The Bimodal Magnetosphere and Radiation Belt, Ring Current and Tail Transducers
R. B. Sheldon
Physics Dept., University of Alabama in Huntsville
301 Sparkman Dr., Huntsville, AL 35899
18 Sep 1998
It has generally been assumed that a geomagnetic storm is entirely
driven by external forces--e.g., solar wind
Ey=Vx X Bz, Vx,
(where the components of the electric field, E, the magnetic field, B
and velocity, V, are given in GSE coordinates)--which would
imply that particle injections in the ring current (RC) or outer
radiation belts should be highly correlated. However the data from
ISTP are showing that the magnetosphere can have at least two very
different responses to the same solar wind (SW) conditions: a classic,
enhanced RC with Dst response, or a 1000-fold increase
in the outer radiation belt MeV electrons (ORBE). August 29, October
14 and 23, 1996 are examples of Dst storms, whereas April 15, 1996 and
January 10, 1997 are examples of MeV storms. It is this second
response that is so deadly to some geosynchronous spacecraft, whereas
geomagnetic storms are categorized by the first response. Neither of these
appear to be correlated to the SW conditions driving substorms. Why should
the SW energy appear in the radiation belts or the ring current
independently? We hypothesize that the RC couples to the electric
power available (Ey), the ORBE couple to
the mechanical power available (Vx), and the Tail
couples to the magnetic
energy (Bz) available in the SW. The transducer for RC may be
subauroral parallel potentials, the transducer for ORBE may be the
cusp, while the Tail substorm transducer is yet a third independent
mechanism for extracting SW energy. Evidence for this theory
comes from the novel POLAR satellite that traverses
the cusp, the plasmasheet and the radiation belts.
With the launch of POLAR in early 1996, we had the first high
spectral resolution data of the outer radiation belt electrons
(ORBE) simultaneous with geosynchronous (GEO) and highly elliptical orbit
(HEO) monitors of the integral flux. Thus we were in a position to
track the source regions and dynamics of the ORBE with
unprecedented precision. Simultaneously, POLAR was also measuring
the lower energy ions of the ring current (RC) which are
responsible for the majority of the energy density of the dipole
trapped plasma and hence for the magnetic disturbances
characterized by the Dst index (e.g., the Dessler-Parker-Sckopke
relation Dessler59,Sckopke66). We confirmed the
well-known observation that ORBE
enhancements are uncorrelated (in magnitude or occurrence) with
Dst or RC on timescales less
than 48 hours (e.g., Baker86,Baker97) though often the occurrence
of ORBE and Dst are correlated on t>2 day timescales. But in addition to
this t<2 day
uncorrelation of ORBE and Dst, we were surprised to observe that longer
time correlations were weak or absent during the first year (April 96 - March 97
) of the
Figure 1 shows in panel a), daily averages of integral electron
measurements made with dosimeters on a HEO spacecraft, and b) the
Dst index from Jan 1996--Mar 1997. The integral measurements have
ranges as noted, with the lowest E>0.5 MeV channel showing the largest
flux and largest variations. The orbit integrates over
all L-shells at high latitudes, and is therefore dominated by the
high energy fluxes at the lowest L-shells. Note that storms
generally harden the spectrum up to a limiting upper energy.
As can be seen from the plot, the
largest injection of MeV electrons occurred on April 15, 1996,
whereas Dst showed little effect. Likewise the largest Dst
in this time period occurred on October 23, 1996, which produced a
relatively small change in MeV electron flux. Thus we shall adopt
the viewpoint in this paper that
whatever the mechanism producing ORBE, it is separate and distinct
from the mechanism that drives the RC and Dst.
FIGURE 1: Left panels show 400 days from Jan 1, 1996 of ORBE
electrons plotted with Dst. Panel a) are HEO dosimeter orbit
averages in rads/orbit corresponding roughly to E> 0.5 MeV, 1.5
MeV and 2.5 MeV electrons respectively. The orbit integrates over
all L-shells at high latitude, and is therefore dominated by the
high energy fluxes at the lowest L-shells. Note that storms
generally harden the spectrum up to a limiting upper energy.
Panel b) is one hour Dst for the same time period with the largest
excursion on 10/23. Right panels display POLAR/CAMMICE
energy-time spectrograms for August 16, 1998 showing a pass through
the radiation belts. The south polar cap is visible
at 1800UT, with radiation belt passes on both sides. Panels from
top are c) O+, d) He++, e) He+, f) H+ and g) a
sector-roll plot of H+. ``S''-curves in panel g) are empty loss
cones visible as the sector look direction rotates through
0 degrees. Note the injections at 1400, 1430, 1500, 1530
and 1600 UT, especially visible in the He++ data. The last
two injections are visible in the O+ as well. These injections
are accompanied by an isotropization of the distribution as
indicated by the full loss cones in panel g).
