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Tutorial on geomagnetic storms and substorms
Article in IEEE Transactions on Plasma Science · January 2001
DOI: 10.1109/27.902214 · Source: IEEE Xplore
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
Tutorial on Geomagnetic Storms and Substorms
Anthony T. Y. Lui
Invited Paper
Abstract—Geomagnetic storms have been studied for more
than a century and substorms for nearly four decades. The space
era which began in the late 1950s has ushered new discoveries
and given new practical importance to this scientific discipline as
we continue to amass technological assets in space. Geomagnetic
storms and substorms pose hazards to our venture into the final
frontier, much like adverse atmospheric weather does to our
outdoor activity. This tutorial provides an overview of the main
characteristics of these space phenomena and a brief review of
the present theories concerning their initiation. For geomagnetic
storms, the two prevailing views on their cause are discussed.
One considers a storm to be the accumulated effects of a series of
substorms while the other considers it to be the result of strong
and prolonged enhancement of the global magnetospheric electric
field. A synergistic model combining elements from both views is
proposed as the likely explanation for the cause of geomagnetic
storms. For substorms, there are generally four categories of
models. The first proposes some plasma instabilities or externally-imposed reduction in the magnetospheric electric field at
the near-Earth region. The second calls for magnetic reconnection
occurring in the mid-tail environment. The third focuses on
coupling the ionosphere to the magnetosphere while the fourth
invokes abstract descriptions in nonlinear dynamics to address
some statistical characteristics of substorms. An evaluation of
observations and these models suggests that substorm onset
may not be uniquely attributed to a single physical process. A
synthesis of the essential elements of the present models in all
four categories may well yield the answer to the mystery on the
initiation of magnetospheric substorms.
Index Terms—Magnetic reconnection, plasma instability, storm,
substorm.
I. INTRODUCTION
T
HERE is enhanced awareness of space weather due to
the coincidence of the new millennium with the approach
of the solar maximum. Before the millennium transition, the
Y2K problem associated with the two-digit designation of
the year by computer software was expected to be a menace.
Anticipating a similar menace to our technological society by
solar activity reaching the maximum of its cycle, some space
scientists had referred to the upcoming solar maximum as the
other Y2K problem. While the Y2K problem turned out to be a
nonproblem as a result of much resources devoted to minimize
Manuscript received January 3, 2000; revised April 27, 2000. This work was
supported by the Atmospheric Sciences Division of the NSF to the Johns Hopkins University Applied Physics Laboratory.
The author is with the Applied Physics Laboratory,The Johns Hopkins University Laurel, MD 20723 USA.
Publisher Item Identifier S 0093-3813(00)10656-3.
its impact beforehand, there is no comparable preparation for
the upcoming solar maximum. Since the maiden voyage of
Sputnik in 1957 which demonstrated the ability to launch artificial satellites, there has been a progressively rapid increase of
technological assets in space. With each new endeavor follows
an ever-increasing dependence on space and ever-growing need
to monitor and forecast the space environment to avoid potential
hazards. These developments can justifiably be viewed as the
dawning of our venture into the final frontier, our first step into
the enormous universe awaiting for our exploration. No longer
is space weather just an academic pursuit or a curiosity but a
practical necessity. This is analogous to the early days of air
travel when the atmospheric environment at airplane altitudes
took on a sudden significance in our daily lives.
Historically, the discovery of magnetic storms may be contributed to Baron Alexander von Humboldt who reported the
observation of the deflection in the local magnetic declination
at Berlin on December 21, 1806 [1]. He also noted the simultaneous auroral activity overhead with the magnetic deflection.
The general description of a geomagnetic storm in the early days
is through the time history of the horizontal or -component of
the magnetic field. The official index called Dst (disturbance
storm time), constructed on the basis of the -components of
four low-latitude magnetic stations, is now routinely used as a
measure for the storm intensity. The Dst index during two magnetic storms is shown in Fig. 1. A storm generally begins with a
sudden increase of the -component of the geomagnetic field
(the storm sudden commencement or SSC), followed by a period of the field remaining enhanced (the initial phase), then
followed by a period of a substantially reduced field (as much
as 1% of the Earth’s main equatorial field) lasting for several hours (the main phase). The eventual return of the field to
its nominal quiet-time value (the recovery phase) usually takes
several days but can last for several weeks. Deviations from the
general picture as shown in Fig. 1(a) exist, e.g., some storms
do not have well defined SSC and initial phase, as illustrated in
Fig. 1(b).
A long time past from the early report of Humboldt before
the source disturbance was traced back to the Sun. The magnetic
field depression during the storm main phase was first attributed
to electrical currents flowing near the Earth from charged particles originating directly at the Sun [2], [3]. However, the Earth’s
intrinsic magnetic field is a very effective barrier to charged particles such that direct entry of solar particles is very limited.
Nevertheless, the idea that magnetic storms are caused by a ring
of electrical current encircling the Earth called the ring current is
0093–3813/00$10.00 © 2000 IEEE
LUI: TUTORIAL ON GEOMAGNETIC STORMS AND SUBSTORMS
(a)
1855
Fig. 2. Schematic diagram to illustrate the trapping of charged particles in the
Earth’s magnetic field by the magnetic mirror points in strong field regions.
[8]. For a charged particle of mass , charge and velocity ,
its equation of motion in a uniform magnetic field is
(1)
If we resolve the velocity into components parallel
to , we find
perpendicular
and
(b)
Fig. 1. (a) Dst index for a classic geomagnetic storm which begins with a
sudden storm commencement, followed by the initial phase, the main phase,
and the recovery phase. (b) The Dst index for a geomagnetic storm which shows
deviation from the classic example, i.e., no recognizable SSC and the initial
phase preceding the main phase. The date labels are placed at the mid-day time.
essentially a correct one. As will be explained in Section II, the
charged particles responsible for the ring current are trapped by
the Earth’s magnetic field similar to the energetic charged particles in the Van Allen radiation belts.
This tutorial will briefly review the underlying physics concerning geomagnetic storms and substorms. Section II deals
with how electric currents exist in space, which necessitates
some basic understanding of how charged particles move in the
near-Earth space. Section III addresses the question of where do
these charged particles come from and eventually go, which relates to the interaction between the Earth’s magnetic field and
the continuous supersonic blast of ionized gas from the Sun.
Section IV summarizes the present two competing views for geomagnetic storm onsets. Section V provides a bird’s eye view
on the myriad of space disturbances associated with substorms.
Section VI discusses theories on onset of substorms, classifying
them into basically four schools of thought. The last section
concludes by highlighting some future outstanding issues to be
solved on these phenomena.
