Ebihara Progress in Earth and Planetary Science
https://doi.org/10.1186/s40645-019-0264-3(2019) 6:16

Progress in Earth andPlanetary Science

REVIEW

Open Access

Simulation study of near-Earth space
disturbances: 1. magnetic storms
Yusuke Ebihara

Abstract
A magnetic storm is the world-wide geomagnetic disturbance taking place in near-Earth space environment, lasting
for a few days. Geomagnetic fields can be depressed by ~ 1% on the ground for large magnetic storms. The primecause of the long-lasting, world-wide geomagnetic disturbance is the development of the ring current that surrounds
the Earth. The ring current is an electric current carried by charged particles. Thus, the growth and decay of the ring
current correspond to accumulation and loss of the ring current particles, respectively. The ring current is strong
enough to modulate near-Earth space environment, and leads to many observable effects. In this sense, the ring current
can be regarded as an important mediator in the near-Earth space environment. Here, the dynamics and structure of
the ring current and its active role are briefly reviewed on the basis of numerical simulation results.
Keywords: Magnetic storms, Computer simulation, Magnetosphere, Ionosphere, Inner magnetosphere, Ring current

Introduction
Magnetic storms are characterized by irregular disturbance of the geomagnetic field. A magnetic storm starts
with an initial phase, followed by a main phase and a recovery phase. The initial phase is characterized by a sharp
increase in the horizontal component (H-component) of
the geomagnetic field, but the initial phase is not always
involved in all the magnetic storms. The main phase ischaracterized by a substantial decrease in the geomagnetic
field, lasting for a few hours, or more (Gonzalez et al.
1994). Magnetic storms were first recognized by von
Humboldt (1808) who observed magnetic declination in
Berlin (Lakhina and Tsurutani 2016). Nowadays, the magnetic storms are known as world-wide magnetic disturbance. In 1917, Schmidt postulated the existence of a ring
current encircling the Earth to cause the decrease in the
H-component of the magnetic field (Egeland and Burke
2012). Satellite observations confirmed the existence ofthe ring current (Frank 1967; Smith and Hoffman 1973;
Lui et al. 1987; Le et al. 2004). In the recovery phase, theH-component of the geomagnetic field returns to thepre-storm level, which is primarily caused by the decay of
the ring current.

Correspondence: ebihara@rish.kyoto-u.ac.jp
Research Institute for Sustainable Humanosphere, Kyoto University, Gokasho,Uji, Kyoto 611-0011, JapanThe term “ring current” gives the impression that the ring
current is completely symmetric about the dipole axis of
the Earth. However, according to ground-based observations, the negative disturbance of the magnetic fielddepends on a magnetic local time (MLT), suggesting asymmetric ring current (Akasofu and Chapman 1964). This isconfirmed by satellite observations (Le et al. 2004). To provide a unified measure of the strength of the magnetic disturbance, a Dst index (disturbance storm time index) isinvented (Sugiura 1964). The Dst index is basically aweighted average of ΔH−Hbase observed at four different
longitudes at low latitudes (Honolulu, San Juan, Hermanus,
and Kakioka), where Hbase is the baseline for quiet days
(Sugiura and Kamei 1991). The Dst index is reasonably predicted by an empirical formula, which is a function of thesolar wind speed, the solar wind density, and the southward
component of IMF Bz (Burton et al. 1975). The Burton etal.’s formula is derived based on an energy balance equation. To understand the growth and decay of the ring
current deeply, one has to take into consideration the particles that are the carrier of the ring current.
The major carrier of the storm-time ring current is
known to be ions with energy of tens of keV (Frank 1967;
Smith and Hoffman 1973). The AMPTEE/CCE satellite
measured substantial contribution from O+ to thestorm-time ring current (Hamilton et al. 1988). This is a

© The Author(s). 2019 Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0
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Ebihara Progress in Earth and Planetary Science(2019) 6:16

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striking finding in the ring current research because it implies that the source of the ring current particles is not only
the Sun, but also the Earth. As for quiet time (non-stormtime), the ring current consists of ions with energy greaterthan 100 keV. This means that the ring current always
exists regardless of magnetic storms. Investigation of
the growth and decay of the ring current is equivalent
to investigating the accumulation and loss of the ionswith energy of the order of tens of keV in the innermagnetosphere.
The charged particles trapped by Earth’s magnetic
field undergo three different types of motion, gyromotion, bounce motion along a field line between two
mirror points, and drift motion perpendicular to themagnetic field. The current density is defined by theelectric current per unit area of cross section. Whenthe first adiabatic invariant is conserved, the current
density is given by summing up the currents associated with gyromotion, grad-B drift and curvature driftas (Parker 1957)
J¼

B
P∥ −P⊥
ðB  ∇ÞB;2  ½∇P ⊥ þ
B
B2

ð1Þ

where B, P⊥, and P|| are the magnetic field, perpendicular
plasma pressure, and parallel plasma pressure, respectively.
Observations show that the first term of the right-hand sideof Eq. (1) dominates the second one, although the second
one is non-negligible in the ring current (Lui et al. 1987).
The first term is called “diamagnetic current,” and is associated with gyromotion of the particles. The peak of the pressure takes place at L ~ 2–3 (Lui et al. 1987). Because of thedominance of the diamagnetic current, the ring current
flows westward in the outer region, and flows eastward in
the inner region. The distribution of the current density isinvestigated by Le et al. (2004) in detail.
The plasma pressure is given by
Z
1 2
P⊥ ¼
mv f ðvÞsin2 αdp;
2
Z
ð2Þ
2
2
P ∥ ¼ mv f ðvÞcos αdp;
where m, v, f, α, and p are mass, velocity, phase spacedensity, pitch angle, and momentum vector, respectively.
For gyrotropic plasma, dp = 2πm3v2 sin αdαdv. The
phase space density f is related to the directional differential flux j as f = j/p2. According to Liouville’s theorem,
the phase space density must be conserved when source
and loss of particles are absent.
Equations (1) and (2) imply that understanding thering current is equivalent to understand the phase spacedensity of the charged particles. Because motion of
charge particles depend on kinetic energy and pitch
angle as well as local magnetic and electric fields, it isessential to track motion of charged particles properly
for the purpose of understanding the ring current andthe magnetic storms.

