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The electric current approach in the solar–terrestrial relationship


Abstract and Figures

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 (V[B²∕8π]) from the sun across the magnetopause. This consideration gives some insight into all the processes involved equally well compared with the magnetic field line approach, which has been adopted almost exclusively in the past.
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Ann. Geophys., 35, 965–978, 2017
© Author(s) 2017. This work is distributed under
the Creative Commons Attribution 3.0 License.
The electric current approach in the solar–terrestrial relationship
Syun-Ichi Akasofu
International Arctic Research Center, University of Alaska Fairbanks, Fairbanks, AK 99775, USA
Correspondence to: Syun-Ichi Akasofu (
Received: 27 March 2017 – Revised: 12 April 2017 – Accepted: 3 May 2017 – Published: 21 August 2017
Abstract. The sequence of phenomena consisting of solar
flares, coronal mass ejections (CMEs), auroral substorms,
and geomagnetic storms is mostly a manifestation of elec-
tromagnetic energy dissipation. Thus, first of all, it is nat-
ural to consider each of them in terms of a sequence of
power supply (dynamo), power transmission (electric cur-
rents/circuits), and dissipation (mostly observed phenom-
ena), i.e., as an input–output process and the electric cur-
rent line approach. Secondly, extending this concept, it is at-
tempted in this paper to consider the whole solar–terrestrial
relationship in terms of electric currents. This approach en-
ables 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 (V[B2/8π]) from the sun across the mag-
netopause. This consideration gives some insight into all the
processes involved equally well compared with the magnetic
field line approach, which has been adopted almost exclu-
sively in the past.
Keywords. Ionosphere (electric fields and currents)
1 Introduction
In as early as 1967, Alfvén (1967) noted the following: “In
some application we can illustrate essential properties of the
electromagnetic state of space either by depicting the mag-
netic field lines or by depicting the electric current lines. Al-
most always the first picture is used exclusively. It is im-
portant to note that in many cases the physical basis of the
phenomena is better understood if the discussion is centered
on the picture of the current lines”. Alfvén (1977) also em-
phasized the following: “Hence in order to understand the
properties of a current-carrying plasma, we must take ac-
count of the properties of the whole circuit in which the cur-
rent flows”. His point is that it is necessary to consider the
whole sequence (dynamo, transmission, and dissipation) as
an input–output process.
Indeed, the current line approach can follow quantitatively
the flow of the power/energy (physical quantities) as a con-
tinuous process through the whole sun–earth system and
thus can link the resulting phenomena. For this reason, it is
worthwhile to consider the sequence of solar flares, coronal
mass ejections, auroral substorms, and geomagnetic storms
in terms of the electric current approach.
2 Power supply
In all the phenomena we consider in this paper, the first im-
portant subject is the power supply produced by plasma flows
in a magnetic field.
The dynamo power Pis given by the Poynting flux:
P=ZE×B·dS=V (B2/8π )S, (1)
where Vand Bdenote the speed of plasma flows and the
magnetic field intensity in the photosphere; Sis the cross
section which depends on the phenomena we deal with (cf.
Akasofu, 1977, chap. 1, Sect. 1.4). The attempt in this paper
is to follow the flow of the dynamo power/energy V (B2/8π)
from solar flares/coronal mass ejections (CMEs) to auroral
substorms/geomagnetic storms on the basis of the current
line approach.
3 Solar flares
In terms of the current line approach, solar flare processes
can be described by the following terms: photospheric dy-
namo, the magnetic arcade current system (the H α emis-
sion), and the loop (prominence) current system (explosive
prominences and CMEs).
Published by Copernicus Publications on behalf of the European Geosciences Union.
966 S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship
This approach may be contrasted with the present mag-
netic field line approach, which involves the following: mag-
netic reconnection (converting magnetic energy) and CMEs
and downward plasma flows (causing flare phenomena, like
the H α emission).
In considering solar flares in terms of the current line ap-
proach, it is important to recognize that there are two cir-
cuits: the magnetic arcade circuit and the loop (prominence)
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 H α
(two-ribbon) emission along the feet of the arcade. In this
case, the dynamo power is dissipated directly at the feet of
the magnetic arcade, so that the magnetic energy conversion
is not needed.
The second one is a loop current system along a filament
(prominence) above and along the arcade, in which the mag-
netic energy is accumulated and then released when the loop
current is reduced (Fig. 3). This current is crucial in gen-
erating and launching CMEs and eventually causing sub-
3.1 Need for photospheric dynamo as the power supply
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), Mil-
ligan 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 Ma-
gara (2011).
Most recent studies of solar flares are based on magnetic
reconnection at the outset as the conversion process of mag-
netic 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 theo-
retical and observational studies on magnetic reconnection,
there has been a puzzling omission of estimating accurately
the magnetic field intensity and the amount of available mag-
netic 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 B=500 G without mentioning the location, and Shibata
and Magara (2011), who mentioned B=1000 G “in a typical
sunspot”. Thus, the first question in this approach is where
magnetic reconnection is supposed to occur and whether or
not there is enough energy there.
Figure 1. (a) Magnetic reconnection model in the corona above a
magnetic arcade (Hirayama, 1974). (b) Two approaching sunspot
pairs, forming an antiparallel magnetic field configuration (Sweet,
1958); a red arrow is added to show the motion of a sunspot pair.
