Longterm loss and reformation of the outer radiation belt



Longterm loss and reformation of the outer radiation belt
JOURNAL OF GEOPHYSICAL RESEARCH: SPACE PHYSICS, VOL. 118, 3297–3313, doi:10.1002/jgra.50357, 2013
Long-term loss and re-formation of the outer radiation belt
D.-Y. Lee,1 D.-K. Shin,1 J.-H. Kim,1 J.-H. Cho,1 K.-C. Kim,2 J. A. Hwang,2 D. L. Turner,3
T. K. Kim,1 and M.-Y. Park 1
Received 14 February 2013; revised 1 May 2013; accepted 24 May 2013; published 21 June 2013.
[1] The Earth’s outer radiation belt is known to vary often and significantly on various time
scales. In this study, we have used the data of various instruments onboard the THEMIS
spacecraft to study long-term changes of the outer radiation belt electrons around the year
2009. We find that the entire outer belt became extremely weak for nearly a year and was
practically lost a few times, each time lasting ~20 days up to ~2 months, before eventually
re-forming. This was revealed at a wide energy range from several tens of keV to up to
719 keV, which was covered by the THEMIS spacecraft measurements. The loss of the
outer belt was associated with extremely weak solar wind conditions, i.e., low interplanetary
magnetic field magnitude and slow solar wind speed. In particular, this set greatly reduced
magnetospheric convection and/or injections for a prolonged time interval, which led to a
large expansion of the plasmasphere, even beyond geosynchronous altitude and thus
invading the majority of the typical outer belt territory for the same prolonged time interval.
Consequently, preexisting electrons inside the plasmasphere had enough time to be lost into
the atmosphere gradually over a time scale of several days without being supplied with fresh
electrons from the plasma sheet under the same reduced convection and/or injections.
Plasmaspheric hiss waves with an amplitude of up to a few tens of pT persisted to exist
during the gradual decay periods, implying that they are likely responsible for the continual
loss of the electrons inside the plasmasphere. A complete re-formation of the outer belt to
full intensity was then realized over an interval of a few months. During the re-formation
process, the magnetospheric convection and/or injections increased, which led to a gradual
increase of whistler chorus wave activity, contraction of the plasmasphere, and supply of the
plasma sheet electrons at high L shells. This set first an outward increasing profile of the
phase space density, which eventually developed into a profile with a peak at low L of ~5
over a time scale of 1–2 days. In this latter stage, a local acceleration at low L shells is found
to be clearly needed although the radial diffusion process can contribute to some extent, in
particular, for particles with a low first adiabatic invariant value.
Citation: Lee, D.-Y., D.-K. Shin, J.-H. Kim, J.-H. Cho, K.-C. Kim, J. A. Hwang, D. L. Turner, T. K. Kim, and
M.-Y. Park (2013), Long-term loss and re-formation of the outer radiation belt, J. Geophys. Res. Space Physics, 118,
3297–3313, doi:10.1002/jgra.50357.
[2] It is well known that the Earth’s electron radiation belts
generally consist of two zones, the inner belt at L < ~2 and
the outer one at L > ~3. While the inner belt is usually stable,
the outer belt can be very dynamic. Previous observations
indicated that the intensity and structure of the outer belt
Department of Astronomy and Space Science, Chungbuk National
University, Cheongju, South Korea.
Korea Astronomy and Space Science Institute, Daejeon, Korea.
Department of Earth and Space Sciences, UCLA, Los Angeles,
California, USA.
Corresponding author: D.-Y. Lee, Department of Astronomy and Space
Science, Chungbuk National University, 52 Naesudong-Ro, Heungduk-Gu,
Cheongju, Chungbuk 361–763, South Korea. ([email protected])
©2013. American Geophysical Union. All Rights Reserved.
can vary significantly on various time scales including solar
cycles, semiannual time scales, solar rotation periods,
geomagnetic storm durations, and sometimes even minutes
[Li et al., 2001; Li and Temerin, 2001; Baker et al., 2004].
Often, the outer belt variation is characterized by a great
enhancement in the particle flux by several orders of magnitude. Spatially, under a strong storm condition, it can penetrate even into the slot region that usually separates the two
belts [Baker et al., 2004] and also can expand outward to
reach a geosynchronous altitude, becoming a potential threat
to geosynchronous satellites [e.g., Kim et al., 2006]. At other
times, some part of the outer belt is lost or weakened by
mechanisms such as magnetopause shadowing followed by
outward radial diffusion and atmospheric precipitation of
particles [Green et al., 2004; Lyons et al., 2005; Bortnik
et al., 2006; Shprits et al., 2006; Ukhorskiy et al., 2006;
Millan and Thorne, 2007; Millan et al., 2007; Onsager
et al., 2007; Ohtani et al., 2009; Saito et al., 2010; Kim
Figure 1. (Top) Monthly averaged >2 MeV electron flux measured by GOES 11, and (bottom) the sunspot number, for the period from 1996 to mid-2010.
et al., 2008, 2010, 2011a; Turner et al., 2012a]. The particle
enhancements and dropout phenomena are often associated
with magnetic storm phases [Kim and Chan, 1997], but the
precise association with a storm is not necessarily robust
[Reeves et al., 2003; Turner et al., 2013; Zhao and Li,
2013]. Various acceleration and loss mechanisms must combine or compete to lead to a net flux change that is observable
by spacecraft [Horne and Thorne, 2003; Green and Kivelson,
2004; Shprits et al., 2009; Kim et al., 2011b].