Storm main phase (development of ring current)
The ring current is known to develop when the interplanetary magnetic field (IMF) is southward (Kokubun 1972).
Coronal mass ejection (CME) and a corotating interaction
region (CIR) are thought to deliver prolonged southward
IMF (Tsurutani et al. 1988). A magnetic cloud is embedded in the ejecta of CME. In front of the magnetic cloud,the solar wind is compressed. This compressed region iscalled a sheath, and strong southward IMF can be formed.
When the strong southward IMF is embedded in either
the sheath or the magnetic cloud, a magnetic storm occurs. The magnetic storm would develop in a two-stepmanner when the strong southward IMF is embedded inboth the sheath and the magnetic cloud (Kamide et al.
1998). The CIR is accompanied with high speed solar
wind streams originating from a coronal hole on the surface of the Sun. In the CIR, IMF is highly fluctuated (Tsurutani and Gonzalez 1987). The southward component of
the fluctuated IMF can cause a magnetic storm. Statisticalstudies show that the CME-driven magnetic storms tend
to be larger than the CIR-driven magnetic storms in termsof the Dst index (Borovsky and Denton 2006; Denton etal. 2006).
The fundamental process for the development of thering current is the accumulation of particle energy in the
inner magnetosphere where the Earth’s dipolar magnetic
field dominates (Dessler and Parker 1959; Sckopke1966). There are two competing processes for the accumulation of the particle energy. One is that the particle
energy is accumulated by a succession of substorms(Akasofu 1968). Hot plasma is known to be injected into
the inner magnetosphere by short-lived impulsive electric field at the substorm expansion (DeForest and McIlwain 1971; Kamide and McIlwain 1974). If the substorm
injection occurs frequently with a sufficiently shortinterval, the particle energy would increase stepwisely.
The other process is that hot plasma is transported by
the persistent, large-scale convection electric field(Axford 1969). As the particles move into the innermagnetosphere, they adiabatically gain kinetic energy,
resulting in a substantial increase in the net particle energy. In both the processes, dawn-dusk electric field is
responsible for the earthward transport of the particles
stored in the plasma sheet on the nightside. A question
arises: What is the essential cause of the storm-time ring
current?
In 1940s–1950s, Hannes Alfvén divided motion of
charged particles into gyromotion and its guiding centermotion. Introducing a uniform electric field and the dipole magnetic field, he suggested drift paths of particles

Ebihara Progress in Earth and Planetary Science(2019) 6:16

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in the equatorial plane, and field-aligned current associated with the asymmetric paths of them (Egeland andBurke 2012). The invention of the guiding-center approximation helps reduce computational cost significantly. The state of charged particles is described by six
dimensional independent parameters, that is, three forreal space and three for momentum space. With theguiding-center approximation, the number of the dimension can be reduced to five because information about
gyro phase is lost. With the bounce-averaged approximation (Roederer 1970), the number of the dimension
can be reduced to four because information about gyrophase and bounce phase are lost. The bounce-averaged
approximation has been preferred to track motion of thecharged particles in the inner magnetosphere because
the gyro phase and the bounce phase do not matter inmany cases.
When there are no sink and source, the number of particles must be conserved in phase space. One of the practicalschemes to solve the evolution of the phase space density isbased on the Boltzmann equation (Fok et al. 1995; Jordanova et al. 1996; Kozyra et al. 1998b; Liemohn et al. 1999).
Another scheme is based on weighted particle tracing (Ebihara and Ejiri 1998; Chen et al. 1998; Ebihara and Ejiri
2000), which is similar to the ones that have employed to
calculate the evolution of the ring current in terms of energy (Lee et al. 1983; Wodnicka 1989; Takahashi et al.
1990). The Rice Convection Model solves the evolution of
the particle content in a flux tube (Toffoletto et al. 2003)
Simulation studies show that the fundamental evolution of the ring current ions can be achieved when
the dipole magnetic field, the convection electric field,
and the corotation electric field are taken into consideration. The strength of the convection electric field
is known to increase when the southward componentof the IMF is strong and the solar wind speed is high(Matsui et al. 2013). The total potential drop of theconvection electric field is ~ 20 kV for quiet time,and is ~ 200 kV and more during the magnetic
storms (Ebihara et al. 2005a; Hairston et al. 2005). In
the equatorial plane, the direction of the convection
electric field is duskward, corresponding to the sunward E × B drift. A simple form of the convection
electric field (Volland 1973; Stern 1975) has been
widely used to describe the transport of charged particles in the inner magnetosphere, which is given byΦcv ¼ A r γ
a

sinϕ;

ð3Þ

where A is the intensity of the convection electric
potential, a is the Earth’s radius, γ is a shielding factor,and ϕ is MLT. The convection electric field is uniform
when γ = 1. The moderately shielded condition, in

which γ = 2, is often used by simulations. Ejiri (1981)
suggested that γ depends on the Kp index as γ = 7.3/Kp.
The corotation electric field arises from the Earth’s
rotation with partially ionized atmosphere. The electric
potential of the corotation electric field is given byZ r
E  dr;ð4Þ
Φcr ðr Þ ¼ −∞where
E ¼ −ðΩ  rÞ  B;

