Statistics of Plasma Sheet Convection
1
L. Juusola,1N. Østgaard, and1E. Tanskanen1,2
L. Juusola, Finnish Meteorological Institute, P.O. Box 503, FIN-00101 Helsinki, Finland.
N. Østgaard, Department of Physics and Technology, University of Bergen, Postboks 7803, NO-5020 Bergen, Norway.
E. Tanskanen, Finnish Meteorological Institute, P.O. Box 503, FIN-00101, Helsinki, Finland.
1Department of Physics and Technology, University of Bergen, Bergen, Norway.
2Finnish Meteorological Institute, Helsinki, Finland.
Abstract. We study statistically plasma sheet convection using ion and
2
magnetic field data obtained by Cluster 1 and 3 (years 2001–2007), Geotail
3
(1995–2006), and THEMIS 1–5 (2007–2009). The condition ionβ > 0.5 is
4
used to find the plasma sheet regime. Plasma sheet convection is observed
5
to be dominated by slow speed (<100 km/s) flows that circulate around Earth
6
on both sides towards the dayside. Higher speeds flows are concentrate around
7
the aberrated midnight meridian. With increasing speed, the sunward com-
8
ponent of the flow velocity becomes more pronounced, such that flows with
9
V >500 km/s are directed almost purely sunward, not circulating around Earth
10
like the slower flows. Interplanetary magnetic field (IMF) y- and z-components
11
are observed to penetrate the plasma sheet, causing a rather uniform change
12
of a few nT in the same magnetic field component. Moreover, during IMFz<0
13
conditions, a channel of increased Bz is created in the nightside around the
14
aberrated midnight axis. It is suggested that the channel is caused by dipo-
15
larization and magnetic flux pileup related to fast flows. Compared to IMFz<0
16
conditions, the nightside region of highest mean flow speed is shifted towards
17
dusk during IMFy<0 conditions, and towards dawn during IMFy>0 condi-
18
tions. For the V >100 km/s flows, no correlation is found between the plasma
19
sheet flow speed and the solar wind electric field magnitude, but between the
20
flow speed and IMF clock angle there is a clear correlation, with increasing
21
speed as IMF turns southward.
22
1. Introduction
According to the open magnetosphere model byDungey [1961], the closed geomagnetic
23
field lines reconnect with the interplanetary magnetic field (IMF) on the dayside mag-
24
netopause. The resulting open field lines are dragged tailwards across the northern and
25
southern polar caps by the solar wind. On the nightside they reconnect again, and the re-
26
sulting closed, but far stretched field lines migrate back toward the dayside magnetopause.
27
This process is known as the magnetospheric convection. Occasionally the dayside and
28
nightside reconnection rates are balanced, resulting in periods of steady magnetospheric
29
convection [e.g., Sergeev et al., 1996], but more often more magnetic flux is either opened
30
or closed [e.g.,Milan et al., 2007]. The substorm, for instance, consists of such periods of
31
loading and unloading.
32
According to the two-fluid approximation, two components contribute to the ion velocity in the plasma sheet. These are the electric drift and the diamagnetic drift:
Vi =qiE× B
qiB2 −∇Pi
Ni × B
qiB2, (1)
whereqi,Pi,Ni, andViare the ion charge, thermal pressure, number density, and velocity,
33
and E and B the electric and magnetic field. In the plasma sheet, ions and electrons
34
drift diamagnetically in opposite direction, creating the cross-tail current. The relative
35
strengths of the two terms in Eq. (1) are determined by two factors. First, the electric
36
field and pressure gradients vary significantly in the near-Earth region. Second, electric
37
drift does not depend on particle energy, but diamagnetic drift does. Thus, the motion
38
of low-energy ions is dominated by electric drift, and the motion of high-energy ions by
39
diamagnetic drift.
40
Several statistical studies based on ion moments computed from satellite measurements
41
have addressed the characteristics of plasma sheet convection. In most cases, the focus
42
has either been on the slow [Angelopoulos et al., 1993; Zhu, 1993; Wang et al., 2006] or
43
fast [Baumjohann et al., 1990;Angelopoulos et al., 1992, 1994; Shiokawa et al., 1997;Raj
44
et al., 2002] plasma sheet flows, and the studied region limited to the nightside plasma
45
sheet.
46
Using data from the AMPTE/IRM satellite (four months from 1986) in the region
47
−19 RE < xGSM < −9 RE (Earth radii) and |yGSM| < 15 RE, Baumjohann et al. [1989]
48
inferred that the average ion flow speed in the central plasma sheet is low, below 100
49
km/s, due to the predominance of low-speed flows. Magnetotail lobe or plasma sheet
50
boundary layer (PSBL) samples were excluded from the data set by assuming that in the
51
plasma sheet spacecraft charging effects should be absent. High-speed flows were found
52
to occur in the plasma sheet, but in bursts mostly less than one minute in duration, with
53
intermittent intervals of near stagnant plasma. The bursts were more frequent during
54
geomagnetically disturbed times, but occurred also during low Auroral Electrojet (AE)
55
index conditions.