One of the generally accepted models assumes magnetic
reconnection above the magnetic arcade (Fig. 1a). Unfortu-
nately, there have so far been neither measurements (not pos-
sible at present) of the magnetic field intensity in the corona
nor estimates of it; most coronal magnetic field models as-
sume the current-free condition, so that there is no expend-
able 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 2.5×104km
(corresponding to the diameter of the earth). Assuming field
intensity of as large as 100 G on both sides of two unipo-
lar regions (corresponding to Bin the polar region of the
earth), the field intensity at the top of the arcade (correspond-
ing to the earth’s equator) will be about 100G/2=50 G. As-
chwanden (2004, p. 601) suggested that magnetic reconnec-
tion occurs above 4.4×104km. Assuming the height to be
5×104km, it is twice the height of the arcade, where an es-
timated Bwill be 50 G/23=6.25 G at that distance. Since
the magnetic field there is not current free, let us assume Bis
10 G there; thus, the corresponding minimum volume needed
for the weakest flares (1030 ergs/[B2/8π]) is a sphere of ra-
dius about 6 ×104km, which seems to be too large even for
the weakest flares, compared with the height of the arcade.
Thus, it is likely that there is not enough magnetic energy for
flares at the height of 5 ×104km.
Ann. Geophys., 35, 965–978, 2017
S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship 967
Figure 2. (a) The magnetic arcade with an antiparallel plasma flow in the photosphere. (b) The current distribution in the magnetic arcade
(Choe and Lee, 1996a, b). (c) Spotless two-ribbon flare (courtesy of H. Zirin, 1985).
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 maintain-
ing flare activities.
Actually, the need for a dynamo in producing an antiparal-
lel configuration was already implicitly mentioned in the ear-
liest study of magnetic reconnection for flares. Sweet (1958)
proposed that two approaching (or colliding) sunspot pairs
produce an antiparallel magnetic configuration, allowing for
magnetic reconnection to release the magnetic energy for
flares (Fig. 1b). It is important to recognize that his hypo-
thetical motion of sunspot pairs implicitly expresses the need
for a photospheric-dynamo process, producing an antiparal-
lel magnetic configuration and maintaining the power/energy
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 P,V,B,S, and the dissipation
rate δ. Here, we use the minimum total energy W=1030 ergs
of solar flares, so that the minimum power Pneeded is esti-
mated to be about 2.8 ×026 erg s1(=1030 erg h1), assum-
ing that flares typically last for 1 h. Large H α flares are asso-
ciated with a dissipation rate of about 1026 erg s1(Svestka,
1976, p. 13). Let us first consider that a sunspot pair with
an area of rectangular size L=5×104km approaches an-
other sunspot pair of intensity B=100 G, with a speed Vof
1 km s1; for simplicity, Vis assumed to be perpendicular to
These numbers are quite common and reasonable in the
vicinity of sunspot groups and can provide power P=2.0×
1026 erg s1(the minimum power needed for solar flares),
assuming dynamo depth of 500 km. There have been sev-
eral measurements of plasma flows beneath active sunspot
areas (0.1–18 Mm; Mm =103km) by Kosovichev and Du-
vall Jr. (2010); although there have been no such observa-
tions specifically associated with solar flares, the speed of
plasma is observed to be up to 50 m s1–1 km s1under ac-
tive sunspots.
The purpose of the above estimates is simply to demon-
strate 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 an-
tiparallel magnetic configuration for magnetic reconnection
and to maintain the power supply.
3.2 The photospheric dynamo and its circuits
3.2.1 The dynamo under a magnetic arcade
and its circuit
Choe and Lee (1996a, b) developed a photospheric-dynamo
model of solar flares, including active prominences. Its ba-
sis is a magnetic arcade which is formed along the bound-
ary (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 re-
connection 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 an-
tiparallel 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 an-
tiparallel plasma flow (V=2 km s1) along the centerline of
the arcade, which is the boundary of two unipolar regions of Ann. Geophys., 35, 965–978, 2017
968 S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship
opposite polarity, and the magnetic field intensity B=12 G
(=6 G +6 G). These values are well within the observational
constraints along the neutral line between two unipolar mag-
netic regions.
Choe and Lee’s (1996a, b) computer simulation is ex-
tended here. An additional calculation shows that the field-
aligned currents flow along the arcade magnetic field lines
generated by this dynamo process. Thus, the arcade magnetic
field lines are the circuit which transmits the dynamo power
to the chromosphere. The current flows along the feet of the
magnetic arcade for a two-ribbon flare (one of the main dis-
sipations). There is no need for magnetic reconnection.
3.2.2 Dissipation
The intensity of the field-aligned current is about
104A m2, corresponding to an electron flux of
1014 m2s1. The results are shown in Fig. 2b. For
the area of typical two ribbons of H α emission
(2 ×2×105km ×2.5×104km), the total current and
the energy carried by the electrons are, respectively, about
1012 A and 1025 erg s1(as demonstrated by auroral elec-
trons, the current-carrying electrons are accelerated to
1000 keV along the magnetic field lines of the arcade, in
order to penetrate into the chromosphere). As mentioned
earlier, large flares are associated with an energy
of about 1026 erg s1(Svestka, 1976, p. 13). Thus, the
photospheric-dynamo model by Choe and Lee (1996a, b)
can provide the current/circuit and the power dissipation
(the two-ribbon H α emission) for the simplest and weakest
flares, that is at least for spotless flares (Fig. 2c). It is
expected that the intensity of the H α emission follows
closely the power of the photospheric dynamo as a function
of time (the so-called “explosive” nature of flaring is due in
part to a speeded-up time-lapse video).
Therefore, the study by Choe and Lee (1996a, b) sug-
gests that the photospheric dynamo alone can directly pro-
duce the two-ribbon H α emission at the feet of the magnetic
arcade, one of the major dissipation processes, and thus that
the power is carried by the current along the arcade mag-
netic field lines to the chromosphere. In this model (spotless
flare), neither sunspots nor magnetic reconnection is involved
in producing the H α emission (one of the major dissipation
processes). In this case, P (t ) =δ(t ).