II. HOW DO ELECTRIC CURRENTS EXIST IN SPACE?
The charged particle population of the storm-time ring current
has been measured directly by spacecraft [4], [5]. The dominant
population, with 95% of the charged particles in the energy
range of 5–500 keV [6], resides in the radial range of 2 to 8
(
km) from the Earth. To understand how these
particles can be responsible for the world wide depression of the
Earth’s magnetic field requires some basic knowledge on how
charged particles move in space. The guiding center concept
for charged particle motion introduced by Alfvén [7] laid the
foundation for the modern day explanation of this ring current
(2)
indicating that the particle’s velocity along the magnetic field
is constant while its motion perpendicular to the magnetic field
, analogous to the basic
is circular with a frequency of
orbital motion of a planet around the Sun due to the gravitational force. The sense of gyration is dependent on the charge.
The frequency of this gyration is called the gyrofrequency and
is typically very high. In the geostationary orbit where the magnetic field may be 100 nT, the gyrofrequency is 2.8 kHz
for electrons and 1.5 Hz for protons. In addition, the gyration motion of a charged particle generates a circular current
loop, equivalent to a small magnet with a magnetic moment
.
When the magnetic field is nonuniform and is converging,
the repelling force (also known as the mirroring force) acting
. This force acts to accelerate
on a charged particle is
the particle away from a strong field region and often leads to
the particle being reflected back (mirrored) from the region. A
magnetic field with a strong field at both ends of a field line,
as in the case for the Earth, traps a charged particle due to this
force. This concept is illustrated in Fig. 2. The particle bounces
between two points called the mirror points at which its component becomes zero. This is the basic principle by which Van
Allen radiation belt particles are trapped in space. Note that the
magnetic field does no work on the particle so that the particle’s
component detotal energy remains constant, i.e., when the
component increases to conserve the total encreases, the
ergy. It is customary to refer to a magnetic field line in terms of
its shell value. The shell coordinate takes into account the
deviation of the magnetospheric field from a perfect dipole and
organizes well the charged particle population in space. The
shell value is basically the equatorial crossing distance in
of the magnetic field line if the magnetic field in space were a
pure dipole.
The guiding center concept introduced by Alfvén [7] considers the average position and motion of a charged particle
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
by neglecting the fast gyration around the magnetic field. With
this approximation (valid when scales of magnetic field inhomogeneities are large compared to the radius of gyration and
when the time scale of variation is slow compared to the gyration period), the drift motion of the gyrocenter (the center of the
fast gyration) of a charged particle under a given force is
(3)
Based on this simplified expression, we can readily obtain the
drift motions of a charged particle moving in a nonuniform magnetic field. For example, the motion along a curved magnetic
is
field with a radius of curvature
, resulting in a drift
associated with a centrifugal force of
, as illustrated in Fig. 3(a).
given by
Since the drift direction is charge dependent, for a particle pop, the curvature
ulation with a velocity distribution given by
drift gives rise to a current density
(4)
where is the particle pressure component parallel to the magnetic field with the assumption that the velocity distribution
is independent on the phase of gyration, i.e., the number of
is
particles in the velocity range and
. In a magnetic field gradient
, the reand the drift
pelling force for a magnetic moment is
, as illustrated in Fig. 3(b). Similarly,
is
as the drift direction is charge dependent, the current density associated with gradient drift for a particle population is
(a)
(b)
(c)
(5)
is the particle pressure component perpendicular to
where
the magnetic field. Furthermore, if there is a density or temperature gradient of the particle population, then there is a current density which does not involve any actual particle drift.
This current density arises from gyration motion of the particles, from crowding of gyration orbits due to a density gradient
or a larger gyration speed due to a temperature gradient, as illustrated in Fig. 3(c) and (d). This is called the magnetization
current and is given by
(6)
The combination of all these real and apparent drift motions
gives rise to electrical currents which are quite ubiquitous in
space. In fact, a weak ring current exists even outside magnetic
storm periods. Quantitatively, all these drifts may be added and
simplified after some vector algebra to give the equation for
the total electric current perpendicular to the magnetic field
(d)
Fig. 3. Electric current arising from the motion of a charged particle in: (a)
a curved magnetic field geometry, (b) a magnetic field gradient, (c) a density
gradient (represented by two circles on the higher density side), and (d) a
temperature gradient (represented by the larger circle on the higher temperature
side). The sense of gyration and the drift motion direction is shown for positive
charged particle. Magnetic field in panels (b)–(d) points out of the paper. The
force F acting on the particle in panels (a) and (b) is explicitly given with the
corresponding guiding center drift v .
carried by charged particles in the nonuniform magnetic field
of the magnetosphere as
(7)
)
This expression is valid for a quasisteady state (i.e.,
and when the gravitational force can be neglected. From in situ
measurements, it is found that the first term in (7) generally
LUI: TUTORIAL ON GEOMAGNETIC STORMS AND SUBSTORMS
1857
is small compared with the total particle kinetic energy. Several good references now exist for extended discussion on topics
covered in this section [12]–[15].
III. SOURCES AND SINKS OF THE RING CURRENT CHARGED
PARTICLES
Fig. 4. Observations during the main phase of a geomagnetic storm showing
the equatorial radial profile of (a) ring current particle pressure components, and
(b) current densities (positive and negative values denote westward and eastward
currents, respectively). The radial distance is represented by the L shell value.
dominates over the second term during storms [9]. As an example, Fig. 4 shows a radial profile of ring current pressure
components measured by the AMPTE/CCE spacecraft and the
deduced ring current densities during a geomagnetic storm on
September 4, 1984. In general, the ring current is directed east2.5 to 3.5) but
ward inward of the peak pressure location (at
is directed predominantly westward beyond the peak. Overall,
the ring current has a net westward component which causes
the world-wide decrease in the geomagnetic field. The magnetic
field reduction at the Earth due to the ring current population
can be obtained from applying the Biot–Savart law based on the
measured electrical current [9]. However, the common practice
is to use the Dessler–Parker–Sckopke relation [10], [11] which
to the
relates the total energy of the ring current particles
on the ground which is given as
magnetic perturbation
(8)
is the magnetic field at the Earth’s equatorial surwhere
face and is the total magnetic energy of the Earth’s dipole
field above the surface. This expression is derived based on the
assumption that the magnetosphere is a closed quasistationary
system and the total magnetic energy inside the magnetosphere
The main issues for geomagnetic storms are the origin of the
ring current particles, how they are transported to the ring current region, and their loss mechanisms. There are two sources
for ring current particles. The first source comes from the interaction between the Earth’s magnetic dipole and the solar wind
which is a supersonic stream of charged particles continuously
emitted from the Sun. The Earth’s magnetic field is confined
by the solar wind to a volume called the magnetosphere and its
outer boundary surface is called the magnetopause (see Fig. 5).
