JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 116, A09220, doi:10.1029/2011JA016562, 2011
On energetic electrons (>38 keV) in the central plasma sheet:
Data analysis and modeling
Bingxian Luo,1 Weichao Tu,2 Xinlin Li,2 Jiancun Gong,1 Siqing Liu,1
E. Burin des Roziers,2 and D. N. Baker2
Received 14 February 2011; revised 8 June 2011; accepted 14 June 2011; published 17 September 2011.
[1] The spatial distribution of >38 keV electron fluxes in the central plasma sheet (CPS)
and the statistical relationship between the CPS electron fluxes and the upstream solar
wind and interplanetary magnetic field (IMF) parameters are investigated quantitatively
using measurements from the Geotail satellite (1998–2004) at geocentric radial distances
of 9‐30 RE in the night side. The measured electron fluxes increase with closer distance
to the center of the neutral sheet, and exhibit clear dawn‐dusk asymmetry, with the lowest
fluxes at the dusk side and increasing toward the dawn side. The asymmetry persists
along the Earth’s magnetotail region (at least to Geotail’s apogee of 30 RE during the
period of interest). Both the individual case and the statistical analysis on the relationship
between >38 keV CPS electron fluxes and solar wind and IMF properties show that larger
(smaller) solar wind speed and southward (northward) IMF Bz imposed on the
magnetopause result in higher (lower) energetic electron fluxes in the CPS with a time
delay of about 1 hour, while the influence of solar wind ion density on the energetic
electrons fluxes is insignificant. Interestingly, the energetic electron fluxes at a given radial
distance correlate better with IMF Bz than with the solar wind speed. Based on these
statistical analyses, an empirical model is developed for the first time to describe the
2‐D distribution (along and across the Earth’s magnetotail) of the energetic electron fluxes
(>38 keV) in the CPS, as a function of the upstream solar wind and IMF parameters.
The model reproduces the observed energetic electron fluxes well, with a correlation
coefficient R equal to 0.86. Taking advantage of the time delay, full spatial distribution of
energetic electron fluxes in the CPS can be predicted about 2 hours in advance using
the real‐time solar wind and IMF measurements at the L1 point: 1 hour for the solar wind
to propagate to the magnetopause and a 1 hour delay for the best correlation. Such a
prediction helps us to determine whether there are enough electrons in the CPS available to
be transported inward to enhance the outer electron radiation belt.
Citation: Luo, B., W. Tu, X. Li, J. Gong, S. Liu, E. Burin des Roziers, and D. N. Baker (2011), On energetic electrons (>38 keV)
in the central plasma sheet: Data analysis and modeling, J. Geophys. Res., 116, A09220, doi:10.1029/2011JA016562.
1. Introduction
[2] The plasma sheet is an extended region of hot, tenuous
plasma near the equatorial plane of the Earth’s magnetotail. It
is a key region to understand the mass and energy transport in
the magnetosphere since it is regarded as a critical source
region for energetic particles in the inner magnetosphere, the
auroral precipitation, and ring current, etc [Baker et al.,
1996]. A review of the transient and localized processes in
the magnetotail is given by Sharma et al. [2008]; such as
bursty bulk flows, beamlets, energy dispersed ion beams, flux
ropes, traveling compression regions, night‐side flux transfer
1
Center for Space Science and Applied Research, Chinese Academy of
Sciences, Beijing, China.
2
Laboratory for Atmospheric and Space Physics, University of
Colorado at Boulder, Boulder, Colorado, USA.
Copyright 2011 by the American Geophysical Union.
0148‐0227/11/2011JA016562
events, and rapid flappings of the current sheet. Additionally,
work concerning the plasma sheet has been performed
focusing on the ion density, temperature, and pressure. It is
now well known that the distribution of ions and their properties are highly correlated with the upstream solar wind and
interplanetary magnetic field (IMF) parameters (such as solar
wind velocity, density, and IMF Bz). For example, Borovsky
et al. [1998] correlated plasma sheet ion properties directly
with solar wind parameters and found that: solar wind density,
velocity, and dynamic pressure are strongly correlated with
plasma sheet density, temperature, and pressure, respectively.
Thomsen et al. [2003] discussed the delivery of plasma sheet
material into the near‐Earth region and concluded that the
formation of a strong geomagnetic storm should be favored
by an extended interval of strong southward IMF that is
preceded by an earlier interval of northward field or very
weak Bz. Wing and Newell [2002] and Wing et al. [2005,
2006] discussed formation, dawn‐dusk asymmetry, and time
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scale of the plasma sheet ion features. Wang et al. [2006,
2007] discussed the distribution and drift of plasma sheet ions
under different IMF conditions. Moreover, Tsyganenko and
Mukai [2003] developed models of plasma sheet ion density,
temperature, and pressure as functions of incoming solar
wind parameters. However, previous work has not focused on
energetic electrons in the plasma sheet.
[3] Since the energetic electrons in the plasma sheet are
considered an important source for the relativistic electrons
in the outer radiation belt [Li et al., 1998; Baker et al., 1998;
Li et al., 2001; Li, 2004], understanding the distribution of
these energetic electrons and their relationship with the
upstream solar wind is crucial for us to understand the
transport and energization of electrons in the outer radiation
belt. Moreover, understanding the source of the outer radiation belt is of both scientific and practical importance, as
we still do not understand the physical processes that are
responsible for forming the radiation belts. Also, we are
becoming more reliant on space‐based technologies that
are susceptible to the hazardous effects resulted from these
energetic particles [Taylor et al., 2004]. During strong convection times, tens of keV plasma sheet electrons can access
to geosynchronous orbit and be accelerated to MeV energies.