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 Vand Bare large within an active sunspot group, so
that the power is also expected to be greater. In the case of
Choe and Lee’s (1996a, b) model, Bis 12G, but it is ex-
pected to be much larger, say 100G or more, along the neu-
tral line (along which two-ribbon flares tend to occur) in an
active sunspot group, so that the power is expected to become
1032 ergs or more. Therefore, their dynamo model discussed
above should also be applicable to much more intense flares.
3.3 Loop current
3.3.1 Circuit
One of the most interesting features of flare phenomena
is active prominences, which require processes other than
the H α emission. Active prominences are often observed
as dark filaments along the top of the magnetic arcade
and expand/explode during flares (Fig. 3a). Electric cur-
rents flow in a filament (prominence) structure (Bothmer and
Schwenn, 1994), forming a current loop (Fig. 3b). Choe and
Lee (1996a, b) also showed the formation of such a current
above and along the magnetic arcade.
3.3.2 Dissipation
A sudden reduction in the loop current is expected to release
its magnetic energy (Alfvén and Carlqvist, 1967). Let us as-
sume that the magnetic energy is accumulated when the loop
current is building up.
The magnetic energy Win a loop current is given by
W=(1/2)J 2L,
where Ldenotes the inductance in the loop circuit. Chen and
Krall (2003) estimated the intensity of their loop current to be
1011 A in their theory of CMEs. For medium-intensity flares
(W=1032 ergs), Lis estimated to be 2000 H.
The conversion of magnetic energy Winto the energy of
prominence eruption can be considered to be a process of
a rapid current reduction and the resulting release of en-
ergy. The reduction process is likely to be a current insta-
bility rather than magnetic reconnection. Indeed, instabilities
of filaments during flares have been observed by Moore et
al. (2001), Rust and LaBonte (2005), and many others. It is
interesting to note that an expanding loop appears to have un-
twisting motions, suggesting a sudden reduction in the loop
current (Kurokawa et al., 1987).
3.3.3 Launching coronal mass ejection
The released magnetic energy is expected to cause CMEs.
Chen and Krall (2003) showed that the Lorentz force (J×B)
is responsible for ejecting CMEs (overcoming the solar grav-
ity) rather than that they are the results of a thermal expansion
(pressure gradient) or magnetic reconnection; thus, the loop
current in prominences is vital in launching CMEs from the
point of view of the current line approach. As shown in the
next section, it is difficult to explain a helical magnetic struc-
ture of CMEs without considering such an expanding current
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 launch-
ing CMEs, when CMEs have a helical magnetic structure
(Sect. 3), which is crucial in predicting the intensity of auro-
ral substorms/geomagnetic storms. Thus, when CMEs have a
Ann. Geophys., 35, 965–978, 2017
S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship 969
Figure 3. (a) An example of expanding prominences (courtesy of W. O. Roberts, 1970). (b) A current loop for a prominence (Alfvén and
Carlqvist, 1967).
Figure 4. (a) The propagation of the shock wave associated with the 14–15 May 1997 geomagnetic storm (Fry et al., 2001); the location of
the earth is indicated by a dot. (b) The reconstructed of the helical magnetic structure (Saito et al., 2007). (c) Comparison of results between
the observation and the reconstructed helical structure (Saito et al., 2007; Akasofu, 2017).
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.
4 CMEs: current loop
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 current loops. However, ma-
gentohydrodynamics (MHD) simulations of CMEs have so
far not clearly showed the observed helical magnetic config-
uration (cf. Odstrci et al., 2004; Wu et al., 2007; Lugaz et al.,
Thus, by assuming currents of 109A along the loop, an
attempt was made to reconstruct the helical magnetic struc- Ann. Geophys., 35, 965–978, 2017
970 S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship
ture (Saito et al., 2007). An example is shown in Fig. 4 (14–
15 May 1997). This reconstruction is made after the event.
Nevertheless, the fact that we can reconstruct crudely some
features of the magnetic structure of CMEs, as well as the
number density and the speed, by assuming a loop current
with the Hakamada–Akasofu–Fry (HAF) model (Fry et al.,
2001), suggests that this approach may help in guiding MHD
simulation models. Indeed, Bothmer and Schwenn (1994)
showed that some prominences have a helical magnetic con-
It is suggested that both methods should work together, in-
stead of considering the MHD simulation approach alone. In
the previous section, we emphasized that the initial condi-
tion 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 struc-
ture 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 θof the inter-
planetary magnetic field (IMF) plays a crucial role in deter-
mining the dynamo process and the power generated by the
interaction between the solar wind and the magnetosphere
(Sect. 4.1); Vand Balone are insufficient. Even if Vand B
can be very large, there will be no power if θ=0. This is the
reason why intense flares at the center of the solar disk often
fail to cause major geomagnetic storms, Thus, it is essential
to predict the magnetic configuration for the intensity of geo-
magnetic storms and auroral substorms, not just the intensity
of flares and plasma flow speed.
5 Auroral substorms
In terms of the current line approach, magnetospheric pro-
cesses associated with auroral substorms can be described as
a combination of the following: the Chapman–Ferraro cur-
rent (see Sect. 5.1), the solar wind–magnetosphere dynamo,
the directly driven (DD) current system, the unloading com-
ponent (UL) current, and the ring current as a result of load-
ing/unloading of magnetic energy in the main body of the
This approach may be contrasted with the magnetic field
line approach, which involves the following: dayside recon-
nection, flux transfer, magnetic reconnection in the magne-
totail, and the resulting plasma flows and their consequences
(in producing the substorm current system and the ring cur-
5.1 Solar wind–magnetosphere dynamo
The solar wind–magnetosphere dynamo power has been em-
pirically expressed by Perrault and Akasofu (1978):
ε=V B2sin4 /2)l2,(2)
where Vand Bdenote the solar wind speed and the mag-
nitude of the IMF and θis the polar angle of the IMF;
l2is the dimensional factor, and lis taken to be 15RE
(earth’s radius). Rewriting the above equation in terms of
the Poynting flux V (B2/8π )sin4/2)l2,lbecome 5 RE,
where S=sin4/2)l2; for this theoretical derivation, see
Akasofu (1977, chap. 1.4).