[3] One fact that is well established is a solar cycle dependence of the outer belt intensity. Previous works using
NOAA POES and SAMPEX data showed that the outer belt
is greatly enhanced during the solar declining phase and it is
greatly depressed near solar minimum and during the solar
ascending phase [Li et al., 2001; Miyoshi et al., 2004]. In particular, Miyoshi et al. [2004] noted from NOAA POES data
that the outer belt nearly disappeared in the first half of
1987 corresponding to the ascending phase of solar cycle
22. Similarly, the SAMPEX data used by Li et al. [2001]
indicate loss of the outer belt in the summer of 1996, corresponding to solar minimum when solar cycle 23 had just
begun. This period is indicated in Figure 1, which shows
the monthly averaged >2 MeV electron flux measured by
GOES 11 with the sunspot number for solar cycle 23 and
early phase of solar cycle 24. The geosynchronous flux
decreased greatly during the summer in 1996. The general
relationship between the outer belt intensity and the sunspot
cycle is also well confirmed in Figure 1. Additionally, it
was first reported by Kataoka and Miyoshi [2010] that
the geosynchronous >2 MeV electron flux was greatly
depressed for a prolonged time interval around the year
2009, which was near solar minimum when solar cycle 24
was just beginning, as marked in Figure 1. This long-term
depression of the MeV electron flux in the outer radiation belt
for 2009 was also noted in the highly inclined observations
by SAMPEX as reported in the paper by Li et al. [2011]
where no detailed examination has been done, however.
[4] In the present work, we focus on the interval around the
year 2009 and examine the outer belt variations using the
observations by the THEMIS spacecraft which provide
near-equatorial measurements. Since the THEMIS spacecraft
cross the entire radiation belt zone routinely, the observations
allow us to examine in detail what happened to the entire
outer belt near the equator when the long-term dropout
occurred at geosynchronous orbit. We find that the entire
outer belt became extremely weak for nearly a year and
was practically lost a few times, each time lasting ~20 days
up to 2 months, until it re-formed eventually. This interesting
phenomenon provides an excellent opportunity to examine
specific processes leading to semipermanent loss and re-formation of the outer radiation belt. In section 2, we describe
overall statistical features associated with the long-term
weakening/loss and re-formation of the outer belt. Then, in
section 3, we focus on some short intervals of days to examine loss and re-formation processes in detail. We summarize
the results and discuss some issues and future works in
section 4.
2. Overall Characteristics of the Outer
Belt Weakening/Loss
[5] For the present study, we used the various data from
instruments onboard the THEMIS spacecraft. First, for the
energetic electron flux, we used the data provided from the
measurements by the Solid State Telescope (SST) for the
energy range from ~30 keV to 719 keV [Angelopoulos,
2008]. To examine the whistler wave activities, we used the
wave magnetic fields that the Digital Fields Board calculates
using the magnetic field data from the Search Coil
Magnetometer (SCM) [Roux et al., 2008]. These filter bank
data are provided in six logarithmically spaced frequency
bands from 0.1 Hz to 4 kHz. The specific way that we used
this data is the same as in Li et al. [2009]. To estimate the
equatorial electron cyclotron frequencies which control the
whistler wave bands, we used the background magnetic field
data measured by the Fluxgate Magnetometer [Auster et al.,
2008]. To identify the plasmasphere, we used the total
electron density inferred from the spacecraft potential and
Figure 2. Top panel shows >2 MeV electron flux (/s/sr/cm2) at GOES 11, and three bottom panels show
omnidirectional electron flux (/s/sr/cm2/eV) at three energies measured by the THEMIS A spacecraft for
2 years interval from 1 July 2008. Five major loss periods are identified as marked by dashed-line box
and named at the top (See Table 1 for the specific dates of the periods).
electron thermal speed measured by the Electric Field
Instrument [Bonnell et al., 2008] and Electro-Static
Analyzer [McFadden et al., 2008], respectively.
[6] Figure 2 shows the 2 year data from 1 July 2008 for the
electron flux with energy >2 MeV from GOES 11 at geosynchronous orbit and the electron fluxes at three energy channels, 52 keV, 203 keV, and 719 keV, from THEMIS-A
spacecraft. Both the GOES and THEMIS data indicate that
the outer belt structure was typical until late 2008 when it
started to become very weak. This greatly weakened belt
period continued until early 2010. The THEMIS data show
that, throughout this roughly 2 year period, the entire outer
belt practically disappeared a few times, each lasting for a
prolonged time period. To guide visual identification of this
feature, we have marked five major loss periods when the
719 keV electron flux of THEMIS was less than 5/cm2/s/sr/
eV for a prolonged time period (note that the >2 MeV electron flux at GOES 11 also decreased significantly, in practice,
to background levels during these periods). These identified
periods are summarized in Table 1. The first loss event,
L1a, lasted roughly 20 days, and the others ~1.5 months to
2 months, making the total period being >a third of a year
around 2009. The loss appears most obvious in the high
energy channel in the THEMIS data and become less prominent, but still identifiable, in the lowest energy channel.
[7] Here we briefly comment on some known caveats
regarding the THEMIS SST data. First, the THEMIS SST
instruments saturate at the heart of the outer belt during very
Table 1. Summary of the Major Event Periods Identified in
Figures 2 and 3
Active Belt Periods
Lost (Diminished) Belt Periods
ID a
Periods c
Naming for identification.
Note that these are approximate determination based on visual inspection
without imposing a quantitative criterion in Figure 3.
Note that these are determined based on the condition that the 719 keV
flux is less than 5/cm /s/sr/eV in Figure 2.
Figure 3. GOES >2 MeV electron flux (/s/sr/cm2/eV), IMF B and Bz (nT), solar wind number density
Nsw (/cm3), speed Vsw (km/s), and three geomagnetic indices, Kp, Dst (nT), and AE (nT) for the 2 year
interval from 1 July 2008. Two active belt periods are approximately identified (highlighted in violet and
named A1 and A2) for comparison with the loss periods (same as in Figure 2).
active times. The saturation effects appear as electron flux
depletion at L shells around 4–5, most clearly seen at
203 keV and 719 keV in April–June 2010 in Figure 2. In
addition, the THEMIS SST electrons channels below
~300 keV are known to be contaminated by > ~300 keV
protons. This is most likely responsible for the finite, though
weak, level of the 203 keV flux at L ~ 3–4, the usual slot
region, in Figure 2, and it is non-negligible particularly when
the outer belt electron intensity became very weak.