Recent particle tracing studies [Elkington et al., 2004] show
that sometimes large disturbances in the magnetosphere may
not cause relativistic electron fluxes in geosynchronous orbit
because there are not enough source electrons in the plasma
sheet, while some small disturbances can result in enhanced
relativistic electron fluxes if there are much more pre‐existing
source electrons in the plasma sheet. Thus, understanding the
variations of the energetic electron fluxes in the plasma sheet
is important for understanding the radiation belt dynamics.
[4] The relationship between energetic electrons in the
central plasma sheet (CPS) and the solar wind has been
investigated by Burin des Roziers et al. [2009a, 2009b], in
which they found that energetic electron fluxes beyond
geosynchronous show good correlation with solar wind
speed, with highest correlation coefficient within hours’ time
lag. However, there was still a large spread (about 6 orders of
magnitude) in the fluxes of CPS electrons for a given solar
wind speed. Some resulting questions are: are there any other
parameters that can influence the CPS electron fluxes besides
the solar wind speed? Could the large spread of fluxes be
described by other spatial or solar wind or IMF parameters?
What is the delay for solar wind to affect the energetic electron fluxes in the CPS? Furthermore, is it possible to develop
an empirical model that can forecast the spatial distribution
of CPS electron fluxes based on their spatial distribution and
correlation with solar wind and IMF parameters? These
considerations led to our studies described in this paper.
[5] We first survey the spatial distribution of the energetic
CPS electron fluxes using seven years of data from the Geotail
satellite. Then, quantitative correlations between the CPS
electron fluxes and the solar wind and IMF parameters are
investigated, including the time lag within each correlation.
Last, a model to describe and predict the energetic electron
flux distribution in the CPS is developed based on the results.
2. Instrumentation
[6] The >38 keV electron fluxes in the CPS are collected
from the Geotail satellite under several selection criteria. A
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total of seven years of Geotail data are used, ranging from
1998 through 2004. The Geotail satellite was launched in
1992 into an eccentric near equatorial orbit. During the
period from 1998 to 2004, Geotail was in an orbit with an
apogee of 30 RE and a perigee of 9 RE. Particle data from two
instruments are used in the study. The first is the Energetic
Particle and Ion Composition (EPIC) [Williams et al., 1994]
instrument, which measured the >38 keV integral electron
flux. The second is the Comprehensive Plasma Instrument
(CPI) [Frank et al., 1994], which provides the ion parameters.
Magnetic field measurements were obtained from the fluxgate search coil (MGF) [Kokubun et al., 1994]. The time
resolution of Geotail data is 1.5‐minutes.
[7] The solar wind data is taken from the Solar Wind
Electron, Proton, and Alpha Monitor (SWEPAM) [McComas
et al., 1998] onboard the Advanced Composition Explorer
(ACE) [Stone et al., 1998]. The magnetometer (MAG) [Smith
et al., 1998] aboard ACE provides the interplanetary magnetic field measurements. The data, which are from the L1
point and have 1‐minute resolution, are propagated to the
subsolar point 10 RE from the earth using a simple ballistic
propagation scheme. Slower solar wind will be replaced if it
is overtaken by a high speed stream. However, this happened
less than 0.02% of the time from 1998 to 2004.
3. Data Selection and Handling
3.1. CPS Crossing Selection Criteria
[8] To determine the time intervals during which the Geotail
satellite was inside the CPS, we use the same selection criteria
used by Burin des Roziers et al. [2009a, 2009b]. A set of
4 criteria (related to the plasma beta (equation (1)), magnetic
field (equation (2)), geometric location (equation (3)), and
time length (equation (4))) must to be satisfied for the measurements to be defined as from within the CPS:
1:0
ð1Þ
Bz
1
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi B2x þ B2y 2
ð2Þ
XGSM < 0RE ; jYGSM j < 10RE ; jZGSM j < 10RE
ð3Þ
Tcrossing 30 min;
ð4Þ
where XGSM, YGSM, and ZGSM are satellite positions in
the geocentric solar magnetospheric (GSM) coordinates, Bx,
By, and Bz are three‐dimensional magnetic fields in GSM
coordinates, b is the ratio of plasma pressure to magnetic
pressure, and Tcrossing is the time length for one CPS crossing.
The plasma beta (equation (1)) criterion requires that the
plasma is hot. The magnetic condition (equation (2)) ensures
that the satellite is close to the neutral sheet by requiring
that Bz be large compared to Bx and By. The geometric conditions (equation (3)) require that the satellite be located
within a certain area in GSM coordinates to ensure that the
satellite is close to the CPS and not in the lobes or flanks. Last,
equation (4) requires the satellite to be inside the CPS for
at least 30 minutes to avoid transit dips into the plasma
sheet due to rapid plasma sheet flapping or other spatial
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Figure 1. Distribution of the CPS crossings in the GSM coordinates.
effects. The time criterion may exclude some thin current
sheet conditions or the reconnection region [e.g., Øieroset
et al., 2002; Imada et al., 2007].