There are two important implications in the above ex-
pression of the power. From the point of view of the en-
ergy flow from the sun, the above expression of the power
indicates that the magnetic energy (B2/8π) is carried out
by the solar wind with the speed Vinto the heliosphere
and that the magnetosphere has a sort of “cross section” or
“filter” [sin4/2)l2] to receive it. At the earth’s distance,
for B=5 nT and V=500 km, the magnetic energy flux is
5×103erg cm2s1, which may be compared with the par-
ticle flux 7.0×102erg cm2s1and the black-body radia-
tion flux of 3.4×105erg cm2s1.
The second implication is that the magnetic energy car-
ried 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 per-
pendicular to the magnetic field lines, so that a significant
amount of the power thus generated flows across the mag-
netopause 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
5.2 Currents/circuits
The substorm current has two components: the DD compo-
nent and the UL; Akasofu (2013). The DD component is di-
rectly driven by the solar wind–magnetosphere dynamo of
power ε, while the UL component is a result of the unload-
ing of the loaded magnetic energy during an early epoch (the
growth phase) in the main body of the magnetosphere (within
a distance of 10 RE). The current line approach succeeded in
identifying the current system UL which is directly respon-
sible for the expansion phase. Both current systems are illus-
trated in Fig. 5a and b. The DD component has been con-
structed by a large number of researchers, including Chap-
man (1935), Dungey (1961), and Axford and Hines (1961).
The UL component was proposed by Bostrom (1964).
Figure 6 shows how the DD and UL components vary dur-
ing substorms, together with ε. It can be seen that the DD
component tends to follow ε, while the UL component is in-
dependent of εand impulsive. It is the UL component which
is responsible for spectacular auroral displays during the ex-
pansion phase (particularly the poleward advance; Sect. 4.6).
In a sense, DD corresponds to the magnetic arch current and
UL to the loop current in solar flares.
Ann. Geophys., 35, 965–978, 2017
S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship 971
Figure 5. The DD current: (a) the solar wind–magnetosphere interaction; (b) a schematic illustration of the circuit; (c) the resulting con-
vection pattern of magnetospheric plasmas (Axford and Hines, 1961); (d) the expected convection pattern of ionospheric plasma, which
is basically the equipotential pattern (Akasofu, 2017); (e) SuperDARN result (Bristow and Jensen, 2007); (f) the realistic ionospheric DD
current (convection) derived from the magnetometer data (Akasofu, 2017). The UL current: (g) the UL component of the ionospheric current
(Akasofu, 2017); (h) Bostrom’s 3-D current system made up of azimuthal and meridional components (Akasofu, 2017).
5.3 Dissipation
5.3.1 Direct dissipation
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 mag-
netosphere can accumulate. The current line approach is so
far the only way to provide this crucial quantity observation-
ally. The Joule heat production is proportional to the inten-
sity of the current in the ionosphere because it is proportional
to J2=(J /σ )J , where σis the ionospheric conductiv-
ity (which is proportional to J). Figure 7 shows an example
of the distribution of dissipation in the ionosphere during a
substorm. By integrating the dissipation over the polar iono-
sphere, one can determine the global dissipation rate δ(t ),
which is about 3–5 ×1018 erg s1. Integrating δ(t) further
during a substorm, one can obtain the total dissipation dur- Ann. Geophys., 35, 965–978, 2017
972 S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship
Figure 6. Time variations in the power ε, the DD current, and the
UL current (Sun et al., 1998). Note that the DD tends to follow ε
but the UL is impulsive (Akasofu, 2013).
ing a substorm; it is on average 5 ×1022 ergs for medium-
intensity substorms.
5.3.2 Loading and unloading
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 REin a symmetric ring current (Aka-
sofu and Chapman, 1961; Akasofu et al., 1961). It can be
seen that the magnetic field is pushed out from the region
where the energy is accumulated. The accumulated magnetic
energy is 2.9 ×1021 ergs, and the βvalue (=nkT/[B2/8π])
becomes close to 1.0 at 6 REin this case. The current density
is 3 ×1018 A cm2at 6 RE.
Unloading and the magnetic energy conversion
There is uncertainty about the limiting amount of magnetic
energy that makes the magnetosphere unstable. Since βbe-
comes close to 1.0, the above amount of magnetic energy is
not far from the maximum amount of energy which can be
loaded or accumulated around 6 RE;β=1.0 may be a mea-
sure of such instabilities, because the magnetic field may not
be able to control the dynamics of the plasma well, and thus
the system will become unstable.
For these reasons, it is expected that the magnetosphere
tries to stabilize itself, resulting in the unloading of the accu-
mulated 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 compo-
nent. The development of individual substorms is very com-
Figure 7. 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) (Aka-
sofu, 2017).
plicated, because the input function ε(t ) is not the same, and
the dissipation depends on various conditions of the iono-
sphere and the magnetosphere, so that several possibilities
can be considered, depending on individual substorms (Zhou
and Tsurutani, 2002, their Fig. 5). However, the basic case is
very simple (Akasofu, 2015, his Fig. 9).
The magnetosphere is capable of accumulating more mag-
netic energy at closer distances (where B2/8πis higher) than
at 6 RE. It is suggested that the accumulated energy is located
between 10 and 4 RE, depending on the intensity of sub-
storms (AE =100 nT >2000nT). Indeed, the onset lati-
tude of the expansion phase can be as low as 48MLAT
(L=2.4) during major storms (although both the plasma
sheet and the ring current shift closer to the earth during ma-
jor storms, it is unlikely that the location of the accumulation
is as close as 2.4 RE). In this respect, it is interesting to know
that the ratio of (B2/8π) at 4 RE/10 REis about 20, corre-
sponding to the substorm intensity ratio of 2000 nT /100 nT.