[8] The responsible solar wind conditions are shown in
Figure 3 along with the three major geomagnetic indices,
Kp, Dst and AE, for the same 2 year period. The main feature
in the solar wind is that both the interplanetary magnetic field
(IMF) magnitude and the solar wind speed are on average
much lower for the same diminished belt periods as identified
in Figure 2 (as highlighted in magenta) than for the active belt
periods (as highlighted in violet and named A1 and A2—see
Table 1 for the specific dates). The solar wind density and the
IMF Bz do not indicate any distinctive difference for the
diminished belt periods as compared to those for the active
belt periods, except for an interesting feature that there are
more periods of high density and fewer high speed streams
for the diminished belt periods. The three geomagnetic
indices during the diminished belt periods are very weak as
compared to those for the active belt periods. Therefore, the
key feature associated with the lost/weakened belt periods
is the very weak IMF/solar wind speed and the associated
quiet geomagnetic state. In particular, we emphasize that
the low AE values during the diminished belt periods imply
reduction in the magnetospheric convection and/or injections. Below, we argue that it is the convection and/or injections level that primarily controls the outer belt structure and
intensity by controlling the size of the plasmasphere, supply
of the plasma sheet electrons, and chorus wave activity.
[9] First, we have used the plasma density data from
THEMIS-A to identify the plasmapause location Lpp. The
method that we employed to determine Lpp is similar to that
in the well-known previous works [Carpenter and
Anderson, 1992; Moldwin et al., 2002; O’Brien and
Moldwin, 2003] except that we have imposed a more stringent
criterion that the change in the plasma density should occur by
a factor of 15 or larger within ΔL =0.5. Also, once Lpp was
identified by an automatic procedure based on the criterion,
we have further inspected them visually to eliminate any
ambiguous cases. Figure 4 shows the mean curves of Lpp separately for the diminished (magenta) and active (blue) belt
periods identified in Figure 3. Since the THEMIS orbits are
limited in their MLT coverage throughout the year, this figure
Figure 4. Mean curves of L values of the plasmapause
location, Lpp, determined from the THEMIS-A plasma density data, separately for the diminished (magenta) and active
(blue) belt periods identified in Figure 3. The short radial
lines indicate standard deviations from the mean Lpp marked
at selected MLTs for visual simplicity where they are larger
than the standard deviation averaged over all MLTs, which
is ~0.67 for both curves.
includes seasonal dependencies in MLT. It is no surprise to see
that the plasmasphere is on average larger for the diminished
belt periods than for the active belt periods. As the standard
deviations in Figure 4 imply, the Lpp can vary quite significantly even on a short time scale. Figure 5 shows the time evolution of Lpp explicitly, shown as red line superposed over the
L-time plot of 719 keV electron flux. The relationship between
the plasmapause location and the outer belt structure can be
seen more specifically in Figure 5. It is clear that the loss/
weakening of the outer belt is mostly associated with a great
expansion of the plasmasphere as Lpp can be large like L = 6
or beyond. This seems like a situation that the largely
expanded plasmasphere practically occupied the territory to
a large extent where the outer belt would otherwise reside.
[10] Incidentally, it is interesting to note in Figure 5 that
the plasmapause location is not necessarily coincident
with the inner edge of the outer belt [Li et al., 2006]. In
particular, during the active belt periods, enhanced electron fluxes can exist for some time even inside Lpp, though
the general trend of a smaller Lpp for a more active period
is still maintained. Several loss mechanisms can operate
inside the plasmasphere. For L > ~3, resonant interactions
with plasmaspheric hiss are known to dominate the pitch
angle scattering of electrons [Meredith et al., 2006,
2007]. Previous studies report that the loss time scale for
plasmaspheric hiss ranges from a few days for hundreds
of keV to tens of days for large MeV energies [Shprits
et al., 2008]. Therefore, it may be due to a longer loss
time scale for electrons inside the plasmasphere into the
atmosphere than an outward expansion time scale of the
plasmapause that a substantial population of the electrons
can exist inside the plasmasphere for a while.
[11] The reduction in convection and/or injections implies
reduction or interruption of the plasma sheet electron supply.
This can be easily confirmed via the phase space density
(PSD) as a function of adiabatic invariants. Using the directional fluxes of the electrons from all five THEMIS spacecraft as long as they are at L = 5–10, we have computed
PSD for various values of first adiabatic invariant m, and we
present the results for m = 300 MeV/G, 500 MeV/G, and
700 MeV/G in Figure 6. For the computation, we have
required that the spacecraft is within 10 in magnetic latitude
so that we can assume that the used electron fluxes are mostly
dominated by near-equatorial particles [Kurita et al., 2011].
Of course, this assumption is not very precise, but it allows
a simplified way to compute PSD in a wide L-MLT domain
without having to compute L* [Roederer, 1970] and the second adiabatic invariant. The error associated with this
assumption can be ignored considering the large difference
in the resulting PSD by at least an order of magnitude between the active and diminished belt periods as seen in
Figure 6. The most interesting feature in Figure 6 lies in the
difference in the radial profile of PSD between the active
and diminished belt periods. Clearly, the PSD profiles are
characterized by some radial gradient for the active belt
periods, which is more evident for higher m cases, while it
is less so for the diminished belt periods. The m dependence
of PSD profiles is fully consistent with that found in Turner
et al. [2012b]. The difference between the active and diminished belts is seen more clearly in Figure 7 which shows the
L value
Flux [ # / cm2 / sr / s / keV ]
Figure 5. Line plot of Lpp (red) determined from the THEMIS-A plasma density data, as superposed on
the 719 keV electron flux plot for the 2 year interval from 1 July 2008.