ð5Þand Ω is the angular frequency of Earth’s rotation. In theequatorial plane, Eq. (4) yields
Z r
ΩrBdr:
ð6ÞΦco ¼∞

Assuming the dipole magnetic field,a3
B ¼ B0 3 ;rð7Þ

where B0 is the magnetic field at the equator. Substituting Eq. (7) into Eq. (6), we haveZ r
ΩB0 a3
dr
Φco ¼
r2
∞
ð8Þ
ΩB0 a3:¼−
r
Equation (8) implies that the Earth is negatively charged
from ambient in quasi-inertial frame of reference due toEarth’s rotation. According to the 12th generation of theInternational Geomagnetic Reference Field (Thébault et al.
2015), B0 is 30,829 nT in 1970, and 29,868 nT in 2015. The
total corotation potential drop is 91 kV in 1970, and 88 kV
in 2015. The decrease in the total potential drop resultsfrom the secular variation of the geomagnetic field.
When the first adiabatic invariant μ is conserved, thebounce-averaged trajectory of a non-relativistic particle
follows the equipotential as1qΦcn þ qΦco þ μB þ mv2∥ ¼ const;2

ð9Þ

where q is charge, m is mass, and v|| is parallel component of the velocity. The bounce-averaged drift velocity
for the grad-B and curvature drifts is provided by Roederer(1970). By summing up the E × B drift velocity and thebounce-averaged drift velocity for the grad-B and curvaturedrifts, one can trace the motion of charged particles in atime-dependent manner. A precise approximation for thebounce-averaged drift velocity in the dipole magnetic fieldis given by Ejiri (1978).
Figure 1 shows an example of calculated Dst (SYM-H)
values for a large magnetic storm (Ebihara et al. 2005a).
SYM-H is essentially equivalent to Dst. The calculationSYM*-H(nT)λPCB (deg)ΦPCP (kV)

Tps (keV)

Nps (cm-3 )Ebihara Progress in Earth and Planetary Science

5
4
3
2
1
0
14
12
10
8
6
4
2
300
250
200
150
100
50
0
75
70
65
60
0
-100

(2019) 6:16

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(1)

(2)

(3)

(4)

(5)

Constant Nps and Tps

-200
-300
-400

Variable Nps and Tps

Observation-500
0000 0600 1200 1800 0000 0600 1200 1800 0000
20 Nov
21 Nov
22 Nov
UT
Fig. 1 Simulated storm-time Dst (SYM-H) index during the magnetic storm of 20–21 November 2003. The input parameters (plasma sheet density Nps,
plasma sheet temperature Tps, strength of the convection electric field ΦPCP, magnetic latitude of the polar cap boundary at which ΦPCP is imposed)
used to drive the simulation are summarized in the top 4 panels. (Ebihara et al. 2005a)

Ebihara Progress in Earth and Planetary Science(2019) 6:16

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Fig. 2 Calculated ring current during the moderate storm of 10–12 April 1997. Perpendicular component of the plasma pressure (P⊥) and the azimuthalcomponent of the current density are provided. (Ebihara and Ejiri 2000)

was performed by the comprehensive ring current model(CRCM) (Fok et al. 2001). The electric potential, which
depends on the solar wind and IMF (Siscoe 2002), is imposed to the outer boundary of the simulation. The
plasma sheet density and temperature measured by geosynchronous satellites are imposed to the outer boundaryof the simulation. The calculated Dst (SYM-H) shows anegative excursion, and roughly follows the observed one.
When the plasma sheet density and temperature are held
constant through the simulation, the amplitude of thenegative excursion is much smaller than that observed.
This suggests that the intensification of the ring current iscaused by not only the enhancement of the convection
electric field but also the enhancement of the plasma sheet
density and/or temperature (Ebihara and Ejiri 1998; Kozyra
et al. 1998b; Ebihara and Ejiri 2000; Liemohn et al. 2001).
The plasma sheet density is known to increase when thesolar wind density is high (Terasawa et al. 1997; Ebihara

and Ejiri 2000). It is thought that the intensity of the ring
current is proportional to the plasma sheet density. However, because of the shielding effect described below, themagnitude of the ring current is no longer proportional tothe plasma sheet density (Ebihara et al. 2005b).
Figure 2 shows the calculated plasma pressure and theazimuthal component of the current density in the equatorial plane (Ebihara and Ejiri 2000). The dawn-dusk
convection electric field, the corotation electric field, andthe dipole magnetic are taken into consideration in thesimulation. The strength of the convection electric field ischanged in accordance with the solar wind parameters. As
the storm main phase proceeds (from A to B), the plasmapressure increases in the midnight-dusk sector, whereas it
decreases in the noon-dawn sector. Figure 3 shows drift
trajectories of the ions originating in the nightside plasma
sheet. When the strength of the convection electric field is
kept constant (left panel of Fig. 3), the drift paths areEbihara Progress in Earth and Planetary Science(2019) 6:16

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Fig. 3 Bounce-averaged drift trajectories of protons with magnetic moment of 0.030 keV/nT with initial equatorial pitch angle of 25° at L = 10 in
the presence of the convection electric field, the corotation electric field, and the dipole magnetic field. A filled circle is marked every 1 h along
the trajectory. (Ebihara et al. 2004)

symmetric about the dawn-dusk meridian. After departing
the nightside plasma sheet, they gradually penetrate into
the inner region. As they approach the Earth, they travel
duskward, and gain kinetic energy, resulting in the enhancement of the plasma pressure. After passing throughthe dusk meridian, they travel dawnward, and lose kinetic
energy. An interesting feature is that the plasma pressure
decreases in the noon-dawn sector as shown in Fig. 2b.
This is explained by the change of the drift paths. Whenthe strength of the convection electric is enhanced in theFig. 4 Energy density of protons with energy 1–200 keV observed by the Polar satellite near the equatorial plane. (After Ebihara et al. 2002)