[9] In order to investigate the statistical relationship between
the solar wind and the CPS electron fluxes, the CPS measurements are averaged over 15 minutes within each CPS
crossing. These criteria result in a total of 4611 data points.
It must be mentioned that the usage of such a 15‐minute
average data means that consecutive data points cannot be
considered as independent measurements. The 15‐minute
time resolution is still sufficient to catch most of the temporal
variations of the CPS.
3.2. Distribution of the CPS Crossing Points
[10] The spatial distributions of the 4611 CPS crossings
projected on the GSM XY, XZ, and YZ planes are shown in
Figure 1. On the GSM XZ plane (Figure 1b), points in the
mid‐tail are more dispersed compared to the points in the
near‐tail due to the rotation of the dipole axis of the geomagnetic field. Most of the crossings in the dawn (dusk)
sector were observed southward (northward) from the GSM
equatorial plane (Figure 1c), due to the fact that most of the
Geotail orbits passed the dawn (dusk) sector in winter
(summer), when the Earth’s dipole tilts away from (toward)
the Sun; hence the plasma sheet is shifted southward (northward) from its average position. Table 1 lists the Geotail orbit
distribution (in percentage of the total time) in the tail region
during 1998–2004. Obviously, Geotail remained longer in
the dawn (dusk) sector, more southward (northward) from
the GSM equatorial plane than northward (southward). The
positions of the CPS crossings relative to the neutral sheet,
which are calculated from the Standard Equatorial‐Neutral
Sheet Model [Xu, 1992] (see CCMC Web site http://ccmc.
gsfc.nasa.gov/modelweb/magnetos/xu.html), are plotted in
Figure 1d. Here DZ = ZGSM − ZSEN, in which ZGSM is the
CPS crossing position and ZSEN is the expected position of
neutral sheet in GSM. The reduced positions of the crossings
form an orderly symmetric cloud, closely grouped around
the DZ = 0 axis, but more dispersed near the tail flanks,
where the plasma sheet becomes more unstable.
4. Analysis
4.1. Spatial Distribution of Energetic Electron Fluxes
in the CPS
[11] Figure 2 shows the spatial distribution of the energetic electron flux data (cm−2sr−1s−1) in the CPS, illustrating
the flux variations with XGSM, YGSM, DZ, and the radial
distance
to the center of the Earth rGSM (rGSM =
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
2
XGSM
þ YGSM
þ ZGSM
). The CPS electron flux is higher
in the near‐tail (XGSM = 0 to −25 RE) than in the mid‐tail
region (XGSM = −25 to −30 RE) (Figures 2a and 2d). One can
also see a dawn‐dusk asymmetry across the tail with higher
fluxes at the dawn side (YGSM < 0 in Figure 2b). This distribution agrees with previously published results [Meng et al.,
1981; Sarafopoulos et al., 2001; Walker and Farley, 1972;
Bame et al., 1967; Imada et al., 2008; Åsnes et al., 2008]. For
example, Korth et al. [1999] and Imada et al. [2008] found
that the dawn‐dusk asymmetry may be due to electrons
Table 1. Geotail Orbit Distribution in Tail Region During
1998–2004
YGSM > 0
YGSM < 0
ZGSM > 0
ZGSM < 0
ZGSM > 0
ZGSM < 0
23.22%
9.28%
16.89%
21.16%
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Figure 2. Spatial distribution of the CPS electron fluxes
(cm−2sr−1s−1) in the GSM coordinates. The red squares indicate the averaged flux in (a) 5, (b) 5, (c) 2, and (d) 5 RE bins
of the horizontal axis.
drifting eastward and filling the dawn side more than the dusk
side. The dawn‐dusk asymmetry will be discussed further in
section 5.3. In addition, Figure 2c shows that the energetic
electron flux is somewhat higher closer to the center of the
neutral sheet, which is clear from the averaged electron fluxes
profile versus DZ (the red squares in Figure 2c).
[12] Figure 3 shows a 2‐D distribution of the logarithm of
electron fluxes averaged over an area of 1 × 1 RE projected
on the GSM XY plane for all the CPS crossings. Again, the
dawn‐dusk asymmetry is clearly shown, and the CPS electron
flux is higher in the near‐tail than in the mid‐tail. Due to our
CPS selection criteria, there are relatively fewer crossing
points in the mid‐tail than in the near‐tail. The time criterion
(staying in the CPS for at least 30 minutes) automatically
excludes some thin current sheet condition as well as the
reconnection region.