Figure 6. Phase space density in units of (c/MeV/cm)3 in polar plot for three representative m values as
distinguished between the active and diminished belt periods.
line plots of PSD for the case of m = 700 MeV/G as averaged
for two selected MLT zones. The PSD profiles are of more
peaked shape for the active belt periods while they are less
peaked or rather flat for the diminished belt periods.
[12] The magnetospheric convection and/or injections
should control wave activities that are critical to the radiation
belt dynamics [e.g., Anderson and Maeda, 1977; Lyons et al.,
2005; Hwang et al., 2007; Li et al., 2008]. In order to confirm
this expectation and the expected difference between the
active and diminished belt periods, we have estimated the
chorus magnetic wave intensities using the filter bank data
of SCM onboard all five THEMIS spacecraft as long as they
are at L = 5–10. This was done by following the same methodology as in Li et al. [2009]. It should be mentioned that the
inner boundary was set at L = 5 since this is approximately
the inner most region where the highest frequency band
(~1.4–4 kHz) of the filter bank data can cover the typical
chorus frequency range (~0.1 fce–0.8 fce). The results are
summarized in Figure 8 as distinguished between near-equatorial and off-equatorial measurements and between the
active and diminished belt periods. The upper plots in
Figure 8 show RMS chorus wave amplitude (in pT), and
the lower plots in Figure 8 indicate the number of samples
in each bin. The overall wave distribution characteristics
are consistent with previous reports [e.g., Li et al., 2009],
and with no surprise, it is clearly seen that the chorus activity
was statistically weaker during the diminished belt periods.
Time evolution of chorus activities is shown in Figure 9
(middle) where only the THEMIS-A data were used and
the chorus magnetic intensities were averaged over each half
orbit of the spacecraft trajectories as long as it was within
L = 5 to 10 and MLT = 21 to 12 h. The afternoon and early
evening sector (MLT = 12 through 21 h) was excluded as
chorus activities are expected not to occur significantly in this
sector (this is the reason that no data points of the averaged
chorus exist in the middle (~July and August of 2009) in
Figure 9 (middle) when THEMIS-A orbit configuration
roughly corresponded to the phase covering this chorus-free
sector). Figure 9 (middle) clearly shows that the average chorus activity declined slowly over a time scale of a few months
when the outer belt became weak in late 2008 through early
2009. The chorus remained weak on average, though active
sometimes, until it started to enhance over a few months’
time scale in early 2010 when the outer belt gradually reformed. Clearly, the chorus activity played a role in re-formation of the outer belt at least in the statistical sense.
[13] Similarly, we have used the same filter bank data of
the THEMIS SCM to examine whistler hiss wave activities inside the plasmasphere. To identify hiss waves, we
followed the same procedure as in Golden et al. [2012a,
2012b] except that we used the plasma density data to specifically determine the plasmapause locations as above
(Figures 4 and 5). Figure 10 shows the determined hiss
wave amplitudes averaged in L-MLT bins in the polar
plot, and Figure 9 (bottom) shows the hiss amplitude averaged over the L range from 2.5 to Lpp along each half-orbit of the spacecraft. Consistent with the result in Golden
et al. [2012a], the day-night asymmetry is clear in the
Figure 7. Line plots of phase space density in units of (c/MeV/cm)3 for m = 700 MeV/G for two selected
MLT zones, distinguished between the active and diminished belt periods. In each panel, the solid traces are
the median curves, and the dashed and dotted traces indicate the upper and lower quartiles, respectively.
polar plot, in particular for the diminished belt periods,
though it is not well confirmed for the active belt periods
due to limited sampling on the nightside. Both the polar
plot and the orbit averaged line plot indicate the overall
trend that the hiss amplitude was larger during the active
belt periods. However, during the diminished belt periods,
the hiss wave activities did not fully diminish and
persisted to exist with some non-negligible amplitude, up
to a few tens of pT. This is in fact consistent with the
CRRES observations [Meredith et al., 2004].
Figure 8. (Top row) Chrous mean amplitude in polar plot as obatined from all five THEMIS spacecraft
measurements. (Bottom row) Statistics of sampling of the identified chorus events.
Figure 9. (Top) 719 keV omnidirectional flux obtained using three inner probes of THEMIS, (middle)
chorus magnetic wave intensity averaged over half-orbit trajectories of THEMIS-A when the spacecraft
is fully inside the domain defined by 21-12 MLT and L = 5–10 for the 2 year period from 1 July 2008,
and (bottom) hiss magnetic wave intensity averaged over half-orbit trajectories of THEMIS-A when the
spacecraft is safely inside the plasmasphere for the same 2 year period.
[14] Here we make some additional comments on the chorus and hiss results in Figures 8, 9, and 10 for clarification.
First, a direct, quantitatively precise, comparison of the chorus and hiss intensities based on Figure 9 is not entirely
straightforward. The main reason is that both wave activities
have strong L and MLT dependences which differ between
the two waves as shown in Figures 8 and 10. The orbit averages may not catch this spatial dependence precisely. The
larger standard deviation for hiss than for chorus also makes
a direct comparison not easy. Second, because of the strong L
and MLT dependences, the orbit averages of both waves in
Figure 9 cannot be expected to represent the time evolution
too precisely, and they should be regarded to represent an
average trend only. Again, note the large standard deviation
particularly for hiss, which however indicates that the hiss
can sometimes exist with a substantial amplitude during the
quite times. Third, while the half-orbit averaging of hiss
was done over L = 2.5 – Lpp, the chorus average was done
over L = 5–10 for the sake of convenience. This might imply
a rather inaccurate inclusion of chorus waves when the
plasmasphere has expanded outside than L = 5. However,
such a situation usually corresponds to a weak convection
state, and thus the corresponding chorus intensity between
L = 5 and L = Lpp would not be significant such that the chorus average in Figure 9 remains roughly valid. Last, the number of data points in Figure 9 is less for hiss than for chorus.