56
Baumjohann et al. [1990] used AMPTE/IRM data (eight months from spring 1985 and
57
spring 1986) to study the occurrence rates and typical characteristics of high-speed (V >
58
400 km/s) ion flows in the plasma sheet and PSBL. The largest occurrence rates of high-
59
speed flows were found near the midnight meridian at the largest radial distances accessible
60
to the spacecraft (≈19 RE), and their occurrence strongly peaked in the sunward direction.
61
The high-speed flows were found to be bursty, with the majority of the flows lasting less
62
than 10 sec.
63
Angelopoulos et al. [1992] studied the high-speed flows reported by Baumjohann et al.
64
[1989] using AMPTE/IRM data (two months from 1985). They found that the high-speed
65
flows organize themselves in 10-min time scale flow enhancements, which they termed
66
bursty bulk flow (BBF) events. The flow peaks were usually associated with magnetic
67
field dipolarization and ion temperature increases.
68
Angelopoulos et al. [1993] constructed the average flow pattern in the quiet, that is,
69
non-BBF, plasma sheet (β > 0.5) using AMPTE/IRM (6 months from 1985) and ISEE
70
2 data (12 months from 1978 and 1979). BBFs were defined as plasma sheet segments of
71
continuous ion flow of V >100 km/s, during which V exceeded 400 km/s at least once.
72
The ISEE 2 orbit extended the analysis beyond the apogee of IRM to 22 RE. The flow
73
was found to be predominantly duskward at local midnight, while closer to the flanks of
74
the examined region it was mostly earthward.
75
Zhu [1993] constructed the average convection pattern in the plasma sheet (β > 0.2)
76
using ISEE 1 and 2 data (14 months in 1977–1979) in the region−20 RE < xGSM <−10 RE
77
and|yGSM|<15 RE. Only flows withqVx2+Vy2 <250 km/s were included. They showed
78
that the convective flows tend to follow contours of constant unit magnetic flux volume
79
as they move around the Earth, which helps to avoid the pressure balance inconsistency
80
found in two dimensional magnetotail models [e.g., Erickson and Wolf, 1980].
81
Angelopoulos et al.[1994] studied the statistical properties of BBFs in the plasma sheet
82
using AMPTE/IRM and ISEE 2 data. The plasma sheet was defined as the regime where
83
β > 0.5, and BBFs as segments of V > 100 km/s in the plasma sheet, during which
84
V exceeded 400 km/s for at least at one sample. Samples of V > 400 km/s that were
85
less than 10 minutes apart were considered to belong to the same BBF event, even if the
86
speed dropped below 100 km/s between these samples. They inferred that BBFs were
87
responsible for 60–100% of the earthward transport of mass, energy and magnetic flux,
88
even though they occurred only 10–15% of the observation time the spacecraft spent in
89
the plasma sheet. Earthward ofxGSM=−19 RE, the occurence rate of BBFs was observed
90
to decrease. Braking of the flow speed was suggested as a possible explanation.
91
Shiokawa et al.[1997] studied possible braking mechanisms of high-speed (>400 km/s)
92
ion flows in the near-Earth plasma sheet using the same data set as Baumjohann et al.
93
[1989]. The high-speed flows were found almost always to be directed earthward between
94
−19 RE< xGSM<−9 RE, indicating that their source was beyondxGSM<−19 RE. The
95
occurrence rate of the high-speed flows was observed to substantially decrease towards
96
Earth, but flows with speeds >600 km/s were still observed at xGSM = −9 RE. It was
97
suggested that the high-speed flows are stopped at a clear boundary between the regions
98
of dipolar and tail-like field in the plasma sheet, which corresponds to the inner edge of
99
the plasma sheet. The average jump of the magnetic field at this boundary was estimated
100
to be 6.7 nT.
101
The fast flows observed in the PSBL typically consist of unidirectional or counter stream-
102
ing ion beams strongly aligned with the magnetic field [e.g.,Raj et al., 2002, and references
103
therein]. These field-aligned beams have sharp cutoffs at low energies, and occur within
104
relatively steady magnetic field and plasma conditions. For counter streaming beams the
105
velocity moments do not represent the bulk motion of the plasma. Quasi-steady recon-
106
nection tailward of the observation point has been suggested as the source of these beams
107
[Onsager et al., 1991]. High speed flows observed in the plasma sheet, on the other hand,
108
typically consist of a single bulk flow population directed mostly sunward, independent of
109
the local magnetic field direction. These bulk flows do not have low-energy cutoffs, and
110
are often associated with magnetic field dipolarization and plasma temperature enhance-
111
ments.
