magnetosphere. Since magnetic reconnection is rare within
10
Lui and Kamide (2003) and Akasofu (2013, 2015) suggested that electrons and protons are separated during the deflation and produce the earthward electric field needed (Fig. 9).
When the magnetic energy is accumulated, the magnetosphere is inflated. Thus,
the unloading (or releasing) of the magnetic energy causes deflation. Because
of the deflation (
It may be noted that Lyons et al. (2001) reported that substorms tend to occur after a northward
turning of the IMF
Auroral substorms have most of the basic features of geomagnetic storms in
terms of
The “standard” type of geomagnetic storms consists of storm sudden
commencement (ssc) and the initial, main, and recovery phases. The ssc is a
step-function-like increase in the earth's magnetic field, which is followed
by a fairly quiet period for a few hours of the initial phase. After the
initial phase, the main phase begins, during which a large southward
(reckoned negative) field develops for about 6–10 h as a result of an
intense ring current. The last phase is the recovery phase. Figure 10 shows
an example of geomagnetic storms. It shows an assembly of low-latitude
magnetic records (the
Chapman and Ferraro (1931) showed that an advancing solar plasma flow toward
the earth's dipole field is stopped, because electric current is induced at
the front of the plasma flow, and the Lorentz force (
The major difference between geomagnetic storms and auroral substorms is an
anomalous development of the ring current, which is produced by a frequent
occurrence (an enhanced accumulation effect) of intense substorms in about
6–12 h (Akasofu and Chapman, 1963). The intense development of the ring
current causes a large depression of the horizontal component and is
recognized as the main phase of geomagnetic storms. It was found that the
main ion in the ring current during intense geomagnetic storms is O
There has been a controversy about the relationship between substorms and storms (Sharma et al., 2003). However, as mentioned earlier, substorms are mini-storms from the point of view of the current line approach, and thus geomagnetic storms are exceptional cases during which the ring current grows anomalously large.
An example of geomagnetic storms. In the upper part, magnetic
records (the
The current and its magnetic field are already shown in Fig. 8. The major
current is the diamagnetic current that flows westward in the outer part and
eastward in the inner part; the westward current has a larger effect on the
earth's surface. The main phase decrease is very asymmetric during an early
epoch of the development of the main phase and larger in the late evening
sector (Akasofu and Chapman, 1964), indicating that the ring current
particles are injected in the midnight sector and drift westward (Fok et al.,
2006; Fig. 11c). The O
Although the heliosphere has become an important topic in recent years, there is so far no adequate model of the heliosphere. Most of the suggested models of the heliosphere in the past are a sort of extension of magnetospheric models based on the magnetic field line approach (cf. Balogh and Izmodenev, 2005; Longcope, 2009) and are not adequate. Thus, a little more realistic model is considered here, which is a simple model based on the principle of the unipolar induction.
The main heliospheric current consists of the meridional current and the circular current in the heliospheric current sheet (HCS).
The basic principle of modeling for the sunspot minimum period is given by
Alfvén (1950). The main point of modeling is to consider the unipolar
induction to drive electric currents in the heliosphere (Alfvén, 1950,
Sect. 1.3; Alfvén, 1977, 279–278; 1981, chap. III). Assuming a spherical
heliosphere of radius 20
There must be spiral current lines perpendicular to Parker's spiral magnetic
field lines, which consist of the radial current (mentioned before) and the
circular current on the HCS during the sunspot minimum period. The solar wind
effect of the stretching of the field lines is represented by this circular
current around the sun on the HCS, which also reverses the direction in each
solar cycle. Alfvén (1981) estimated the intensity of the polar current
from one hemisphere to be
Two models of the heliosphere (the northern hemisphere).
In the confined case, a field line from the polar angle
If the heliospheric magnetic field is not confined, high-latitude field lines
of the heliosphere are expected to be connected with magnetic field lines of
galactic magnetic field lines. Figure 12 shows an example of a high-latitude field line (
Obviously, the radius of the spherical heliosphere should be about 100 au, instead of 20 au. The motion of the solar system in the interstellar plasma can be simulated by the image dipole method (Chapman and Ferraro, 1931). In spite of this being a very primitive and crude model, it is hoped that it will be useful in studying more Ulysses observations, as well as future observations.
Most of our observed phenomena are various manifestations of electromagnetic energy dissipation, so that it is natural to study them as a chain of processes, which consists of power supply (dynamo), transmission (circuits/currents) and dissipation (flares, substorms).
In this paper, an attempt is made to study the whole solar–terrestrial relationship in terms of electric currents. The electric current line approach enables us also to study not only the flow of power/energy (the basic physical quantities) from their production to the end (dissipation) in each phenomenon (solar flares, CMEs, and auroral substorms/geomagnetic storms) but also to provide the link between them in terms of their initial condition. Further, some of the crucial quantities (such as the energy consumed by a single substorm) can be obtained so far only by studying electric currents.
Electromagnetic phenomena can be studied by considering either the magnetic
field line approach or the electric current line approach because of the
relationship given by curl
The 1978 magnetograms are individually collected from the observatories listed in the paper by Kamide et al. (1982).
The authors declare that they have no conflict of interest.
The author would like acknowledge the late Sydney Chapman and the late Hannes Alfvén for their guidance in his early days. He would like to thank also Lou-Chuan Lee and Guangson Choe for their discussion on solar flares. The topical editor, Georgios Balasis, thanks two anonymous referees for help in evaluating this paper.