4.2. Event Study on CPS Electron Flux Enhancement
[13] Here we introduce an individual event with energetic
electron flux enhancement in the CPS to see what may
influence the energization process and how long the CPS
electron flux response time is. The event occurred on 02/07/
1999 (Figure 4). The start and stop times of the event (indicated
by vertical lines in Figure 4) is from the plasma sheet criteria
discussed in section 3.1 (e.g., b > 1 in Figure 4f), although an
inspection of Geotail data showed that the satellite actually
entered the plasma sheet about tens of minutes earlier and
crossed the neutral sheet from north to south. The low ion
density (<0.5 cm−3, Figure 4d) and high temperature (>1 keV,
Figure 4e) are typical CPS observation characteristics. The
x‐component of the Geotail magnetic field showed several
direction changes (Figure 4b), most likely caused by magnetotail flapping. Figure 4a shows that at 12:45 UT (marked
by the red arrow), the CPS >38 keV electron flux increased
by two orders of magnitude in 15 minutes. The IMF Bz turned
southward at about 11:30 UT (red arrow in Figure 4h),
75 minutes before the flux enhancement in Figure 4a, and
remained southward for almost two hours. Meanwhile, solar
wind speed and dynamic pressure were very steady during
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the event (Figures 4g and 4i). The geomagnetic field was
quiet (Kp ∼3 and AE ∼200 nT). Thus, it seems that under
the steady solar wind speed and dynamic pressure condition, the southward turning of IMF Bz caused the energetic
electron flux enhancement in CPS, with about 1 hour’s time
lag.
[14] The >2 MeV electron flux at geosynchronous orbit
increased about one day after the energetic electron flux
enhancement described above (not shown here), which
might be due to the inward radial diffusion of the source
electrons observed in the CPS during the event. To see if the
enhancement of >38 keV CPS electrons generated a source
population for the radiation belt electrons, the phase space
density (PSD) for the same first adiabatic invariant (m) in the
CPS and at GEO are calculated. If the PSD in the CPS is
higher than that in the inner magnetosphere (e.g., the electron radiation belt), it means that the electrons in the CPS
can be transported and energized via radial diffusion into the
radiation belt. Radial diffusion conserves m and thus inward
transport increases the energy of the transported electrons,
which is an important non‐adiabatic acceleration mechanism
for radiation belt electrons. The inward radial diffusion is
non‐adiabatic because at least the third adiabatic invariant is
violated [e.g., Li and Temerin, 2001; Tu et al., 2009]. If so,
knowing the precondition of electrons in the plasma sheet
would help to understand the radiation belt.
[15] Flux measurements from two energy channels of the
Los Alamos National Laboratory (LANL) 1994‐084 satellite
at GEO are used to calculate the PSD in geosynchronous
orbit (data on 02/07/1999 are shown in Figure 5b). The
magnitude of magnetic field is required to calculate m. However, the LANL satellite does not have onboard magnetometers, so the local magnetic field is estimated by a dipole
approximation:
B¼
0:317
;
L3
ð5Þ
where L is about 6.6 at GEO. Thus, B at GEO is approximately 110 nT. The local magnetic field in the CPS can be
obtained from the Geotail satellite. The differential flux is
required to calculate PSD, but the electron flux data from
Geotail and LANL are integral fluxes. The differential flux
is estimated by assuming an energy spectra of power law
j = AE −l. For CPS energetic electrons we set l to be 4 to fit
the >38 keV integral flux, which has been investigated by
Figure 3. Distribution of the log of CPS electron fluxes
(cm−2sr−1s−1) on GSM XY plane.
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Figure 4. (a) An event of CPS electron flux enhancement on 7 February 1999. (b) The magnetic field
components, (c) ion speed, (d) ion density, (e) ion temperature, and (f) plasma b detected by Geotail as
well as (g) solar wind speed, (h) interplanetary magnetic field and (i) solar wind dynamic pressure. Geotail
positions are listed at bottom.
Burin des Roziers et al. [2009a]). For the differential flux at
LANL, the equivalent energy for each channel is assumed:
E¼
pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
Emin Emax ;
ð6Þ
where the Emin and Emax are the lower and upper bounds of
the channels [Chen et al., 2005], and the observed flux
energy spectrum is fitted with a power law (j = AE−l). Following Chen et al. [2005], the PSD is calculated using:
f ¼
j
1:66 1010 200:3;
2
E ð E þ m0 c Þ
ð7Þ
where f is PSD in GEM (Geospace Environment Modeling)
units (c/MeV/cm)3, j is electron differential flux in units
of cm−2sr−1s−1keV−1, E is energy in MeV, and m0c2 is the
rest energy of an electron. The comparison of the PSD for
m = 1000 MeV/G in the CPS and at GEO is shown in
Figure 5c. It can be seen that, during the enhancement period
of energetic electron flux, the PSDs in the CPS are higher
than that at GEO. For this case, there appears to be a sufficient
source of electrons in the CPS to account for the enhancement
of electrons in the inner magnetosphere.
[16] From this event, we can see that the upstream solar
wind can cause electron enhancements in the CPS, and these
electrons could be a source for the outer electron radiation
belt. Thus, understanding the solar wind and IMF influence
on electrons in the CPS provides insight toward the transport
of electrons to the inner magnetosphere.
4.3. Correlation Between Interplanetary Parameters
and the CPS Electrons
[17] The overall equatorial distribution (crossing points
projected on the GSM XY plane) of the CPS electron fluxes
under different solar wind and IMF conditions are shown in
Figure 6, similar to the format in Figure 3. The electron
fluxes are sorted into six solar wind and IMF conditions:
(1) solar wind number density Np > 7 cm−3, (2) solar wind
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Figure 5. (a) Geotail >38 keV electron flux, (b) LANL 1997‐84 electron flux, and (c) phase space density
(PSD) for m = 1000 MeV/G in the CPS and at GEO.
Figure 6. Distribution of the log of the CPS electron fluxes (cm−2sr−1s−1) on the GSM XY plane under
different solar wind and IMF conditions.