A fraction of the solar wind particles enters through the magnetopause to the plasma sheet, creating a large reservoir of charged
particles in the Earth’s distorted nightside magnetic field known
as the magnetotail. These solar wind particles are transported
inward to the ring current region during magnetic storms. The
second source is the ionosphere which provides a significant
outflow of charged particles to the plasma sheet in association
with the physical processes for auroral arc formation [16], [17].
Whether the dominant source for the ring current is the solar
wind or the ionosphere depends on a number of parameters
such as the storm intensity, the phase of the solar cycle, and the
strength of solar ultraviolet emission which influences the ionization rate in the ionosphere. Observations have indicated that
ionospheric ions like singly charged oxygen ions may dominant
over the usually most abundant protons in intense geomagnetic
storms briefly around their main phase [18]. Protons which are
most abundant during less intense storms may also be originated
from the ionosphere.
The storm-time ring current population gradually becomes
depleted by a number of processes. A charged particle may collide with a neutral particle (i.e., one which carries no electric
charge) in the magnetosphere, exchange the charge with it and
escape from the confinement of the magnetic field. A ring current particle may loose its energy by Coulomb collision with
another charged particle of lower energy in the magnetosphere.
A ring current particle may also get into a trajectory, perhaps
through its interaction with plasma waves, which brings it down
to the ionosphere where it collides with a dense atmosphere and
loses its energy. A ring current particle may diffuse through the
magnetosphere due to electric and magnetic fluctuations or be
transported by electric field inside the magnetosphere, eventually escaping from the magnetosphere. In fact, this flux leakage
is an important source of energetic charged particles outside the
magnetosphere [19].
IV. FORMATION OF THE STORM-TIME RING CURRENT
The most significant increase in the ring current population
during magnetic storms is in the inner magnetosphere within a
. At present, there are two basic
geocentric distance of
views on the storm-time ring current formation. The conventional idea is that a magnetic storm results from the accumulation of many elementary disturbances, termed magnetospheric
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
Fig. 5. Illustration of the various electric currents in space from the interaction between the solar wind and the Earth’s magnetic field. Enclosing the magnetosphere
are the dayside and nightside magnetopause currents. The magnetosphere is shaped like a comet with the magnetic field stretched in the nightside to form the
magnetotail. A cross-tail current flows in the equatorial plane of the magnetotail within the plasma sheet. This current links with the auroral ionosphere through
field-aligned currents. Earthward of the plasma sheet is the ring current encircling the Earth.
substorms, manifested most vividly in the polar region [20].
Each substorm produces an enhanced westward electric field
in the outer ring current boundary and brings the particles in
from the plasma sheet, a phenomenon known as substorm injection [21], as illustrated in Fig. 6(a). Equation (3) indicates
that an electric field leads to particle motion called convection
which is independent of charge and mass so that all particles
move in a coherent fashion (no electric current is generated by
convection). Enhanced convection competes in the radial transport of the ring current particles with the curvature and gradient
drifts which move the particles azimuthally instead. The plasma
sheet population may be modified during the substorm process
such that more ionospheric particles contribute to the ring current population as magnetic storms evolve. Subsequently, the
ring current particles move further inward by electric field fluctuations as predicted by early theoretical study of ring current
formation which describes the ring current formation by a diffusion equation [22]. The time evolution of the distribution funcfor ring current particles with energy
on the
tion
-shell (averaged over their bounce motion and their phase of
gyration) can be described by [23]
(9)
where the radial diffusion coefficient due to electric impulses is
given by
(10)
is the distance to the subsolar dayside magHere
is the equatorial magnetic field at the subsolar
netopause,
is the power spectral density of elecmagnetopause, and
tric impulses at the frequency of the particles’ drift motion
around the Earth. Note that the radial diffusion coefficient depends on the sixth power of the value so that the diffusion becomes less efficient as the particles approach closer to the Earth.
Overall, this view on storm onset implies that the cause and the
intensity of magnetic storms may be traced to the factors which
determine the frequency and intensity of each substorm.
A challenge to the view of a storm as a sum of substorms
has surfaced early on and has become more noticeable recently.
Observations indicate that magnetic storms arise from a specific
solar wind condition which is favorable for setting up a largescale electric field in the magnetosphere to transport charged
particles from the plasma sheet to the inner magnetosphere. The
favorable condition is long-duration ( 3 h) of strong southward
nT) [24]. In addition,
interplanetary magnetic field (
LUI: TUTORIAL ON GEOMAGNETIC STORMS AND SUBSTORMS
(a) Storm as a sum of frequent substorms.
(b) Storm as a prolonged strong convection.
Fig. 6. Schematic diagrams to illustrate the two views for the onset of
a geomagnetic storm: (a) it is the accumulated effects of frequent intense
substorms which progressively build up the storm-time ring current, and (b) it
is an enhanced and prolonged magnetospheric convection event.
as mentioned earlier, the Dst index is commonly used to measure the storm intensity. From a study of the substorm effect on
the Dst index, it was found that the rate of increase in the magnitude of the Dst index during magnetic storms does not become
greater with substorm development [25]. In other words, if we
take the Dst index to be a true indicator on the buildup of the
storm-time ring current, then a substorm tends to cause the ring
current to develop less rapidly than before the substorm onset.
Furthermore, it is estimated that the induction electric field associated with substorms is not effective in the radial transport of
where the ring current
particles to geocentric distances
population increases most significantly during magnetic storms
[26], [27]. These points are used to justify the new view that
sustained enhancement of magnetospheric electric field rather
than frequent occurrence of intense substorms is the reason for
the ring current formation. In other words, a magnetic storm is
a result of sustained strong magnetospheric convection, as illustrated in Fig. 6(b).
However, this new view is not without its own challenges. Numerical simulations have shown that the buildup of the ring current is effective from an enhanced convection only initially (for
the first 3 h) [28], [29]. Continual presence of a steady convection gives no further increase in the ring current thereafter.
This is understandable because strong convection also removes
particles from the magnetosphere through the dayside magnetopause. On the other hand, the ring current can be continuously
built up after this initial rise by electric field fluctuations, which
may be substorm-related or variations in the convection electric
field. Nevertheless, there is little doubt that each substorm injects particles into the ring current region and thus is expected
to contribute to the strengthening of the ring current. The lack
of clear indication of ring current buildup from substorm development in the Dst index may well be a defect of the Dst index
in portraying the true ring current intensity [31]. Note that the
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ring current gives a negative perturbation of the -component
on the ground while the current system associated with a substorm (to be discussed later) gives a positive perturbation [30].
As a result, the true strengthening of the ring current may well
be masked by the substorm current system. A better index than
the Dst index in monitoring the ring current population needs
to be developed to overcome this deficiency [31], [32]. The argument that substorms are ineffective in radial transport can be
countered by evidence that substorm onsets during storms occur
at very low latitudes on the ground, i.e., very close to the Earth
in the magnetosphere, so that substorm-energized particles need
not be transported from far to contribute to the ring current population.
