Propagation properties of foreshock cavitons: Cluster observations
Wang Mengmeng, Yao Shutao, 史 全岐, zhang hui, Tian Anmin, Degeling Alexander, Zhang Shuai, Guo Ruilong, Sun Weijie, Liu Ji, Bai Shichen, Shen
Xiaochen, Zhu Xiaoqiong, Fu Suiyan and Pu Zuyin
Citation: SCIENCE CHINA Technological Sciences ; doi: 10.1007/s11431-018-9450-3
View online: http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
Published by the Science China Press
Articles you may be interested in
Statistical research on the motion properties of the magnetotail current sheet: Cluster observations
SCIENCE CHINA Technological Sciences 53, 1732 (2010);
Propagation of interplanetary shock excited ultra low frequency (ULF) waves in magnetosphere-ionosphere-atmosphere —Multi-spacecraft
“Cluster” and ground-based magnetometer observations
SCIENCE CHINA Technological Sciences 53, 2528 (2010);
Statistical survey on the magnetic field in magnetotail current sheets: Cluster observations
Chinese Science Bulletin 55, 2542 (2010);
Low-frequency fluctuations in the magnetosheath: Double Star TC-1 and Cluster observations
Science in China Series E-Technological Sciences 51, 1626 (2008);
Structures of magnetic null points in reconnection diffusion region: Cluster observations
Chinese Science Bulletin 53, 1880 (2008);
Fo
ed
SCIENCE CHINA Technological Sciences
rR
pt
Propagation properties of foreshock cavitons: Cluster
observations
Journal: Science China Technological Sciences
Manuscript ID SCTS-2018-0487.R3
ev
Manuscript Type: Original Article
iew
Ac
ce
Date Submitted by the
23-Nov-2018
Author:
ly
On
Complete List of Authors: Wang, Mengmeng; Shandong University; Chinese Academy of Sciences,
National Space Science Center
Yao, Shutao; Shandong University at Weihai
史, 全岐; Shandong University, School of Space Science and Physics
zhang, hui; Geophysical Institute, University of Alaska Fairbanks
Tian, Anmin; School of Space Science and Physics, Shandong University
at Weihai
Degeling, Alexander
Zhang, Shuai; Shandong University at Weihai
Guo, Ruilong; Chinese Academy of Sciences, Institute of Geology and
Geophysics
Sun, Weijie; University of Michigan, Department of Climate and Space
Sciences and Engineering
Liu, Ji; Chinese Academy of Sciences
Bai, Shichen; Shandong University at Weihai
Shen, Xiaochen
Zhu, Xiaoqiong
Fu, Suiyan; Peking University, School of Earth and Space Science
Pu, Zuyin; Peking University, School of Earth and Space Science
foreshock transient phenomena, cavitons, nonlinear evolution of ULF
Keywords: waves, propagation and evolution properties of structures, multipoint
spacecraft methods
Speciality: Space Sciences
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
ed
Fo
iew
Ac
ce
ev
rR
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
pt
Page 1 of 41
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
Propagation properties of foreshock cavitons: Cluster
2
observations
3
WANG MengMeng1,2, YAO ShuTao1, SHI QuanQi1*, ZHANG Hui3, TIAN AnMin1,
4
DEGELING Alexander William1, ZHANG Shuai1, GUO RuiLong4, SUN WeiJie5,
5
LIU Ji2, BAI ShiChen1, SHEN XiaoChen1, ZHU XiaoQiong1, FU SuiYan6, PU
6
ZuYin6
7
1School
8
2National
9
3Geophysical
10
11
12
4Institute
5Department
Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China
Institute, University of Alaska Fairbanks, Fairbanks, Alaska, 99775, USA
of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China
of Space Physics and Applied Technology, Peking University, Beijing, 100871, China
*Corresponding author (email: sqq@sdu.edu.cn)
Abstract
rR
14
of Space Science and Physics, Shandong University, Weihai, 264209, China
of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, 48113, USA
6Institute
13
pt
ed
1
Fo
15
Foreshock cavitons are transient phenomena observed in the terrestrial foreshock region.
16
They are characterized by a simultaneous depression of magnetic field magnitude and plasma
17
density, which are bounded with enhancements of these two parameters and surrounded by
18
ultra low frequency (ULF) waves. Previous studies focused on the interplanetary magnetic
19
field (IMF) conditions, solar wind (SW) conditions, and the growth of the foreshock waves
20
related to the generation of foreshock cavitons. Previously, a multipoint spacecraft analysis
21
method using Cluster data was applied to analyze only two foreshock cavitons, and this
22
method did not consider uncertainties. In this study, multipoint spacecraft analysis methods,
23
including the timing method, the Minimum Directional Difference (MDD) method, and the
24
Spatiotemporal Difference (STD) method are applied to determine the velocity in both
25
spacecraft and solar wind frames. The propagation properties show good agreement with
26
previous results from simulations and observations that most cavitons move sunward in the
27
solar wind frame, with the velocities larger than the Alfvén speed. The propagation properties
28
of foreshock cavitons support the formation mechanism of cavitons in previous simulations,
29
which suggested that cavitons are formed due to the nonlinear evolution of compressive ULF
30
waves. We find that there is clear decreasing trend between the size of cavitons and their
31
velocity in the solar wind frame. In addition, the timing method considering errors has been
32
applied to study the evolution properties by comparing the velocities with errors of the
33
leading and trailing edges, and we identify three stable cavitons and one contracting caviton,
34
which has not been studied before. Most cavitons should remain stable when they travel
35
toward the Earth’s bow shock. The relationship between the size of foreshock cavitons and
36
their distance from the bow shock is also discussed.
iew
Ac
ce
ev
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 2 of 41
Page 3 of 41
37
Key words foreshock transient phenomena, cavitons, nonlinear evolution of ULF waves,
38
propagation and evolution properties of structures, multipoint spacecraft methods
39
1 Introduction
40
When the supermagnetosonic magnetized solar wind encounters the Earth’s magnetosphere,
41
the bow shock forms. The nature of the bow shock depends on the angle  Bn between the
42
interplanetary magnetic field (IMF) and the shock normal [1]. The shock is either
43
quasi-parallel
44
upstream of the quasi-parallel shock and the “shock foot” of the quasi-perpendicular shock [2]
45
[3] [4], is populated with particles backstreaming from the bow shock, ULF waves [5][6]
46
[7][8], hot flow anomalies (HFAs) [9], spontaneous hot flow anomalies (SHFAs) [10] [11],
47
and foreshock cavities [12] [13]. These transients can modify the solar wind before they
48
encounter the bow shock.
pt
ed
( Bn  45 ) or quasi-perpendicular ( Bn  45 ) . The foreshock, located
Fo
49
Global hybrid simulations performed by Omidi [14] and Blanco-Cano et al. [15] [16]
50
suggested that a new category of transient structure called foreshock caviton exist in the
51
foreshock region. Foreshock cavitons are transient phenomena as common as HFAs and
52
SHFAs in the foreshock region, which saturate at a width of several RE , with a depressed core
53
plasma density and magnetic field strength bounded by a rim of enhanced plasma density and
iew
Ac
ce
ev
rR
54
magnetic field strength [14] [15] [16]. Cavitons are not associated with IMF discontinuities,
55
and there is no plasma heating or flow deflection inside the structures, which is in contrast to
56
HFAs. Omidi et al. [14] referred to cavitons as ‘foreshock cavities’ in their simulation of
57
formation of foreshock cavitons. However, foreshock cavitons are always embedded in a sea
58
of ULF waves, which is in contrast to other isolated cavities with no ULF waves nearby.
59
Diffuse ions are found inside and outside foreshock cavitons, while diffuse ions are only
60
found inside foreshock cavities. Schwartz et al. [13] suggested foreshock cavities are formed
61
by thermal expansion because of the magnetic field in cavities connected to the bow shock,
62
which contrasts with notion that the wave interactions generate foreshock cavitons. Hence,
63
Blanco-Cano et al. [15] [16] used the term, foreshock cavitons, to describe these new
64
structures.
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
65
The interaction of ULF waves in the foreshock contributes to the formation of foreshock
66
cavitons. Under the condition of radial IMF, the foreshock region is permeated by parallel
67
propagating sinusoidal fluctuations with right- or left-hand circular polarization, and fast,
68
linearly polarized, oblique (FLO) waves. The nonlinear evolution of these two types of
69
ultra-low frequency (ULF) waves generates foreshock cavitons [14] [15][16]. Global hybrid
70
simulations performed by Blanco-Cano et al. [16] showed that foreshock cavitons could exist
71
under a wide range of IMF [17] [18] orientations depending on the Mach number. They found
72
that major features of foreshock cavitons do not vary with the IMF orientation. Statistical
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
73
studies of foreshock cavitons [20] [21] have shown that foreshock cavitons are observed for a
74
wide range of IMF orientation and SW conditions. The time duration of cavitons is 65s and
75
the size is 4.6 RE on average. Inside cavitons, the variations of plasma density and magnetic
76
field magnitude are highly correlated.
The foreshock-bow shock system is a significant region for the solar wind-magnetosphere
78
coupling process. There are a plethora of multi-scale plasma physics processes and
79
phenomena in foreshock, making it an important and excellent laboratory to study plasma
80
physics. The generation and evolution of foreshock cavitons are an intrinsic process of the
81
foreshock-bow shock system and play a considerable role in reformation of the system.
82
Hybrid simulations suggest that the interaction between foreshock cavitons and the bow
83
shock generate another transient phenomenon, namely, SHFAs [10][11]. Several cavitons
84
even generate complicated and large structures if they arrive at the bow shock at the same
85
time. They play an important role in the deformation of the bow shock and can lead to ripples
86
on the surface of bow shock. Cavitons may lead to disturbances in the magnetosheath and
87
surface waves on the magnetopause [10] [11] [22] [23] [24]. Considering the magnetospheric
88
response [25], foreshock cavitons are no less important than foreshock transients such as
89
HFAs with large dynamic pressure pulses [26] [27]. Given that cavitons exhibit similar
90
sudden dynamic pressure decreases, cavitons may generate ULF waves in the magnetosphere
91
[28] [29] [30] [31] [32] and drive magnetospheric vortices [33]. Foreshock cavitons may
92
evolve into SHFAs, which can make the plasma more inhomogeneous and contribute to the
93
formation of magnetosheath jets [34] and magnetosheath filamentary structures (MFS) [35].