Ebihara Progress in Earth and Planetary Science(2019) 6:16

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Table 1 Decay processes for ring current (Ebihara and Ejiri 2003)
Process

Region or cause

Charge exchange

Geocorona

Fate
Energetic neutral atom (Dessler and Parker 1959)

Coulomb collision

Plasmasphere

Precipitation into ionosphere (Wentworth et al. 1959;
Fok et al. 1991; Jordanova et al. 1996)

Wave-particle interaction

Resonant interaction withion cyclotron wave

Precipitation into ionosphere (Cornwall et al. 1970)

Adiabatic loss cone loss

Inward transport of ions

Precipitation into ionosphere (Jordanova et al. 1996)

Field line curvature

Curved magnetic field line

Precipitation into ionosphere (Sergeev et al. 1983;
Ebihara et al. 2011)

Sudden decrease inplasma sheet density

Entire ring current

Replacement of ring current ions with tenuous ones
(Ebihara and Ejiri 1998)

course of the earthward drift motion (right panel of Fig. 3),
the ions start traveling sunward immediately. In the noondawn sector, the preexisting ions also start travelingsunward, resulting in the removal of the preexisting ones
from the noon-dawn sector. The sudden decrease in theion flux in the noon-dawn sector is observed by global
images of energetic neutral atoms when the convection
electric field is enhanced (Brandt et al. 2002). The simulation result is also consistent with the magnetic disturbances on the ground (Hashimoto et al. 2002).
The bottom panel of Fig. 2 shows the current density,that is, the electric current per unit area. The westward
current flows in the outer region, and the eastward one
flows in the inner region. The current density also shows
the asymmetric distribution during the main phase,

Fig. 5 The ratio of the gyroradius of protons with energy of 50 keV
to the curvature radius of the magnetic field line for intense storm.
(Ebihara et al. (2011)

which is consistent with the observation (Le et al. 2004).
Because of the dipolar geometry, the cross-sectional areaof the outer region where the westward current flows islarger than the inner region where the eastward current
flows. Thus, the net current flowing westward is larger
than that flowing eastward (Ebihara and Ejiri 2000). The
dominance of the net westward current causes thedecrease in the geomagnetic field on the ground.
Figure 4 shows the averaged energy density of the protons with energy from 1 to 200 keV (Ebihara et al. 2002).
For isotropic pressure (P⊥ = P||), the energy density is 1.5
times larger than the plasma pressure. The data was
acquired when the Polar satellite traversed the equatorial
plane. During the storm main phase, the energy density
significantly increases on the nightside, whereas it decreases on the decreases. The increase and decrease in
the energy density can be reasonably explained by theintensification and relaxation of the convection electricfield as shown in Fig. 2.
In addition to the convective transport, substorm-associated transport has also been simulated (Fok et al. 1999).
Fok et al. (1999) calculated the substorm-associated electric field by differentiating empirical magnetic field, andFig. 6 Calculated Dst for run 1, run 2, and run3. Run 1 considers the
charge exchange and the field-line curvature scattering. Run 2 considers
the charge exchange only. Run3 considers no loss process. The blackline indicates the observed one. Ebihara et al. (2011)

Ebihara Progress in Earth and Planetary Science(2019) 6:16

(a)

(b)

(d)

(e)

Page 8 of 20(c)Fig. 7 Example of ring current-radiation belt coupling. Top panels show proton and electron pitch angle distributions observed by the Polar satellite.
Bottom panels show proton pitch angle distribution obtained by simulation. (After Ebihara et al. 2008a). a 80–100 keV observed proton. b 125–173 keV
observed proton. c 1698–2101 keV observed electron. d 80–100 keV simulated proton. e 125–173 keV simulated proton

solved the evolution of the phase space density of the ions.
The ring current is intensified well when the strong convection electric is incorporated. This suggests that thesubstorm without enhancement of the convection electricfield has little impact on the ring current.

Storm recovery phase (decay of ring current)
The storm recovery phase is known to start when thesouthward IMF becomes weak, or turns northward(Burton et al. 1975). The northward turning of IMF results
in an immediate reduction of the convection electric field.
The characteristic decay time of the Dst value is estimatedto be 7.7 h for the magnetic storms (Burton et al. 1975).

Shorter decay time, less than 1 h, is also suggested forlarge storms (Macmahon and Llop-Romero 2008). Observations show that the plasma pressure (energy density) of
the ring current protons becomes symmetric during therecovery phase as shown in Fig. 4. This symmetrization of
the storm-time ring current can be understood to thechange in the drift paths of the ions. When the convection
electric field becomes weak, the azimuthal drift motion(the grad-B drift and the curvature drift) dominates the
E × B drift. The plasma sheet ions cannot penetrate deep
earthward any more, and the ions that had been previously transported to the inner magnetosphere during themain phase cannot escape from the inner magnetosphere.