A synthesis of the old and new ideas may well be the correct scenario for storm development. Both steady convection
and substorms play important roles in storm-time ring current
formation. The former provides the initial rise of the ring current
population while the latter provides the particle source as well
as the continual buildup after the initial rise from convection by
diffusion due to electric field impulses generated by substorm
activity. While solar wind fluctuations may generate convection electric field fluctuations, the ones generated by substorms
are larger in magnitude and thus are more efficient in inward
transport of particles. On the other hand, numerical simulations
show that transport (convective or diffusive) cannot account for
a large storm unless there is a stormtime enhancement of the
plasma sheet distribution [28], [29], [33]. This suggested scenario of ring current buildup is consistent with numerical simulations which can isolate these different factors and is also compatible with observations indicating that larger storms generally
have two or more distinct episodes of ring current enhancements
[34].
V. SUBSTORM PHENOMENA
Substorm disturbances are seen over many regions in the
near-Earth space. Three different phases of a substorm have
been defined: growth, expansion, and recovery [35], [36]. Substorms may occur so frequently that they overlap. Therefore, the
best way to identify clearly substorm features in each of these
phases is to examine an isolated substorm with observations
from multiple ground stations and satellites distributed within
the magnetosphere [37]. From such investigations, the key
substorm phenomena are identified.
The very quiet magnetospheric condition corresponds typically to northward interplanetary magnetic field (IMF) and a
small polar cap encircled by the global distribution of auroral
arcs. The polar cap is the region at Earth which contains magnetic field lines connected to the IMF. Growth phase usually
begins with the start of southward turning of the IMF. In the
ionosphere, the polar cap size increases as the ionospheric electrojets (currents) in the polar region intensify. In the magnetosphere, the cross-section of the magnetotail enlarges. Plasma
sheet thinning develops in the near-Earth magnetotail ( 5–15
downstream), altering the dipolar field there to become taillike.
Fig. 7 illustrates some key disturbances attributed to substorm expansion activity. At substorm expansion onset one of
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
netic stations (opposite in effect to the storm-time ring current).
Referring back to Fig. 7(e), thinning of the plasma sheet commences at further downstream distances in the mid-tail. Transient fast plasma flows are detected in the central plasma sheet,
along with impulsive and highly fluctuating electric and magnetic fields.
Recovery phase begins when the poleward expansion of the
auroral bulge halts. The last episode of expansion usually exhibits a major auroral arc brightening over an extended portion
of the poleward front of the auroral bulge. In the mid-tail region
( 15–80
downstream), plasma sheet suddenly thickens
with fast plasma flows, predominantly field-aligned, at the
plasma sheet boundary. In the distant tail region [Fig. 7(f)],
magnetic field shows a northward then southward swing. This
is typically accompanied by tailward streaming of energetic
electrons at the plasma sheet boundary. These features are
interpreted as signatures of a plasmoid in which energized
particles are enclosed by closed loops of magnetic field.
VI. SUBSTORM THEORIES
Fig. 7. Diagram to illustrate several key substorm phenomenon. The substorm
onset time is indicated by the vertical dashed lines in the panels. The ground
activity is shown by the H -component of the magnetic field at high latitude
stations (H -high) and at mid-latitude stations (H -mid). The micropulsation at
onset is indicated by the H trace. The increased fluxes of energetic particles at
the geostationary altitude and in the near-tail region are indicated by the J traces.
The magnetic field dipolarization in these regions is indicated by the B trace.
Magnetic turbulence at the current sheet is often seen prior to dipolarization
in the near-tail at substorm onset. Plasma sheet thinning in the mid-tail region
is often seen by drops in number density (N trace) and temperature (T trace).
Plasma flow (V trace) may occasionally be tailward before dropout and become
earthward at plasma sheet recovery. Observation in the distant tail often show a
transient increase in the total magnetic field magnitude (B trace) accompanied
by a north-then-south excursion of the B component and tailward plasma flow
(V trace). These are interpreted as signatures of a plasmoid being ejected down
the tail.
1
the nightside auroral arcs, typically the most equatorward one
in the midnight sector, brightens suddenly, breaks up, and expands poleward [Fig. 7(a)]. This activity builds up to an auroral bulge in which its westward end exhibits one or multiple
surge forms. The -components at high-latitude ground magnetic stations show large negative excursions while those at midlatitude and equatorial stations show small positive excursions
[Fig. 7(b)]. Micropulsations with periodicities in the 40–150s
range, called Pi2, are often observed in these magnetograms.
In the near-tail region [Fig. 7(c)] and at the geostationary altitude [Fig. 7(d)], the stretched tail-like configuration developed
during the growth phase relaxes abruptly to a dipolar-like field
geometry. Earthward injection of energetic particles and thickening of the plasma sheet are seen. This field dipolarization is
often preceded by large magnetic fluctuations suggestive of a
turbulent state. The change in the current system can be regarded
as a rerouting of a portion of the cross-tail current from the tail
to the ionosphere, as illustrated in Fig. 8. This current system is
called the substorm current wedge and produces positive perturbation in the -component at mid-latitude and equatorial mag-
There are many theories for substorm. In general, they may
be classified into four categories: (a) those based on some internally triggered or externally driven processes in the near-Earth
region, (b) those based on magnetic reconnection occurring in
in the tail, (c) those
the mid-tail region downstream of 20
based on coupling between the ionosphere and magnetosphere,
and (d) those based on abstract descriptions of nonlinear dynamics without specifying the physical process.
Fig. 9 shows a schematic diagram for the first category of substorm theories. The most equatorward arc is associated with an
intense cross-tail current and an electric field which enhances
the local current density to excite a current-driven instability.
The onset of the instability and its ensuing turbulence disrupt
the cross-tail current and diverts its path to the ionosphere. The
disruption injects particles earthward and thickens the plasma
sheet. Tailward of the disruption, a rarefaction wave is launched
which causes further thinning of the plasma sheet. Magnetic reconnection develops later at a current disruption site which then
produces overall thickening of the plasma sheet and tailward
ejection of a plasmoid.
The possible candidates for current disruption are the
cross-field current instability [38], [39], the ballooning instability [40]–[42], or the convection electric field reduction
due to external solar wind condition [43]. Fig. 10 illustrates
the basic physics principle behind the cross-field current
instability which encompasses the modified two-stream and the
Ion-Weibel instabilities [44]. The existence of an intense current indicates a large relative drift between ions and electrons
which is a form of free energy available to excite waves. An
obliquely propagating wave (generated out of thermal noise)
may be excited through its interaction with both ions and
electrons. Since electrons have small gyroradius and are tied to
the magnetic field line, they have to go a long distance along
the field to interact with the ions, as illustrated in Fig. 10(a).