94
Successive expansion and contraction of the magnetosphere caused by SHFAs are significant,
95
which may excite ULF waves in the inner magnetosphere [36] [37] [38] [39] [40] [41].
pt
ed
77
iew
Ac
ce
ev
rR
Fo
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
96
As foreshock cavitons form, they are convected by the solar wind towards the bow shock.
97
Blanco-Cano et al. [16] found that cavitons propagate sunward in the solar wind frame, as
98
weakly compressive waves. In their simulations, the velocity of the example caviton in the
99
solar wind frame is 98 km/s, which equals 1.9 VA [16]. Kajdič et al. [19] analyzed two
100
foreshock cavitons observed by the multi-spacecraft Cluster mission. The two cavitons
101
propagate sunward in the solar wind frame at a speed of 188 km/s and 120 km/s. However,
102
only the timing method without calculating errors has been applied to calculate the velocities
103
of these two cavitons [19]. Although theories and simulations provide the formation
104
conditions and the evolution of foreshock cavitons, no observations of the evolution of
105
foreshock cavitons have been reported.
106
In this paper, we perform a study of the propagation properties of a series of foreshock
107
cavitons using several multipoint spacecraft analysis methods, including the timing method
108
[42], the Minimum Directional Derivative (MDD) method [43] and the Spatiotemporal
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 4 of 41
Page 5 of 41
109
Difference (STD) method [44]. Four cavitons with both velocities of leading edge and trailing
110
edge considering errors are classified into three stable structures and one contracting structure.
111
We also examine the possible relationship between the size of foreshock cavitons and the
112
distance from cavitons to the bow shock.
113
2 Data and Methods
114
2.1 Data and Event Selection
Cluster mission consists of four identical spacecraft (C1, C2, C3, C4). We obtain the
116
magnetic field data with 0.2s resolution from the Fluxgate Magnetometer (FGM) [45] [46]
117
[47] onboard all four spacecraft, and we obtain the ion data with 4s resolution from the Hot
118
Ion Analyzer (HIA) of the Cluster Ion Spectrometer (CIS) [48] on C1. We obtain the solar
119
wind and IMF data with 1-min resolution from the OMNI database, which indicate
120
parameters near the nose of the Earth’s bow shock.
pt
ed
115
Fo
121
All foreshock caviton events analyzed here are taken from [20], which presented 92
122
foreshock cavitons selected using C1 data from 2001 to 2006. Firstly, foreshock cavitons
123
observed by all four Cluster spacecraft are selected. Then, we select the cavitons with clear
124
leading and trailing boundaries and with the similar profiles observed by four spacecraft.
125
Following these criteria, twelve foreshock cavitons are selected and their propagation
126
properties are investigated. Further criteria, including the shape parameters of the tetrahedral
127
spacecraft configuration can improve the precision of the timing analysis, MDD analysis, and
128
STD analysis.
129
2.2 Timing method
iew
Ac
ce
ev
rR
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
The timing method has been widely applied to determine the velocity and normal direction
131
of shocks, magnetic holes, magnetic peaks, and HFAs [42] [49] [50] [51] [52] [53]. To
132
calculate the velocities and normal of the boundaries of foreshock cavitons, we apply a
133
similar method by analyzing magnetic field data detected by four Cluster spacecraft [54] [55].
134
By solving the following equation,
ly
On
130
135
r ur r
U (t i  t j )  (ri  rj )gn ,
136
the unit normal direction n and velocity magnitude U of the foreshock caviton leading
137
and trailing boundaries are obtained. Here, t  ti  t j is the time lag between two spacecraft
138
observing the same boundary, and r ij  r i  r j is their corresponding difference in position
139
vectors. As Cluster mission consists of four spacecraft, three differences in position vectors,
140
r r r
r12 , r13 , r14 and three time lags,
t12  t1  t2 , t13  t1  t3 , t  t1  t4 are determined.
141
Furthermore, we estimate the uncertainty of velocity magnitude and normal direction
142
according to [54]. An empirical relative error of time lag is  t  0.1t . the relative
143
uncertainty of the distance between satellites is 0.01, the time lag uncertainty contributes
(1)
r
r
r
r
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
144
more to the error of results and is considered dominant. A pair of satellites can give an
145
interval [t   t , t   t ] . The interval is divided into 11 equidistant points. In total 113
146
calculations of velocity and normal are given due to three time intervals determined by four
147
satellites. The mean velocity and normal are given and the standard deviations estimate the
148
uncertainty.
2.3
The MDD method
150
The Minimum Directional Derivative (MDD) method is a dimensionality determination
151
technique with the help of multipoint measurements described by Shi et al. [43]. The
152
eigenvalues and eigenvectors of
153
principal directions of the structure (where T denotes the transposition). Three directions
154
corresponding to the maximum, intermediate and minimum variations of magnetic field are
155
determined straightforwardly by the MDD method, which can help us investigate the time
156
variation of a structure’s characteristic direction. It is proved that the MDD method is feasible
157
for the determination of the normal direction of 1-D structures including magnetic holes [50]
158
[51] [56], and magnetic peaks [52].
pt
ed
149
ur
ur
L  ( B)( B)T indicate the dimensionality and the
159
2.4
160
The Spatiotemporal Difference (STD) method [44] can be applied to calculate the velocity
161
of quasi-stationary structures in any dimensionality using multipoint magnetic field
162
measurements. Further, we can resolve time-variations of the velocity from the STD results.
163
By estimating the time variation of the magnetic field and the magnetic gradient tensor  B ,
164
the velocity of the structure in the spacecraft frame, V str , is obtained from the equation of
166
ur
ur
ly
On
165
iew
Ac
ce
ev
The STD method
rR
Fo
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 6 of 41
ur
ur
 B ur
 V str g B  0 .
t
3 Propagation and evolution properties of foreshock cavitons
167
3.1
168
3.1.1
169
Timing method is applied to calculate the velocity of foreshock cavitons in the spacecraft
170
and the solar wind frames. Here, the GSE coordinate system is used. We obtain the velocity
171
of foreshock cavitons in the solar wind frame from
172
Propagation properties
Timing analysis
r r
V  U  v sw gn .
(2)
173
Here U is the velocity of caviton in the spacecraft frame obtained from the timing analysis,
174
as before. U is along the normal direction, n . The average value of the solar wind velocity
175
measured by CIS-HIA over a 10 minute interval including the cavitons is used to eliminate
176
fluctuations. In accordance with [48], an uncertainty in the solar wind velocity v sw of 10%
177
in magnitude and +/-5° in direction are considered. We carried out four timing calculations
r
r
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 7 of 41
178
and considered all four calculations to generate our results, including velocities, normal
179
directions and uncertainty estimates, represented as error bars in Figure 4. If the error bar
180
crosses zero, the caviton is probably stationary with respect to the solar wind. Examples of
181
timing analysis are shown in Figure 1. Figure 1(a-d) show the results for the leading boundary,
182
and figure 1(e-h) show the results for the trailing boundary. The mean speed of the leading
183
boundary in the spacecraft frame is 98.6 km/s and the uncertainty is 4.1 km/s as shown in
184
Figure 1b. The average velocity of leading boundary in the solar wind frame is
r
219.2  32.9km / s along n L  (0.97,0.14,0.17) with uncertainty of 1.8 . Figures
186
1e-1h show the detailed velocity of the trailing boundary with VT  212.7  33.7 km / s
187
and nT  ( 0.93,0.18,0.33) . Magnetic field data with different resolutions were employed
188
to check the reliability of the results. The results agree with those using data with 0.2 s
189
cadence. The velocity with error not including zero shows that the caviton is moving in the
190
solar wind plasma.
r
pt
ed
185
rR
Fo
191
3.1.2
MDD and STD analysis
192
Here, we apply the MDD and STD methods to calculate the dimensionality and velocity
193
vector and compare the results with those from the timing method. The analysis results of the
194
same case shown in Figure 1 are shown in Figure 2. As the MDD method suggested, the
iew
Ac
ce
ev
195
relative size of the three eigenvalues indicate the dimensionality information of the structure.
196
If 1 ? 2 , 3 , we can regard the structures as quasi-1D, and 1 is the eigenvalue of the
197
maximum variant direction of the magnetic field. The maximum variant direction n1
198
represents the normal of the boundary of foreshock caviton. The ratio of the average
199
and 2 in the limited period indicated by orange shadow is 8.7 for the leading boundary. For
200
the trailing boundary, the ratio in the limited period indicated by the blue shadow is 19.6.
201
Therefore, we regard this caviton as quasi-1D structure.
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
r
1
202
The propagation velocity of the leading boundary in the solar wind frame is -219.3 km/s
203
along n L  (0.88, 0.29,0.37) and for trailing boundary, the velocity is -222.0 km/s
204
along nT  (0.96, 0.27,0.02) . Here, L denotes the leading boundary and T denotes the
205
trailing boundary. These results fall within the velocity error from timing method as shown in
206
Figure 4(a).
r
r
207
3.1.3
Statistical results
208
The propagation velocity along the normal of the foreshock cavitons are given by equation
209
(2). The velocity vector of the cavitons in the spacecraft frame is equal to U multiplied by n ,
210
while the velocity vector of the cavitons in the solar wind frame is equal to V multiplied by
r
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
r
n . Velocity magnitudes and directions of the twelve foreshock cavitons calculated by timing,
212
MDD and STD methods are plotted in GSE-XY and GSE-XZ planes. Velocity vectors in both
213
the spacecraft frame and the solar wind frame are plotted in Figure 3. In the spacecraft frame,
214
foreshock cavitons are moving towards the Earth. Eleven cavitons are propagating sunwards
215
in the solar wind frame, which is consistent with previous observations [19] and the
216
predictions of simulations [16]. Another caviton observed on Mar 26, 2005 has a velocity in
217
the solar wind frame that is close to zero, for which the error bar crosses zero.
pt
ed
211
218
Sizes of foreshock cavitons are calculated using both the timing velocities and STD
219
velocities in the spacecraft frame. As foreshock cavitons propagate in the solar wind frame,
220
we estimate the spatial extents of the cavitons by multiplying their speed in the spacecraft
221
frame by their durations, rather than multiplying their durations by the solar wind velocity
222
[20]. Since foreshock cavitons remain stable when they travel towards the bow shock, the
223
velocities of one boundary are used to calculate the extents of cavitons.