However, both ORBE and RC are ultimately driven by the Sun and its
interaction with the magnetosphere; the solar wind is the energy
driver for both systems. How then can they respond separately?
Shouldn't an increase in solar wind energy (say, a high
speed stream) produce an increase in both ORBE and RC? Not if their
acceleration mechanisms, their solar wind energy transducers, are
different. It may even be possible that conditions that favor one
transducer suppress the other, such that the magnetosphere operates
in a bimodal fashion. This paper, then, examines the question
whether the magnetosphere has multiple transducers, and if so,
whether they operate bimodally.
Since one of the goals of the international solar-terrestrial
program (ISTP) was to determine, using multiple spacecraft, ``the
flow of mass, momentum and energy through the magnetosphere'', by
investigating the energy transducers of the RC and ORBE, we are
completing a necessary step in achieving that goal. Therefore in
section 2 we consider the energy storage of the
magnetosphere and its properties. In section 3 we consider
some aspects of the Tail transducer. In section 4 we
examine the ORBE transducer and its coupling to the solar wind. In
section 5 we analyze the RC transducer in the light of new
simulations. In section 6 we reexamine the correlation
of RC with ORBE and the effect of solar cycle variations.
There are three main regions of energy storage in the
magnetosphere, persisting on the order of hours to days and months.
The long geomagnetic tail stores energy in the lobe fields and the
associated current sheet that maintains its structure. The RC
stores energy primarily in the 30 keV/L to 0.12 keV/nT (10-400 keV at L=3)
ions that grad B
drift around the earth in the L=3-5 Re region of the dipole trap.
And the radiation belts, while not storing as great a quantity as
the other two, nonetheless store it in a particularly dangerous
form, hazardous to both humans and mechanized spacecraft.
The time histories of these storage regions are all different. The
tail shows a gradual increase, as solar wind magnetic fields
accumulate, caught by the snag of the earth's dipole field. This
gradual growth is punctuated by sudden releases, substorms, whose
triggering and onset remain areas of ongoing controversy. In
contrast, RC or Dst show long periods of gradual decay broken by
periods of very rapid increase, ``storm injections'' whose precise
mechanism remains elusive, despite increasingly sophisticated
computer simulations. The radiation belts show a similar history as
RC, injections followed by decay. The decay of the RC is generally
days, whereas the ORBE decays on the order of months and the inner
zone protons decay on the order of years. RC injections also occur
in a few hours, whereas ORBE injections generally span a few days.
Each of these storage regions appears to be only weakly correlated
with the others. Substorms can occur before, during or after RC
storms, with no apparent connection to the Dst index. Some have
argued (e.g., Chapman68,Akasofu70)
that storms are generated by multiple intense substorms, though
counter-examples abound. Others contend (e.g., Siscoe97)
that substorms actually divert energy from
the RC into joule heating, acting as brake on the development of
Dst during main phase. The source of ORBE injections has also been
somewhat mysterious for 30 years, with some postulating substorms
as a possible driver, others choosing storms. It is interesting to
note that the ORBE neural net predictor of Koons91
found the best correlation with neither AE nor Dst, but
with Kp. Thus we hypothesize that the magnetosphere
has not one, not two, but at least three separate transducers that
tap into the solar wind energy and store it in the magnetosphere.
We schematically tabulate the properties of these three transducers
in Table 1.
TABLE 1: The Three Solar Wind Transducers
|Property || Tail || storm RC || ORBE
|Geomagnetic Index || AE || Dst || none
|Energy Growth || gradual || sudden || sudden
|Injection Onset || minutes || hours || days
|Energy Decay || sudden || gradual ||gradual
|Decay Rate || minutes || days || months
|Median Energy || few keV || 10-100 keV ||few MeV
|Location || midnight,L>6 ||L=3-6 || L=3-7
|SW Coupling ||Bz || +Ey=VxBz || large Vx
|Nomenclature|| Magnetic|| Electric|| Mechanical
The tail lobe fields store energy and release it depending on the
precise interplanetary magnetic field (IMF) Bz component
(in GSE or GSM coordinates). The
orientation and strength of IMF is by far the controlling factor in
substorm growth and development. In contrast, RC is far better
correlated to the solar wind electric field, given by the product of
solar wind velocity and magnetic field,
E = v X B , which we write in component form,
Ey=VxBz. In fact,
non-linear or quadratic filters have found up to 84% correlation
of Dst with solar wind Ey making this the best understood of
all the transducers (e.g., Gleisner96). Differing from both
of these are the ORBE, which at least during solar minimum, show
the highest correlation to solar wind velocity Vx
This can be seen very nicely in Figure 1a, where a
double coronal hole in the first months of 1996 brought a high
speed solar wind stream to the earth twice in a 27-day solar
rotation. The big ORBE injection of April 15, then, was associated
with the merging and disappearance of this solar stream structure.