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Figure 7. Scatterplot of the CPS electron fluxes (>38 keV,
cm−2sr−1s−1) from Geotail taken from [−30, −25] RE in XGSM
versus (a) solar wind speed Vx, (b) IMF Bz, (c) solar wind
ion density Np, and (d) VxBz.
number density Np < 7 cm−3, (3) solar wind speed Vx >
430 km/s, (4) solar wind speed Vx < 430 km/s, (5) IMF Bz < 0,
(6) IMF Bz > 0. Here the solar wind and IMF parameters
75 minutes in advance of Geotail CPS electron flux are
adopted. Later we will demonstrate that the time‐lag of
75 minutes is indeed appropriate. Based on the distributions in
Figure 6, we find that larger (smaller) solar wind speed and
southward (northward) IMF Bz result in higher (lower) energetic electron flux in the CPS, but there are no clear differences
for the CPS electron fluxes for higher or lower solar wind
number density.
[18] Here we investigate the quantitative correlation
between each of the solar wind and IMF parameters and the
CPS electron fluxes. The solar wind and IMF parameters are
also chosen to be 75 minutes prior to the CPS electron
fluxes. We organize the plasma data by distance down the
tail and divide it into 6 regions: 5 RE bins from 0 to −30 RE
in XGSM. We take the CPS crossing points in the mid‐tail
(XGSM = −25 to −30 RE) in consideration. Figure 7 shows a
comparison of the CPS electron fluxes with the solar wind
speed, IMF Bz, solar wind number density Np, and VxBz
(representing the electric field strength at the subsolar point),
respectively, propagated to the magnetopause. Linear correlation coefficients between the solar wind speed Vx, IMF
Bz, solar wind number density Np, VxBz and the logarithm of
the CPS electron flux were calculated (indicated in each
panel of Figure 7). There is a clear positive correlation
between the CPS electron fluxes and the solar wind speed
Vx. The correlation between the flux and Bz as well as VxBz
is also high, but is insignificant for Np.
[19] Even though the CPS electron fluxes correlate well
with the solar wind speed Vx, we find that at a given Vx such
as Vx = 400 km/s, there is still a wide dynamic range of CPS
electron fluxes over several orders of magnitude (Figure 7a).
In order to understand the cause of the wide spread of CPS
electron fluxes, we further divided points with solar wind
speed ranging from 300 km/s to 550 km/s (Figure 7a) into
50 km/s bins, shown in different colors in Figure 8a. The
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points with solar wind speed greater than 550 km/s are
sorted into one subset due to relatively fewer points. The
correlation coefficient between the CPS electron fluxes and
IMF Bz (indicated in Figures 8b–8d for three subsets) is
calculated for each subset. Higher correlation coefficients
than those in Figure 7 are obtained. Based on the results
from Figures 7 and 8, we conclude that both the solar wind
speed and the IMF Bz can influence the CPS electron fluxes.
[20] In the CPS electron flux enhancement on 7 February
1999 described in section 4.2, there is about one hour time
delay of the flux enhancement after the IMF Bz turning
southward. To investigate the average time delay between
solar wind and IMF parameters and the CPS electron fluxes,
different time delays from 0 to 300 minutes in 15 minutes
bin resolution were applied to the calculation of the correlation coefficients between Vx, Np, Bz, VxBz and the CPS
electron flux from a range of distances down the tail. The
results are shown in Figure 9. Figure 9d shows that the
correlation coefficients between VxBz and the CPS electron
flux are highest for time delays of 60–90 minutes after the
solar wind arrives at the magnetopause. The correlation
between IMF Bz and the CPS electron fluxes (Figure 9b)
shows similar results. However, the correlation between Vx
and the CPS electron flux does not change much within
several hours’ time lag (Figure 9a). The correlation coefficients between solar wind density Np and the CPS electron
flux again are much weaker (Figure 9c). Based on these
statistical results, the highest correlated time delay between
solar wind and IMF parameters at the magnetopause and the
CPS electron fluxes is 1–2 hours.
4.4. Modeling the Energetic Electron Flux in the CPS
4.4.1. Modeling Equation
[21] From previous analysis we find that the spatial
distribution of CPS electron flux shows the following
characteristics:
Figure 8. Scatterplot of the CPS electron flux (>38 keV,
cm−2sr−1s−1) taken from [−30, −25] RE in XGSM versus solar
wind speed and IMF Bz. (a) The same as Figure 7a, but with
points in color corresponding to their solar wind speed, and
one color representing one solar wind speed bin (50 km/s).
(b–d) Points are subsets of Figure 8a, with each subset
covering one bin of solar wind speed.
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Figure 9. Correlation coefficients between solar wind parameters and the log of the CPS electron flux
under different time lags. The red squares indicate the best correlation coefficients.
[22] 1. The CPS electron flux increases with decreasing
distance to the Earth;
[23] 2. The CPS electron flux increases with decreasing
distance to the center of the neutral sheet;
[24] 3. The CPS electron flux has a dawn‐dusk asymmetry
with higher flux at the dawn side;
[25] Furthermore, the CPS electron fluxes are strongly
correlated with the upstream solar wind and IMF parameters,
which can be described as following:
[26] 1. Higher solar wind speed results in the higher CPS
electron flux;
[27] 2. Higher southward IMF Bz results in the higher CPS
electron flux;
[28] 3. Solar wind number density is not correlated with
the CPS electron flux;
[29] 4. The time delay of upstream solar wind and IMF
(already propagated to the magnetopause) effects on the
CPS electron flux is 60–90 minutes.