This long path essentially makes electrons behaving like the
heavy ions in the sense that their apparent inertia in interacting
with the waves is like that of ions. This effect allows them
LUI: TUTORIAL ON GEOMAGNETIC STORMS AND SUBSTORMS
1861
Fig. 8. Diagram of the equatorial cross-section of the magnetosphere to illustrate the diversion of the cross-tail current during substorm expansion. Current paths
are drawn with arrows indicating the current flow direction. The times below each panel refers to the time after substorm expansion onset.
Fig. 9. Main features of the category of substorm models which places the
substorm onset in the near-Earth magnetotail. The sequential developments are
numbered from 1 to 6 accordingly.
to exchange momentum with the ions efficiently through the
wave. As a result, the relative drift between ions and electrons
is reduced, i.e., current disruption. In cold plasma theory, the
instability is described by
(11)
Fig. 10. (a) Modified two-stream instability. The excited wave propagates
obliquely to the magnetic field as indicated by the wavenumber vector k.
Ions have large gyroradius and can interact with the wave readily while
electrons have small gyroradius and have to travel a long distance along the
magnetic field line to interact with the wave. (b) The Ion–Weibel instability.
The wave propagating along the magnetic field causes bunching (n >0) of
the current-carrying ions which in turn amplify the wave. For both instabilities,
the free energy from the relative drift between ions and electrons, i.e., electric
current, is reduced in exciting the wave.
Here,
and
plasma frequency and gyrofrequency for electrons, respectively;
ion plasma frequency;
relative drift between ions and electrons;
angle between magnetic field and wave propagation direction;
wavenumber;
complex quantity in which the real part is the
wave frequency and the imaginary part is the
growth or damping rate.
For the Ion–Weibel instability, the ion response to a wave
propagating along the magnetic field can be written as
(12)
represents the relative drift between ions and elecAgain,
, the wave magnetic
trons, as illustrated in Fig. 10(b). At
accelerates the ions upward while at a distance of half
field
wavelength away, the wave magnetic field changes direction and
accelerates the ions there downward. This causes a bunching
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
Fig. 12. Diagram to illustrate the idea that a substorm current wedge can be set
up by reduction in convection and differential drifts of particles in the plasma
sheet [43].
Fig. 11. Ballooning instability is analogous to the Rayleigh–Taylor instability
for a heavy fluid resting on a light one. The normal orientation of the
magnetosphere is rotated 90 to express the centrifugal force in ballooning
instability being analogous to the gravitational force in the Rayleigh–Taylor
instability. The centrifugal force acts on the particles within the magnetic flux
tube and displaces them tailward when the particle pressure is sufficiently high.
Particle pressure is relieved by inflating the weakest point in the magnetic flux
tube.
of ions in layers (parallel to the -plane in the figure) half a
wavelength apart. Since the ions are carrying the current, the ion
bunching causes an enhanced current layer which further amplifies the initial wave magnetic field. The ensuing turbulence
of this current filamentation extracts the free energy from the
relative drift of ions and electrons and disrupts the current. In
cold fluid theory, this instability is a purely growing mode with
, where is the velocity of light.
growth rate
The basic physics of the ballooning instability can be gained
by drawing its analogy to the Rayleigh–Taylor instability
for a heavy fluid resting on a light one. In the ballooning
instability, the centrifugal force associated with magnetic field
line curvature takes up the role of gravitational force in the
Rayleigh–Taylor instability, as illustrated in Fig. 11 [45]. The
buildup of current density at the inner edge of the plasma sheet
produces a large pressure gradient, similar to the inflation of
a balloon. If the tailward displacement of particles is energetically favorable, the system relaxes by releasing its pressure
tailward, thus reducing the pressure gradient [and the current
density, see (7)] locally. The consequence of this instability
actually leads to a thinner plasma sheet with a higher current
density tailward of the disruption site than before.
For the idea of externally driven reduction in the magnetospheric convection electric field, it is postulated that the interplanetary electric field can readily penetrate into the magnetosphere. Northward turning or reduction of the dawn–dusk component of the IMF could reduce magnetospheric convection.
Once the convection electric field is reduced sufficiently, higher
energy ions will drift more rapidly westward than the lower energy ions due to the energy dependence of the curvature and
gradient drifts. The change of field-aligned current is
(13)
where is the particle pressure and
is the thermal energy.
The dawn–dusk profile of the thermal energy due to the paron the dusk side and
ticle drifts would lead to
on the dawn side. As a result, a current system
consistent with the substorm current wedge is set up. The development under this scheme is illustrated in Fig. 12 [43].
Fig. 13 depicts the model in the second category which
is known as the near-Earth neutral line model [46], [47]. In
essence, a near-Earth X-type magnetic neutral line is formed
a few minutes
at the downstream distance beyond 20
before substorm expansion onset on the ground. Fast Earthward
plasma flows are created Earthward of the X-line. Braking of
this flow in the near-Earth region creates an eastward inertial
current in the equatorial plane which closes in the ionosphere
to form the substorm current wedge. Tailward of the X-line, the
plasma sheet is severed and a plasmoid is formed and ejected
downstream. The neutral line stays in the near-Earth region
until substorm recovery, at which time it moves downstream,
causing the plasma sheet Earthward of the neutral line to
thicken. The process responsible for the X-line formation is
still an open question. Early studies suggested tearing mode
instability [48], [49] but later studies found the mode to be
heavily damped in a realistic current sheet whenever a small
magnetic field normal to the current sheet is present [50], [51].
This instability appears to require imposing a large nonlinear
tearing mode perturbation on the tail current sheet to drive it to
a nonlinear stage or to require the aid of another process [52],
[53].
The third category of substorm models emphasizes on the amplification of field-aligned currents by Alfvén waves bouncing
between the ionosphere and the magnetosphere [54]–[56]. Due
to a mismatch of impedance between the two regions, each reflection of Alfvén waves at the ionosphere amplifies the associated field-aligned current, thus producing a large positive
feedback mechanism to generate the substorm current wedge.
No specific prediction about the plasma sheet dynamics emerge
from this approach. For instance, there is no definite prediction
about thinning and thickening of plasma sheet, magnetic turbulence, plasma flows, and plasmoid formation.
LUI: TUTORIAL ON GEOMAGNETIC STORMS AND SUBSTORMS
1863
Fig. 13. Main features for the near-Earth neutral line model. Magnetic reconnection in the mid-tail creates earthward plasma flows which brake at the near-Earth
region. An eastward inertial current is set up which closes in the ionosphere by driving field-aligned currents downward at its eastward end and upward at its
westward end [38].
The fourth category of substorm models uses abstract
descriptions from nonlinear dynamics to obtain the statistical
characteristics of substorms [57]–[61]. Under this approach,
the power law slope found in distributions of energy dissipation, size, and duration associated with substorms could be
understood in terms of a simple avalanche system. However,
these models do not provide any specific physical process for
substorm onsets which can be evaluated with observations.