Describing these different mechanisms, we refer to the substorm
transducer as magnetic, the RC transducer as electric, and the ORBE
transducer as mechanical.
A second piece of information can be gleaned from Table 1
regarding the timescales of the respective
transducers. The energy storage for the tail is gradually increasing with a
sudden release, which has been likened to a water drop falling from
a faucet. Any acceleration observed during this release
must then occur in minutes, and must be highly efficient. Such
efficient, fast acceleration implies a direct ``first order''
mechanism, e.g., a first order Fermi acceleration. In contrast, the
two day rise of the ORBE mechanism imply a gradual, stochastic,
``second order'' acceleration mechanism. The RC acceleration is a
puzzle, with characteristics of both a slow (several hour)
stochastic and a fast (tens of minutes) direct acceleration
mechanisms. Both mechanisms have been proposed for the RC, though
perhaps their coexistence has not heretofore been postulated. The
key point is that not only do the transducers couple to different
aspects of the solar wind, but their coupling, their acceleration
mechanisms are also fundamentally different. Therefore we examine
each transducer in turn.
The nature of the tail transducer, and particularly its triggering
mechanism has been the focus of intense research over the last
decade. All are agreed, however, that one of the results of a
substorm is a ``dipolarization'' of the magnetic fields in the region
L=5-8 near midnight simultaneous with a strong current driven
through the high latitude ionosphere (e.g., McPherron79). Such a
dipolarization results in two basic accelerations in the
magnetosphere, a betatron acceleration associated with enhanced
field within the gyroorbit (Fillius67 and a first
order Fermi acceleration associated with the decreasing distance
between the mirror points.
The observation of accelerated particles in this ``dipolarization''
region have primarily been made at geosynchronous orbit, generally
with plasma instruments using electrostatic deflection with 10eV-10
keV spectral bandwidth. Within these limitations, McIlwain74
observed two types of substorm injections, those with simultaneous
appearance of all energies, ``dispersionless'', and those with higher
energies arriving first, ``dispersed''. He postulated that dispersed
injections are found earthward of a dispersionless injection, and
time-of-flight effects associated with gradB transport allow
the more energetic particles faster access. Using a semi-empirical
magnetic field model, he was able to derive a spiral
``dispersionless particle injection boundary'' consistent with all
the available observations.
Several observations of the POLAR/CEPPAD may modify this model. On
an inbound pass on August 16, 1996, five dispersed injections were
observed within 2 hours. (See Figure 1 panels c-g).
Each successive injection showed a faster time-of-flight, which by
McIlwain's analysis, would indicate a closer proximity to the
injection boundary. Yet the satellite was inbound, and therefore
moving away from the canonical boundary. It is difficult to
reconcile this with the theory without invoking further assumptions
about moving boundaries.
Furthermore, nearly dispersionless injections are also observed by
POLAR, showing an upper bound to the injection energy of several
tens of keV, a bit above the highest energy resolvable by
electrostatic deflection. The nature of the injections can be seen by
careful inspection of Figure 1. ``S''-curves in panel g) are empty loss
cones visible as the sector look direction rotates through
0o. The injections occur at 1400, 1430, 1500, 1530
and 1600 UT, and are especially visible in the He++ data. The last
two injections are visible in the O+ as well. These injections
are accompanied by an isotropization of the distribution as
indicated by the full loss cones in panel g). Therefore if one truncates
the energy spectrum at 20 keV, as in the first
injection of Figure 1f) at 1400UT for example,
the injection would appear dispersionless and isotropic.
However the experimentally measured
upper cutoff energy of this first dispersionless
injection remains far below the highest energies observed
in the subsequent dispersed injections of
Figure 1f). So we have a puzzle,
the highest energies in dispersed injections are not seen in
dispersionless injections, suggesting that dispersionless
injections may not be the source of the dispersed injections.
The Inductive Gyrobetatron:
Our conjecture is that dispersionless injections have all the
characteristics of the plasmasheet, though at slightly higher
energies. We propose that the southward Bz, which normally
accompanies the substorm growth phase, produces earthward
convection and may displace the inner edge of the plasmasheet
inward while adiabatically heating it, to generate the signature
that POLAR or geosynchronous satellites observe. (There is also some
evidence that a dipolarization also acts to convect the plasmasheet
inward toward geosynchronous orbit Baker91,Li98.) In contrast, the
dispersed signature may be caused by the dipolarization acting on
trapped RC particles, and the resulting spectrum is characteristic of
the dB/dt acceleration. Admittedly, the dB/dt is operating on
this convected plasmasheet population as well, but in principle the
seed population need not have come from a dispersionless injection.
Now as Fillius67 demonstrate, dB/dt acceleration is
energy dependent. The induced voltage on a gyroorbit is
proportional to the area of the orbit, which is energy dependent.