[30] Considering the above spatial distribution and solar
wind effects on the CPS electron flux, the following form
was adopted to model the CPS electron flux:
logð f Þ ¼
A
A0 BAt 1 1 þ A2 sin A3 ðVx*ÞA4 Np* 5 þ A6
A
A7 þ A8 BAt 9 1 þ A10 sin A11 ðVx*ÞA4 Np* 13 þ A14
A15
sin ð1 þ A16 DZ Þ;
¼ ðarccosðBz =Bt Þ Þ=2;
¼ ðarctanðYGSM =XGSM Þ =2Þ=2;
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
2
2
2
þ YGSM
þ ZGSM
¼ XGSM
;
DZ ¼ jZGSM ZSEN j;
Vx* ¼ VX =430;
NP* ¼ Np =7;
ð8Þ
where Bt is the magnitude of the IMF in nT and A0, A1, …, and
A16 are model parameters. Solar wind variables were normalized using a typical average magnitude, e.g., Vx/430 (km/s)
and Np/7 (cm−3). The three terms related to the spatial distribution of the energetic electrons in equation (8) are: radial
dependence rA7, dawn‐dusk asymmetry, rA15 sin and distance to the center of the neutral sheet (1 + A16DZ). The
influence of solar wind and IMF parameters are presented
as a factor before each spatially related term. In the model
function, the term related to the solar wind and IMF parameters is adopted from both physical and mathematical
consideration, in which it is easy to see the significance of
different solar wind parameters. Li et al. [2007] developed a
model predicting the AL index using the solar wind parameters and used a similar form, considering the energy input of
solar wind into the magnetosphere. A similar form regarding
the close relationship between the substorm and electron
enhancement in the CPS was adopted in our model.
4.4.2. Model Parameters
[31] The best fit values of the coefficients and nonlinear
parameters are achieved by a least squares‐fit between the
model prediction and the observed 15‐min averaged CPS
electron fluxes and are given in Table 2. Figure 10 shows the
correlation between the observed values of CPS electron fluxes
and those predicted by the model, illustrating the overall
quality of the model. The correlation coefficient between the
observed and predicted CPS electron fluxes is R = 0.86.
[32] The model captures the spatial distribution and
dynamic variation of the fluxes and can also reflect the
relative importance of different parameters of the solar wind
and IMF when modeling the CPS electron flux. From the
model parameters we can see that A3 and A4 are larger than
A5, which implies that the mechanisms which may control
the CPS electron fluxes are mainly influenced by Vx and
IMF Bz. A16 is negative, which means that the CPS electron
flux will decrease with increasing perpendicular distance to
the center of the neutral sheet. These results are consistent
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Table 2. Parameters of the >38 keV CPS Electron Flux Model
Parameter
Value
A0
A1
A2
A3
A4
A5
A6
A7
A8
A9
A10
A11
A12
A13
A14
A15
A16
1.57
−0.02
0.72
1.63
1.46
0.02
10.14
−0.35
−0.24
0.20
−0.67
1.93
−0.59
−0.10
0.16
0.80
−0.02
with the features from previous statistical correlation analysis in section 4.3.
4.4.3. Full Distribution of the CPS Electron Flux
and Response to the Interplanetary Parameters
[33] The spatial distribution of the CPS electron flux can
be quantitatively described using the solar wind speed Vx
and the IMF Bz as principal driving parameters of the model,
which is useful for magnetospheric modeling research which
needs plasma sheet electron flux as boundary conditions,
considering that satellites can only supply single point data
while the model can provide full spatial distribution. Since
there is about one hour delay for solar wind on the L1 point
to propagated to the magnetopause and there is an additional about one hour delay for the best correlation, we can
use the model to predict the distribution of energetic electron fluxes in the CPS about 2 hours in advance (supposing
that the real‐time solar wind and IMF data can be achieved).
Such a forecast is helpful to determine whether there are
sufficient electrons in the CPS to be transported to the inner
magnetosphere, such as the outer electron radiation belt. To
visualize the impact of the state of the interplanetary medium,
and the full distribution of the CPS electron fluxes, color‐
coded maps of the CPS electron fluxes on GSM XY plane
for different solar wind and IMF conditions are plotted in
Figure 11. Comparison between the graphs clearly illustrates the effect of changing individual input parameters.
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number density Np, and IMF Bz), as well as the GEOTAIL
CPS electron flux used in the calculation of the input variables for the model (equation (8)). In each of the three
panels, three vertical dashed lines correspond to the 5, 50,
and 95 percent of the total number of samples. As can be
seen, our data set provides a fair coverage of the average
observed condition of the solar wind; that is, solar wind
speed between 300 km/s and 600 km/s, IMF Bz between
−5 nT and +5 nT, solar wind density between 2 and 15 #/cc,
but contains very few data with unusually fast, dense solar
wind, or strongly southward or northward IMF. This is a
common problem in any kind of data based modeling, caused
naturally by the relative rarity of unusual events. Comparing
the solar wind and IMF distributions of our data set with that
used by Tsyganenko and Mukai [2003], we find that, although
the parametric spaces are very similar, there are more unusual
events in our data set. This is because our data set covers the
solar maximum of solar cycle 23, while the data set used by
Tsyganenko and Mukai [2003] covers the solar minimum
from 1994–1998.