A synthesis of these models seems likely to be the most
probable scenario of substorm development [62]. This is illustrated in Fig. 14 in which the columns depict, respectively, the
auroral activity, the magnetospheric activity in the noon–midnight cross-section and at the equatorial projection during the
different phases of a substorm. The location of substorm onset
to be linked with the most equatorward auroral arc is due to
the electric field associated with an auroral arc and the intense cross-tail current associated with the most equatorward
arc [63]. The substorm expansion onset occurs when the intense
cross-tail current built up in the near-Earth region suddenly becomes reduced drastically within a narrow longitudinal sector,
as illustrated in the second row of the middle column. This current disruption arises from the onset of internal instabilities or
convection reduction as described in the first category of substorm models, producing magnetic turbulence in the disruption
region. The ionosphere plays a significant role in restraining or
promoting further current diversion, incorporating an essential
feature of the third category of models. The magnetosphere also
plays a role in determining the eventual outcome of the activation by the free energy content in the activity site. If the free
energy content is limited, even a favorable ionospheric response
will not lead to a large dissipation. Current disruption, which
can occur in multiple sites, leads to substorm injection and
plasma sheet thickening. One of these current disruption sites
may eventually develop to a large-scale magnetic reconnection
site as envisioned by the second category of substorm models.
This is one possible sequence, probably the most common scenario for substorms.
Since solar wind condition can be very different for different
substorms, it is quite conceivable that substorm development
under some solar wind condition and past history of magnetospheric activity may deviate from the above scenario and resemble the sequence described by the second category. Therefore, it may not be meaningful to attribute one physical process
to be responsible for all substorm onsets or a fixed sequence of
for all substorm evolution [64]. Ideas developed along the category of current disruption are consistent with this philosophy.
For instance, the latest theoretical work attributes turbulence associated with current disruption to more than one plasma instability, kinetic ballooning and cross-field current instabilities
[65]. Furthermore, the threshold of current disruption depends
crucially on the local condition and can be triggered over a wide
range of downstream distance in the magnetotail. Therefore,
current disruption occurring first in mid-tail region for some
substorms is not unexpected. In addition, current disruption at
one site instigates current disruption at the adjacent regions [38],
[39] and therefore fits in well with the nonlinear dynamics treatment of substorms as a kind of avalanche event [66], [67].
VII. SOME OUTSTANDING QUESTIONS
We conclude this tutorial by highlighting some important issues to be resolved in future work to gain better understanding
of onsets of storms and substorms. The evidence for storms not
due to the accumulated effects of substorms relies heavily on
how well the Dst index portrays the true intensity of the ring
current. The reliability of the Dst index in monitoring the ring
current strength has been in question for a while [31]. There
is another means to measure the ring current intensity which is
being investigated only recently. This is through the monitoring
of the energetic neutral atoms emissions [68]–[72] which could
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IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
Fig. 14. Schematic diagram to illustrate the major elements in the substorm synthesis model. The substorm onset occurs in the near-Earth region with current
disruption. The ionosphere plays a major role in enhancing or quenching further disruption of the cross-tail current. Current disruption spreads tailward and a
near-Earth neutral line eventually develops at one of the current disruption sites. This synthesis incorporates key features in many substorm models.
be used to infer the total energy content of the ring current ion
population. This method will offer a way to determine the ring
current intensity without the interference from the tail current
system which the Dst index suffers. Another important issue on
storms is to address the relative importance of different loss processes for the storm-time ring current during all the phases of a
storm.
For substorms, a large number of the onset mechanisms are
not well understood. For instance, the near-Earth neutral line
model calls for the formation of a neutral line in the mid-tail region. How is this crucial region formed? What is the non-MHD
process operating in the diffusion region of magnetic reconnection? How is the mid-tail reconnection linked to field line
of the most equatorward arc in the near-Earth region? How
are magnetic fluctuations in current disruption events formed
in this model? For models with near-Earth instabilities as the
onset mechanisms, what is the nonlinear evolution of these instabilities? How do these instabilities couple to the large-scale
evolution of the magnetosphere? Most of these questions are
quite challenging, but their answers would definitely advance
significantly our present understanding of storms and substorms.
LUI: TUTORIAL ON GEOMAGNETIC STORMS AND SUBSTORMS
ACKNOWLEDGMENT
The author is grateful to M. W. Chen and E. E. Hume, Jr., for
discussions on the early version of the manuscript.
REFERENCES
[1] B. T. Tsurutani, W. D. Gonzalez, Y. Kamide, and J. K. Arballo, “Magnetic storms,” in AGU Monograph 98 Washington, DC, 1997.
[2] A. Schmidt, “Erdmagnetisumus,” in Enzyklopädie der mathematischen
wissenschaften: Band VI, Leipzig, Germany, 1917.
[3] S. Chapman, “An outline of a theory of magnetic storms,” Proc. R. Soc.
London, Ser. A, vol. 95, p. 61, 1918.
[4] L. A. Frank, “On the extraterrestrial ring current during geomagnetic
storms,” J. Geophys. Res., vol. 72, p. 2753, 1967.
[5] P. H. Smith and R. A. Hoffmann, “Ring current particle distributions
during the magnetic storms of December 16–18, 1971,” J. Geophys.
Res., vol. 78, p. 4731, 1973.
[6] D. J. Williams, “Ring current composition and sources: An update,”
Planet. Space Sci., vol. 29, p. 1195, 1981.
[7] H. Alfvén, Cosmical Electrodynamics, Oxford, U.K.: Oxford University
Press, 1950.
[8] S. F. Singer, “A new model of magnetic storms and aurorae,” EOS Trans.
AGU, vol. 38, p. 175, 1957.
[9] A. T. Y. Lui, R. W. McEntire, and S. M. Krimigis, “Evolution of the ring
current during two geomagnetic storms,” J. Geophys. Res., vol. 92, pp.
7459–7470, 1987.
[10] A. J. Dessler and E. N. Parker, “Hydromagnetic theory of geomagnetic
storms,” J. Geophys. Res., vol. 64, p. 2239, 1959.
[11] N. Sckopke, “A general relation between the energy of trapped particles
and the disturbance field near the earth,” J. Geophys. Res., vol. 71, p.
3125, 1966.
[12] L. R. Lyons and D. J. Williams, Quantitative Aspects of Magnetospheric
Physics. Dordrecht, The Netherlands: Reidel, 1984.
[13] G. K. Parks, Physics of Space Plasmas. Redwood City, CA: AddisonWesley, Reidel, 1991.
[14] M. G. Kivelson and C. T. Russell, Eds., Introduction to Space Physics,
Cambridge, U.K.: Cambridge Univ. Press, 1995.
[15] T. I. Gombosi, Physics of Space Environment, Cambridge, U.K.: Cambridge Univ. Press, 1998.