Likewise, the integrated voltage gain is proportional to the number
of gyroorbits during an acceleration interval, which is also energy
dependent. They give the power of a magnetic field
disturbance, Pg, acting on the gyrobetatron as:
Pg = DE/Tg = (g m0 v^2/2B)(dB/dt)
where DE is the energy change, Tg is the period of gyration,
g m0 v^2 is the relativistic kinetic energy, and B is
the magnetic field strength.
This mechanism has more power for higher energy particles, so it
imparts an acceleration that is some percentage of original energy.
Thus it does not change the spectral index of the distribution.
However we did not constrain the dB/dt area in our calculation,
nor the motion of the ions during the acceleration time, both of
which act to limit the highest energies attainable (and make the
adiabatic heating irreversible). In reality, dB/dt varies with
position, and one would expect a higher value near the equator near
midnight at the inner edge of the current sheet. Thus the spectra
evolves continuously through this region, becoming harder as one
approaches the center. The subsequent drift and evolution of these
ions make the ``dispersionless injection'' theorem a zeroeth order
approximation to the actual spectra, and the derivation of an
injection boundary somewhat problematic.
Bimodal with RC:
As a transducer, most of the energy released in a substorm appears
as Joule heating in the ionosphere. Only a small part of the total
is used to inductively heat the near earth plasmasheet. Thus we
should not attribute to the Tail transducer the responsibility for
driving either the storm-time RC or the ORBE. And if Siscoe97
are correct, this transducer parasitically removes energy from the
storm-time RC and dumps it in the auroral zone, thereby making the
Tail transducer bimodal with respect to the storm-time RC
transducer. Alternatively, we could say that the cross-tail
convective electric field is the energy driver for the RC
transducer, which the Tail transducer, by diverting current into
auroral zone, short-circuits. Thus the two transducers may be considered
to be mutually exclusive and ``bimodal''.
This is not to say that the Tail transducer has no enhancing effect
on Dst. Rather, the inductively heated region is important as a
seed population for the quiet RC, and forms the basis of the Dst
increases seen during non-storm injections. We consider this
secondary coupling later in section 5.
Characteristics of the ORBE transducer have been known for 30 years
(McIlwain96), which we summarize briefly. The ORBE show
rapid, non-adiabatic injections, gradual decay, and occasional
adiabatic response to the RC. The decay is consistent with
scattering loss processes, and the adiabatic response has been
modelled very nicely with the Dst index. However the
nature of the non-adiabatic injections have never been sufficiently
explained nor predicted. The best prediction model available,
Koons91, claims to get 70% of the logarithmic variation for
daily average fluences using daily average Kp, but in practice,
they model quiet-time, low-Kp exceptionally well and fail utterly
to predict either onset or magnitude of the injections on high-Kp
days. Since it is these high-Kp injections that are of critical
importance for satellite electronics, NOAA's SEC relies on monitors
rather than predictors of ORBE to warn the community. Normally the
2-day rise time of the ORBE allows at least a 1-day warning of
hazardous conditions, but the Jan 10--11, 1997 storm produced a
T < 8 hour rise time, possibly correlated to a subsequent
communication satellite failure 24 hours later (SN97).
The lesson is clear: we cannot circumvent our ignorance of the ORBE
transducer by playing with neural nets or relying on statistics. If
we want to protect our expensive space assets, we must model the
transducer accurately. To this end, we list some characteristics of
the transducer and a physical model that may predict it. We also
buttress our model with recent observations that verify certain
aspects of the model.
The origin of the MeV electrons is somewhat mysterious. The phase
space density of the solar wind or magnetosheath is much smaller
than the ORBE, excluding them from being a source. Similarly, the
solar wind and magnetosheath normally lack the MV potentials that
can generate the observed energies. Shock acceleration is possible
only during extreme solar wind conditions (e.g., the March 1991
shock, Li93), which are far too rare to explain the
frequency of ORBE injections. Thus most proposed mechanisms rely on
multiple small acceleration steps to reach MeV energies which can be
either resonantly monotonic (e.g., a cyclotron) or randomly
accelerating/decelerating (stochastic energy diffusion).
Although resonant processes have been proposed, they presuppose a
degree of coherence through the magnetosphere or across a gyroorbit
that has rarely been observed. An additional problem occurs as the
gyrofrequency of the accelerated particle changes with energy,
necessitating not just a cyclotron, but a synchrocyclotron
accelerator. Stochastic acceleration solves both these problems at
the price of being far less efficient, such that a second order Fermi
process (Fermi49) shows exponentially longer time for
accelerating to higher energy. This feature, however, may explain
the 2-day rise time of a typical ORBE injection as the
characteristic time of the stochastic accelerator.