Ebihara Progress in Earth and Planetary Science(2019) 6:16

Consequently, in the noon-dusk sector, the plasma pressure increases in comparison with the main phase. The
simulation results (Fig. 2) are consistent with the observations (Fig. 4). The reduction of the convection electricfield, however, cannot result in the net decay of the ring
current because most of the particles still remain trappedin the inner magnetosphere (Ebihara and Ejiri 2003). At
least, there are six processes that may be related to the
decay of the storm-time ring current. They are summarized in Table 1.
Charge exchange is one of the dominant loss process forthe ring current ions (Dessler and Parker 1959). The charge
exchange frequently occurs where neutral atoms are dense,such as low L-shells, and low altitude. According to an empirical model (Rairden et al. 1986), the geocorona density is
660 cm−3 at geocentric distance of 3 Re. At L = 3, thecharge exchange lifetime for H+ is 4 h at 10 keV, and 96 h
at 100 keV. For O+, it is 16 h at 10 keV, and 11 h at
100 keV (Ebihara and Ejiri 2003). As the ion travels toward
Northern Hemisphere, or Southern Hemisphere along afield line, the ion undergoes short lifetime because of dense
neutral atoms. Therefore, the lifetime depends on the equatorial pitch angle. The two-step recovery of Dst is attributed

Page 9 of 20

to the lifetime depending on ionic species. On the basis of
the observation that O+ dominates H+ in the storm-timering current, it is suggested that the first rapid recovery iscaused by the charge exchange of O+, followed by the slow
recovery caused by the charge exchange of H+ (Hamilton etal. 1988). Numerical simulation, however, shows that the
charge exchange is insufficient to explain the rapid recovery, and that precipitation into the ionosphere is necessary(Kozyra et al. 1998a). Kozyra et al. (1998a) pointed out thatin addition to charge exchange, the precipitation loss is significant for the rapid recovery of Dst. This is supported by
the evidence of a filled loss cone observed by satellites(Amundsen et al. 1972; Williams and Lyons 1974; Hultqvist
et al. 1976; Sergeev et al. 1983; Walt and Voss 2001). However, the mechanism for the pitch angle scattering that
leads to the filled loss cone is not well known.
Coulomb collision with thermal plasma, and resonantinteraction with ion cyclotron waves result in the pitch
angle scattering, but their role in the overall reduction of
the ring current is suggested to be minor (Jordanova et al.
2001). As recently suggested, resonant interaction with ion
cyclotron waves may cause pitch angle scattering significantly during extremely intense magnetic storms (Tsurutani

Fig. 8 Adiabatic deceleration (near the equatorial plane) and acceleration (at off-equator) of ions in the storm-time magnetic field. The dashed line
indicates the magnetic field line in the pre-storm time, and the solid line indicates the magnetic field line deformed by the storm-time ring current

Ebihara Progress in Earth and Planetary Science

(a)

(b)

(c)

(d)

(e)

Fig. 9 (See legend on next page.)(2019) 6:16

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Ebihara Progress in Earth and Planetary Science(2019) 6:16

Page 11 of 20(See figure on previous page.)
Fig. 9 Example of ring current-ionosphere coupling (overshielding). In b, the fan shape indicates the field of view of the SuperDARN Hokkaido radar, andthe contour indicates the ionospheric electric potential. (After Ebihara et al. 2008b). a Simulated plasma pressure in the equatorial plane. b Simulated fieldaligned current in the ionosphere and electric potential. c Observed IMF Bz d Observed line-of-sight velocity. e Simulated line-of-sight velocity

et al. 2018). The field-line curvature (FLC) scattering occurs
where the curvature of a magnetic field line is short incomparison with the gyroradius of the particle (Sergeev etal. 1983; Birmingham 1984; Büchner and Zelenyi 1989;
Young et al. 2002). Using empirical magnetic field model,
one can predict the region where the FLC scattering occurs.
For example, the ratio of the gyroradius of a 50 keV H+ tothe curvature radius of the field line exceeds 0.1 at L ~ 4.8,
and 1 at L ~ 5.5 for a large storm condition as shown in
Fig. 5 (Ebihara et al. 2011). Strong pitch angle scattering is
expected to occur in such limited regions.
Figure 6 shows the calculated Dst together with observed one. The Dst is calculated by comprehensive ring
current model (CRCM) (Fok et al. 2001) together with
self-consistent magnetic field (Ebihara et al. 2008a). Run 1
takes into account the charge exchange and the FLC scattering, showing that Dst recovers with an e-folding time of~ 3 h. The difference between the observation and thesimulation is probably attributed to the underestimationof the plasma sheet density. Run 2 takes into account the
charge exchange only. The e-folding time is ~ 12 h. Obviously, inclusion of the FLC scattering appears to give rise
to rapid recovery of Dst. However, the impact of the FLC
scattering on the rapid recovery of Dst may be limited tosmall and moderate magnetic storms. For large magnetic
storms, the inner edge of the ring current could reach very
close to the Earth, like L ~ 1.5 (Ebihara et al. 2005a). In
the deep inner region (L < 3), the magnetic field is rigid(that is, low plasma beta), so that the magnetic field ishardly stretched.
Precipitation of particles can occur without pitch angle
scattering. The adiabatic loss cone loss, which arises whendαL dα0
<
;
dL
dL

ð10Þ

where αL and α0 are the loss cone angle and the equatorial pitch angle. As an ion moves earthward adiabatically,
the equatorial pitch angle becomes large to conserve thefirst two adiabatic invariants. The loss cone angle also
becomes large. As the ion moves earthward, the loss coneangle increases faster than the equatorial pitch angle does
(Ebihara and Ejiri 2003). Some of the ions with equatorial
pitch angle near the loss cone will precipitate into theionosphere as the ions drift earthward. The contribution
from the adiabatic loss cone loss is estimated to be verysmall (Jordanova et al. 1997). It amounts to ~ 1–2% of the
net loss of the ring current (Ebihara and Ejiri 2003).