[16] C. R. Chappell, T. E. Moore, and J. H. Waite, Jr., “The ionosphere as
a fully adequate source of plasma for the Earth’s magnetosphere,” J.
Geophys. Res., vol. 92, p. 5896, 1987.
[17] A. W. Yau, E. G. Shelley, and W. K. Peterson, “Energetic auroral and
polar ion outflow at DE 1 altitudes: Magnitude, composition, magnetic
activity dependence, and long-term variations,” J. Geophys. Res., vol.
90, p. 8417, 1985.
[18] D. C. Hamilton, G. Gloeckler, F. M. Ipavich, W. Studemann, B. Wilken,
and G. Kremser, “Ring current development during the great geomagnetic storm of February 1986,” J. Geophys. Res., vol. 93, p. 14 343, 1988.
[19] S. M. Krimigis, D. Venkatesan, J. C. Barichello, and E. T. Sarris, “Simultaneous measurements of energetic protons and electrons in the distant
magnetosheath, magnetotail and upstream in the solar wind,” Geophys.
Res. Lett., vol. 5, p. 961, 1978.
[20] S.-I. Akasofu, Polar and Magnetospheric Substorms. Norwell, MA.:
Reidel, 1968, p. 5.
[21] C. E. McIlwain, “Substorm injection boundaries,” in Magnetospheric
Physics, B. M. McCormac, Ed. Hingham, MA: Reidel, 1974, p. 143.
[22] L. R. Lyons and M. Schulz, “Access of energetic particles to stormtime
ring current through enhanced radial diffusion,” J. Geophys. Res., vol.
94, p. 5491, 1989.
[23] C.-G. Fälthammar, “Effects of time dependent electric fields on geomagnetically trapped radiation,” J. Geophys. Res., vol. 70, p. 2503, 1965.
[24] W. D. Gonzalez and B. T. Tsurutani, “Criteria of interplanetary parameters causing intense magnetic storms (
100 nT),” Planet. Space
Sci., vol. 35, p. 1101, 1987.
[25] T. Iyemori and D. R. K. Rao, “Decay of the
field of geomagnetic
disturbance after substorm onset and its implication to storm-substorm
relation,” Ann. Geophysicae, vol. 14, p. 608, 1996.
[26] R. A. Wolf, J. W. Freeman, Jr., B. A. Hausman, R. W. Spiro, R.
B. Hilmer, and R. L. Lambour, “Modeling convection effects in
magnetic storms,” in Magnetic Storms, B. T. Tsurutani and Y. Kamide,
Eds. Washington, D.C.: AGU, 1996, p. 161.
[27] M.-C. Fok, T. E. Moore, and D. C. Delcourt, “Modeling of inner plasma
sheet and ring current during substorms,” J. Geophys. Res., vol. 104, p.
14 557, 1996.
Dst < 0
Dst
1865
[28] M. W. Chen, M. Schulz, and L. R. Lyons, “Simulations of phase space
distributions of stormtime proton ring current,” J. Geophys. Res., vol.
99, p. 5745, 1994.
[29] M.-C. Fok , T. E. Moore , and M. E. Greenspan, “Ring current development during storm main phase,” J. Geophys. Res., vol. 101, p. 15 311,
1996.
[30] G. Rostoker, W. Baumjohann, W. D. Gonzalez, Y. Kamide, S.
Kokubun, R. L. McPherron, and B. T. Tsurutani, “Comment on
field of geomagnetic disturbance after substorm
‘Decay of the
onset and its implication to storm-substorm relation’,” Ann. Geophys.,
vol. 15, p. 848, 1997.
[31] W. H. Campbell, “Geomagnetic storms, the
ring-current myth and
lgonormal distributions,” J. Atm. Terr. Phys., vol. 58, pp. 1171–1181,
1996.
[32] W. Sun and S.-I. Akasofu, “On the formation of the storm-time ring
current belt,” , submitted for publication.
[33] J. U. Kozyra, V. K. Jordanova, J. E. Borovsky, M. F. Thomsen, D. J.
Knipp, D. S. Evans, D. J. McComas, and T. E. Cayton, “Effects of
a high-density plasma sheet on ring current development during the
November 2–6, 1993, magnetic storm,” J. Geophys. Res., vol. 103,
p. 26 285, 1998.
[34] N. Yokoyama and Y. Kamide, “Statistical nature of geomagnetic
storms,” J. Geophys. Res., vol. 102, no. 86, p. 189, 1981.
[35] S.-I. Akasofu, “The development of the auroral substorm,” Planet. Space
Sci., vol. 12, pp. 273–282, 1964.
[36] R. L. McPherron, C. T. Russell, and M. Aubry, “Satellite studies of magnetospheric substorms on August 15, 1968, 9, Phenomenological model
for substorms,” J. Geophys. Res., vol. 78, p. 3131, 1973.
[37] A. T. Y. Lui, D. J. Williams, R. W. McEntire, S. Ohtani, L. J. Zanetti,
W. A. Bristow, R. A. Greenwald, P. T. Newell, S. P. Christon, T. Mukai,
K. Tsuruda, T. Yamamoto, S. Kokubun, H. Matsumoto, H. Kojima, T.
Murata, D. H. Fairfield, R. P. Lepping, J. C. Samson, G. Rostoker, G. D.
Reeves, A. S. Rodger, and H. J. Singer, “Multi-point study of a substorm
on February 9, 1995,” J. Geophys. Res., vol. 103, pp. 17 333–17 343,
1998.
[38] A. T. Y. Lui, C.-L. Chang, A. Mankofsky, H.-K. Wong, and D. Winske,
“A cross-field current instability for substorm expansions,” J. Geophys.
Res., vol. 96, p. 11 389, 1991.
[39] A. T. Y. Lui, “Current disruption in the Earth’s magnetosphere: Observations and models,” J. Geophys. Res., vol. 101, p. 13 067, 1996.
[40] A. Roux, S. Perraut, P. Robert, A. Morane, A. Pedersen, A. Korth, G.
Kremser, B. Aparicio, D. Rodgers, and R. Pellinen, “Plasma sheet instability related to the westward traveling surge,” J. Geophys. Res., vol. 96,
p. 17 697, 1991.
[41] G. M. Erickson, “Substorm theories: United they stand, divided they
fall,” Rev. Geophys., vol. 33, p. 685, 1995.
[42] W. W. Liu, “Disruption of thin current sheets: A two-fluid theory,” J.
Geophys. Res., vol. 102, p. 14 331, 1997.
[43] L. R. Lyons, “Substorms: Fundamental observational features, distinction from other disturbances, and external triggering,” J. Geophys. Res.,
vol. 101, p. 13 011, 1996.
[44] A. T. Y. Lui, P. H. Yoon, and C.-L. Chang, “Quasi-linear analysis of ion
Weibel instability in the Earth’s neutral sheet,” J. Geophys. Res., vol. 98,
p. 153, 1993.