Fo
224
Figure 4 (a) shows a plot of the estimated size in RE of foreshock cavitons against their
225
propagation velocity in the solar wind frame. This figure shows the trend that smaller
226
foreshock cavitons have significantly higher velocity than larger ones in the solar wind frame.
227
Since the normal of one edge of foreshock cavitons is obtained from the timing method and
228
MDD & STD method, we calculate the angle between the normal direction and the ambient
229
magnetic field vector. This indicates the direction of propagation for a 1-D structure [43] [44].
230
The results are shown in Figure 4 (b). The average magnetic field value over a 10 minute
231
interval excluding the cavitons is used. We can see that the foreshock cavitons are
232
propagating along the parallel or anti-parallel direction. These results are obtained using two
233
independent techniques (timing and MDD and STD analysis as described above), with both
234
techniques revealing the same trend.
iew
Ac
ce
ev
rR
Evolution of foreshock cavitons
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
235
3.2
236
Here we show a stable caviton structure observed on 16 February 2002 by comparing the
237
velocities with errors of the leading edge and the trailing edge. The detailed process is as
238
follows. The timing analysis shows that the leading edge travels at a speed of about
239
r
219.2  32.9km / s along the direction n L  (0.93,0.14,0.17) in the solar wind, while
240
the trailing edge moves at a speed of about 212.7  33.7 km/ s along the direction
241
r
n T  (0.93,0.18,0.33) in the solar wind frame. Here, L denotes the leading boundary
242
and T denotes the trailing boundary as before. We calculate the difference of velocities
243
between the leading boundary and trailing boundary by projecting the trailing boundary
244
velocity to the normal of the leading boundary and subtracting the leading boundary velocity
245
magnitude:
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 8 of 41
Page 9 of 41
246
 V | VT cos nr L , nr T  VL |
247
where  nr L , nr L
248
V  9.3km / s   L   T  32.9  33.7  66.6km / s , we conclude that the leading edge
249
and the trailing edge of the caviton move at velocities that are indistinguishable given the
250
error estimates of the measurements. Consequently, the caviton can be regarded as a stable
251
structure as suggested in Xiao et al [53].
(3)
the angle between the normal of the leading edge and trailing edge. As
Only four out of twelve cavitons have usable timing velocities considering errors of both
253
the leading boundary and trailing boundary, and we investigate the evolution properties of
254
these four cavitons. Three cavitons are stable, and only one shows property of contraction.
255
Our results indicate that cavitons remain stable when they are convected toward the bow
256
shock.
pt
ed
252
Fo
257
4 Summary and Discussions
258
By using the timing method, MDD and STD method, we analyze the propagation and
259
evolution properties of twelve foreshock cavitons. We find that all cavitons move earthward
260
in the spacecraft frame and the normal of the edge of cavitons are nearly parallel or
261
anti-parallel to the ambient magnetic field. The velocities of cavitons in the solar wind frame
262
are also calculated. Eleven cavitons of all cavitons move sunward in the solar wind frame.
263
These results are consistent with previous ones from simulations and observations. We also
264
find that the caviton observed on March 26, 2005 has features consistent with those of a
265
mature caviton structure.
266
and their propagation velocity in the solar wind frame. As for the evolution properties, the
267
results suggest that most foreshock cavitons remain stable when they propagate towards the
268
bow shock. We find that there is no clear correlation between the size of foreshock cavitons
269
and their distance from the bow shock.
iew
Ac
ce
ev
rR
We find a clear decreasing trend between foreshock caviton size
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
270
In the simulation of [16], one caviton moves upstream in the solar wind frame at a speed
271
of 1.9 times of the Alfven speed. By Cluster observations, Kajdič et al. [19] found that two
272
cavitons move at 188 km/s and 120 km/s towards the sun in the solar wind frame. We have
273
also found that foreshock cavitons have a variety of propagation velocities, which is
274
consistent with simulation [16]. The nature of ULF waves and the nonlinear evolution of the
275
waves contribute to the propagation properties of cavitons. Weakly compressive waves
276
propagate upstream in the reference frame of background plasma, which is similar to the
277
propagation direction of cavitons. The normal of the edge of cavitons are nearly parallel or
278
anti-parallel to the ambient magnetic field, which suggests that parallel propagating weakly
279
compressive waves are necessary for the generation of foreshock cavitons. Consequently, the
280
propagation properties imply that foreshock cavitons form due to the nonlinear evolution of
281
circularly polarized, parallel propagating ULF waves and compressive, linearly polarized,
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
282
oblique ULF waves. We find that in all but one case, foreshock cavitons propagate sunward,
283
and their speed can be shown to be larger than the Alfvén speed. Previous results from
284
simulations and observations have found sunward propagating foreshock cavitons with speeds
285
greater than the Alfvén speed. We appear to have found one counter-example.
For the caviton observed on Mar 26, 2005, the uncertainty in its velocity in the solar wind
287
frame is greater than its magnitude – in other words it has an error bar across zero. In this case
288
we consider that it is likely that the caviton is stationary with respect to the solar wind,
289
however the size of the uncertainty in velocity for this event is significant; on the order of the
290
Alfven speed. Compared to other cavitons in our study, this event is observed within a higher
291
speed solar wind (larger than 600 km/s) and lower plasma density (less than 3 cm-3)
292
environment. This caviton does not show a double peak internal structure [19]. There are few
293
small fluctuations or high-frequency waves in the interior, and the profile of magnetic field
294
magnitude is similar to that of plasma density. Blanco-Cano et al. finds that the width of
295
cavitons should increase slightly during their evolution [16], and that towards the end of their
296
evolution, the profiles of magnetic field magnitude and density should become similar.
297
Therefore, this caviton appears to be a mature structure with fewer wave features compared to
298
the newly generated cavitons, possibly because these fluctuations have dissipated over time in
299
this case.
pt
ed
286
iew
Ac
ce
ev
rR
Fo
300
The correlation between the size of foreshock cavitons and their velocity in the solar wind
301
frame shows that the bigger scale the foreshock caviton has, the slower it moves in the solar
302
wind flow. There is clear decreasing trend between the size of foreshock cavitons and their
303
velocity in the solar wind frame. It is reasonable to expect that, although the structures were
304
found to be 1-D based on the scale-size of the Cluster satellite configuration, they may be at
305
least 2-D on a larger scale. If we assume that they have roughly the same shape, then size
306
measurements we have obtained are a proxy for their scale size. A structure of a given size
307
propagating with respect to the solar wind will be subject to an effective drag force that
308
increases with the structure’s size (which can be calculated by integrating the total pressure
309
forces around the structure). This may make the larger cavitons more easily be slowed down
310
in the solar wind plasma frame, explaining our observations.
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
311
We studied the propagation properties of foreshock cavitons, which are similar to the
312
propagation properties of solitary waves reported in [50] [59]. Both cavitons and solitary
313
waves are fast-mode structures/waves, and they propagate in the background plasma frame.
314
However, the size of foreshock cavitons exceeds tens to several hundred ion gyroradii and
315
there is no correlation between the propagation velocity in solar wind and the velocity of fast
316
magnetosonic waves. Therefore, foreshock cavitons do not correspond to these kinds of
317
solitary waves.
318
Page 10 of 41
Among the four foreshock cavitons in our study, three cavitons are stable and one is
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 11 of 41
contracting, indicating these are mature or near mature structures. The mature foreshock
320
cavitons are structures with a high correlation between the decrements in density and
321
magnetic field magnitude [20]. Due to the enhancement of the pressure of suprathermal ions,
322
the total pressure inside and outside foreshock cavitons is very similar, [16] [19] and the
323
cavitons can maintain equilibrium. However, when the cavitons are steepening and evolving,
324
their sizes evaluated from the density profile become larger as the structures will expand.
325
These cavitons cannot be selected using rigorous criteria [20] and we are still unable to
326
diagnose their evolution from generation to maturity using spacecraft data.
pt
ed
319
327
We find that there is no clear correlation between the size of foreshock cavitons and their
328
distance from the bow shock, which may be due to the origin of foreshock cavitons and their
329
evolution properties. The bow shock model presented in [54] [55] [56] under the
330
corresponding IMF and solar wind conditions is used to calculate the distance from the
331
cavitons to the bow shock. Hybrid simulations have shown that foreshock cavitons can appear
332
in a broad area of the ion foreshock [16] and be carried by the solar wind toward the bow
333
shock. The foreshock region is populated by the weakly compressive waves generated by
334
field-aligned ions [63]. Fast, linearly polarized, oblique waves will grow significantly on the
335
condition that the backstreaming ions are cold. The density striations in the perpendicular
336
direction caused by waves are essential for the formation of foreshock cavitons. The nonlinear
337
interaction of the two kinds of waves generates foreshock cavitons. The process does not need
338
a trigger and can be generated self-consistently around the bow shock, which is an intrinsic
339
process in foreshock region. Foreshock cavitons will not disappear on the way to the bow
340
shock. The evolution properties in our study show that cavitons will not expand or contract,
341
instead, caviton width will change only slightly when they are carried toward the bow shock.