This is mainly because we determined hiss amplitude only
when the plasmapause location Lpp could be well determined. This reduces the number of the events suitable for
the hiss averaging process.
3. Specific Processes of the Loss and Re-formation
of the Outer Belt
3.1. Loss Process
3.1.1. Description of Observations of a Specific Event
[15] Here we examine in more detail how the loss process
develops by taking a close look at some specific interval.
Figure 10. (Top row) Hiss mean amplitude in polar plot as obatined from THEMIS A spacecraft measurements. (Bottom row) Statistics of sampling of the identified hiss events.
First, we present relevant observations in Figure 11, where
the middle panel shows the AE data for 10 days from 15
November 2008. This corresponds to the first half period of
the first major loss event, L1a, identified in Figure 2 and
Table 1. Figure 11 (bottom) also shows the plasma density
and energetic electron fluxes at three energy channels,
52 keV, 203 keV, and 719 keV, as a function of L covered
by roughly half orbit of THEMIS-A trajectories on selected
dates. (Note that while the color scale in the L-time plot of
the flux in Figure 11 (top) is linear, the line profiles of the flux
in Figure 11 (bottom) where the flux drop appears much less
abrupt are presented in log scale for the purpose of
demonstration here.)
[16] Comparison of the first two of the bottom panels in
Figure 11, covering one full-orbital period on 15–16
November, indicates a major contraction of the plasmasphere
with Lpp moving from ~7 to ~4. This is in response to the
large increase in AE. Also, it shows a major increase of the
lowest energy flux by an order of magnitude at L > ~4 and
an overall decrease of the higher energy fluxes by a factor
of 3–4 (except for the discontinuous drops of the higher
energy fluxes across L > ~8.5 seen in the first panel).
[17] Then, for the next 8 days or so, the AE index
decreased and remained low for most of the times.
Correspondingly, the plasmasphere expanded continuously
out to L = 7 or beyond, and simultaneously, the energetic
electron fluxes decreased gradually at all energies (see the
last three of the bottom panels in Figure 11). The flux
decrease is most significant in the lowest energy, being by
two orders of magnitude. It is by ~40% in the highest energy
over the ~8 days, but note that there was already an earlier
dropout in this high energy (between the first two panels)
when AE increased on 16 November as mentioned above,
such that the total flux drop rate over the entire ~10 days is
by a factor ~5 (Though not shown here, the 719 keV flux
dropped even further by a factor of ~3 for the subsequent
two days).
3.1.2. Interpretation and Suggested Scenario
for Long-Term Loss
[18] First, we discuss the flux changes during the initial
full-orbital period on 15–16 November (shown in the first
two of the bottom panels in Figure 11). Since AE increased
largely, the lowest energy flux increase must be due to
enhanced convection and/or injections. The higher energy
flux decrease seen over the same orbital period must be a
result of loss-dominant process over acceleration. In our
separate work (J. A. Hwang et al., Significant loss of
energetic electrons at the heart of the outer radiation belt
during weak magnetic storms, submitted to Journal of
Geophysical Research: Space Physics, 2013), we attempted
to show that the dominant loss process in this short interval
is magnetopause shadowing effect in combination with radial
diffusion [e.g., Shprits et al., 2006; Kim et al., 2008, 2010,
2011a; Ohtani et al., 2009; Turner et al., 2012a, 2012b].
[19] For the loss process during the next ~8 days, we suggest the following scenario. First, we emphasize that the
prolonged interval of weak convection and/or injections, as
indicated by the low AE, allows a large expansion of the
plasmasphere outward to or even beyond geosynchronous
altitude, thus invading the usual outer belt territory. This is
Figure 11. (Top) 719 keV omnidirectional flux obtained using three inner probes of THEMIS for the
2 year interval from 1 July 2008, (middle) plot of AE (nT) for 10 days from 15 November 2008, and
(bottom) the plasma density (cm3; filled black curves) and electron omnidirectional flux (/s/sr/cm2/eV)
in three energies (52 keV in red, 203 in blue, and 719 keV in magenta) vs. L obtained from THEMIS-A.
indeed well seen in Figure 11. Once the plasmasphere
expands to a large size and remains so for several days, much
part of the particle flux profile (including the peak) remains
located “inside the plasmasphere” for the same period.
Thus, there is an opportunity of several days for the
preexisting electrons to get lost into the atmosphere by presumably whistler hiss waves, but no chance is available for
acceleration by whistler chorus waves which usually exist
outside the plasmasphere. If the initially contracted
plasmasphere (on 16 November) had remained so for some
sufficient time like a few days such that the electron flux peak
had remained “outside the plasmasphere,” then the electrons
might have been given a chance to be accelerated by chorus
waves leading to high energy flux enhancement (this effect
is in fact seen in the example associated with belt re-formation discussed below in section 3.2).
3.1.3. Loss Time Scales for the Major Loss Periods and
Their Relation With Hiss
[20] In order to assess the interpretation and scenario
above, we estimated the loss time scales and checked their
relation with plasmaspheric hiss waves. First, we defined
the loss time scale, to, by fitting an exponential function of
the form, J ~ exp(t/to), to periods of gradual decay of the
flux J. Similar to, but not exactly same as, the procedure in
Meredith et al. [2006], we measured the strength of the goodness of linear fit between the natural logarithm of the flux and
the decay time for a certain size of the data points, which was
varied systematically throughout the whole data set. The procedure was applied to three selected energies, 52 keV,
203 keV, and 719 keV, separately. Figure 12 shows the natural logarithm of the peak fluxes (in linear scale) identified
during each half-orbit of THEMIS spacecraft. The three
panels in Figure 12 cover three separate periods to which
the fitting procedure was applied. Each of these periods
includes the major loss periods, L1a and L1b, L2, and L3,
respectively, as identified in Figure 2 and Table 1. The red
solid lines overplotted on the flux data are the best fits to
the determined decay periods. It should be mentioned that
the 52 keV flux level is easily subject to transient convection
effect, which is why the flux level with the black symbol in
Figure 12 is often quite large and appears rather scattered.