[45] S.-I. Ohtani and T. Tamao, “Does the ballooning instability trigger
substorms in the near-Earth magnetotail,” J. Geophys. Res., vol. 98, p.
19 369, 1993.
[46] E. W. Hones, Jr., J. R. Asbridge, S. J. Bame, and S. Singer, “Substorm
= 6
to
variations of the magnetotail plasma sheet from
= 60 ,” J. Geophys. Res., vol. 78, p. 109, 1973.
[47] K. Shiokawa, G. Haerendel, and W Baumjohann, “Azimuthal pressure
gradient as driving force of substorm currents,” J. Geophys. Res., vol.
25, p. 963, 1998.
[48] B. Coppi, G. Laval, and R. Pellat, “Dynamics of the geomagnetic tail,”
Phys. Rev. Lett., vol. 16, p. 1207, 1966.
[49] K. Schindler, “A theory of the substorm mechanism,” J. Geophys. Res.,
vol. 79, p. 2803, 1974.
[50] R. Pellat, F. V. Coroniti, and P. L. Pritchett, “Does ion tearing exist?,”
Geophys. Res. Lett., vol. 18, p. 143, 1991.
[51] M. Brittnacher, K. B. Quest, and H. Karimabadi, “A study of the effect
of pitch angle and spatial diffusion on tearing instability using a new
finite element based linear code,” J. Geophys. Res., vol. 103, p. 4587,
1998.
[52] A. P. Kropotkin, O. O. Trubachev, and A. T. Y. Lui, “Nonlinear instability of the geomagnetotail current sheet combining the features of
tearing and cross-field current instabilities,” J. Geophys. Res., vol. 104,
p. 371, 1999.
Dst
Dst
X
0 R
X
0R
1866
[53] M. I. Sitnov and A. T. Y. Lui, “Cross-field current instability as a catalyst
of the explosive reconnection in the geomagnetotail,” J. Geophys. Res.,
vol. 104, p. 6941, 1999.
[54] P. L. Rothwell, L. P. Block, M. B. Silevitch, and C.-G. Falthammer,
“A new model for substorm onsets: The pre-breakup and triggering
regimes,” Geophys. Res. Lett., vol. 15, p. 1279, 1988.
[55] J. R. Kan, “A global magnetosphere-ionosphere coupling model of substorms,” J. Geophys. Res., vol. 98, p. 17 263, 1993.
[56] R. L. Lysak, “Feedback instability of the ionospheric resonant cavity,”
J. Geophys. Res., vol. 96, p. 1553, 1991.
[57] T. S. C. Chang, “Low dimensional behavior and symmetry breaking
of stochastic systems near criticality—Can these effects be observed in
space and in the laboratory?,” IEEE Trans. Plasma Sci., vol. 20, p. 691,
1992.
[58] G. Consolini, M. F. Marcucci, and M. Candidi, “Multifractal structure of
auroral electrojet index data,” Phys. Rev. Lett., vol. 76, no. 21, p. 4082,
1996.
[59] A. J. Klimas, D. Vassiliadis, D. N. Baker, and D. A. Roberts, “The organized nonlinear dynamics of the magnetosphere,” J. Geophys. Res., vol.
101, p. 13 089, 1996.
[60] G. Consolini and P. D. Michelis, “Non-Gaussian distribution function of
AE-index fluctuations: Evidence for time intermittency,” Geophys. Res.
Lett., vol. 25, p. 4087, 1998.
[61] S. C. Chapman, N. W Watkins, R. O. Dendy, P. Helander, and G. Rowlands, “A simple avalanche model as an analogue for magnetospheric
activity,” Geophys. Res. Lett., vol. 25, p. 2397, 1998.
[62] A. T. Y. Lui, “A synthesis of magnetospheric substorm models,” J. Geophys. Res., vol. 96, p. 1849, 1991.
[63] A. T. Y. Lui and J. S. Murphree, “A substorm model with onset location
tied to an auroral arc,” Geophys. Res. Lett., vol. 25, p. 1269, 1998.
[64] A. T. Y. Lui, “Magnetospheric substorms,” Phys. Fluids B, vol. 4, no. 7,
p. 2257, 1992.
[65] C. Z. Cheng and A. T. Y. Lui, “Kinetic ballooning instability for substorm onset and current disruption observed by AMPTE/CCE,” Geophys. Res. Lett., vol. 25, p. 4091, 1998.
[66] G. Consolini et al., “Sandpile cellular automata and magnetospheric dynamics,” in Cosmic Physics in the Year 2000, Aiello et al., Eds, Bologna,
Italy: SIF, 1997, vol. 58.
View publication stats
IEEE TRANSACTIONS ON PLASMA SCIENCE, VOL. 28, NO. 6, DECEMBER 2000
[67] S. C. Chapman, N. W. Watkins, R. O. Dendy, P. Helander, and G. Rowlands, “A simple avalanche model as an analogue for magnetospheric
activity,” Geophys. Res. Lett., vol. 25, p. 2397, 1998.
[68] E. C. Roelof, D. G. Mitchell, and D. J. Williams, “Energetic neutral
atoms (
50 keV) from the ring current IMP-7/8 and ISEE-1,” J.
Geophys. Res., vol. 90, p. 10 991, 1985.
[69] A. T. Y. Lui, D. J. Williams, E. C. Roelof, R. W. McEntire, and D. G.
Mitchell, “First composition measurements of energetic neutral atoms,”
Geophys. Res. Lett., vol. 23, p. 2641, 1996.
[70] A. Milillo and S. Orsini, “Low-altitude energetic neutral atoms imaging
of the inner magnetosphere: A geometrical method to identify the energetic neutral atoms contributions from different magnetospheric regions,” J. Geophys. Res., vol. 101, p. 27 123, 1996.
[71] M. G. Henderson, G. D. Reeves, H. E. Spence, R. B. Sheldon, A. M.
Jorgensen, J. B. Blake, and J. F. Fennell, “First energetic neutral atom
images from polar,” Geophys. Res. Lett., vol. 24, p. 1167, 1997.
[72] A. M. Jorgensen, H. E. Spence, M. G. Henderson, G. D. Reeves, M.
Sugiura, and T. Kamei, “Global energetic neutral atom (ENA) measureindex,” Geophys. Res. Lett.,
ments and their association with the
vol. 24, p. 3173, 1997.
E
Dst
Anthony T. Y. Lui received the Ph.D. degree from
the University of Calgary, Calgary, AB, Canada, in
1974.
He is a Principal Professional Staff at the Applied
Physics Laboratory, The Johns Hopkins University,
Baltimore, MD. His main interests are substorms,
magnetotail, and aurora in which he has performed
data analyses and developed theories to understand
these natural phenomena.