342
The width of cavitons depends on their initial size. Therefore, the relationship between the
343
size of cavitons and their distance from the bow shock is not clear. On the other hand, even if
344
foreshock cavitons will expand or contract during their travel toward the bow shock, we
345
cannot obtain the correlation between the size of foreshock cavitons and their distance from
346
the bow shock, as cavitons can be observed on their way to the bow shock and their evolution
347
stages are different from one-another.
iew
Ac
ce
ev
rR
Fo
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
348
As hybrid simulations performed by Omidi et al. [10] suggested that SHFAs form due to
349
the interaction between foreshock cavitons and the bow shock, more work is required to
350
understand the relation between foreshock cavitons and SHFAs. Using high-resolution plasma
351
data from the Magnetospheric Multiscale (MMS) mission, the particles properties inside
352
foreshock cavitons can be analyzed.
353
Acknowledgments We acknowledge the Cluster Team for providing data. All Cluster data is
354
obtained from the Cluster Science Archive (http://www.cosmos.esa.int/web/csa/). We also
355
acknowledge NASA's Space Physics Data Facility (SPDF) for providing OMNI data
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
356
(https://omniweb.gsfc.nasa.gov/). This work was supported by the National Natural Science
357
Foundation of China (grants 41574157, 41628402, and 41774153), and Hui Zhang is
358
partially supported by NSF AGS-1352669. We are grateful to the International Space Science
359
Institute-Beijing for supporting the international team “Dayside Transient Phenomena and
360
Their Impact on the Magnetosphere-Ionosphere”. The project was also supported by the
361
specialized research fund for State Key Laboratories.
362
Reference
364
365
366
367
368
370
Space Sci Rev, 2005, 118: 155–160
2. J P Eastwood, E A Lucek, C Mazelle, et al. The foreshock. Space Science Reviews,
2005,118: 41–94
3. Hao Y F, Lu Q M, Gao X L, et al. Ion dynamics at a rippled quasi-parallel shock: 2D
hybrid simulations, Astrophys J, 2016, 823, 7-18
4. Hao Y F, Gao X L, Lu Q M, et al. Reformation of rippled quasi-parallel shocks:2-D
rR
369
1. Balogh A, Schwartz S J, Bale S D, et al. Cluster at the Earth’s Bow Shock: Introduction.
pt
ed
363
Fo
hybrid simulations, J Geophys Res Space Physics, 2017, 122, 6385-6396
371
5. Hoppe M, Russell C T, Frank L A, et al. Upstream Hydromagnetic Waves and Their
372
Association with Backstreaming Ion Populations ISEE 1 and 2 Observations. J
373
Geophys Res, 1981, 86: 4471-4492
374
375
iew
Ac
ce
ev
6. Greenstadt E W, Le G, Strangeway R J. ULF waves in the foreshock. Adv Space Res,
1995, 15: 71-84
376
7. Su Y Q, Lu Q M, Huang C, et al. Particle acceleration and generation of diffuse
377
superthermal ions at a quasi-parallel collisionless shock: hybrid simulations, J
378
Geophys Res Space Physics, 2012, 117, A08107
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
379
8. Wu M Y, Hao Y F, Lu Q M, et al. The role of large amplitude upstream low-frequency
380
waves in the generation of superthermal ions at a quasi-parallel collisionless shock:
381
CLUSTER observations, Astrophys J, 2015, 808, 2-8
382
383
9. Schwartz S J. Hot Flow Anomalies near the Earth’s bow shock. Adv Space Res, 1995, 15:
107-116
384
10. Omidi N, Zhang H, Sibeck D, Turner D. Spontaneous hot flow anomalies at
385
quasi-parallel shocks: 2. Hybrid simulations. J Geophys Res Space Physics, 2013, 118:
386
173–180
387
11. Zhang H, Sibeck D G, Zong Q G, et al. Spontaneous hot flow anomalies at
388
quasi-parallel shocks: 1. Observations, J Geophys Res Space Physics, 2013, 118:
389
3357–3363
390
391
392
Page 12 of 41
12. Sibeck D G, Phan T D, Lin R, et al. Wind observations of foreshock cavities: A case
study. J Geophys Res, 2002, 07: 1271-1272
13. Schwartz S J, Sibeck D, Wilber M, et al. Kinetic aspects of foreshock cavities.
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 13 of 41
393
Geophys Res Lett, 2006, 33: L12103
394
14. Omidi N. Formation of cavities in the foreshock. AIP Conf Proc, 2007, 932: 181-190
395
15. Blanco-Cano X, Omidi N, and Russell C T. Global hybrid simulations: Foreshock
396
waves and cavitons under radial interplanetary magnetic field geometry. J Geophys
397
Res, 2009, 114: A01216
16. Blanco-Cano X, Kajdič P, Omidi N, et al. Foreshock cavitons for different
399
interplanetary magnetic field geometries: Simulations and observations. J Geophys
400
Res, 2011, 116: A09101
pt
ed
398
401
17. Shi Q Q, Zong Q -G, Zhang H, et al. Cluster observations of the entry layer
402
equatorward of the cusp under northward interplanetary magnetic field. J Geophys Res
403
Space Physics, 2009, 114: A12219
404
18. Pu Z Y, Zong Q G, Fritz T A, et al. Multiple flux rope events at the high-latitude
405
magnetopause: cluster/rapid observation on 26 January, 2001. SURVEYS IN
406
GEOPHYSICS, 2005, 26: 193-214
408
upstream of the quasi-parallel bow shock. Planet Space Sci, 2011, 59: 705–714
20. Kajdič P, Blanco-Cano X, Omidi N, et al. Statistical study of foreshock cavitons. Ann
Geophys, 2013, 31: 2163–2178
411
412
413
21. Kajdič P, Blanco-Cano X, Omidi N, et al. Traveling foreshocks and transient
foreshock phenomena. J Geophys Res: Space Physics, 2017, 122: 9148–9168
22. Lin Y, Global-scale simulation of foreshock structures at the quasi-parallel bow shock.
J Geophys Res, 2003, 108: 1390
ly
On
414
iew
Ac
ce
410
19. Kajdič P, Blanco-Cano X, Omidi N, et al. Multispacecraft study of foreshock cavitons
ev
409
rR
407
Fo
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
415
23. Lin Y, and Wang X, Three-dimensional global hybrid simulation of dayside dynamics
416
associated with the quasi-parallel bow shock. J Geophys Res, 2005, 110: A12216
417
24. Shi Q Q, Zong Q G, Fu S Y, et al. Solar wind entry into the high-latitude terrestrial
418
magnetosphere during geomagnetically quiet times. Nat Commun, 2013, 4:1466-1472
419
25. Zhou, X. -Z.; Ge, Y. S.; Angelopoulos, V.; et al. Dipolarization fronts and associated
420
auroral activities: 2. Acceleration of ions and their subsequent behavior. J Geophys
421
Res, 2012, 117: A10227
422
26. Eastwood J P, Sibeck D G, Angelopouloset V et al. THEMIS observations of a hot
423
flow anomaly: Solar wind, magnetosheath, and ground-based measurements, Geophys
424
Res Lett, 2008, 35: L17S03
425
27. Eastwood J P, Schwartz S J, Horbury T S et al. Transient Pc3 wave activity generated
426
by a hot flow anomaly: Cluster, Rosetta, and ground‐based observations. J Geophys
427
Res, 2011, 116: A08224
428
28. Zhao L L, Zhang H, and Zong Q G. Global ULF waves generated by a hot flow
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
429
anomaly. Geophys Res Lett, 2017, 44: 5283–5291
430
29. Zhang X Y, Zong Q G, Wang Y F et al. ULF waves excited by negative/positive solar
431
wind dynamic pressure impulses at geosynchronous orbit. J Geophys Res Space
432
Physics, 2010, 115: A10221
433
30. Shen X C, Shi Q Q, Zong Q G, et al. Dayside magnetospheric ULF wave frequency
434
modulated by a solar wind dynamic pressure negative impulse. J Geophys Res Space
435
Physics, 2017, 122: 1658–1669
31. Shen X C, Zong Q G, Shi Q Q, et al. Magnetospheric ULF waves with increasing
437
amplitude related to solar wind dynamic pressure changes: The Time History of
438
Events and Macroscale Interactions during Substorms (THEMIS) observations. J
439
Geophys Res Space Physics, 2015, 120: 7179–7190
pt
ed
436
440
32. Shi Q Q, Hartinger H, Angelopoulos V et al. THEMIS observations of ULF wave
441
excitation in the nightside plasma sheet during sudden impulse events. J Geophys Res
442
Space Physics, 2013, 118: 284–298
rR
Fo
443
33. Shi Q Q, Hartinger H, Angelopoulos V et al. Solar wind pressure pulse-driven
444
magnetospheric vortices and their global consequences, J Geophys Res Space Physics,
445
2014, 119: 4274–4280
ev
34. Hao Y, Lembege B, Lu Q M, et al. Formation of downstream high-speed jets by a
447
rippled nonstationary quasi-parallel shock: 2-D hybrid simulations, J Geophys Res
448
Space Physics, 2016, 121, 2080-2094
iew
Ac
ce
446
449
35. Hao Y F, Lu Q M, Gao X L, et al. Two-dimensional hybrid simulations of filamentary
450
structures and kinetic slow waves downstream of a quasi-parallel shock, Ap J, 2018,
451
861, 57-65
452
453
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 14 of 41
36. Omidi N, Zhang H, Chu C, et al. Parametric dependencies of spontaneous hot flow