The processes related to the power εand thus the DD current
process, namely an enhanced convection, may be responsible
for shifting the accumulation location.
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 RE(Ge and Russell, 2006), a
new process of conversion may be needed. In explaining the
expansion phase, the most important requirement is that the
converted magnetic energy must produce the UL current sys-
tem (Fig. 5h) and thus an earthward electric field; the avail-
Ann. Geophys., 35, 965–978, 2017
S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship 973
Figure 8. Changes in the earth’s magnetic configuration when magnetic energy is accumulated centered around 6 RE(red dot); (a) the earth’s
field change and (b) the distribution of the magnetic field produced by the model ring current. (c) The distortion (inflation) of the magnetic
field lines (Akasofu et al., 1961; Akasofu, 2017).
ability of energy is not enough. The current line approach
can provide such a crucial requirement, which is also needed
as the requirement for the magnetic field line approach; the
plasma flow from the magnetotail must produce an earthward
electric field.
Lui and Kamide (2003) and Akasofu (2013, 2015) sug-
gested 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 mag-
netosphere is inflated. Thus, the unloading (or releas-
ing) of the magnetic energy causes deflation. Because
of the deflation (Bz>0) in the inflated location, an
earthward electric field of 5 mV m1[=(∂Bz/∂ t ×
R∂y)= +50 nT/20 min ×20 RE] can be produced, which
can drive the UL current system. Depending on the values of
the parameters in the above, the electric field could be as high
as 50 mV m1. The UL current system is mainly responsible
for various expansion phase phenomena, including visible
auroras and the auroral electrojet in the ionosphere. This pro-
cess will continue as long as the magnetosphere is being de-
flated or until the accumulated energy is spent. The deflation
time is less than 1.5 h (5 ×1022 ergs /3–5 ×1018 erg s1),
which is similar to the period of the growth phase. Note that
this short life similar to the period of the growth phase is also
a requirement for the magnetic energy conversion; the dura-
tion of the expansion phase (which is similar to the duration
of the growth phase) is also a requirement in explaining the
expansion phase.
It may be noted that Lyons et al. (2001) reported that sub-
storms tend to occur after a northward turning of the IMF
after a southward turning. It is likely that the northward turn-
ing could trigger the onset. Freeman and Morley (2009) and
Newell and Liou (2011) emphasized that the initial south-
ward turning is crucial, not just the northward turning.
6 Geomagnetic storms
Auroral substorms have most of the basic features of geo-
magnetic storms in terms of electric currents. Geomagnetic
storms can be considered as a consequence of the accumu-
lated effects of the ring current formation by auroral sub-
storms. In fact, a substorms is a mini-storm. The period of
geomagnetic storms is the period when intense substorms oc-
cur very frequently (Akasofu and Chapman, 1963), accumu-
lating the ring current particles.
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 south-
ward (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 geomag-
netic storms. It shows an assembly of low-latitude magnetic
records (the Hcomponent); its average gives the Dst index.
Figure 10 also shows an assembly of magnetic records (the
Hcomponent) from high latitudes; the range between the up-
per and lower envelopes gives the auroral electrojet (AE) in-
dex. Except for the Chapman–Ferraro current, the main cur-
rents during geomagnetic storms are same as those of sub-
storm currents. Ann. Geophys., 35, 965–978, 2017
974 S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship
Figure 9. (a) A schematic representation of how the charge separa-
tion and the eastward electric field might occur during the deflation
(Akasofu, 2017). (b) An example of a series of all-sky photographs
(Fairbanks, 65gm lat), showing the initial brightening (shown by
a red allow) and the subsequent poleward expansion.
6.1 Chapman–Ferraro current and ssc
Chapman and Ferraro (1931) showed that an advancing so-
lar 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 (J×B) resulting from
it is responsible for the stoppage; this current is called the
Chapman–Ferraro current. Note that the magnetic field line
approach cannot determine the stopping distance of the solar
wind or the distance of the front side of the magnetopause.
Although the advancing plasma flow is now replaced by the
interplanetary shock wave, the basic process is the same. Fur-
ther, since the solar wind and magnetosphere are a perma-
nent feature of the earth, an enhancement of the plasma flow
increases the Chapman–Ferraro current, reducing the stop-
ping distance, and its effects propagate to the earth’s surface,
recorded as ssc.
6.2 The ring current and the main phase
The major difference between geomagnetic storms and au-
roral substorms is an anomalous development of the ring
current, which is produced by a frequent occurrence (an en-
hanced accumulation effect) of intense substorms in about
6–12 h (Akasofu and Chapman, 1963). The intense devel-
opment of the ring current causes a large depression of the
horizontal component and is recognized as the main phase
Figure 10. An example of geomagnetic storms. In the upper part,
magnetic records (the Hcomponent) from low-latitude stations are
assembled; the Dst index is the average of the records. In the lower
part, magnetic records (the Hcomponent) from high latitudes are
assembled; the range between the upper and lower envelopes pro-
vides the AE index.
of geomagnetic storms. It was found that the main ion in the
ring current during intense geomagnetic storms is O+ions
which are ejected from the ionosphere during intense sub-
storms (Shelley et al., 1972; Daglis, 1977); Fig. 11a.
There has been a controversy about the relationship be-
tween substorms and storms (Sharma et al., 2003). How-
ever, as mentioned earlier, substorms are mini-storms from
the point of view of the current line approach, and thus geo-
magnetic storms are exceptional cases during which the ring
current grows anomalously large.