A second objection to a stochastic process arises from the same
inefficiency. If it takes two days to energize this population,
there must be a trap that can hold the particles for two days with
sufficient available wave energy. Although the dipole trap has trapping
times of months, phase space densities of ORBE show that the
particles are diffusing into the dipole trap from an exterior
source, rather than being accelerated in situ
(Li97,Selesnick97,Selesnick97b). Furthermore, the strong
magnetic field strength of the inner magnetosphere necessitates
either unrealistically large perturbations or resonant
perturbations to energize the ORBE. One proposed stochastic
mechanism that satisfies these constraints, Nishida recirculation
(Nishida76), is unfortunately also far too inefficient.
The Outer Cusp:
This impasse was cleared by the fortuitous observation of MeV ions
and electrons in the outer cusp (Chen98a,Sheldon98b) which
have only recently been discovered and modelled. Summarizing the
results of these papers, we find MeV electrons trapped in the outer
cusp, L=8--10, near the topological minimum |B| point, with
pitchangle distributions consistent with a ``leaky bottle'' (see
figure 1 of Sheldon98b (S98b)). Tracing electrons through a
Tsyganenko 96 model B-field showed that they were trapped with 3
invariants of the motion, and these invariants had periods much
closer together than the dipole trap (see figure 2 and table 1 of
S98b). Thus they define a second permanent trapping
region of the earth's magnetosphere.
Furthermore, data from the POLAR magnetometer as well as the EFI
electric field instrument and the PWI plasma wave instrument show
extremely large electromagnetic fluctuations with dB/B~1
Chen98a,Chen98b. The combination of weak magnetic fields, large
fluctuations and converging periods of the motion, make the outer
cusp an ideal place for stochastic chaotic acceleration
(Arnold64). And indeed, all the measurements of the outer
cusp events show enhanced phase space densities that exceed both
the neighboring solar wind, magnetosheath, and magnetosphere
populations, indicating a locally accelerated source.
The Energy Driver:
The energy source for these fluctuations in the outer cusp are
related primarily to topology changes. Because the magnetic field
is so weak at the center of the outer cusp, nearby current systems
dominate the topology and the fluctuation wave field. The strongest
such current system is the Chapman-Ferraro (CF) currents of the
magnetopause, but field-aligned currents can also have an effect.
So the source of fluctuation power are not waves per se but
the buffetting that the magnetosphere receives from the solar wind.
Thus the speed of the solar wind, and even more important, the
turbulence of the solar wind should be an important factor in
powering this transducer, which would finally explain the somewhat
mysterious correlation with solar wind Vx.
Now high speed solar wind streams are also found to have very high
levels of Alfvenic turbulence (related to their origin in the
open field-lines of the sun), which at the bow shock, are converted
into pressure pulses. It may be that the higher correlation with
solar wind speed, is really a correlation with solar wind
fluctuation power. Temerin (GGS Goddard workshop, 1997) presented
results showing not only the well-known 70% correlation of ORBE
with solar wind speed, but a 75% correlation with dVSW.
Therefore it appears quite plausible that the ORBE are accelerated
in the stochastic wave field of the outer cusp, and later diffuse
into the dipole region of the magnetosphere.
With the hypothesis of a cusp acceleration region providing ORBE,
we are now skirting with the opposite problem, the great
variability of ORBE injections versus the continuous input of the
cusp. That is, the energy input to the cusp may vary by a factor of
5 or 6, as the solar wind speed changes from a slow 300 km/s to a
blistering 800 km/s, but the ORBE injections typically show
enhancements of 100-1000. Some other process must be invoked to
explain the variability in onset and magnitude of the ORBE
The same feature of the cusp that allows large perturbation fields
also permits large changes in topology. Stronger CF currents put a
larger kink in the cusp fields and make the trap ``deeper'' by
enhancing the mirror fields; substorms remove lobe fields and cause
the cusp to tilt forward. The daily rotation of the earth tips the
cusp forward and backward as well. But most importantly, plasma in
the cusp trap produce a profound modification of the cusp itself,
much as a strengthened RC produces an inflated dipole. But in the
case of the cusp, the trapped plasma generate a diamagnetic cavity
which produces a deeper trap that then holds more plasma, driving a
positive feedback mechanism. The mechanism operates when the
diamagnetic cavity increases the curvature of the field lines that
must go around it. This enhanced curvature leads to faster grad
B drift around the cusp. The cusp ``plasmapause'' is defined by the
competition between E X B drift which would tend to empty
the cusp plasma, and the gradB drift which would constrain
it. Both a heated plasma and a higher curvature field would
increase the volume of the cusp plasmapause, thereby producing a
positive feedback. It this positive feedback, we believe, that so
non-linearly amplifies the solar wind variability in the ORBE
The scenario for an ORBE injection may have the following chain of
events. The cusp is normally empty of any significant trapped
plasma. Then some fortuitous arrangement of dipole tilt and solar
wind speed succeeds in injecting a substantial amount of
magnetospheath plasma down the throat of the cusp. This plasma
generates a deep well that can trap energetic particles. The
ever-present wave field begins to accelerate these particles to
higher and higher energies, which also make the particles more
trapped. Simultaneously the plasma begins to diffuse out of the
trap due to pitchangle scattering. Over the next few days,
exponentially greater numbers of MeV particles are found in the
trap, and begin to diffuse into the outer radiation belts. At some
point, either because sufficient low energy plasma has evaporated,
or because a second solar wind disturbance distorts the cusp, the
cusp loses its ``plug'' of trapped particles and a sudden injection
is observed in the outer radiation belts.