Our criterion in applying the linear fit is rather strictly set
such that a fit is abandoned when the data points suffer from
a large scatter. Also, the 203 keV electron flux suffers from
proton contamination such that it eventually saturates to the
background proton flux level as the electron loss process continues. Thus, our identification of the peak flux at 203 keV
stops sometime prior to this saturation level. This is why
the 203 keV data points are sometimes missing and some of
the best fit lines are shorter for 203 keV than for 719 keV.
Table 2 summarizes the determined loss time scales.
Table 2 (bottom) indicates that the average loss time scales
are 5.32, 6.88, and 8.32 days for 52 keV, 203 keV, and
719 keV, respectively. This confirms that the identified loss
is indeed a gradual process and the trend is clear that the time
scale is longer for a higher energy.
[21] In Figure 5, we have already presented the
plasmapause location Lpp. The plasmasphere expanded
greatly during the gradual decay of the flux such that a large
portion of the outer radiation belt remained inside the
plasmasphere for much of the decay times, which we have
demonstrated also in the example shown in Figure 11 above.
We have also shown the plasmaspheric hiss activities in
Figures 9 and 10. The plasmaspheric hiss did not completely
diminish but remained non-negligible, its amplitude ranging
from ~10 pT to a few tens of pT, during the gradual
decay periods.
[22] Comparing our results with previous results, the
CRRES satellite observations examined by Meredith et al.
[2006] indicate that the loss time scales in the region
Figure 12. Peak fluxes of electrons at three energies identified during each half-orbit of THEMIS spacecraft for three selected periods. The red solid lines overplotted on the electron flux data are the best fits. The
major loss periods identified in Figure 2 and Table 1 are marked for reference.
3 < L < 5 during quiet periods (Kp <3) are 1.5–3.5 days for
214 keV electrons and 5.5–6.5 days for 1.09 MeV electrons.
Also, the model calculations by Shprits et al. [2008] reveal
that the hiss-induced loss time scales for L = 3–7 are a few
days for 500 keV and ~10 days for 1 MeV. Clearly, the specific numbers for the loss time scale differ among different
reports including ours, which must be due to different
methods and event periods used to estimate the time scales,
but the general trend of a longer time scale for a higher
energy is consistent among them. Meredith et al. [2006]
computed loss time scales for pitch angle scattering by
plasmaspheric hiss using the PADIE code with wave properties based on CRRES observations (with hiss amplitude of a
few tens of pT). They concluded that pitch angle scattering
Table 2. Summary of Loss Time Scales for Three Energies as Obtained in Figure 12
52 keV
203 keV
Loss time scales in units of days.
Average time scales.
719 keV
tο b
by plasmaspheric hiss propagating at small or intermediate
wave normal angles is responsible for electron loss over a
wide range of energies and L shells. In the recent simulations
to explain the formation of the slot region, Kim et al. [2011b]
used the hiss amplitude given by 80*kp/4 [pT], which thus
implies a few tens of pT for low geomagnetic states, consistent with what our THEMIS observations indicate. Thus, all
these support the possibility that the main loss mechanism
for the gradual loss during our event periods is hiss waveelectron interaction.
[23] In addition to the hiss-induced atmospheric precipitation inside the expanded plasmasphere, we speculate that
there might be some contribution by inward radial diffusion
which transports lower energy electrons of enhanced flux
from higher L shells to lower L shells, resulting in higher energy electrons (For the specific period in Figure 11, we
attempted to calculate PSD and L* for various m and K
values, but our calculations could be made only for limited
L* ranges, which makes it difficult to quantitatively assess
radial diffusion process). There must a competition between
radial diffusion source effects and atmospheric loss effects,
as shown in the work by Kim et al. [2011b] for CRRES
observations which simulated this kind of competition. We
suspect that the source effect by radial diffusion may be a
weaker process due to the weak geomagnetic conditions,
and the net result must have been the gradual decrease in
the high energy flux as seen in Figures 11 and 12.
3.2. Re-formation Process
3.2.1. Description of Observations of a Specific Event
[24] Next, we examine the detailed process of re-formation
of the outer belt after a long-term loss. The re-formation of
the outer belt that we are considering here occurred over a
time scale of a few months in early 2010 (see Figure 2).
During this time period, the formation of the outer belt back
to full strength was realized through a few repeated formation
of a weaker strength belt. Here we focus on one of these
weakly formed belts in March 2010.
[25] Figure 13 shows the relevant data for 4 days from 9
March 2010. The AE largely increased in the middle of 10
March and remained active for the next few days. This
caused the plasmapause to move from L ~ 6.5 to ~4. This also
implies enhancement in convection and/or injections which
supplied the plasma sheet electrons. This is well reflected
through the increase in the lowest energy electron flux on
10 March (as marked by thick vertical arrow). But it should
be emphasized that this increase occurred mostly at higher
L shells, L > ~5. On the same day, the 203 keV electron flux
also increased at higher L shells, but not as much significantly as the 52 keV electron flux did, and the 719 keV electron flux decreased, reflecting loss-dominant process. Then,
on 11 March, while the plasmasphere remained contracted
under the enhanced convection and/or injections, the electron
fluxes at 719 keV and 203 keV increased substantially, in
particular, at lower L shells, making the flux profiles more
peaked in radial distance (as marked by thick vertical arrow).
The lowest energy flux decreased, however.