Alternative idea to explain the rapid decay of the ring
current is a replacement of the ring current population
with tenuous one. This can be achieved when the plasma
sheet density rapidly decreases and the convection electricfield remains high (Ebihara and Ejiri 1998; Ebihara and Ejiri
2000). During the large magnetic storm on 20–21 November 2003, the rapid recovery of Dst can be explained by thesudden decrease in the plasma sheet density Nps as shownin Fig. 1 (Ebihara et al. 2005a). When the plasma sheet
density is constant in time, Dst shows slow recovery.

Active role of ring current
The ring current is strong enough to change the magnetic
field in the inner magnetosphere (Akasofu and Chapman
1961). One of the observable effects of this is an adiabaticchange in the trapped particles. Relativistic particle flux
tends to decrease during the storm main phase, and increase during the recovery phase as if the flux follows theDst variation (McIlwain 1966). This is called a ring current
effect. Satellite observations also show energy-dependent
variation during the magnetic storms. The ion flux with energy greater than 200 keV substantially decreases, whereas
the ion flux with energy less than 63 keV increases at L ~ 4
during an intense storm (Lyons and Williams 1976; Lyons
1977). The increase in the low-energy ions (< 63 keV) most
likely corresponds to the storm-time ring current, which
decreases the magnetic field near the equatorial plane,
resulting in the adiabatic deceleration of the high energy
ions (> 200 keV) (Williams 1981). This can be regarded asenergy-domain coupling. Temporin and Ebihara (2011)
show the similar tendency. They also show that during therecovery phase, the high-energy ion flux (125–173 keV) increases, and sometimes it exceeds the pre-storm level. This
may imply the presence of non-adiabatic processes.
Figure 7 shows the pitch angle distribution of the protons and electrons measured by the Polar satellite near theequatorial plane (Ebihara et al. 2008a). The flux of protons(80–173 keV) and electrons (1.7–2.1 MeV) near the pitch
angle of ~ 90° appears to decrease in comparison with thepre-storm condition. The simulated pitch angle distribution is shown in the bottom panels of Fig. 7. The differential flux of the ions is calculated by comprehensive ring
current model (CRCM) (Fok et al. 2001) together with
self-consistent magnetic field (Ebihara et al. 2008a). The
flux near the pitch angle of ~ 90° decreases in comparison
with the pre-storm condition, which is consistent with theobservation (Lyons and Williams 1976; Lyons 1977). A
remarkable point to be noted is the increase in the flux ofEbihara Progress in Earth and Planetary Science(2019) 6:16

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(a)

(b)

(c)

Fig. 10 Another example of ring current-ionosphere coupling (subauroral polarization stream). (After Ebihara et al. 2009). (top) Simulated plasmapressure. a SuperDARN Hokkaido radar observation of the line-of-sight velocity of ionospheric plasma flow. b Simulated line-of-sight velocity with
time-varying plasma sheet density. c Simulated one with constant plasma sheet density

Ebihara Progress in Earth and Planetary Science(2019) 6:16

Page 13 of 20

Fig. 11 Influence of ring current-ionosphere coupling on the plasmasphere. An indentation of the plasmapause propagates sunward. Top panels
show the observation by the IMAGE satellite. The bottom ones show the cold electron density obtained by the simulation. (Fok et al. 2005)

nearly field-aligned particles (< 30° and > 150°). The decrease (at pitch angles of ~ 90°) and increase (at pitch
angles of < 30° and > 150°) in the flux of the ions correspond to deceleration and acceleration of the ions.
The deceleration occurs near the equatorial planewhere the magnetic field decreases. The acceleration(a)occurs at off-equator where the magnetic field increases. The acceleration can also be explained in termsof Fermi acceleration because the distance between two
mirror points in the Northern Hemisphere and theSouthern Hemisphere becomes short. Figure 8 provides
schematic illustration for the deceleration and(b)Fig. 12 Influence of ring current-ionosphere coupling on the ring current protons in terms of shielding. The flux of energetic neutral atoms is indicatedby red color in the unit of 1/cm2 s str keV. Precipitating proton flux into the ionosphere is indicated by blue color in the unit of 1012 eV/cm2 s. The left
panel shows the observation made by the IMAGE satellite. The right one shows the simulation result. (Ebihara et al. 2011). a Observation (39–50 keV).
b Simulation (44 keV)

Ebihara Progress in Earth and Planetary Science(2019) 6:16

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Fig. 13 Influence of ring current-ionosphere coupling on the ring current protons in terms of Rayleigh-Taylor type instability. Proton flux
with energy 32 keV is shown in the left panel. The outer edge of the flux population shows undulation due to interaction between themagnetosphere and the ionosphere. The contour indicates the ionospheric potential. The schematic illustration is provided in the rightpanel. (After Ebihara et al. 2005a)