The prototypical example of such a scenario is the Jan 10--11, 1997
storm (see Fig 1 and Geophys. Res. Lett. 25(14), 15 July 1998). A
magnetic cloud brought a weak shock of moderate speed solar wind
that struck the earth at a time very close to winter solstice and
at the maximum diurnal tilt of the southern polar cusp. These
conditions were optimal for driving a plug of plasma deep into the
southern cusp. The southward IMF of the cloud began to produce a
great deal of substorm activity that generated the turbulent energy
needed for accelerating the electrons found in the trap. Roughly
eight hours into the magnetic cloud event, around 1100 UT, the
IMF rotated northward, and a small pressure pulse
arrived at the earth. Either of these events may have been
sufficient to dislodge the plug, and a thousand-fold increase in 2
MeV electrons was observed by POLAR. The eight-hour duration of the
injection was unusually short, and as expected by the Fermi
mechanism, the high energy cutoff of the injection (<3.5 MeV) was
lower (softer) than usual as well.
The Bimodal Cusp:
As we sketched above, the Tail transducer can provide turbulent
energy input into the cusp as well as give the cusp a favorable
topology. So it is clear that the ORBE and Tail transducers may
indeed work together. It is not so clear, however, what the
relationship is between the storm RC and ORBE transducer. We know
that solar wind electric field, Ey, is crucial for driving the
plasmasheet into the RC region. This same electric field can also
appear across the cusp, enhancing the loss of cold plasma from the
cusp, and shrinking the cusp plasmasphere. Therefore conditions
that favor the storm RC will often not favor the ORBE transducer.
On the other hand, major Dst storms are often preceded by an
interplanetary shock that produces the ``storm sudden commencement''
(SSC). This same shock may produce a large enough ``plug'' to survive
an enhanced cusp electric field. Under these conditions, the CF
currents and/or magnetopause electric fields, driven by the same
reconnection that drives the Ey in the plasmasheet, may be
driving enhanced fluctuation power through the cusp, and energizing
any trapped plasma found in the plug. This scenario appears to
describe the conditions of the April 15, 1996 storm, which produced
a large 1-minute SYM and ASY (low-latitude magnetic H-component
index published by Kyoto) as well as the largest ORBE enhancement
of the year.
Therefore it appears that small, |Dst| < 100 nT, storms can
suppress the ORBE injection, whereas large, |Dst| > 150 nT
storms can enhance it. The important feature is the way in which
the storm starts, which depends to a large extent on the nature of
the solar wind disturbance. High speed solar wind streams, which
appear near solar minimum, will have a very different effect than
magnetic clouds or solar flares. This leads to an interesting solar
cycle phenomenon, that correlations between ORBE and storm-RC will
depend on the phase of the solar cycle. With all these caveats, it
is probably not prudent to call these transducers exclusive
or bimodal until we have defined the storm-RC transducer more
Of all the ways to convert solar wind energy to storage in the
magnetosphere, the theory of the RC transducer has the longest
history and the greatest success. Space constrains us from
describing the long history of the theory, from Chapman32 to
Singer57 and Parker60 up to the present computer
models (e.g., Sheldon94a,Fok95,Jordanova99), but we can
describe the present theory.
Since the RC is a trapped plasma, one must non-adiabatically move
plasma into this region, which leads to two related mechanisms:
convection and diffusion. The convective mechanism uses an enhanced
plasmasheet electric field to shift the Alfven boundary, the
near-earth edge of the plasmasheet, closer to the earth. This
enhancement, if sustained long enough, will convect the plasmasheet
past the earth and on out into the magnetosheath, but if an abrupt
change in the electric field occurs, some plasma will be stranded
on closed drift paths near the earth. This abrupt change in
electric field violates the third adiabatic invariant and allows
the plasma to change its L-shell without modifying the first two
invariants. A variation on this method uses a stochastic on/off
fluctuating electric field to diffuse plasmasheet particles into
the trapped dipole region (Chen94).
The second method relies on diffusion to transport the particles.