[36] There are some error sources associated with the
model. First, there is uncertainty in the assumed propagation
of the solar wind to the Earth [Weimer et al., 2003; Bargatze
et al., 2005]. Additionally, there is error associated with the
model equation due to missing spatial, solar wind, or other
IMF parameters that may also affect the CPS electron flux.
However, the good performance of our model demonstrates
it includes the major factors (especially of the upstream solar
wind) in modeling the energetic electron flux in the CPS.
[37] A future project to test the validity of the model
would be to use the same model dependences reported,
but use energetic particle data available from the ISEE 1 and
2 satellites in the tail and the ISEE‐3 satellite upstream
providing the solar wind/IMF data, and see if a plot similar to
Figure 10 is found.
5. Discussion
5.1. Model Limitation and Error Sources
[34] Data based models are naturally limited by the coverage of data used in the derivation of model parameters. As
discussed in section 3 and shown in Figure 1, the spatial
distribution of the Geotail observations in our data set
spanned radial distances from 9 to 30 RE. Thus, the model is
restricted to the near‐tail (XGSM = −0 to −25 RE) and the
mid‐tail (XGSM = −25 to −30 RE) regions.
[35] The values of the input parameters to provide reliable
result should be within the solar wind and IMF range in our
data set. This is also the common limitation in data based
models. Figure 12 shows distributions of the values of solar
wind and IMF parameters (solar wind speed Vx, solar wind
Figure 10. Scatterplot of the modeled CPS electron flux
against the observed ones.
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Figure 11. Color‐coded plots of the distribution of the CPS electron flux (cm−2sr−1s−1) from the model
under different solar wind speed conditions (described on top of each plot).
5.2. Time Lag of SW Influence on the CPS Electrons
[38] Significant work has been done on the time delay
between the upstream solar wind and IMF effects and the
CPS properties, mostly the ion density, temperature, and
pressure. Previous studies [e.g., Terasawa et al., 1997; Wang
et al., 2007; Øieroset et al., 2003] suggest that northward
IMF averaged over 8–9 hours prior to the CPS observation
best determines the CPS properties. Borovsky et al. [1998]
found that the highest correlation between solar wind density
and plasma sheet density in the mid‐tail (17–22 RE), nightside
at geosynchronous orbit, and dayside plasma sheets occurred
with time lags of 0–2.5 hours, 0–7 hours, and 11–18 hours,
respectively. Wing et al. [2006] reported that the transport
time depends on the direction of the IMF: solar wind
density enhancements precede mid‐tail plasma sheet density enhancements by 3 hours during times of northward IMF.
[39] Unlike the above studies which use the ion response
in the CPS, the work presented here focuses on the >38 keV
Figure 12. Histograms illustrating the coverage of the solar wind and IMF data as well as the CPS electron
fluxes. Three vertical dashed lines correspond to the 5, 50, and 95 percent of the total sample numbers.
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electrons in the CPS. From both individual case and statistical analysis, we found a delay of 60–90 minutes for the
upstream solar wind to affect the CPS electrons. Considering
the energetic electron flux enhancement in the CPS, which is
quite often caused by substorms related to southward IMF
periods, the time lag is similar to the substorm time scale,
reported to be about 1–2 hours [McPherron, 1991].
[40] From Figure 9, it can be seen that the time delay for
energetic electron flux in region −15 to −10 RE is shorter
than in the region −25 to −15 RE (in XGSM down the tail). If
all the electrons are transported and energized from the distant tail (100 RE) to the near Earth region through the CPS,
the time delay should be increasing with decreasing XGSM.
This is not the case based on the statistical analysis presented
here. One possible explanation is that there might be some
local energization of electrons in the region around −15 RE
in XGSM in the CPS. Energization of these electrons may be
caused by magnetic reconnections, but in the quasi‐steady
state, reconnection on the nightside is believed to occur in the
distant magnetotail beyond 100 RE [e.g., Zwickl et al., 1984;
Slavin et al., 1985; Nishida et al., 1996]. However, when
open field lines are stored in the tail lobes, magnetic reconnection can occur explosively in the near Earth magnetotail
and is an important element of magnetospheric substorms
[e.g., Russell and McPherron, 1973; Hones, 1979; McPherron,
1991; Baker et al., 1996; Nagai et al., 2005]. Nagai et al.
[2005] investigated the radial distance of the magnetic reconnection site using the criterion of strong electron acceleration
in the magnetotail under different solar wind and IMF conditions. They found that magnetic reconnection takes place
closer to the Earth when the efficiency of energy input is
higher. Even when the energy input reaches the threshold
value needed for mid‐tail (XGSM = −25 to −31 RE) reconnection, it does not start in the mid‐tail before the near‐tail
(XGSM = −15 to −25 RE). This might be an explanation of the
local heating at around −15 RE in XGSM.