acceleration of the charged particles in the magnetic
field line changed by the ring current.
The current density of the ring current is stronger on
the nightside than on the dayside during the magnetic
storms (Le et al. 2004). This means that the storm-timering current is essentially asymmetric, and that thecurrent cannot be closed in the inner magnetosphere.
From the requirement of the current continuity, theremnant of the current must flow into and out of theionosphere as previously suggested by Hannes Alfvén(Egeland and Burke 2012). In the ionosphere, secondary
electric field must be established to satisfy the current
continuity. The electric field is expected to feed back to
the magnetosphere. Motion of particles trapped in the
inner magnetosphere will be modified by the additional
electric field. This feedback process is suggested by
Vasyliunas (1970) and Wolf (1970).
The ring current tends to generate downward FAC on
the duskside, and upward FAC on the dawnside. A pair ofthese FACs is called region 2 current (Iijima and Potemra1976). To close the current originating from the ring
current, dusk-dawn electric field is expected to appear in
the ionosphere. The direction of the electric field is opposite to that of the convection electric field. The additional
electric field is called shielding electric field, and is substantially investigated by Spiro and Wolf (1984). Figure 9shows an example of the ionospheric plasma flow associated with shielding electric field (Ebihara et al. 2008b).
The second panel from the bottom shows the ionosphericplasma flow observed by the SuperDARN Hokkaido radar.
The warm color represents the flow away from the radar,which is approximately in the geomagnetically north-east
direction. The field of view of the radar was situated in
the afternoon sector as shown in Fig. 9. The observationshows that the north-east flow (away from the radar) is intensified when IMF turns northward (event 1). The flow
direction is opposite to the usually expected direction.
This can be regarded as the overshieldling in which theshielding electric field dominates the convection electricfield. The bottom panel shows the simulation result. The
flow toward the radar is intensified, which is consistent
with the observation for event 1. In the second row fromthe top, the FACs associated with the ring current are provided, together with ionospheric convection pattern. The
downward current (positive value) and the upward current(negative value) persist for this interval, whereas the ionospheric potential pattern is significantly changed by an
abrupt reduction of the convection electric field. The direction of the ionospheric flow is changed from westward
to eastward (as indicated by blue allows near a fan shape).
The fan shape shows the field of views of the SuperDARN
Hokkaido radar, which observed an abrupt intensificationof the flow away from the radar. The plasma pressure in
the inner magnetosphere, as shown in the top panel,decreases due to the dominance of the dusk-dawn electricfield. The maximum pressure decreases from ~ 90 to ~ 60
nPa in 6 min. After a while, another overshielding occurs
during the prolonged southward IMF (event 2). Event 2 is

Ebihara Progress in Earth and Planetary Science(2019) 6:16

Page 15 of 20

Fig. 14 Active role of the storm-time ring current; 1 inflation of the magnetic field, 2 development of the shielding/overshielding electric field(dusk-dawn electric field), 3 development of fast ionospheric flow (poleward electric field), and 4 development of multiple fast ionospheric flow(poleward electric field)

associated with a substorm activity, and is not reproducedby the ring current simulation (CRCM) that considers theinner magnetosphere only. Later on, the global MHD
simulation, REPPU, is found to reproduce the overshielding condition during the recovery phase of a substorm(Ebihara et al. 2014). The geomagnetic field variation associated with the overshielding is consistent with theobservation.
Another observable effect of the ring current-ionosphere
coupling is a localized westward flow in the subauroral
ionosphere. Region 1 current flows poleward of the region
2 current. To satisfy the current continuity, the poleward

electric field is established on the duskside, resulting in a
localized westward flow in the subauroral ionosphere(Anderson et al. 1993). Figure 10 shows the SuperDARN
Hokkaido radar observation of the ionospheric fast flow atmagnetic latitudes from ~ 50° to ~ 55° (Ebihara et al. 2009).
The direction of the fast flow is westward as indicated byblue color. The fast flow occurs intermittently, not continuously. The fast flow belongs to a class of subauroralpolarization stream (SAPS) (Foster and Vo 2002). In the
top panels of Fig. 10, the plasma pressure distribution calculated by the CRCM simulation is shown. The simulation
employs time-varying plasma sheet density observed byEbihara Progress in Earth and Planetary Science(2019) 6:16

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Fig. 15 Cross energy and cross region coupling in the inner magnetosphere and the ionospheregeosynchronous satellites as a boundary condition of thering current. Because of the time-varying plasma sheet
density, the plasma pressure shows multiple-peak distribution. The multiple-peak distribution of plasma pressure
moves earthward due to the sunward convection. The FAC
accompanied by the plasma pressure distribution also
moves westward equatorward. As the FAC moves, the electric field changes accordingly. In the third panel, the calculated line-of-sight velocity of the ionospheric plasma isprovided, which is roughly consistent with the observation.
When the plasma sheet density is kept constant in time,the ionospheric flow is rather continuous as shown in thebottom panel of Fig. 10.
Figure 11 shows an example of the impact of the ring
current-ionosphere coupling on the plasmasphere (Fok et
al. 2005). The top panels show the plasmasphere observedby the IMAGE satellite. An indentation appears suddenlyon the duskside, and propagates sunward. The bottom
panels show the cold electron density calculated by the
CRCM. When the plasma sheet density increases abruptly,
the ring current grows locally, generating localized FACs.

The electric field associated with the localized FACs initiates the indentation propagating sunward. Thus, the indentation of the plasmasphere may be regarded as thering current-plasmasphere coupling.
Figure 12 shows an example of the impact of the ring
current-ionosphere coupling on the energetic protons in
the inner magnetosphere (Ebihara et al. 2011). The redcolor indicates the flux of energetic neutral atom (ENA)
with energy of ~ 44 keV. The peak flux of ENA takes placein the post-midnight sector, which is different from theconventional understanding. Conventionally, the ions originating from the nightside plasma sheet gain the kinetic
energy most in the pre-midnight sector where the ions get
closer to the Earth, as shown in Fig. 3. Thus, the peak of
the ENA is expected to take place in the pre-midnight sector. The eastward shift of the ENA peak as observed by
the IMAGE satellite can be explained by the developmentof the shielding electric field (Fok et al. 2003). The shielding electric field changes the drift trajectories, and someions originating in the plasma sheet get closer to the Earthin the post-midnight sector.