anomalies. J Geophys Res Space Physics, 2014, 119: 9823–9833
454
37. Omidi N, Berchem J, Sibeck D, and Zhang H. Impacts of spontaneous hot flow
455
anomalies on the magnetosheath and magnetopause, J Geophys Res Space Physics,
456
2016, 121: 3155–3169
457
38. Zong Q G, Wang Y F, Zhang H, et al. Fast acceleration of inner magnetospheric
458
hydrogen and oxygen ions by shock induced ULF waves. J Geophys Res Space
459
Physics, 2012, 117: A11206
460
39. Yang B, Zong Q G, Wang Y F et al. Cluster observations of simultaneous resonant
461
interactions of ULF waves with energetic electrons and thermal ion species in the
462
inner magnetosphere. J Geophys Res Space Physics, 2010, 115: A02214
463
40. Zong Q G, Zhou X Z, Wang Y F, et al. Energetic electron response to ULF waves
464
induced by interplanetary shocks in the outer radiation belt. J Geophys Res Space
465
Physics, 2009, 114: A10204
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 15 of 41
466
467
41. Zong Q G, Zhou X Z, Li X, et al. Ultralow frequency modulation of energetic particles
in the dayside magnetosphere. Geophys Res Lett, 2007, 34: L12105
468
42. Russell C T, Mellott M M, Smith E J, et al. Multiple spacecraft observations of
469
interplanetary shocks: Four spacecraft determination of shock normal. J Geophys Res,
470
1983, 88(A6): 4739–4748
43. Shi Q Q, Shen C, Pu Z Y, et al. Dimensional analysis of observed structures using
472
multipoint magnetic field measurements: Application to Cluster. Geophys Res Lett,
473
2005, 32: L12105
pt
ed
471
474
44. Shi Q Q, Shen C, Dunlop M W, et al. Motion of observed structures calculated from
475
multi-point magnetic field measurements: Application to Cluster. Geophys Res Lett,
476
2006, 33: L08109
477
45. Balogh A, Carr C M, Acuña M H, et al. The Cluster Magnetic Field Investigation:
478
overview of in-flight performance and initial results. Ann Geophys, 2001,
479
19:1207-1217
481
plasmoid in the tail. Geophys Res Lett, 2004, 31: L18803
47. Zong Q G, Fritz T A, Zhang H, et al. Triple cusps observed by Cluster - Temporal or
spatial effect? Geophys Res Lett, 2004, 31: L09810
iew
Ac
ce
483
46. Zong Q G, Fritz T A, Pu Z Y, et al. Cluster observations of earthward flowing
ev
482
rR
480
Fo
484
48. Rème H, Aoustin C, Bosqued J M. et al. First multispacecraft ion measurements in
485
and near the Earth’s magnetosphere with the identical Cluster ion spectrometry (CIS)
486
experiment. Ann Geophys, 2001, 19: 1303-1354
487
49. Schwartz S J. Shock and discontinuity normals, Mach numbers, and related
488
parameters. In Analysis Methods for Multi-Spacecraft Data, Report, edited by G
489
Paschmann and P W Daly, Bern, International Space Science Institute ISSI, 1998,
490
249–270,
491
492
493
494
495
496
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
50. Yao S T, Shi Q Q, Li Z Y et al. Propagation of small size magnetic holes in the
magnetospheric plasma sheet. J Geophys Res Space Physics, 2016, 121: 5510–5519
51. Yao S T, Wang X G, Shi Q Q, et al. Observations of kinetic-size magnetic holes in the
magnetosheath. J Geophys Res Space Physics, 2017, 122: 1990–2000
52. Yao S T, Shi Q Q, Guo R L, et al. MMS observations of electron scale magnetic peak.
Geophys Res Lett, 2017, 45: 527-537
497
53. Xiao T, Zhang H, Shi Q Q, et al. Propagation characteristics of young hot flow
498
anomalies near the bow shock: Cluster observations. J Geophys Res Space Physics,
499
2015, 120: 4142–4154
500
54. Knetter T. A new perspective of the solar wind micro-structure due to multi-point
501
observations of discontinuities. Doctoral Dissertation, Köln: Univ. zu Köln, 2005,
502
88-108, 185-241
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
503
55. Knetter T, Neubauer F M, Horbury T et al. Four-point discontinuity observations
504
using Cluster magnetic field data: A statistical survey. J Geophys Res, 2004, 109:
505
A06102
506
507
56. Sun W J, Shi Q Q, Fu S Y, et al. Cluster and TC-1 observation of magnetic holes in
the plasma sheet. Ann Geophys, 2012, 30: 583-595
57. Sun W J, Slavin J A, Fu S Y, et al. MESSENGER observations of Alfvénic and
509
compressional waves during Mercury’s substorms. Geophys. Res. Lett., 2015, 42:
510
6189–6198
pt
ed
508
511
58. Eastwood J P, Balogh A, Mazelle C, et al. Oblique propagation of 30 s period fast
512
magnetosonic foreshock waves: A Cluster case study. Geophys Res Lett, 2004,31,
513
L04804
514
515
517
518
60. Chao J K, Wu D J, Lin C H, et al. Models for the size and shape of the Earth’s
magnetopause and bow shock. Cospar Colloq Ser, 2002, 12: 127–135
61. Liu J, Shi Q Q, Tian A M, et al. Shape and position of Earth’s bow shock near-lunar
ev
519
waves in magnetotail plasmas. J Geophys Res Space Physics, 2014, 119: 4281–4289
rR
516
59. Ji X F, Wang X G, Sun W J, et al. EMHD theory and observations of electron solitary
Fo
orbit based on ARTEMIS data. Science China Earth Sciences, 2016, 59: 1700–1706
62. Zhang H, Khurana K K, Kivelson M G, et al. Three-dimensional lunar wake
521
reconstructed from ARTEMIS data. J. Geophys. Res. Space Physics, 2014, 119:
522
5220–5243
523
524
iew
Ac
ce
520
63. Sun W J, Fu S Y, Parks G K, et al. Field-aligned currents associated with
dipolarization fronts. Geophys. Res. Lett., (2013),40: 4503-4508
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 16 of 41
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
iew
Ac
ce
ev
rR
Fo
525
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
pt
ed
Page 17 of 41
526
Figure 1 Timing analysis results for one typical foreshock caviton. The left four panels (a-d) are for the
527
leading boundary, and the right four panels (e-h) are for the trailing boundary. Four different magnetic
528
field magnitudes marked by the four colored horizontal lines in Figures 1(a) are used to determine the
529
time when the spacecraft crossed the caviton, corresponding to the different histograms of the same
530
color in Figures 1b-1d. The magnetic field observed by the Cluster spacecraft (Figure 1a). And the
531
black, red, green, and blue curve denotes Cluster 1, 2, 3, 4, respectively. Histograms of the velocities of
532
the boundary in the spacecraft frame (Figure 1b). Histograms of the velocities in the solar wind frame
533
(Figure 1c). Histograms of angles between any two normal vectors of leading boundary (Figure 1d).
534
And the ultimate results of velocity, normal and their uncertainty considering four calculations are
535
written in bold in every subgraph. Figures 1e-1h are results for the trailing boundary of this caviton,
536
and the formats are the same as in Figures 1a-1d.
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
pt
ed
538
ev
rR
Fo
539
Figure 2 MDD and STD analysis result: (a) magnetic field magnitude in GSE coordinates. (b)
541
eigenvalues
542
velocity along the maximum direction. The red shadowed area indicates the leading edge, while the
543
blue shadowed area is the trailing edge.
iew
Ac
ce
540
1 , 2 , and 3 . (c) normal along the maximum derivative direction of magnetic field. (d)
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 18 of 41
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 19 of 41
545
pt
ed
546
rR
Fo
547
ev
Figure 3 Distribution of foreshock cavitons in GSE XY and XZ plane, with velocity vector in
549
the spacecraft frame (a and b) and in the solar wind frame (c and d). GSE coordinate system
Ac
ce
548
is used. The azure arrows denote the timing results, and the pink arrows denote the MDD and
551
STD results. A bow shock model presented by Chao et al. [60] is used, under typical solar wi
552
nd conditions ( Bz  0.35nT , D p  2.48nT , M ms  6.96,and   2.08) . The green curve
553
denotes the nominal bow shock. The caviton observed on Mar 26, 2005 is marked by
554
a black solid dot.
iew
550
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
558
pt
ed
556
557
Fo
559
Figure 4 (a) The size of foreshock cavitons versus their propagation velocity of foreshock cavitons in
560
the solar wind frame. The X axis shows the velocity from the timing or the MDD and STD methods in
561
the solar wind frame, and the Y axis denotes the size of foreshock cavitons. The blue horizontal and
562
vertical lines denote error bars. (b) The angle between the normal direction of the boundary of
563
foreshock cavitons and the ambient magnetic field. The caviton observed on Mar 26, 2005 is
564
marked as ’1’. In both plots, the blue thin diamonds denote the timing result, while the pink asterisks
565
denote the MDD and STD results.