112
Generally, it is assumed that field-aligned beams and bulk flows occur in the PSBL and
113
plasma sheet, respectively, and these two regions can be distinguished from each other
114
based on, for instance, plasma β. Raj et al. [2002] surveyed all high-speed (>250 km/s)
115
flows detected by Wind during 17 perigee passes across the near-Earth (−25 RE < xGSE <
116
0) plasma sheet between 1995 and 1997. Instead of plasma moments or the regions in
117
which the flows were detected, they classified the high-speed flow events based on their
118
ion distribution characteristics. They discovered that bulk flows are perpendicular to
119
the magnetic field when detected at the neutral sheet (Bx ≈ 0) but have a large field-
120
aligned component at higher magnetic latitudes. Field-aligned bulk flow and field-aligned
121
beams were similar in terms of their velocity moments and could occur at the same
122
magnetic latitudes, but were easily distinguishable based on their ion distributions. No
123
single moment-based parameter or threshold could cleanly separate beam from bulk flow
124
distributions, because a range of values of these parameters existed where both types of
125
fast flows were observed. Moreover, they observed little or no temperature enhancements
126
in cases where the spacecraft resided near the neutral sheet before the arrival of bulk
127
flows, suggesting that the temperature enhancements seen in other bulk flow events might
128
in part be a spatial effect instead of true heating of the plasma. The occurrence of high-
129
speed bulk flow events had a dawn-dusk asymmetry, with higher occurrence rates in the
130
premidnight sector of the plasma sheet, while beam events occurred with equal probability
131
on both sides of midnight.
132
Wang et al. [2006] used Geotail data (November 1994 to April 1998) in the region
133
|yGSM| < 22.5 RE and −30 RE < xGSM < 0 to study the distributions of plasma sheet
134
(β >1) ions and magnetic fields under northward and southward IMF conditions. They
135
utilized the condition VGSM,x > −100 km/s to exclude magnetosheath crossings, and
136
V⊥ < 200 km/s to exclude large BBFs. The perpendicular flow around |yGSM| = 10 RE
137
was observed to be stronger in the premidnight than in the postmidnight region, and this
138
asymmetry was shown to result from the westward diamagnetic drift. The flow pattern
139
was not significantly different during northward and southward IMF conditions, but the
140
overall flow speed was higher during southward IMF.
141
The several years of Geotail, Cluster, and THEMIS data now available provide an excel-
142
lent opportunity to revisit the question of the characteristics of plasma sheet convection.
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The abudance of data enables us to reveal more detailed as well as new infomation on
144
this important process, by which disturbances are communicated from the tail to the
145
inner magnetosphere. In this study, we analyze statistically plasma sheet bulk flows at
146
radial distances<30 RE from Earth. In Sect. 3.1, we construct the average plasma sheet
147
flow pattern, and discuss the relative abundance of sunward and tailward flows. Such
148
convection maps could also be useful, when validating magnetospheric simulation codes.
149
Sect. 3.2 deals with dawn-dusk symmetries and asymmetries observed in the plasma sheet
150
parameters, and in Sect. 3.3 the effect of the IMF clock angle is examined. As noted
151
by Angelopoulos et al. [1992], the often used fast flow speed threshold of 400 km/s does
152
not represent any physically significant quantity, and also flows with speeds below the
153
threshold are an integral part of the BBF structure. Thus, in Sect. 3.4, we have divided
154
all samples according to speed into 10 bins (0–100 km/s, 100–200 km/s, ..., 900–1000
155
km/s), and examined the properties of each bin separately. The convection electric field
156
related to the average flow pattern is derived in Sect. 3.5. The final Sect. 4 contains dis-
157
cussion and conclusions. We begin by introducing the used instruments and data analysis
158
techniques (Sect. 2).
159
2. Data
In this study we have used magnetospheric ion and magnetic field data obtained by the
160
Cluster 1 and 3 satellites from 2001 to 2007, by the Geotail satellite from 1995 to 2006,
161
and by the THEMIS 1–5 satellites from September 2007 to the end of 2009.
162
From the Cluster 1 and 3 spacecraft we have used 4-s (spin average) resolution data
163
from the Fluxgate magnetometer [FGM,Balogh et al., 2001] and ion moments from Cluster
164
Ion Spectrometry [CIS,R`eme et al., 2001] Hot Ion Analyser (HIA) instrument. CIS/HIA
165
measures energies from 5 eV/q to 32 keV/q. From the Geotail spacecraft we have utilized
166
3-s (spin average) resolution data from the Magnetic Field experiment [MGF, Kokubun
167
et al., 1994], and 12-s resolution ion moments from the Low Energy Particle experiment
168
[LEP, Mukai et al., 1994]. LEP/EA measures energies from several eV/q to 43 keV/q.