Ebihara Progress in Earth and Planetary Science(2019) 6:16

The ring current-ionosphere interaction can lead to aRayleigh-Taylor type instability (interchange-like instability)(Sazykin et al. 2002; Ebihara et al. 2005a). Figure 13 shows
the differential flux of protons with energy 32 keV for theintense magnetic storm of 20–21 November 2003. CRCM
is used to calculate the ions, and plasma sheet density andtemperature observed at geosynchronous orbit are used asa boundary condition of the simulation. A remarkable
point is the spatial distribution of the flux showing undulation. At the early stage of the recovery phase of thisstorm, the plasma sheet density suddenly decreases asshown in Fig. 1. Then, tenuous ion population propagates
earthward. Consequently, the earthward gradient of theplasma pressure is established near the interface between
the outer edge of the preexisting high-pressure (dense
plasma) and the inner edge of the newly coming
low-pressure (tenuous plasma). When the interface has asmall hump, localized FACs are generated around it.
Downward FAC flows on the westside of the hump, andupward one flows on the eastside. To satisfy the current
continuity, eastward electric field is generated. When theeastward electric field is mapped to the magnetosphere,
the ions that are constitute of the hump start drifting outward so as to enlarge the hump. This process is schematically illustrated in the right panel of Fig. 13.
The ring current is also known to result in auroral phenomena. The energy of the ring current ions is transferred
to plasmaspheric thermal electrons by way of the Coulomb collisions. The heat flux propagates to the ionosphere, resulting in stable auroral red (SAR) arcs
(Cole 1965). ENAs originating from the ring current ionsprecipitate into the ionosphere, resulting in aurora at low
latitudes (Zhang et al. 2006). Magnitude of the lowlatitude aurora is inversely proportional to the Dst index.
Temperature anisotropy of the ring current ions excites
electromagnetic ion cyclotron (EMIC) waves (Kennel andPetschek 1966). The cold and hot plasma densities determine the linear growth rate of the EMIC wave. The pitch
angle of the protons is scattered when they encounter the
EMIC waves. Some of the scattered protons precipitate
into the ionosphere, resulting in the proton aurora(Yahnin et al. 2007). Jordanova et al. (2007) calculated
wave gain of the EMIC waves in the ring current simulation, and confirmed that the EMIC waves grow efficiently
in the regions where the energetic ring current protons
overlaps with the dayside plasmaspheric plumes andwhere density gradients are steep at the plasmapause. The
precipitating protons significantly increase the ionosphericconductivity proton near the equatorward edge of the auroral oval on the duskside (Galand and Richmond 2001).
The ring current is shown to have a large influence on
the magnetosphere and the ionosphere. Figure 14 summarizes the active role of the ring current. (1) The ring
current is strong enough to distort the magnetic field,

Page 17 of 20

leading to adiabatic changes in the trapped particle fluxes.
The magnetic field decreases near the equatorial plane,
whereas the magnetic field increases at off-equator. This
causes the dual acceleration process (betatron deceleration
and Fermi acceleration), resulting in butterfly-like pitch
angle distribution of trapped particles (Ebihara et al.
2008a). (2) The asymmetric ring current results in a formation of the region 2 FAC (flowing into the ionosphereon the duskside and away from the ionosphere on thedawnside). Dusk-dawn electric field appears to establish
the current continuity in the ionosphere. This electric fieldis called a shielding/overshielding electric field because thedirection is opposite to that of the convection electric field(dawn-dusk electric field). (3) The region 2 FAC is locatedequatorward of the region 1 FAC. Poleward electric fieldappears to establish the current continuity in the ionosphere. The poleward electric field gives rise to the westward fast ionospheric flow in the subauroral ionosphere. (4)When the plasma pressure shows multiple-peak distribution, multiple fast ionospheric flow appears. One observeschanges in the speed of the ionospheric flow as the multiple
plasma pressure distribution drifts.
Figure 15 summarizes possible cross energy and crossregion coupling in the inner magnetosphere and the ionosphere. One causes another, so that the system is rather
complicated. When the magnetic storms take place, allthese components play active and passive roles. Numericalsimulation is obviously a powerful tool to understand thecomplicated system.

Conclusion
The development and the decay of the magnetic storm
are understood to accumulation and loss of the charged
particles trapped by the Earth’s magnetic field, respectively. The enhancement of the convection electric field
is necessary to explain the accumulation of the particles
and the development of the ring current during themagnetic storms. The ring current is strong enough tochange the magnetic field in the near-Earth space environment, resulting in the significant changes in thetrapped particles. The asymmetric distribution of thering current, which can be reasonably explained by
the development of the convection, results in the formation of the field-aligned current. The field-aligned current
flows into and away from the ionosphere, giving rise to
additional electric field. The simulation demonstrates thatthe ring current is not a consequence, but can be a causeof many observable effects during the magnetic storms.
Abbreviations
ENA: Energetic neutral atom; FAC: Field-aligned current
Acknowledgements
A part of the computer simulation was performed on the KDK computer
system at Research Institute for Sustainable Humanosphere, Kyoto University.
The author thanks Drs. Atsuhiro Nishida, Takashi Tanaka, Masaki Ejiri, Takashi

Ebihara Progress in Earth and Planetary Science(2019) 6:16

Kikuchi, Mei-Ching H. Fok, Richard A. Wolf, Pontus C:son Brandt, Nozomu
Nishitani, Tadahiko Ogawa, Lynn M. Kistler, and Hans Nilsson for fruitful
discussion and valuable suggestion.
Funding
This work was supported by JSPS KAKENHI Grant Number 15H03732 and
15H05815, as well as Flagship Collaborative Research and Research Mission
3 “Sustainable Space Environments for Humankind” at RISH, Kyoto University.
Availability of data and materials
This is a review paper. All data used here are in the original papers cited in
the text.
Authors’ contributions
The author read and approved the final manuscript.
Competing interests
The author declares that he has no competing interests.

Publisher’s NoteSpringer Nature remains neutral with regard to jurisdictional claims inpublished maps and institutional affiliations.
Received: 5 October 2018 Accepted: 21 January 2019

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