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 dur-
ing an early epoch of the development of the main phase
and larger in the late evening sector (Akasofu and Chap-
man, 1964), indicating that the ring current particles are in-
jected in the midnight sector and drift westward (Fok et al.,
2006; Fig. 11c). The O+ions in the ring current belt become
mostly neutral hydrogen atoms and can leave from the mag-
netosphere (the major dissipation).
7 Heliosphere
Although the heliosphere has become an important topic in
recent years, there is so far no adequate model of the helio-
sphere. 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 in-
Ann. Geophys., 35, 965–978, 2017
S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship 975
Figure 11. (a) A large asymmetric development of the main phase for two geomagnetic storms; the nightside is indicated by a dark shade
(Akasofu and Chapman, 1964). (b) The O+ion flux and the Dst index (Daglis, 1977) and the simulated distribution of O+ions (Fok et al.,
The main heliospheric current consists of the meridional
current and the circular current in the heliospheric current
sheet (HCS).
Unipolar induction and the circuit
The basic principle of modeling for the sunspot minimum pe-
riod 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 RE, Akasofu and Covey (1981) constructed a
model in which one component of the current flows from
both poles of the sun to both poles of the heliosphere. Af-
ter reaching both poles of the spherical heliosphere, the two
currents flow along the spherical surface and join at the equa-
tor of the heliopause and then flow radially toward the sun
(radial current); the current direction reverses in each solar
There must be spiral current lines perpendicular to
Parker’s spiral magnetic field lines, which consist of the ra-
dial 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 re-
verses the direction in each solar cycle. Alfvén (1981) esti-
mated the intensity of the polar current from one hemisphere
to be 1.5×109A on the basis of the observed spiral mag-
netic field. Figure 12 shows two cases; in the first one, the
magnetic field is confined in the heliosphere, and the second
one shows the connection with an intergalactic magnetic field
of intensity 0.22 nT.
In the confined case, a field line from the polar angle
θ=10, namely the latitude 80, is shown as an example in
both the meridional and equatorial projections in the northern
hemisphere. All the field lines from lower latitudes cross the
HCS after reaching the highest latitude and cross the HCS at
shorter distances from the sun (Fig. 12). Although our model Ann. Geophys., 35, 965–978, 2017
976 S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship
Figure 12. Two models of the heliosphere (the northern hemisphere). (a) A confined case. (b) An open case.
is very crude, the general aspect of the configuration of the
field lines is expected to be similar. Such a 3-D configuration
of magnetic field lines has not been shown in the past. This
model satisfies both div ·J=0 and div ·B=0.
If the heliospheric magnetic field is not confined, high-
latitude field lines of the heliosphere are expected to be con-
nected with magnetic field lines of galactic magnetic field
lines. Figure 12 shows an example of a high-latitude field line
(θ=30; lower-latitude field lines are similar to the confined
case). The model seems to reproduce the spiral structure con-
sidered by cosmic ray studies (cf. Fisk et al., 1999).
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 im-
age 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.
8 Concluding remarks
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 dissi-
pation (flares, substorms).
In this paper, an attempt is made to study the whole solar–
terrestrial relationship in terms of electric currents. The elec-
tric 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 quanti-
ties (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 consider-
ing either the magnetic field line approach or the electric
current line approach because of the relationship given by
curl B=J. Although the magnetic field line approach has
been almost exclusively considered in the past, it is worth-
while to take the current line approach to see if one can learn
more about the processes involved. Indeed, the current line
approach suggests a different way by which the power and
energy are converted for our phenomena. In either case, our
phenomena are quite complex and difficult. In climbing a
mountain, there are at least two routes.
Data availability. The 1978 magnetograms are individually col-
lected from the observatories listed in the paper by Kamide et
al. (1982).
Competing interests. The authors declare that they have no conflict
of interest.
Acknowledgements. 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
Ann. Geophys., 35, 965–978, 2017
S.-I. Akasofu: The electric current approach in the solar–terrestrial relationship 977
Guangson Choe for their discussion on solar flares.
The topical editor, Georgios Balasis, thanks two anonymous ref-
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Ann. Geophys., 35, 965–978, 2017
... This is partly because there has been no study to predict the power of flare-producing dynamo. Since solar flares must be powered by a photospheric dynamo [34], it is important to monitor the power or at least VB 2 and Hα emission together (where V is the plasma speed B is the magnetic field intensity where flares are expected to occur; note that the power equation is the same for auroral substorms and solar flares), enabling us to infer the accumulated energy for the explosive process-in predicting the intensity of flares (the minimum energy is about 10 30 ergs). So far, there has been no quantitative efforts (other than finding an anti-parallel magnetic field). ...
... This is the amount of power which is needed for the minimum energy of flares 10 30 erg which last for one hour. 3 Thus, an important task in predicting solar flares is to monitor the power P and resulting accumulated energy. If the power (P x the [the duration of magnetic shear before flare onset in an active region or where the precursors are present] reaches 10 30 erg, the occurrence of weak flares could occur. ...
The effects of ionospheric weather on RF and GNSS systems are summarized in terms of the resulting consequences for radio communications, systems supporting space-based navigation and positioning, and surveillance, together with a description of the monitoring facilities and mapping techniques available for prediction, nowcasting, forecasting, post-event analysis, along with final operational tools, products, and services.
The science underpinning the study of space weather is discussed, starting from dynamic processes on the Sun, in the interplanetary medium, and in the Earth’s magnetosphere, ionosphere, and atmosphere. The focus is on the dominant features of the plasma medium under normal and extreme solar-terrestrial conditions during the last few Solar Cycles.