[26] For this period, we were able to calculate the
Roederer’s L* [Roederer, 1970] for a meaningful range and
calculated PSD as a function of m, K, and L* (recall that we
did not attempt to express PSD as a function of L* in
Figure 6 for simplicity). Figure 13 (bottom) shows the
calculation results of PSD for three values of m and a fixed
K value of 0.01G0.5RE corresponding to a near-equatorial
pitch angle. Note that in Figure 13, while the PSDs are shown
as a function of L*, the electron flux and plasma density data
are still given as a function of L for the sake of consistency
with the way the other data being presented throughout the
paper, but the essence of our results here can be addressed
without causing much confusion. The PSDs in Figure 13
(bottom) were obtained for a ~2.5 day period covered by each
half-orbit of THEMIS-A. Note that the first of the bottom
panels includes PSD profiles for the first two half-orbits
together. It is then clearly seen that, for the next two inbound
and outbound orbits on 10–11 March, the PSD level
increased primarily at higher L*, making its profile increasing outward (although our calculations are limited, we expect
that the PSD level must then decrease farther outside
(L* > ~7). Last, for the inbound orbit on 11 March, the
PSD profiles became peaked at lower L*, slightly beyond
L* = 5. This is definite for m = 200 MeV/G and 500 MeV/G,
and is still likely for m = 700 MeV/G (blue line) despite the
limited calculation of PSD only for L* >5 due to the maximum available energy for the THEMIS SST electron flux.
3.2.2. Interpretation and Modeling Test
[27] The PSD results in Figure 13 demonstrate how the
PSD evolved over <2 days until it reached a profile of a fully
peaked shape (peaks at low L* ~ 5) with an enhanced level.
We suggest that the convection and/or injections effect at
higher L* shells first provided the PSD profiles with an outward radial gradient before the fully developed peaked profiles were finally achieved. Then, the next question is “what
drove the evolution from the outward gradient PSD profiles
to the peaked PSD profiles?” Can radial diffusion alone lead
to the final PSD profiles?
[28] In order to assess the possible contribution of the
radial diffusion, we have solved the well-known radial diffusion equation [Schulz and Lanzerotti, 1974] with the diffusion coefficient DL*L* given by Brautigam and Albert
[2000] below.
@ D
¼ L*2 L*L* @t
L*2 @L
where f is the PSD, t is the atmospheric loss time scale, and
DL*L* K p ; L ¼ 10ð0:506K p 9:325Þ L*10 =day:
[29] We solved this equation for the two successive halforbits on 10–11 March (the outbound orbit on 10–11
March and the inbound orbit on 11 March in Figure 13) to
see the extent to which the resulting solution can reproduce
the observed evolution of PSD. We took the outbound PSD
profiles from the observations as the initial PSD profiles that
are needed in solving the radial diffusion equation. In this
procedure, we applied a simple extrapolation to the initial
PSD profiles to cover a wider L* range than those estimated
from observations. The most critical factor in determining the
radial diffusion is the PSD condition at the outer boundary.
We tried two cases, one with a fixed boundary condition
and the other with a variable boundary condition. The latter
one was designed to reflect loss effect caused by the magnetopause shadowing [Shprits et al., 2006; Loto’aniu et al.,
Figure 13. (Top three rows) 719 keV omnidirectional electron flux obtained using three inner probes of
THEMIS for the 2 year interval from 1 July 2008, 4 days plot of AE (nT), and the plasma density and electron omnidirectional flux in three energies, in the same format as in Figure 11. (Bottom) The phase space
density in units of (c/MeV/cm)3 as a function of L* for three different m values.
2010; Kim et al., 2011a; Turner et al., 2012a]. Also, we
solved equation (1) with and without the precipitation loss
term. When we included that term, the electron lifetime t
was set to be 10 days inside the plasmasphere and to be
scaled by 4/Kp outside the plasmasphere [cf. Shprits et al.,
2005]. Since the THEMIS inner probes crossed the
plasmapause at least two times each full orbit, we took
advantage of this fact whenever the plasmapause location
could be identified. In fact, we identified the plasmapause
locations at three instances from THEMIS-A on 10–11
March, which was incorporated in solving the radial
diffusion equation.
[30] The results shown in Figure 14 are the simulation case
with the variable boundary condition without the precipitation loss term both inside and outside the plasmasphere. In
fact, including the loss term contributes to lowering PSD
level at low L*, thus making the chance for reproduction of
the observed PSD peaks less likely. The observation-based
PSDs for the two successive half-orbits on 10–11 March
are shown as black lines with symbol and red lines with symbol, respectively. The lines of different colors without symbol refer to time evolution of PSD during the diffusion
process. In this run, the variable boundary condition was
reflected in such a way that the PSD at the outer boundary
is deliberately reduced at a constant time rate until it eventually becomes identical to the final observed PSD value. Also,
we were able to identify the plasmapause locations Lpp at
three occasions. Specifically, Lpp was set to be 4.4 for the first
16 h, 3.8 for the next 4 h, and 4.6 for the last 4 h.
[31] Comparison between the observed final PSDs and the
diffusion-calculated final PSDs in Figure 14 indicates that
while the radial diffusion can be a substantial contributor to
the peaked PSD profile formation for the lowest m case, it is
not for the higher m cases. Clearly, this latter result implies
the necessity of local acceleration effect for formation of
peaks in PSD at low L*, which is in fact consistent with previous works [Green and Kivelson, 2004; Shprits and Thorne,
2004; Chen et al., 2006; Miyoshi et al., 2006; Shprits et al.,
2007; Turner et al., 2013]. It is now well known that a very
likely mechanism for local acceleration is interaction with
whistler chorus waves. Indeed, we find from the THEMIS
wave observations that chorus waves were excited for this
re-formation interval (note that the statistical trend has been
already presented in Figure 9 above) and plan to further
Figure 14. Evolution of the phase space density as a result of the radial diffusion by taking the observations for the 03/10-11 outbound orbit as the initial PSDs (black with symbol). The color code for the
different curves with no symbol means the time evolution with “red line without symbol” referring to
the final PSDs. The final PSDs from the observations for the 03/11 inbound orbit (red with diamond) are
also shown for comparison.
examine details of the possible role of the waves in a
separate work.