566
iew
Ac
ce
ev
rR
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 20 of 41
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 21 of 41
Leading Edge:2002−02−16 08:32:56−08:32:59
Leading Edge:2002−02−16 08:33:07−08:33:10
8
10.5
Bt (nT)
(a)
Bt (nT)
10
9.5
9
7.5
(e)
7
8.5
8
08:32:57
08:32:58
Time
40
rR
σ3=3.8km/s
U3=97.8km/s
σ4=3.7km/s
U4=98.3km/s
20
0
50
100
150
percentage
(c)
40
20
0
ie
Ac
ce
U(km/s)
60
ev
200
−300
−200
V1=−218.7km/s
σ1=32.7km/s
V2=−219.2km/s
σ2=32.7km/s
V3=−221.4km/s
σ3=32.6km/s
V4=−217.5km/s
σ4=32.6km/s
V =−219.2km/s
σ =32.9km/s
−100
0
100
200
60
40
20
σ =4.1km/s
U =98.6km/s
0
percentage
σ2=4.1km/s
U2=99.9km/s
0
w
U1=100.3km/s
σ1=4.7km/s
U2=91.2km/s
σ2=4.1km/s
U3=90.8km/s
σ3=4.2km/s
U4=87.4km/s
σ4=4.2km/s
U =92.4km/s
σ =6.4km/s
0
50
On
60
ly
40
20
0
300
−300
−200
U−dot(Vsw,n)(km/s)
20
150
200
V1=−200.1km/s
σ1=32.4km/s
V2=−217.4km/s
σ2=32.6km/s
V3=−216.0km/s
σ3=32.6km/s
V4=−217.3km/s
σ4=32.5km/s
V =−212.7km/s
σ =33.7km/s
−100
0
100
200
(g)
300
60
o
n1=(−0.97 0.05 0.22)
σ1=1.1
n2=(−0.98 0.11 0.18)
σ2=1.0o
n3=(−0.98 0.16 0.14)
σ3=1.0o
n4=(−0.96 0.24 0.14)
σ4=1.0o
n =(−0.97 0.14 0.17)
σ =1.8o
−20
−10
0
θn ,n
i
10
20
percentage
(d)
100
(f)
U−dot(Vsw,n)(km/s)
60
40
08:33:09
U(km/s)
percentage
percentage
Fo
σ1=4.4km/s
U1=98.6km/s
60
80
08:33:08
Time
80
80
(b)
08:33:07
pt
ed
08:32:56
percentage
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
30
40
20
n1=(−0.91 0.22 0.35)
σ1=0.4o
n2=(−0.94 0.17 0.30)
σ2=0.7o
n3=(−0.93 0.16 0.32)
σ3=0.6o
n4=(−0.93 0.15 0.34)
σ4=0.6o
n =(−0.93 0.18 0.33)
σ =1.8o
−20
j
−10
0
θn ,n
i
10
j
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
20
(h)
30
Cluster MDD and STD Analysis 2002−02−16
(a)
Bt [nT]
10
9
8
rR
7
−5
10
−10
10
1
0.5
λ3
−0.5
−1
200
nx
ny
ly
On
0
n1
λ2
iew
Ac
ce
(b)
Vn1 [km/s]
λ1
ev
λvalues
6
(c)
C1
C2
C3
C4
Fo
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 22 of 41
pt
ed
SCIENCE CHINA Technological Sciences
nz
Vx
100
(d)
Vy
0
Vz
−100
−200
08:32:43
08:32:53
08:33:03
Vt
08:33:13
08:33:23
08:33:33
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 23 of 41
Spacecraft Frame
Solar Wind Frame
Timing results
MDD & STD results
Timing results
MDD & STD results
Timing results
MDD & STD results
100km/s
100km/s
100km/s
100km/s
iew
On
ly
0
10
Ac
10
ev
ZGSE(RE)
0
rR
ce
ZGSE(RE)
Fo
20
0
10
XGSE(RE)
(a)
20
0
(b)
10
20
XGSE(RE)
0
(c)
10
20
XGSE(RE)
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
20
10
pt
10
ed
Timing results
MDD & STD results
YGSE(RE)
20
YGSE(RE)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
SCIENCE CHINA Technological Sciences
0
(d)
10
20
XGSE(RE)
20
2.5
2.0
1.5
1.0
0.5
ed
160
140
1
For
120
Rev
iew
B, U
3.0
1
pt
3.5
Timing results
MDD & STD results
ce
4.0
Page 24 of 41
180
Ac
4.5
Size (RE)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
SCIENCE CHINA Technological Sciences
100
Timing results
MDD & STD results
O80n
60
ly
1
1
40
(a)
0.0300 250 200 150 100 50 0 50 100
Velocity of cavitons in the solar wind frame (km/s)
20
00
(b)
2
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
4
6
8
Series number
10
12
Page 25 of 41
Propagation properties of foreshock cavitons: Cluster
2
observations
3
WANG MengMeng1,2, YAO ShuTao1, SHI QuanQi1*, ZHANG Hui3, TIAN AnMin1,
4
DEGELING Alexander William1, ZHANG Shuai1, GUO RuiLong4, SUN WeiJie5,
5
LIU Ji2, BAI ShiChen1, SHEN XiaoChen1, ZHU XiaoQiong1, FU SuiYan6, PU
6
ZuYin6
7
1School
8
2National
9
3Geophysical
10
11
12
4Institute
5Department
Space Science Center, Chinese Academy of Sciences, Beijing, 100190, China
Institute, University of Alaska Fairbanks, Fairbanks, Alaska, 99775, USA
of Geology and Geophysics, Chinese Academy of Sciences, Beijing, 100029, China
of Space Physics and Applied Technology, Peking University, Beijing, 100871, China
*Corresponding author (email: sqq@sdu.edu.cn)
Abstract
rR
14
of Space Science and Physics, Shandong University, Weihai, 264209, China
of Climate and Space Sciences and Engineering, University of Michigan, Ann Arbor, 48113, USA
6Institute
13
pt
ed
1
Fo
15
Foreshock cavitons are transient phenomena observed in the terrestrial foreshock region.
16
They are characterized by a simultaneous depression of magnetic field magnitude and plasma
17
density, which are bounded with enhancements of these two parameters and surrounded by ultra
18
low frequency (ULF) waves. Previous studies focused on the interplanetary magnetic field
19
(IMF) conditions, solar wind (SW) conditions, and the growth of the foreshock waves related
20
to the generation of foreshock cavitons. Previously, a multipoint spacecraft analysis method
21
using Cluster data was applied to analyze only two foreshock cavitons, and this method did not
22
consider uncertainties. In this study, multipoint spacecraft analysis methods, including the tim-
23
ing method, the Minimum Directional Difference (MDD) method, and the Spatiotemporal Dif-
24
ference (STD) method are applied to determine the velocity in both spacecraft and solar wind
25
frames. The propagation properties show good agreement with previous results from simula-
26
tions and observations that most cavitons move sunward in the solar wind frame, with the ve-
27
locities larger than the Alfvén speed. The propagation properties of foreshock cavitons support
28
the formation mechanism of cavitons in previous simulations, which suggested that cavitons
29
are formed due to the nonlinear evolution of compressive ULF waves. We find that there is
30
clear decreasing trend between the size of cavitons and their velocity in the solar wind frame.
31
In addition, the timing method considering errors has been applied to study the evolution prop-
32
erties by comparing the velocities with errors of the leading and trailing edges, and we identify
33
three stable cavitons and one contracting caviton, which has not been studied before. Most
34
cavitons should remain stable when they travel toward the Earth’s bow shock. The relationship
35
between the size of foreshock cavitons and their distance from the bow shock is also discussed.
iew
Ac
ce
ev
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
36
Key words foreshock transient phenomena, cavitons, nonlinear evolution of ULF waves, prop-
37
agation and evolution properties of structures, multipoint spacecraft methods
38
1 Introduction
When the supermagnetosonic magnetized solar wind encounters the Earth’s magnetosphere,
40
the bow shock forms. The nature of the bow shock depends on the angle 𝜃𝐵𝑛 between the
41
interplanetary magnetic field (IMF) and the shock normal [1]. The shock is either quasi-parallel
42
(𝜃𝐵𝑛 < 45°) or quasi-perpendicular (𝜃𝐵𝑛 > 45°) . The foreshock, located upstream of the
43
quasi-parallel shock and the “shock foot” of the quasi-perpendicular shock [2] [3] [4], is popu-
44
lated with particles backstreaming from the bow shock, ULF waves [5][6] [7][8], hot flow
45
anomalies (HFAs) [9], spontaneous hot flow anomalies (SHFAs) [10] [11], and foreshock cav-
46
ities [12] [13]. These transients can modify the solar wind before they encounter the bow shock.
47
Global hybrid simulations performed by Omidi [14] and Blanco-Cano et al. [15] [16] sug-
48
gested that a new category of transient structure called foreshock caviton exist in the foreshock
49
region. Foreshock cavitons are transient phenomena as common as HFAs and SHFAs in the
50
foreshock region, which saturate at a width of several 𝑅𝐸 , with a depressed core plasma density
51
and magnetic field strength bounded by a rim of enhanced plasma density and magnetic field
52
strength [14] [15] [16]. Cavitons are not associated with IMF discontinuities, and there is no
53
plasma heating or flow deflection inside the structures, which is in contrast to HFAs. Omidi et
54
al. [14] referred to cavitons as ‘foreshock cavities’ in their simulation of formation of foreshock
55
cavitons. However, foreshock cavitons are always embedded in a sea of ULF waves, which is
56
in contrast to other isolated cavities with no ULF waves nearby. Diffuse ions are found inside
57
and outside foreshock cavitons, while diffuse ions are only found inside foreshock cavities.
58
Schwartz et al. [13] suggested foreshock cavities are formed by thermal expansion because of
59
the magnetic field in cavities connected to the bow shock, which contrasts with notion that the
60
wave interactions generate foreshock cavitons. Hence, Blanco-Cano et al. [15] [16] used the
61
term, foreshock cavitons, to describe these new structures.
pt
ed
39
iew
Ac
ce
ev
rR
Fo
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 26 of 41
62
The interaction of ULF waves in the foreshock contributes to the formation of foreshock
63
cavitons. Under the condition of radial IMF, the foreshock region is permeated by parallel prop-
64
agating sinusoidal fluctuations with right- or left-hand circular polarization, and fast, linearly
65
polarized, oblique (FLO) waves. The nonlinear evolution of these two types of ultra-low fre-
66
quency (ULF) waves generates foreshock cavitons [14] [15][16]. Global hybrid simulations
67
performed by Blanco-Cano et al. [16] showed that foreshock cavitons could exist under a wide
68
range of IMF [17] [18] orientations depending on the Mach number. They found that major
69
features of foreshock cavitons do not vary with the IMF orientation. Statistical studies of fore-
70
shock cavitons [20] [21] have shown that foreshock cavitons are observed for a wide range of
71
IMF orientation and SW conditions. The time duration of cavitons is 65s and the size is 4.6𝑅𝐸
72
on average. Inside cavitons, the variations of plasma density and magnetic field magnitude are
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 27 of 41
73
highly correlated.