169
From the THEMIS 1–5 spacecraft we have used 3-s (spin average) resolution data from
170
the Fluxgate magnetometer [FGM,Auster et al., 2008], and ion moments from the Elec-
171
trostatic Analyzer [ESA, McFadden et al., 2008a, b]. ESA measures energies from 1.6
172
eV/q to 25 keV/q. Solar wind data at 1-min resolution propagated to Earth’s bow shock
173
nose were extracted from NASA/GSFC’s OMNI data set through the OMNIWeb interface
174
(http://omniweb.gsfc.nasa.gov/).
175
Figure 1 displays the observation times of ion β > 0.5 (this choice is discussed below)
176
on a 2.5 RE×2.5 RE grid (a): for Cluster 1 and 3 from 2001 to 2007, (b): for Geotail
177
from 1995 to 2006, and (c): for THEMIS 1–5 from 2007 to 2009, presented as a functionx
178
and y. Here and elsewhere in this study we have used Cartesian (x,y,z) Geocentric Solar
179
Magnetospheric (GSM) coordinates. The gray circle represents the geostationary orbit at
180
the 6.6 RE radial distance, and the gray curve the magnetopause according toShue et al.
181
[1997], with Pdyn = 1 nPa and IMF Bz = 0. Both the magnetopause and the solid grid
182
have been rotated 4.8◦ clockwise to take into account the aberration due to Earth’s orbital
183
motion. The thick gray line shows the aberrated noon-midnight axis. Approximately a
184
circle of 30 RE radius was covered by the observations.
185
Our aim is to study statistically plasma sheet bulk flows, which means that first we had
186
to separate those data from other samples. With such a large amount of data involved,
187
it was not feasible to examine every particle distribution. Therefore, we compromised
188
between the amount of data and accurate selection of plasma sheet bulk flows by using
189
moment-based criteria. We chose the criterion ionβ >0.5 for the plasma sheet. According
190
to Raj et al. [2002], this would include 95% of high-speed (V > 250 km/s) bulk flow
191
samples, but at the same time, 55% of undesired high-speed field-aligned beam samples
192
would also satisfy the criterion. Although increasing the limit to β > 2 would eliminate
193
more than 95% of beam samples, only 45% of bulk samples would be included, decreasing
194
the amount of data significantly. As is obvious from Fig. 1, towards plasma sheet flanks,
195
particularly on the dayside, the criterion also included magnetosheath and solar wind
196
samples.
197
Because of the large amount of data, we began by dividing our samples into “flow events”, represented by averages of the ion and magnetic field measurements during the event. Also other parameters describing the ambient conditions, such as solar wind data,
were included. Because plasma sheet convection is dominated by slow speed flows, a flow event was defined as a continuous block of samples during which β > 0.5 and the flow speed remained within one of the bins: 0–100 km/s, 100–200 km/s, ..., 900–1000 km/s.
Typical durations of the events varied from seconds to minutes. In order to emphasize the bulk flows in the center of the plasma sheet, the ion moment and magnetic field averages were weighted by β:
x=
Pn i=1βixi
Pn i=1βi
. (2)
The solar wind averages tagged to each event included not just the event period but
198
also the preceding 30 min in order to better reflect the conditions in the plasma sheet.
199
These event-averages were then gridded according to their xy-locations, and averages of
200
the event-averages, weighted by the durations of the events, were computed for each grid
201
point. The results are displayed in plots such as those in Figure 2.
202
3. Results
3.1. Sunward and Tailward Flows
The color scale in panel (a) of Fig. 2 shows the time Cluster 1 and 3, Geotail, and
203
THEMIS 1–5 had altogether spent observing β >0.5. Due to the orbits of the satellites,
204
some parts within the 30 RE radius circle were better covered than others, but almost
205
everywhere there was at least one day of observations. The vectors in panel (a) of Fig.
206
2 display the mean velocity. The pattern revealed three distinct regions: Upstream the
207
undisturbed solar wind flow had an average angle of 4.8◦ with the −x axis due to Earth’s
208
orbital motion, in the magnetosheath the solar wind flow was deflected around the magne-
209
topause, and inside the magnetosphere the average flow was near stagnant at the displayed
210
scale.