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Auroral substorms are mostly manifestations of dissipative processes of electromagnetic energy. Thus, we consider a sequence of processes consisting of the power supply (dynamo), transmission (currents/circuits) and dissipations (auroral substorms-the end product), namely the electric current line approach. This work confirms quantitatively that after accumulating magnetic energy during the growth phase, the magnetosphere unloads the stored magnetic energy impulsively in order to stabilize itself. This work is based on our result that substorms are caused by two current systems, the directly driven (DD) current system and the unloading system (UL). The most crucial finding in this work is the identification of the UL (unloading) current system which is responsible for the expansion phase. A very tentative sequence of the processes leading to the expansion phase (the generation of the UL current system) is suggested for future discussions. The solar wind-magnetosphere dynamo enhances significantly the plasma sheet current when its power is increased above 1018erg/s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{18}~\mbox{erg}/\mbox{s}$\end{document} (1011\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{11}$\end{document} w). The magnetosphere accumulates magnetic energy during the growth phase, because the ionosphere cannot dissipate the increasing power because of a low conductivity. As a result, the magnetosphere is inflated, accumulating magnetic energy. When the power reaches 3–5×1018erg/s\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3\mbox{--}5\times 10^{18}~\mbox{erg}/\mbox{s}$\end{document} (3–5×1011\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3\mbox{--}5\times 10^{11}$\end{document} w) for about one hour and the stored magnetic energy reaches 3–5×1022\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$3\mbox{--}5\times10^{22}$\end{document} ergs (1015\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$10^{15}$\end{document} J), the magnetosphere begins to develop perturbations caused by current instabilities (the current density ≈3×10−12A/cm2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\approx}3\times 10^{-12}~\mbox{A}/\mbox{cm}^{2}$\end{document} and the total current ≈106A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${\approx}10^{6}~\mbox{A}$\end{document} at 6 Re). As a result, the plasma sheet current is reduced. The magnetosphere is thus deflated. The current reduction causes ∂B/∂t>0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\partial B/\partial t > 0$\end{document} in the main body of the magnetosphere, producing an earthward electric field. As it is transmitted to the ionosphere, it becomes equatorward-directed electric field which drives both Pedersen and Hall currents and thus generates the UL current system. A significant part of the magnetic energy is accumulated in the main body of the magnetosphere (the inner plasma sheet) between 4 Re and 10 Re, because the power (Poynting flux [E×B])\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[ \boldsymbol{E} \times \boldsymbol{B} ])$\end{document} is mainly directed toward this region which can hold the substorm energy. The substorm intensity depends on the location of the energy accumulation (between 4 Re and 10 Re), the closer the location to the earth, the more intense substorms becomes, because the capacity of holding the energy is higher at closer distances. The convective flow toward the earth brings both the ring current and the plasma sheet current closer when the dynamo power becomes higher. This proposed sequence is not necessarily new. Individual processes involved have been considered by many, but the electric current approach can bring them together systematically and provide some new quantitative insights.
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During the last 50 years, we have made much progress in studying auroral substorms (consisting of the growth phase, the expansion phase, and the recovery phase). In particular, we have quantitatively learned about auroral substorms in terms of the global energy input–output relationship. (i) What powers auroral substorms? (ii) Why is there a long delay (1 h) of auroral activities after the magnetosphere is powered (growth phase)? (iii) How much energy is accumulated and unloaded during substorms? (iv) Why is the lifetime of the expansion phase so short (1h)? (v) How is the total energy input–output relationship? (vi) Where is the magnetic energy accumulated during the growth phase? On the basis of the results obtained in (i)–(vi), we have reached the following crucial question: (vii) how can the unloaded energy produce a secondary dynamo, which powers the expansion phase? Or more specifically, how can the accumulated magnetic energy get unloaded such that it generates the earthward electric fields needed to produce the expansion phase of auroral substorms? It is this dynamo and the resulting current circuit that drive a variety of explosive auroral displays as electrical discharge phenomena during the expansion phase, including the poleward advance of auroral arcs and the electrojet. This chain of processes is summarized in Section 4.2. This is the full version of work published by Akasofu (2015). A tentative answer to this crucial question is attempted. Phase occurs impulsively seems to be that the magnetosphere within a distance of 10 Re becomes inflated and unstable (β ∼ 1.0), when the accumulated energy W during the growth phase (at the rate of about ε = 5 × 10 18 erg/s in about 1.5 h) reaches 2 × 10 22 —or at most 10 23 —ergs. Thus, the magnetosphere unloads and dissipates the energy in order to stabilize itself by deflating at the rate of about 5 × 10 18 erg/s (mainly as the Joule heat in the ionosphere), resulting in an impulsive (1 h, 2 × 10 22 ergs ÷ 3.5 × 10 18 erg/s) expansion phase. The deflating process results in a dynamo in a thin magnetic shell near the earthward end of the current sheet by separating electrons from protons and produces an earthward electric field of more than ∼10 mV/m. The separated electrons are discharged along the circuit of the expansion phase, constituting an electrical discharge currents of 5 × 10 6 A and causing brightening an arc, the first indication of the onset of the expansion phase.
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How much electromagnetic energy crosses the photosphere in evolving solar active regions (ARs)? With the advent of high-cadence vector magnetic field observations, addressing this fundamental question has become tractable. In this paper, we apply the “PTD-Doppler-FLCT-Ideal” (PDFI) electric field inversion technique of Kazachenko et al. to a 6-day vector magnetogram and Doppler velocity sequence from the Helioseismic and Magnetic Imager on board the Solar Dynamics Observatory to find the electric field and Poynting flux evolution in NOAA 11158, which produced an X2.2 flare early on 2011 February 15. We find photospheric electric fields ranging up to 2 V cm‑1. The Poynting fluxes range from [‑0.6 to 2.3] × {10}10 {erg} cm‑2 s‑1, mostly positive, with the largest contribution to the energy budget in the range of [{10}9-{10}10] erg cm‑2 s‑1. Integrating the instantaneous energy flux over space and time, we find that the total magnetic energy accumulated above the photosphere from the initial emergence to the moment before the X2.2 flare to be E=10.6× {10}32 {erg}, which is partitioned as 2.0×1032erg and 8.6× {10}32 {erg}, respectively, between free and potential energies. Those estimates are consistent with estimates from preflare nonlinear force-free field extrapolations and the Minimum Current Corona estimates, in spite of our very different approach. This study of photospheric electric fields demonstrates the potential of the PDFI approach for estimating Poynting fluxes and opens the door to more quantitative studies of the solar photosphere and more realistic data-driven simulations of coronal magnetic field evolution.