In practice, this may be due to stochastic electric fields, but it
also may be due to stochastic magnetic fields or time-varying local
perturbations. The key difference is that the diffusion method
specifies a diffusion coefficient, whereas the convection method
specifies a time-varying electric field. Traditionally, diffusion
was thought to operate best on trapped drift orbits whose grad
B drift was significantly greater than E X B drift, which
occurs roughly for energies (E >> 30 keV/L). Early theory
derived a diffusion coefficient in the limit that the particles
were oblivious to the convection electric field and therefore
drifted around the earth on perfect circles (Falthammar65).
Recent theory, Sheldon97, relaxes these constraints and
permits a very general derivation of radial transport for any type
of perturbation on any drift orbit. In fact, convection and
diffusion become limiting cases of the generalized transport
Despite these advances in the theory of plasmasheet transport into
the RC, sophisticated models of various storms indicate that only
about half of the Dst excursion can be attributed to cross-L
transport (Jordanova98). That is, every model of the storm
time RC which normalizes to main phase, finds unaccounted ``losses''
in the recovery-time RC (e.g., Fok95). Another way of saying
this, is that the phase space density of the RC can never exceed
the phase space density of the plasmasheet, since the transport is
``adiabatic''. Yet during the biggest Dst storms, with |Dst| >
300 nT, it is hard to imagine how the plasmasheet could provide the
densities required. Some have proposed a ``super-dense
plasmasheet'', possibly loaded by plasmasphere erosion several hours
earlier (Elphic97,Thomsen98). Yet the biggest RC storms occur
immediately after a large interplanetary shock, with no apparent
time lag to load up the plasmasheet density. And if the shock
compresses the plasmasheet adiabatically, the phase space density
will not change.
Added to this problem are several other anomalies. Since the AMPTE
mission, we have known that large Dst storms have a greater
proportion of oxygen (Hamilton88). This has been ably
confirmed by the CRRES and POLAR satellites. Yet if the oxygen is
coming from the plasmasheet, which is normally deficient in oxygen,
it suggests some pre-storm seeding of this population. Timing
studies (R. Sheldon, GGS workshop, 1998) of the composition changes
observed in the RC with POLAR show that there is insufficient time
from the onset of the storm for oxygen to reach the plasmasheet
through either the polar wind or the cusp ion fountain. Nor does
such a priming explain why the ratio of O/H increases with
increasing Dst (Daglis96).
Finally we mention the hoary problem of the two time constant
recovery of Dst. Early suggestions that the ring current formed two
rings during storms (and therefore had two time constants) were not
supported by spacecraft observations. Hamilton88 suggest
that since large storms contain more oxygen, we are observing the
two charge exchange time constants for the dominant species, H+
and O+. If this were true, then the ratio of the two empirical
loss time constants, (by charge exchange with the most abundant
neutral species, H) reduces to a constant,
R = (Nh Sp Vp)/(Nh So Vo) = 4 <Sp>/<So>
where Nh is the density of neutral H, Sp is the cross section for
proton charge exchange, Vp is the velocity of the protons, So is the
cross section for oxygen charge exchange, Vo is the velocity of the
oxygen, and <> denotes an average. Then the ratio becomes
proportional to the average cross section at some intermediate energy.
However a study of several storms (personal
communication, SEC 1995) show that this ratio is not constant,
leading to additional assumptions about the average energies.
A New Storm Model:
We propose that these difficulties could be overcome if there were
a way to in situ accelerate ionospheric ions to RC energies,
thereby increasing the RC phase space density to larger values than
the plasmasheet. If such an acceleration process were more
efficient with increasing |Dst|, it would explain the
increasing O+ content of the RC with an ionospheric source.
Finally, if the acceleration produced a different pitchangle
distribution than the plasmasheet diffusion/convection population,
it would have a different loss time constant while occupying the
Just such a population was discovered by POLAR in the April 15,
1996 storm (Sheldon98a), with a peculiar, field-aligned beam
component at about 40% of the energy of the convecting plasmasheet
population (See figure 1 of Sheldon98a). We proposed that
this beam was generated by parallel electric fields set up by the
convecting population Sheldon98z.
The complete kinetics of the parallel field generation has not been
worked out fully, but apparently the convecting ions, moving in an
inhomogeneous magnetic field, have substantial gradB drift
that separates them from electrons. This separation of charges is
normally neutralized by the cold magnetospheric electrons, but
under storm conditions, the supply of such electrons runs out, and
ionospheric electrons must be extracted to neutralize this space
charge. This sets up the conditions for a 1-D non-neutral plasma
trap, a ``Malmberg'' trap, which exibits ``anti-shielding''
(Hansen95,Hansen95b). The net result is that the ionospheric
electrons overshield the magnetospheric ions, leading to the
extraction of keV ions from the ionosphere.