211
Panel (b) of Fig. 2 displays the percentage of time spent observing Vx ≥ 0 relative to
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all β > 0.5 samples. On the dawn and dusk flanks of the plasma sheet the flows had
213
predominantly a sunward component, but towards the dayside the percentage decreased
214
due to the increasing amount of antisunward magnetosheath flow samples. Also in the
215
nightside plasma sheet, mainly in the region −30 RE < x < −18 RE and −6 RE < y <
216
12 RE, a significant percentage of the flows were antisunward.
217
At the equatorial plane, antisunward flows observed on open field lines behind an X-line
218
would generally be expected to be associated with a southward magnetic field component,
219
while flows on closed field lines would have a northward component. Panels (c) and (d)
220
of Fig. 2 display the percentage of time spent observingBz <0 relative to all β >0.5 and
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Vx ≥0 and Vx <0 samples. As expected, most sunward flows in the tail were associated
222
with a northward magnetic field component, but so were the majority of antisunward
223
flows. The majority of both sunward and antisunward flows had very low speeds, as is
224
demonstrated by the small mean velocities displayed in panels (e) and (f). Time series
225
of the velocity moments of such low speed flows typically fluctuate around zero, thus
226
containing both positive and negative values. Although the geomagnetic field generally
227
has a positive z component at the equatorial plane, north and south of this plane the sign
228
depends on the distance from Earth, such that close to Earth Bz < 0 and farther away
229
>0. Thus, there are large numbers of samples inside the geostationary orbit in panel (c)
230
of Fig. 2, originating from high magnetic latitudes. Instead of midnight, the majority of
231
the flows with a southward magnetic field component were observed in the premidnight
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region. Fast flows with Vx > 0 and Bz < 0 or Vx < 0 and Bz > 0 could be observed,
233
for instance, during passages of magnetic flux ropes or plasmoids. On closed field lines,
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antisunward flows also take place at the flanks of sunward fast flow channels.
235
Panels (e) and (f) of Fig. 2 show the mean speed (color) and flow direction (vectors)
236
for β > 0.5 and Vx ≥ 0 or Vx < 0. The lengths of the velocity vectors have been
237
normalized to unity, and the xy-component is displayed. For the Vx ≥0 flows, the mean
238
speed was largest inside the approximate nightside region −30 RE < x < −18 RE and
239
−6 RE < y <12 RE, and diminished rather sharply towards Earth and the dawn and dusk
240
sides. In this region the flows were mainly aligned with the x-axis, with a small positive
241
y-component, which strengthened towards Earth. Outside this region, the flows diverged
242
towards the dawn and dusk flanks. The convection circulated azimuthally around Earth,
243
and converged towards noon on the dayside. Outside the magnetopause there were some
244
flows with a sunward component diverging away from the subsolar point. These could
245
be reflected magnetosheath flows. For the Vx <0 flows, only the nightside plasma sheet
246
could be seen, as the dayside and flanks were dominated by magnetosheath flows. The
247
mean flow pattern resembles that of the sunward flows with negative y-components in the
248
postmidnight region and positive elsewhere.
249
Because of the large amount of data, it was not feasible to examine every orbit for
250
magnetopause crossings. As there is no other clean way to separate antisunward mag-
251
netosheath flows from antisunward plasma sheet flows based on moment data only, from
252
now on only samples with a sunward velocity component have been included.
253
3.2. Dawn-Dusk Symmetries and Asymmetries
The convection pattern in panel (e) of Fig. 2 shows some dawn-dusk asymmetries:
254
In GSM coordinates, the nightside region of higher mean flow speed was not located
255
symmetrically around the x-axis, but shifted to the premidnight side. However, the region
256
appears to have been fairly symmetrical with respect to the aberrated midnight axis.
257
Furthermore, the diamagnetic drift causes the positive ions to drift westward around
258
Earth, and this effect became stronger closer to Earth due to the magnetic field gradient.
259
Figure 3 displays the mean ion number density, temperature, magnetic field strength,
260
and plasma β. The scales are logarithmic. The ion number density distribution did not
261
present any clear dawn-dusk asymmetries, but in the near-Earth region the temperature
262
appeared to be higher on the duskside than on the dawnside. In the plasmasphere inside
263
the geosynchronous orbit and in the magnetosheath, the plasma was colder and denser
264
than in the plasma sheet.
265
The magnetic field strength, on the other hand, was clearly weaker in the premidnight
266
region tailward of aboutx≈ −20 RE than elsewhere. The magnetic field strength dawn-
267
dusk asymmetry also caused the mean β, which is the ration between ion thermal and
268
magnetic pressures, to be asymmetric with larger values in the premidnight region than
269
in the postmidnight region. To make sure that the effect was not artificial and caused by
270
orbital bias, panels (e) and (f) of Fig. 2 show β separately for the northern (Br <0) and
271
southern (Br > 0) hemispheres. As the effect is still present in both panels, it seems to
272
be real.