The foreshock-bow shock system is a significant region for the solar wind-magnetosphere
75
coupling process. There are a plethora of multi-scale plasma physics processes and phenomena
76
in foreshock, making it an important and excellent laboratory to study plasma physics. The
77
generation and evolution of foreshock cavitons are an intrinsic process of the foreshock-bow
78
shock system and play a considerable role in reformation of the system. Hybrid simulations
79
suggest that the interaction between foreshock cavitons and the bow shock generate another
80
transient phenomenon, namely, SHFAs [10][11]. Several cavitons even generate complicated
81
and large structures if they arrive at the bow shock at the same time. They play an important
82
role in the deformation of the bow shock and can lead to ripples on the surface of bow shock.
83
Cavitons may lead to disturbances in the magnetosheath and surface waves on the magneto-
84
pause [10] [11] [22] [23] [24]. Considering the magnetospheric response [25], foreshock cavi-
85
tons are no less important than foreshock transients such as HFAs with large dynamic pressure
86
pulses [26] [27]. Given that cavitons exhibit similar sudden dynamic pressure decreases, cavi-
87
tons may generate ULF waves in the magnetosphere [28] [29] [30] [31] [32] and drive magne-
88
tospheric vortices [33]. Foreshock cavitons may evolve into SHFAs, which can make the
89
plasma more inhomogeneous and contribute to the formation of magnetosheath jets [34] and
90
magnetosheath filamentary structures (MFS) [35]. Successive expansion and contraction of the
91
magnetosphere caused by SHFAs are significant, which may excite ULF waves in the inner
92
magnetosphere [36] [37] [38] [39] [40] [41].
pt
ed
74
iew
Ac
ce
ev
rR
Fo
93
As foreshock cavitons form, they are convected by the solar wind towards the bow shock.
94
Blanco-Cano et al. [16] found that cavitons propagate sunward in the solar wind frame, as
95
weakly compressive waves. In their simulations, the velocity of the example caviton in the solar
96
wind frame is 98 km/s, which equals 1.9 𝑉𝐴 [16]. Kajdič et al. [19] analyzed two foreshock
97
cavitons observed by the multi-spacecraft Cluster mission. The two cavitons propagate sunward
98
in the solar wind frame at a speed of 188 km/s and 120 km/s. However, only the timing method
99
without calculating errors has been applied to calculate the velocities of these two cavitons [19].
100
Although theories and simulations provide the formation conditions and the evolution of fore-
101
shock cavitons, no observations of the evolution of foreshock cavitons have been reported.
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
102
In this paper, we perform a study of the propagation properties of a series of foreshock cavi-
103
tons using several multipoint spacecraft analysis methods, including the timing method [42],
104
the Minimum Directional Derivative (MDD) method [43] and the Spatiotemporal Difference
105
(STD) method [44]. Four cavitons with both velocities of leading edge and trailing edge con-
106
sidering errors are classified into three stable structures and one contracting structure. We also
107
examine the possible relationship between the size of foreshock cavitons and the distance from
108
cavitons to the bow shock.
109
2 Data and Methods
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
110
2.1 Data and Event Selection
111
Cluster mission consists of four identical spacecraft (C1, C2, C3, C4). We obtain the mag-
112
netic field data with 0.2s resolution from the Fluxgate Magnetometer (FGM) [45] [46] [47]
113
onboard all four spacecraft, and we obtain the ion data with 4s resolution from the Hot Ion
114
Analyzer (HIA) of the Cluster Ion Spectrometer (CIS) [48] on C1. We obtain the solar wind
115
and IMF data with 1-min resolution from the OMNI database, which indicate parameters near
116
the nose of the Earth’s bow shock.
All foreshock caviton events analyzed here are taken from [20], which presented 92 fore-
118
shock cavitons selected using C1 data from 2001 to 2006. Firstly, foreshock cavitons observed
119
by all four Cluster spacecraft are selected. Then, we select the cavitons with clear leading and
120
trailing boundaries and with the similar profiles observed by four spacecraft. Following these
121
criteria, twelve foreshock cavitons are selected and their propagation properties are investi-
122
gated. Further criteria, including the shape parameters of the tetrahedral spacecraft configura-
123
tion can improve the precision of the timing analysis, MDD analysis, and STD analysis.
124
2.2 Timing method
pt
ed
117
rR
Fo
125
The timing method has been widely applied to determine the velocity and normal direction
126
of shocks, magnetic holes, magnetic peaks, and HFAs [42] [49] [50] [51] [52] [53]. To calculate
127
the velocities and normal of the boundaries of foreshock cavitons, we apply a similar method
128
by analyzing magnetic field data detected by four Cluster spacecraft [54] [55]. By solving the
129
following equation,
iew
Ac
ce
ev
130
𝑈(𝑡𝑖 − 𝑡𝑗 ) = (𝑟⃗𝑖 − 𝑟⃗𝑗 ) ∙ 𝑛⃗⃗,
131
the unit normal direction 𝑛⃗⃗ and velocity magnitude U of the foreshock caviton leading and
132
trailing boundaries are obtained. Here, ∆𝑡 = 𝑡𝑖 − 𝑡𝑗 is the time lag between two spacecraft
133
observing the same boundary, and 𝑟⃗𝑖𝑗 = 𝑟⃗𝑖 − 𝑟⃗𝑗 is their corresponding difference in position
134
vectors. As Cluster mission consists of four spacecraft, three differences in position vectors,
135
𝑟⃗12 , 𝑟⃗13 , 𝑟⃗14and three time lags, ∆𝑡12 = 𝑡1 − 𝑡2 , ∆𝑡13 = 𝑡1 − 𝑡3 , ∆𝑡14 = 𝑡1 − 𝑡4 are determined.
136
Furthermore, we estimate the uncertainty of velocity magnitude and normal direction according
137
to [54]. An empirical relative error of time lag is δt = 0.1∆t . As the relative uncertainty of
138
the distance between satellites is 0.01, the time lag uncertainty contributes more to the error of
139
results and is considered dominant. A pair of satellites can give an interval [∆t − δt, ∆t + δt].
140
The interval is divided into 11 equidistant points. In total 113 calculations of velocity and normal
141
are given due to three time intervals determined by four satellites. The mean velocity and nor-
142
mal are given and the standard deviations estimate the uncertainty.
(1)
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 28 of 41
143
2.3 The MDD method
144
The Minimum Directional Derivative (MDD) method is a dimensionality determination
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 29 of 41
technique with the help of multipoint measurements described by Shi et al. [43]. The eigenval-
146
⃗⃗)(∇𝐵
⃗⃗)𝑇 indicate the dimensionality and the principal direcues and eigenvectors of L = (∇𝐵
147
tions of the structure (where T denotes the transposition). Three directions corresponding to
148
the maximum, intermediate and minimum variations of magnetic field are determined straight-
149
forwardly by the MDD method, which can help us investigate the time variation of a structure’s
150
characteristic direction. It is proved that the MDD method is feasible for the determination of
151
the normal direction of 1-D structures including magnetic holes [50] [51] [56], and magnetic
152
peaks [52].
pt
ed
145
153
2.4 The STD method
154
The Spatiotemporal Difference (STD) method [44] can be applied to calculate the velocity
155
of quasi-stationary structures in any dimensionality using multipoint magnetic field measure-
156
ments. Further, we can resolve time-variations of the velocity from the STD results. By esti-
157
⃗⃗, the vemating the time variation of the magnetic field and the magnetic gradient tensor ∇𝐵
158
⃗⃗𝑠𝑡𝑟 , is obtained from the equation of
locity of the structure in the spacecraft frame, 𝑉
159
⃗⃗ = 0.
∇𝐵
160
3 Propagation and evolution properties of foreshock cavitons
⃗⃗𝑠𝑡𝑟 ∙
+𝑉
iew
Ac
ce
Propagation properties
⃗⃗
𝜕𝐵
𝜕𝑡
ev
3.1
rR
161
Fo
162
3.1.1 Timing analysis
163
Timing method is applied to calculate the velocity of foreshock cavitons in the spacecraft
164
and the solar wind frames. Here, the GSE coordinate system is used. We obtain the velocity of
165
foreshock cavitons in the solar wind frame from
166
𝑉 = 𝑈 − 𝑣⃗𝑠𝑤 ∙ 𝑛⃗⃗.
On
(2)
167
Here U is the velocity of caviton in the spacecraft frame obtained from the timing analysis,
168
as before. U is along the normal direction, 𝑛⃗⃗. The average value of the solar wind velocity
169
measured by CIS-HIA over a 10 minute interval including the cavitons is used to eliminate
170
fluctuations. In accordance with [48], an uncertainty in the solar wind velocity 𝑣⃗𝑠𝑤 of 10% in
171
magnitude and +/-5° in direction are considered. We carried out four timing calculations and
172
considered all four calculations to generate our results, including velocities, normal directions
173
and uncertainty estimates, represented as error bars in Figure 4. If the error bar crosses zero,
174
the caviton is probably stationary with respect to the solar wind. Examples of timing analysis
175
are shown in Figure 1. Figure 1(a-d) show the results for the leading boundary, and figure 1(e-
176
h) show the results for the trailing boundary. The mean speed of the leading boundary in the
177
spacecraft frame is 98.6 km/s and the uncertainty is 4.1 km/s as shown in Figure 1b. The average
178
velocity of leading boundary in the solar wind frame is −219.2 ± 32.9km/s along 𝑛⃗⃗𝐿 =
179
(−0.97, 0.14, 0.17) with uncertainty of 1.8°. Figures 1e-1h show the detailed velocity of the
180
trailing boundary with 𝑉𝑇 = −212.7 ± 33.7 𝑘𝑚/𝑠 𝑎𝑛𝑑 𝑛⃗⃗ 𝑇 = (−0.93,0.18,0.33) . Magnetic
ly
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
181
field data with different resolutions were employed to check the reliability of the results. The
182
results agree with those using data with 0.2 s cadence. The velocity with error not including
183
zero shows that the caviton is moving in the solar wind plasma.