5.3. Dawn‐Dusk Asymmetry of Energetic
Electron Flux
[41] The dawn‐dusk asymmetry of ion density in the
plasma sheet has been investigated by various researchers
[e.g., Wing et al., 2005; Wang et al., 2006, 2007, and references therein]. The ion density is higher on the dusk side in
the plasma sheet, due to the electric and magnetic drift
transport from mid‐tail to the near Earth region [Wang
et al., 2006]. The dawn‐dusk asymmetry of electrons in the
Figure 13. Distribution of dawn‐dusk asymmetric part of
the CPS electron fluxes (cm −2 sr −1 s −1 ) (same format as
Figure 3).
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Figure 14. Dawn‐dusk asymmetric part of the CPS electron
fluxes (cm−2sr−1s−1) averaged in 6 regions across the tail.
plasma sheet has also been investigated. Previous studies
have found that the asymmetry is species and energy
dependent, and can be well reproduced using a diffusion
convection model [e.g., Åsnes et al., 2008; Imada et al.,
2008]. However, the feature of the dawn‐dusk asymmetry
of energetic electron flux along the tail at different down‐tail
distance has not been investigated, and it is very important
for studying the transport process of particles in the plasma
sheet from the distant tail source region. In our CPS electron
flux model there are two terms corresponding to the symmetric and asymmetric spatial distribution, which are presented by rA7 and rA15 sin , respectively, in equation (8).
The asymmetric fluxes of the 4611 CPS crossings can be
achieved by subtracting the modeled symmetric fluxes from
the observed total fluxes, which are shown in Figure 13. The
points in Figure 13 are further divided into six XGSM regions,
with the averaged asymmetric fluxes profile for each region
shown in Figure 14. It can be seen that the intensities of
asymmetry do not change significantly along the CPS at
different radial distances, except in the mid‐tail (blue and
black lines), which might be due to the relatively fewer
crossing points on the mid‐tail dawn side in our data set.
Moreover, it must be mentioned that we constrain YGSM to be in
from −10 to 10 RE when selecting the CPS crossing samples.
Further analysis should be done with wider YGSM range of
plasma sheet selection to look into the asymmetry of energetic
electrons across the magnetotail, because the asymmetry
might be intensified as more electrons drifted dawn‐ward in
wider YGSM regions.
5.4. Solar Activity and the CPS Electron Flux
[42] From above investigations, we found that solar wind
speed and IMF Bz are important in affecting the physical
process that control the electron flux in the CPS. The relative
significance of these two effects can not be easily separated.
Slow solar wind is preferentially observed in solar active
phase, but there are many CMEs that resulted in very high
solar wind speed as well as large southward IMF Bz. In the
present work, our data covered years 1998–2004, mainly
around the solar maximum. The difference of electron fluxes
between the solar maximum and minimum can be investigated by including more data (e.g. 2005–2008).
6. Summary and Conclusions
[43] We investigate in detail the spatial distribution of
>38 keV electron fluxes in the Earth’s magnetotail central
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plasma sheet (CPS) and their responses to the solar wind
and IMF conditions. This work was based on the data from
the Geotail Energetic Particle and Ion Composition instrument (EPIC), between 1998 and 2004, and the concurrent
solar wind and IMF data propagated to the magnetopause.
[44] It was found that the CPS energetic electron fluxes
increase with decreasing geocentric radial distance, showing
a clear dawn‐dusk asymmetry with higher flux on the dawn
side. The dawn‐dusk asymmetry does not show any difference along the magneotail to Geotail’s apogee of 30 RE
during the period of interest. Furthermore, the energetic
electron flux increases with the decreasing distance to center
of the neutral sheet.
[45] Solar wind speed and IMF Bz are the most significant
parameters that can influence the mechanisms which control
the CPS electron fluxes, while solar wind number density
plays a negligible role. Time lag analysis between interplanetary medium conditions and the CPS energetic electron
fluxes shows a one hour delay for the CPS energetic electrons to be enhanced after high speed solar wind reaches the
dayside magnetopause and the IMF Bz turns southward.
[46] Based on the spatial distribution of the CPS electron
fluxes as well as their correlation with upstream interplanetary parameters, an empirical model of the CPS electron
flux was developed. The correlation coefficient between the
observed and predicted values of the CPS electron fluxes is
0.86. Full spatial distributions of energetic electron fluxes in
the CPS can be predicted about 2 hours in advance based on
the solar wind and IMF measurements at the L1 point. The
CPS forecast can be applied to determine whether there are
enough electrons in the CPS available to be transported to
enhance the outer electron radiation belt.
[47] Acknowledgments. This work was supported by the National
Basic Research Program of China (2011CB811406) and the Knowledge
Innovation Program of the Chinese Academy of Sciences (YYYJ‐1110).
It was also supported by NASA grants (NNX‐09AJ57G, and ‐09AF47G)
and NSF grants (ATM‐0842388 and ‐0902813). We thank the OMNI
group at NASA/Goddard Space Flight Center and Geotail team for making
data available.
[48] Masaki Fujimoto thanks the reviewers for their assistance in
evaluating this paper.
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1234 Innovation Dr., Boulder, CO 80303, USA.
J. Gong, S. Liu, and B. Luo, Center for Space Science and Applied
Research, Chinese Academy of Sciences, PO Box 8701, Beijing 100190,
China. (luobx@cssar.ac.cn)
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