273
3.3. Effect of IMF Clock Angle
Panel (a) of Figure 4 displays Byduring IMFBy<0 conditions (clock angle|θ+ 90◦|<
274
45◦) with a background of IMFBz>0 (|θ|<45◦) conditions subtracted. Similarly, panels
275
(c) and (e) display By during IMF By > 0 (|θ−90◦| < 45◦) conditions, and Bz during
276
IMF Bz<0 (|θ|>135◦) conditions.
277
All three panels indicate that an ambient IMFByorBzcauses a rather uniform change
278
of a few nT in the same magnetic field component in the plasma sheet. However, during
279
southward IMF conditions, a channel of enhanced positive Bz was also created around
280
the aberrated midnight axis. In x-direction, the channel extended from x ≈ −30 RE
281
to approximately to the geostationary orbit. In y-direction, the width of the channel
282
was roughly 20 RE, and corresponded to the region where higher mean flow speeds were
283
observed in panel (e) of Fig. 2. The channel could have been caused by dipolarization and
284
magnetic flux pileup related to the sunward fast flows.
285
Panel (b) of Fig. 4 displaysV during IMFBy<0 conditions with a background of IMF
286
Bz >0 conditions subtracted. Similarly, panels (d) and (f) display V during IMF By >0
287
and IMF Bz <0 conditions. In general, the mean flow speed on the nightside was in all
288
cases higher than during northward IMF conditions, but highest during southward IMF
289
conditions. Compared to IMF Bz < 0 conditions, the nightside region of highest flow
290
speed was shifted towards dusk during IMFBy<0 conditions, and towards dawn during
291
IMF By >0 conditions.
292
3.4. Flow Speed
The color scales in Figure 5 display the percentage of time spent observing flows with
293
β > 0.5, Vx ≥ 0, and (a): 0 ≤ V < 100 km/s, (b): 100 km/s ≤ V < 200 km/s,
294
(c): 200 km/s ≤ V < 300 km/s, (d): 300 km/s ≤ V < 400 km/s, (e): 400 km/s ≤
295
V < 500 km/s, (f): 500 km/s ≤ V < 600 km/s, (g): 600 km/s ≤ V < 700 km/s, (h):
296
700 km/s ≤ V < 800 km/s, (i): 800 km/s ≤ V < 900 km/s, and (j): 900 km/s ≤
297
V < 1000 km/s relative to flows with β > 0.5, Vx ≥ 0, and 0 ≤ V < 1000 km/s. Note
298
that the scales vary between the panels. The vast majority of the flows in the plasma
299
sheet had speeds <100 km/s. Only around the aberrated midnight axis, in the region
300
−6 RE < y < 12 RE and −30 RE < x < −18 RE, about 50% of the flows had higher
301
speeds. With increasing flow speed, the flows became more concentrated around midnight
302
and farther downtail. The duration of each speed bin relative to all β >0.5, Vx≥0, and
303
0≤V < 1000 km/s observations are also shown in panel (a) of Figure 6. The centers of
304
the bins have been used as the x-axis, and the y-axis scale is logarithmic. 95% of the time
305
the flows had speeds <100 km/s.
306
The vectors in Fig. 5 show the mean flow direction for each speed bin. The slow speed flows were mainly azimuthal with respect to Earth, but with increasing speed the flow direction turned sunward. This is illustrated more quantitatively in panel (b) of Fig. 6, which shows an mean of the angle α of all flow events in each 100 km/s speed bin. α for one flow event was defined as
cos(α) = Vxy·Bxy
VxyBxy . (3)
As the angles would otherwise be α and 180◦ −α for the oppositely oriented magnetic
307
field lines of the southern and northern hemispheres for the same velocity vector, all field
308
lines of the southern hemisphere (Br > 0) were turned anti-parallel: Bxy → −Bxy. The
309
lengths of the error bars correspond to 20 × the standard deviation of the mean. The
310
very small values indicate that the means are significant.
311
Panel (c) of Fig. 6 displays the mean solar wind electric field| −Vsw×IMF|of all flow
312
events in each speed bin. The electric field was clearly weakest for the slow speed (<100
313
around 2 mV/m. Panel (d) of Fig. 6 shows the mean of the absolute value of the IMF clock
315
angle (|θ|) of all flow events in each speed bin. Again, the V <100 km/s bin was clearly
316
different from the others, with |θ| <90◦. For the other bins, |θ|>90◦, and increased for
317
higher speeds.
318
3.5. Convection Electric Field
Figure 7 shows the meanE=−V×Bmagnitude (color) and direction (vectors) for the
319
β >0.5 and Vx ≥ 0 samples. The lengths of the vectors have been normalized to unity,
320
and the xy-component is displayed. As the sunward flows on the nightside tended to occur
321
around the aberrated midnight axis, also the relatively pure y-directed field was restricted
322
to that region. Towards dusk and dawn, the field direction turned radially away from and
323
towards Earth, respectively, although the effect was more strong on the duskside. Near
324
the outer reaches of the magnetosphere, the field became normal to the magnetopause.