Summary and Discussion
[32] In section 2, we have reported the general characteristics of the outer radiation belt during the 2 year interval
around the year 2009 based on the THEMIS observations.
The most astonishing result is that the outer belt became
overall very weak in 2009 and was practically lost a few
times, each time lasting for a prolonged time interval such
as ~20 days up to 2 months, until it re-formed eventually.
This loss phenomenon was associated with the greatly
weakened solar wind conditions particularly in the solar
wind speed and IMF B. Correspondingly, the Earth’s magnetosphere was geomagnetically very quiet. In particular,
during the loss periods, the plasmasphere expanded greatly,
often even beyond geosynchronous altitude and thus invading the typical outer belt territory, the plasma sheet electron
supply was greatly reduced, and the chorus wave activities
were very weak. Though not presented here, we have confirmed the general feature of the long-term loss and re-formation of the outer belt by checking the electron data
measured by NOAA POES low-Earth orbiting satellites for
the same period. This supports our findings from the
THEMIS observations.
[33] Then, in section 3, we presented two specific events to
describe the loss and re-formation process of the outer belt in
more detail. Further, we proposed a scenario based on convection and/or injections and the dynamic evolution of the
plasmasphere. Figure 15 demonstrates the basic idea of our
scenario with an intention to apply to a high energy electron
population such as 719 keV electrons used in this study.
Figure 15a represents the outer radiation belt structure under
a typical normal solar wind condition. The plasmasphere is
also sketched for reference, which we claim plays a critical
role in the outer belt evolution. We consider two opposite situations according to the solar wind conditions. First, when
the solar wind condition becomes weak, the plasmasphere
expands as shown in Figure 15b. If the solar wind condition
Figure 15. Cartoon demonstrating the solar wind dependence of the outer radiation belt and
plasmasphere. This is a modification to the cartoon in Figure 3 of Baker et al. [2004].
is very weak and if such a condition prevails for a prolonged
time interval such as several to tens of days, the plasmasphere
greatly expands to a large size occupying the typical outer
belt territory and remains so for a long time. Then, the outer
belt suffers primarily from loss processes inside the
plasmasphere, and thus becomes weak and can even be lost
in practice. This is demonstrated in Figure 15c. In contrast,
when the solar wind condition is very strong, the
plasmasphere contracts and the high energy electrons at high
L are lost largely to the dayside magnetopause which
approaches closer to the Earth. This is the situation in
Figure 15d. If such a strong solar wind condition is
maintained for a certain period at least on the order of hours,
then the time is sufficient such that the magnetospheric convection and/or injections brings new particles from the
plasma sheet into the outer radiation belt territory. This can
create a positive radial gradient of PSD, resulting in inward
radial diffusion. It can also create chorus waves, eventually
leading to electron acceleration outside the contracted
plasmapshere. Consequently, the outer electron belt becomes
intensified as demonstrated in Figure 15e. Last, we stress that
the solar wind conditions, the associated convection and/or
injections strength (representing the source of particles and
waves), and the associated response of the plasmasphere,
all being interconnected to one another, should determine
the evolution of the outer electron belt in an interactive way.
[34] In the present work, we have not rigorously distinguished between convection and injection effects but rather relied on the geomagnetic index AE, which may include both
effects but with often no clear distinction [See Ahn et al.,
2005, Tsurutani et al., 2004 for details related to this issue].
The substorm injection usually occurs in the energy range
from a few tens of keV (typically ~50 keV) up to a few hundreds of keV (rarely 300–400 keV, depending on particle species, level of the geomagnetic state, and substorm intensity,
etc.) [e.g., Reeves, 1998; Lee et al., 2004, 2006 and references
therein]. The energy range that the convection covers also
depends on its intensity, but that of a normal intensity usually
brings earthward the particles of a much lower energy than the
lower cutoff energy for the substorm injection. Because of the
generally different energy domain, the specific effects in the
inner magnetosphere may differ between convection and
substorm injections. The convection should be more relevant
in determining the plasmapause location, and the substorm injections should be more related to the excitation of plasma
waves as many previous works report [e.g., Anderson and
Maeda, 1977; Meredith et al., 2002; Li et al., 2008].
[35] An attempt to reproduce the outer belt structure during
the 2 year period studied here by a 3-D diffusion or 4-D transport/diffusion simulation should prove worthwhile [Zheng
et al., 2003; Varotsou et al., 2008; Albert et al., 2009; Fok
et al., 2011; Shprits et al., 2009; Subbotin et al., 2011]. A
difficult part in doing this is to incorporate accurate wave
spectrum information into the simulation code to compute
the diffusion coefficients [e.g., Glauert and Horne, 2005],
which is rather limited and has not been done for the
THEMIS wave observations. There are still advantageous
aspects in using THEMIS data. One is the fact that one can
use realistic boundary flux values at the outer belt boundary
such as r = 7–8 RE where the THEMIS inner probes cross
routinely. Indeed, as a separate work, our group has recently
determined the outer boundary flux conditions using the
comprehensive set of the THEMIS particle data [Shin and
Lee, 2013]. Also, the THEMIS observations provide the
plasma density to identify the plasmapause locations, which
can also be incorporated into any simulation model as we
did in the radial diffusion test in section 3. Our attempt with
a 3-D simulation code is under progress, and the results will
be published separately.
[36] Acknowledgments. The work at Chungbuk National University
was supported by an NSL grant (2011-0030742) of the National Research
Foundation of Korea. We acknowledge NASA contract NAS5-02099 and
V. Angelopoulos for use of data from the THEMIS Mission. D.-Y. Lee is
grateful to Vassilis Angelopoulos, Michael Hartinger, Wen Li, and Binbin
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