Therefore during a storm, at approximately half way into main
phase, the convecting plasmasheet ions at dusk trigger this
``quasi-neutrality catastrophe'' (QNC) instability and extract
ionospheric ions while simultaneously accelerating them to RC
energies. This instability continues as long as the supply of
convecting plasmasheet ions is available. A cessation of either
convection electric field or plasma density would terminate the
instability. At the end of main phase the convection electric field
turns off, and the ions pitchangle scatter erasing the primary
characteristic of their peculiar origin. Thus the ``fast'' time
constant in recovery may be charge exchange of small pitchangle
Support for this model comes from observations of Pc1 waves, which
have the greatest intensities during main phase, rotate toward dusk
during main phase, and drop in frequency during main phase down to
the oxygen gyrofrequency (Mursula96). Studies of partial
ring current (Suzuki85) also indicate that there is a
current out of the ionsphere post-dusk and into the ionosphere
pre-dusk, consistent with this picture. Even the evidence that a
super-dense plasmasheet leads to larger Dst (private communication,
M. Thomsen, 1998) remains consistent, since the strength of
the mechanism depends upon the density of convecting ions.
Is this mechanism mutually exclusive with either the Tail
transducer or the ORBE transducer? As we discussed earlier, the
dipolarization of the substorm current wedge effectively shuts off
the convection electric field by shorting out the tail currents
into the ionosphere, making the Tail transducer bimodal with the
storm-RC. Likewise, the greater the Dst, the stronger the
convection electric field, which might inhibit the cusp trap for
small storms by sweeping away the ``plug'', making the storm RC
weakly bimodal with ORBE. A recent publication takes exception to
this argument, which we treat in the next section.
Reeves98 uses a daily averaged LANL MeV electron flux and a
25-hour average applied to Dst to show that every MeV
injection observed at geosynchronous in 1993 had a corresponding
Dst injection seen on the ground. He argues that the converse may
not be true, but certainly the ORBE and RC transducers are not
mutually exclusive or bimodal. Close examination of the Dst average
shows that many of the Dst injections Reeves identifies are
|Dst| < 10 nT, which is curious, because the ``noise
threshold'' of Dst is around 7-10 nT. Of course, if this is random
noise, then a 25-hour average should reduce this to 1--2 nT, making
Reeves identification more solid. However, the literature has never
presented a Dst ``injection'' of such small magnitude. What then has
Similar injections can be seen in Figure 1
accompanying the 27-day recurrence of high speed solar wind streams
with ORBE injections until April 15. At 1-hour resolution, however,
these Dst injections do not appear as sharp, and in fact, appear to
be rather gradual or ragged 5-10 hour increases. Thus they have
never been identified as storms because the injection time
constants were several times longer than the storm-time RC. It is
only because of the 1-day averages used by Reeves that they
appeared to be storms at all.
We argue that these slow, 10-hour increases in Dst are not caused
by convection (and a possible QNC instability), rather they are
generated by enhanced diffusion from the plasmasheet. Since
classical diffusion theory (Nakada65,Falthammar65) argues that
solar wind variations determine the diffusion coefficient, it is
not at all surprising that enhanced solar wind speed, accompanied
by increased Alfvenic turbulence, should increase the diffusion
rate. As Sheldon93a showed, a higher diffusion rate leads to
an enhanced quiet time RC (by moving inward the inner edge of the
RC), and a resulting higher Dst. Therefore we interpret Reeves
observations to be that the quiet-time RC is coincident with
the ORBE transducer, but by definition mutually exclusive of the
convection driven storm-time RC. That is, storm-RC requires
a large convection E-field, whereas quiet-RC requires a
large diffusion coefficient in the absence of a large
Since these high-speed solar wind streams are most frequent in the
portion of the solar cycle after sunspot maximum, Reeves found a
very good occurrence correlation for 1993 (but little or no
magnitude correlation). By 1996, we can see the end of such a
regular solar wind structure on April 15, with very poor occurrence
correlation afterward. Thus the puzzle that began this paper was
finally explained: 1996 had neither fast
solar wind streams nor fast interplanetary shocks so that Dst and
ORBE appear quite uncorrelated.
We have attempted to describe the ways in which solar wind energy
is captured and stored by the earth's magnetosphere. Our
investigation was sparked by the apparently anti-correlated ORBE
and RC populations. We have tried to understand these correlations,
and find that indeed, several of the transducers are mutually
exclusive or bimodal. Our investigation was greatly facilitated by
the excellent instrumentation on NASA's fleet of spacecraft
dedicated to measuring the flow of mass, momentum and energy
through the magnetosphere. We hope that these mechanisms, sketched
here in outline form, will be further developed into a quantitative
model of the coupled Sun-Earth system.
POLAR/CAMMICE teams, and in particular Harlan Spence and Ted Fritz.
We are also indebted to Jim Sullivan, David Matthews, and Jiasheng
Chen who provided helpful comments.
We thank J. Blake for the HEO data in figure 1, and the referee who helped
clarify the distinction between occurrence and magnitude correlations.
This study was supported by NASA contract NAS5-30368 and NSF grant
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