325
Mapped to the ionospheric Hall currents, which can be observed by ground-based mag-
326
netometers, the azimuthal flow in the dusk and dawn flanks would correspond to the
327
eastward and westward electrojets, respectively. The Harang discontinuity would be ex-
328
pected to correspond to the region where the sunward flow of the midnight region turned
329
azimuthal, or electric field direction turned from y to radial. In this region, the mean flow
330
speed was also observed to brake down significantly.
331
4. Discussion and Conclusions
In this study, magnetospheric ion and magnetic field data obtained by Cluster 1 and 3
332
between 2001 and 2007, by Geotail between 1995 and 2006, and by THEMIS 1–5 between
333
2007 and 2009 have been used to construct statistical maps of the plasma sheet convection.
334
Radial distances from Earth up to approximately 30 RE were covered. The condition ion
335
β > 0.5 was used to find the plasma sheet regime. However, on the dayside and near
336
the flanks of the magnetosphere, this condition also included magnetosheath and solar
337
wind flow samples. As we did not want to restrict our study only to the nightside plasma
338
sheet, and checking every orbit for magnetopause crossings was not feasible because of
339
the large amount of data, we concentrated mainly on the flows with a sunward velocity
340
component, which were the dominant population in the plasma sheet. As the produced
341
convection maps are statistical, they do not represent the actual convection pattern at
342
any given instant.
343
On the nightside, the mean configuration was observed to comprise mainly sunward
344
convection around midnight that diverged towards the dawn and dusk flanks. The con-
345
vection circulated azimuthally around Earth, and converged towards noon on the dayside.
346
The mean speed was largest inside a roughly 20 RE wide channel around the aberrated
347
midnight axis, and diminished rather sharply towards Earth and the dawns and dusk
348
sides. This is consistent with the results of Baumjohann et al.[1990], according to whom
349
the largest occurrence rates of high-speed flows are found near the midnight meridian. Al-
350
though flows with speeds as high as 900–1000 km/s could still be observed atx≈ −10 RE,
351
the occurrence frequency of high-speed flows started to decrease noticeably earthward of
352
about x ≈ −20 RE. This is in agreement with the observations of Baumjohann et al.
353
[1990] and Shiokawa et al. [1997] between−19 RE< x <−9 RE.
354
The ion number density distribution did not present any obvious dawn-dusk asym-
355
metries, and the temperature asymmetries were restricted near Earth (r < 10 RE), in
356
agreement with Wang et al. [2006]. The magnetic field strength, on the other hand, was
357
noticeably weaker in the premidnight region than in the postmidnight region. This caused
358
the mean ion β also to be asymmetric, with larger values in the premidnight region than
359
in the postmidnight region.
360
Ambient IMFByand Bz were observed to penetrate the plasma sheet, causing a rather
361
uniform change of a few nT in the same magnetic field component. Moreover, during
362
southward IMF conditions, a channel of enhanced positiveBz was created in the nightside
363
around the aberrated midnight axis. In y-direction, the width of the channel corresponded
364
to the region where fast flows were most frequently observed, but in x-direction it extended
365
closer to Earth, approximately to the geostationary orbit. We suggest that the channel
366
was caused by dipolarization and magnetic flux pileup related to fast flows. Consistent
367
with the results of Zhu [1993] and Wang et al. [2006], flow speeds on the nightside were
368
observed to be higher during southward IMF conditions than during northward IMF
369
conditions. We also found that compared to IMFBz<0 conditions, the nightside region
370
of highest flow speed was shifted towards dusk during IMFBy <0 conditions, and towards
371
dawn during IMF By >0 conditions.
372
During 95% of all β >0.5 and Vx ≥0 observation time, plasma sheet flows had speeds
373
<100 km/s. Only in the region −30 RE < x < −18 RE and −6 RE < y < 12 RE
374
about 50% of the flows had higher speeds. With increasing flow speed, the flows became
375
more and more concentrated around midnight and farther downtail. The slow speed
376
flows were mainly azimuthal with respect to Earth, but with increasing speed, the flow
377
direction turned increasingly sunward. This is consistent with the results ofBaumjohann
378
et al. [1990], who found that the occurrence of high-speed (V > 400 km/s) flows peaked
379
strongly in the sunward direction.
380
During times when slow flows (<100 km/s) were observed in the plasma sheet, the
381
solar wind electric field was on average weaker and IMF more northward than during
382
times when faster flows (>100 km/s) were observed. For the faster flows, no correlation is
383
found between the observed flow speeds and the mean solar wind electric field magnitude.