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We calculated the time evolution of the free magnetic energy during the 2014-Mar-29 flare (SOL2014-03-29T17:48), the first X-class flare detected by IRIS. The free energy was calculated from the difference between the nonpotential field, constrained by the geometry of observed loop structures, and the potential field. We use AIA/SDO and IRIS images to delineate the geometry of coronal loops in EUV wavelengths, as well as to trace magnetic field directions in UV wavelengths in the chromosphere and transition region. We find an identical evolution of the free energy for both the coronal and chromospheric tracers, as well as agreement between AIA and IRIS results, with a peak free energy of $E_{free}(t_{peak}) \approx (45 \pm 2) \times 10^{30}$ erg, which decreases by an amount of $\Delta E_{free} \approx (29 \pm 3) \times 10^{30}$ erg during the flare decay phase. The consistency of free energies measured from different EUV and UV wavelengths for the first time here, demonstrates that vertical electric currents (manifested in form of helically twisted loops) can be detected and measured from both chromospheric and coronal tracers.
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We present the second part of a project on the global energetics of solar flares and CMEs that includes about 400 M- and X-class flares observed with AIA/SDO during the first 3.5 years of its mission. In this Paper II we compute the differential emission measure (DEM) distribution functions and associated multi-thermal energies, using a spatially-synthesized Gaussian DEM forward-fitting method. The multi-thermal DEM function yields a significantly higher (by an average factor of ~14), but more comprehensive (multi-)thermal energy than an isothermal energy estimate from the same AIA data. We find a statistical energy ratio of $E_{th}/E_{diss} ≈ 2%-40%$ between the multi-thermal energy $E_{th}$ and the magnetically dissipated energy $E_{diss}$, which is an order of magnitude higher than the estimates of Emslie et al. 2012. For the analyzed set of M and X-class flares we find the following physical parameter ranges: $L=10^{8.2}-10^{9.7}$ cm for the length scale of the flare areas, $T_p=10^{5.7}-10^{7.4}$ K for the DEM peak temperature, $T_w=10^{6.8}-10^{7.6}$ K for the emission measure-weighted temperature, $n_p=10^{10.3}-10^{11.8}$ cm$^{-3}$ for the average electron density, $EM_p=10^{47.3}-10^{50.3}$ cm$^{-3}$ for the DEM peak emission measure, and $E_{th}=10^{26.8}-10^{32.0}$ erg for the multi-thermal energies. The deduced multi-thermal energies are consistent with the RTV scaling law $E_{th,RTV} = 7.3 × 10^{-10} \ T_p^3 L_p^2$, which predicts extremal values of $E_{th,max} ≈ 1.5 × 10^{33}$ erg for the largest flare and $E_{th,min} ≈ 1 × 10^{24}$ erg for the smallest coronal nanoflare. The size distributions of the spatial parameters exhibit powerlaw tails that are consistent with the predictions of the fractal-diffusive self-organized criticality model combined with the RTV scaling law.
One of the most idiosyncratic aspects of space physics is the central role assigned to magnetic field lines. Particularly in studies of the Sun, the heliosphere, and the magnetosphere, magnetic field lines are treated as fully fledged physical objects with their own dynamics. The electrical current, when needed, is derived from the magnetic field lines. These practices appear to be at odds with the basic approach, followed in elementary electrodynamics, of deriving the magnetic field from a current distribution and treating magnetic field lines as at best fictitious curiosities. However, physical laws such Ampère's law (excluding the displacement current), do not attribute a causative nature to either side of the equality; they simply state the equality of two quantities. So either approach to satisfying Eq. (4.1), beginning with either j or B, must be valid. This curious approach is adopted in space physics because magnetic fields are found in highly conductive plasmas. Denoting by E and B the electric andmagnetic fields in the stationary (laboratory) frame, a fluid element traveling at velocity v will experience a local electric field E′ = E + v × B. If the fluid is a sufficiently good conductor, evolving sufficiently slowly, then E′ will be extremely small. For example, Ohm's law in a conductor of conductivity σ is E′ = j/σ, so E′ will be small when σ is large compared with something else with the same units. The so-called magnetic Reynold's number, Rm = υLσμ0, serves as a dimensionless version of the conductivity.
The most violent space weather events (eruptive solar flares and coronal mass ejections) are driven by the release of free magnetic energy stored in the solar corona. Energy can build up on timescales of hours to days, and then may be suddenly released in the form of a magnetic eruption, which then propagates through interplanetary space, possibly impacting the Earth's space environment. Can we use the observed evolution of the magnetic and velocity fields in the solar photosphere to model the evolution of the overlying solar coronal field, including the storage and release of magnetic energy in such eruptions? The objective of CGEM, the Coronal Global Evolutionary Model, funded by the NASA/NSF Space Weather Modeling program, is to develop and evaluate such a model for the evolution of the coronal magnetic field. The evolving coronal magnetic field can then be used as a starting point for magnetohydrodynamic (MHD) models of the corona, which can then be used to drive models of heliospheric evolution and predictions of magnetic field and plasma density conditions at 1AU.