Simulation study of near-Earth space disturbances: 1. magnetic storms
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 prime cause 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.
KeywordsMagnetic storms Computer simulation Magnetosphere Ionosphere Inner magnetosphere Ring current
Energetic neutral atom
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 is characterized 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 of the ring current (Frank 1967; Smith and Hoffman 1973; Lui et al. 1987; Le et al. 2004). In the recovery phase, the H-component of the geomagnetic field returns to the pre-storm level, which is primarily caused by the decay of the ring current.
The 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 field depends on a magnetic local time (MLT), suggesting asymmetric ring current (Akasofu and Chapman 1964). This is confirmed 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) is invented (Sugiura 1964). The Dst index is basically a weighted 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 the solar wind speed, the solar wind density, and the southward component of IMF Bz (Burton et al. 1975). The Burton et al.’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 the storm-time ring current (Hamilton et al. 1988). This is a 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-storm time), the ring current consists of ions with energy greater than 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 ions with energy of the order of tens of keV in the inner magnetosphere.
Equations (1) and (2) imply that understanding the ring current is equivalent to understand the phase space density 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 is essential to track motion of charged particles properly for the purpose of understanding the ring current and the 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 is called 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-step manner when the strong southward IMF is embedded in both 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. Statistical studies show that the CME-driven magnetic storms tend to be larger than the CIR-driven magnetic storms in terms of the Dst index (Borovsky and Denton 2006; Denton et al. 2006).
The fundamental process for the development of the ring current is the accumulation of particle energy in the inner magnetosphere where the Earth’s dipolar magnetic field dominates (Dessler and Parker 1959; Sckopke 1966). 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 short interval, 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 inner magnetosphere, 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 center motion. Introducing a uniform electric field and the dipole magnetic field, he suggested drift paths of particles in the equatorial plane, and field-aligned current associated with the asymmetric paths of them (Egeland and Burke 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 for real space and three for momentum space. With the guiding-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 gyro phase and bounce phase are lost. The bounce-averaged approximation has been preferred to track motion of the charged particles in the inner magnetosphere because the gyro phase and the bounce phase do not matter in many cases.
When there are no sink and source, the number of particles must be conserved in phase space. One of the practical schemes to solve the evolution of the phase space density is based 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)
Equation (8) implies that the Earth is negatively charged from ambient in quasi-inertial frame of reference due to Earth’s rotation. According to the 12th generation of the International 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 results from the secular variation of the geomagnetic field.
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, which is consistent with the observation (Le et al. 2004). Because of the dipolar geometry, the cross-sectional area of the outer region where the westward current flows is larger 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 the decrease in the geomagnetic field on the ground.
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, and 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 the substorm without enhancement of the convection electric field has little impact on the ring current.
Storm recovery phase (decay of ring current)
Decay processes for ring current (Ebihara and Ejiri 2003)
Region or cause
Energetic neutral atom (Dessler and Parker 1959)
Resonant interaction with ion 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
Sudden decrease in plasma sheet density
Entire ring current
Replacement of ring current ions with tenuous ones (Ebihara and Ejiri 1998)
Charge exchange is one of the dominant loss process for the 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, the charge 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 a field 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 to the lifetime depending on ionic species. On the basis of the observation that O+ dominates H+ in the storm-time ring current, it is suggested that the first rapid recovery is caused by the charge exchange of O+, followed by the slow recovery caused by the charge exchange of H+ (Hamilton et al. 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 that in 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.
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 electric field 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 the sudden decrease in the plasma sheet density Nps as shown in 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 adiabatic change 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 the Dst 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 as energy-domain coupling. Temporin and Ebihara (2011) show the similar tendency. They also show that during the recovery 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.
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-time ring current is essentially asymmetric, and that the current cannot be closed in the inner magnetosphere. From the requirement of the current continuity, the remnant of the current must flow into and out of the ionosphere 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 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 ions precipitate into the ionosphere, resulting in aurora at low latitudes (Zhang et al. 2006). Magnitude of the low-latitude aurora is inversely proportional to the Dst index. Temperature anisotropy of the ring current ions excites electromagnetic ion cyclotron (EMIC) waves (Kennel and Petschek 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 and where density gradients are steep at the plasmapause. The precipitating protons significantly increase the ionospheric conductivity proton near the equatorward edge of the auroral oval on the duskside (Galand and Richmond 2001).
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 the magnetic storms. The ring current is strong enough to change the magnetic field in the near-Earth space environment, resulting in the significant changes in the trapped particles. The asymmetric distribution of the ring 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 that the ring current is not a consequence, but can be a cause of many observable effects during the magnetic storms.
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 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.
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.
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