384
However, there is a clear correlation between the IMF clock angle and flow speed, with
385
increasing speed when IMF turns southward. According to our knowledge, this has not
386
been reported earlier.
387
Acknowledgments. We acknowledge the principal investigators E. Lucek (Clus-
388
ter/FGM), I. Dandouras (Cluster/CIS), T. Nagai (Geotail/MGF), and Y. Saito (Geo-
389
tail/LEP). We acknowledge NASA contract NAS5-02099 and V. Angelopoulos for use of
390
data from the THEMIS Mission. Specifically: C. W. Carlson and J. P. McFadden for
391
use of ESA data and K. H. Glassmeier, U. Auster and W. Baumjohann for the use of
392
FGM data provided under the lead of the Technical University of Braunschweig and with
393
financial support through the German Ministry for Economy and Technology and the
394
German Center for Aviation and Space (DLR) under contract 50 OC 0302. Cluster data
395
were acquired through Cluster Active Archive, and Geotail (Editor-A) and THEMIS data
396
through CDAWeb. We acknowledge NASA/GSFC’s Space Physics Data Facility’s OM-
397
NIWeb service, and OMNI data. This study was supported by the Norwegian Research
398
Council, through the Norwegian Cluster project 197639/V30.
399
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−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E]
yGSM [RE] Duration [days]
(a)
0 1 2 3 4 5 6 7 8 9 10
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E]
yGSM [RE] Duration [days]
(b)
0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE]
yGSM [RE] Duration [days]
(c)
0 0.5 1 1.5 2 2.5 3
Figure 1. Observation times of β > 0.5 for (a): Cluster 1 and 3 from 2001 to 2007, (b):
Geotail from 1995 to 2006, and (c): THEMIS 1–5 from September 2007 to the end of 2009, presented as a function of GSM x and y. The gray circle represents the geostationary orbit at the 6.6 REradial distance, and the gray curve the magnetopause according toShue et al. [1997], withPdyn = 1 nPa and IMFBz= 0. Both the magnetopause and the solid grid have been rotated 4.8◦ clockwise to take into account the aberration due to Earth’s orbital motion. The thick gray line shows the aberrated noon-midnight axis.
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E] yGSM [RE]
V
GSM,xy = 500 km/s
Duration [days]
(a)
0 1 2 3 4 5 6 7 8 9 10
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E]
yGSM [RE] Duration [%]
(b)
0 10 20 30 40 50 60 70 80 90 100
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE]
yGSM [RE] Duration [%]
(c)
0 5 10 15 20 25 30 35 40 45 50
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE]
yGSM [RE] Duration [%]
(d)
0 5 10 15 20 25 30 35 40 45 50
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE] yGSM [RE]
V
GSM,xy/V = 1
V [km/s]
(e)
0 10 20 30 40 50 60 70 80 90 100
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE] yGSM [RE]
V
GSM,xy/V = 1
V [km/s]
(f)
0 10 20 30 40 50 60 70 80 90 100
Figure 2. (a): Time spent observingβ >0.5 (color). The vectors display the xy-component of the mean velocity. (b): Percentage of time spent observingVx≥0 relative to allβ >0.5 samples.
(c): Percentage of time spent observing Bz <0 relative to all β >0.5 and Vx ≥0 samples. (d):
Percentage of time spent observingBz<0 relative to allβ >0.5 andVx<0 samples. (e): Mean speed (color) and flow direction (vectors) for β > 0.5 and Vx ≥ 0 samples. The lengths of the velocity vectors have been normalized to unity, and the xy-component is displayed. (f ): Mean speed (color) and flow direction (vectors) for β >0.5 and Vx <0 samples.
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE] yGSM [RE]
10x N [cm−3]
(a)
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [RE] yGSM [RE]
10x
T [keV]
(b)
−1
−0.8
−0.6
−0.4
−0.2 0 0.2 0.4 0.6 0.8 1
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E] yGSM [RE]
10x
B [nT]
(c)
−2
−1.5
−1
−0.5 0 0.5 1 1.5 2
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E] yGSM [RE]
10x
β
(d)
−1
−0.5 0 0.5 1 1.5 2 2.5 3
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E] yGSM [RE]
10x
β
(e)
−1
−0.5 0 0.5 1 1.5 2 2.5 3
−30 −20 −10 0 10 20 30
−30
−20
−10 0 10 20 30
xGSM [R E] yGSM [RE]
10x
β
(f)
−1
−0.5 0 0.5 1 1.5 2 2.5 3
Figure 3. (a): Mean ion density. (b): Mean ion temperature. (c): Mean magnetic field
strength. (d): Mean plasma β. (e): Mean β in the northern hemisphere (Br <0)(f ): Mean β in the southern hemisphere (Br >0). Only data with Vx ≥0 are included. The color scales are logarithmic.