3.1.2 MDD and STD analysis
185
Here, we apply the MDD and STD methods to calculate the dimensionality and velocity
186
vector and compare the results with those from the timing method. The analysis results of the
187
same case shown in Figure 1 are shown in Figure 2. As the MDD method suggested, the relative
188
size of the three eigenvalues indicate the dimensionality information of the structure. If 𝜆1 ≫
189
𝜆2 , 𝜆3 ,we can regard the structures as quasi-1D, and 𝜆1 is the eigenvalue of the maximum
190
variant direction of the magnetic field. The maximum variant direction 𝑛⃗⃗1 represents the nor-
191
mal of the boundary of foreshock caviton. The ratio of the average 𝜆1 and 𝜆2 in the limited
192
period indicated by orange shadow is 8.7 for the leading boundary. For the trailing boundary,
193
the ratio in the limited period indicated by the blue shadow is 19.6. Therefore, we regard this
194
caviton as quasi-1D structure.
pt
ed
184
rR
Fo
195
The propagation velocity of the leading boundary in the solar wind frame is -219.3 km/s
196
along 𝑛⃗⃗𝐿 = (−0.88, −0.29, 0.37)and for trailing boundary, the velocity is -222.0 km/s along
197
𝑛⃗⃗ 𝑇 = (−0.96, −0.27, 0.02). Here, L denotes the leading boundary and T denotes the trailing
198
boundary. These results fall within the velocity error from timing method as shown in Figure
199
4(a).
Statistical results
iew
Ac
ce
ev
200
3.1.3
201
The propagation velocity along the normal of the foreshock cavitons are given by equation
202
(2). The velocity vector of the cavitons in the spacecraft frame is equal to U multiplied by 𝑛⃗⃗,
203
while the velocity vector of the cavitons in the solar wind frame is equal to V multiplied by 𝑛⃗⃗.
204
Velocity magnitudes and directions of the twelve foreshock cavitons calculated by timing,
205
MDD and STD methods are plotted in GSE-XY and GSE-XZ planes. Velocity vectors in both
206
the spacecraft frame and the solar wind frame are plotted in Figure 3. In the spacecraft frame,
207
foreshock cavitons are moving towards the Earth. Eleven cavitons are propagating sunwards in
208
the solar wind frame, which is consistent with previous observations [19] and the predictions
209
of simulations [16]. Another caviton observed on Mar 26, 2005 has a velocity in the solar wind
210
frame that is close to zero, for which the error bar crosses zero.
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 30 of 41
211
Sizes of foreshock cavitons are calculated using both the timing velocities and STD veloci-
212
ties in the spacecraft frame. As foreshock cavitons propagate in the solar wind frame, we esti-
213
mate the spatial extents of the cavitons by multiplying their speed in the spacecraft frame by
214
their durations, rather than multiplying their durations by the solar wind velocity [20]. Since
215
foreshock cavitons remain stable when they travel towards the bow shock, the velocities of one
216
boundary are used to calculate the extents of cavitons.
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 31 of 41
217
Figure 4 (a) shows a plot of the estimated size in RE of foreshock cavitons against their
218
propagation velocity in the solar wind frame. This figure shows the trend that smaller foreshock
219
cavitons have significantly higher velocity than larger ones in the solar wind frame.
220
normal of one edge of foreshock cavitons is obtained from the timing method and MDD & STD
221
method, we calculate the angle between the normal direction and the ambient magnetic field
222
vector. This indicates the direction of propagation for a 1-D structure [43] [44]. The results are
223
shown in Figure 4 (b). The average magnetic field value over a 10 minute interval excluding
224
the cavitons is used. We can see that the foreshock cavitons are propagating along the parallel
225
or anti-parallel direction. These results are obtained using two independent techniques (timing
226
and MDD and STD analysis as described above), with both techniques revealing the same trend.
pt
ed
Since the
227
3.2 Evolution of foreshock cavitons
228
Here we show a stable caviton structure observed on 16 February 2002 by comparing the
229
velocities with errors of the leading edge and the trailing edge. The detailed process is as fol-
230
lows. The timing analysis shows that the leading edge travels at a speed of about −219.2 ±
231
32.9 km/s along the direction n
⃗⃗L = (−0.93, 0.14, 0.17) in the solar wind, while the trailing
232
edge moves at a speed of about −212.7 ± 33.7km/s along the direction n
⃗⃗T =
233
(−0.93, 0.18, 0.33) in the solar wind frame. Here, L denotes the leading boundary and T de-
234
notes the trailing boundary as before. We calculate the difference of velocities between the
235
leading boundary and trailing boundary by projecting the trailing boundary velocity to the nor-
236
mal of the leading boundary and subtracting the leading boundary velocity magnitude:
237
∆V = |𝑉𝑇 𝑐𝑜𝑠𝜃𝑛⃗⃗𝐿,𝑛⃗⃗𝑇 − 𝑉𝐿 |
238
where θn⃗⃗L,n⃗⃗T is the angle between the normal of the leading edge and trailing edge. As ∆V =
239
9.3km/s < σL + σT = 32.9 + 33.7 = 66.6km/s, we conclude that the leading edge and the
240
trailing edge of the caviton move at velocities that are indistinguishable given the error esti-
241
mates of the measurements. Consequently, the caviton can be regarded as a stable structure as
242
suggested in Xiao et al [53].
iew
Ac
ce
ev
rR
Fo
(3)
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
243
Only four out of twelve cavitons have usable timing velocities considering errors of both the
244
leading boundary and trailing boundary, and we investigate the evolution properties of these
245
four cavitons. Three cavitons are stable, and only one shows property of contraction. Our results
246
indicate that cavitons remain stable when they are convected toward the bow shock.
247
4 Summary and Discussions
248
By using the timing method, MDD and STD method, we analyze the propagation and evo-
249
lution properties of twelve foreshock cavitons. We find that all cavitons move earthward in the
250
spacecraft frame and the normal of the edge of cavitons are nearly parallel or anti-parallel to
251
the ambient magnetic field. The velocities of cavitons in the solar wind frame are also calculated.
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
Eleven cavitons of all cavitons move sunward in the solar wind frame. These results are con-
253
sistent with previous ones from simulations and observations. We also find that the caviton
254
observed on March 26, 2005 has features consistent with those of a mature caviton structure.
255
We find a clear decreasing trend between foreshock caviton size and their propagation velocity
256
in the solar wind frame. As for the evolution properties, the results suggest that most foreshock
257
cavitons remain stable when they propagate towards the bow shock. We find that there is no
258
clear correlation between the size of foreshock cavitons and their distance from the bow shock.
259
In the simulation of [16], one caviton moves upstream in the solar wind frame at a speed of
260
1.9 times of the Alfven speed. By Cluster observations, Kajdič et al. [19] found that two cavi-
261
tons move at 188 km/s and 120 km/s towards the sun in the solar wind frame. We have also
262
found that foreshock cavitons have a variety of propagation velocities, which is consistent with
263
simulation [16]. The nature of ULF waves and the nonlinear evolution of the waves contribute
264
to the propagation properties of cavitons. Weakly compressive waves propagate upstream in
265
the reference frame of background plasma, which is similar to the propagation direction of
266
cavitons. The normal of the edge of cavitons are nearly parallel or anti-parallel to the ambient
267
magnetic field, which suggests that parallel propagating weakly compressive waves are neces-
268
sary for the generation of foreshock cavitons. Consequently, the propagation properties imply
269
that foreshock cavitons form due to the nonlinear evolution of circularly polarized, parallel
270
propagating ULF waves and compressive, linearly polarized, oblique ULF waves. We find that
271
in all but one case, foreshock cavitons propagate sunward, and their speed can be shown to be
272
larger than the Alfvén speed. Previous results from simulations and observations have found
273
sunward propagating foreshock cavitons with speeds greater than the Alfvén speed. We appear
274
to have found one counter-example.
pt
ed
252
iew
Ac
ce
ev
rR
Fo
On
275
For the caviton observed on Mar 26, 2005, the uncertainty in its velocity in the solar wind
276
frame is greater than its magnitude – in other words it has an error bar across zero. In this case
277
we consider that it is likely that the caviton is stationary with respect to the solar wind, however
278
the size of the uncertainty in velocity for this event is significant; on the order of the Alfven
279
speed. Compared to other cavitons in our study, this event is observed within a higher speed
280
solar wind (larger than 600 km/s) and lower plasma density (less than 3 cm-3) environment.
281
This caviton does not show a double peak internal structure [19]. There are few small fluctua-
282
tions or high-frequency waves in the interior, and the profile of magnetic field magnitude is
283
similar to that of plasma density. Blanco-Cano et al. finds that the width of cavitons should
284
increase slightly during their evolution [16], and that towards the end of their evolution, the
285
profiles of magnetic field magnitude and density should become similar. Therefore, this caviton
286
appears to be a mature structure with fewer wave features compared to the newly generated
287
cavitons, possibly because these fluctuations have dissipated over time in this case.
288
ly
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 32 of 41
The correlation between the size of foreshock cavitons and their velocity in the solar wind
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 33 of 41
frame shows that the bigger scale the foreshock caviton has, the slower it moves in the solar
290
wind flow. There is clear decreasing trend between the size of foreshock cavitons and their
291
velocity in the solar wind frame. It is reasonable to expect that, although the structures were
292
found to be 1-D based on the scale-size of the Cluster satellite configuration, they may be at
293
least 2-D on a larger scale. If we assume that they have roughly the same shape, then size
294
measurements we have obtained are a proxy for their scale size. A structure of a given size
295
propagating with respect to the solar wind will be subject to an effective drag force that in-
296
creases with the structure’s size (which can be calculated by integrating the total pressure forces
297
around the structure). This may make the larger cavitons more easily be slowed down in the
298
solar wind plasma frame, explaining our observations.
pt
ed
289
299
We studied the propagation properties of foreshock cavitons, which are similar to the propa-
300
gation properties of solitary waves reported in [50] [59]. Both cavitons and solitary waves are
301
fast-mode structures/waves, and they propagate in the background plasma frame. However, the
302
size of foreshock cavitons exceeds tens to several hundred ion gyroradii and there is no corre-
303
lation between the propagation velocity in solar wind and the velocity of fast magnetosonic
304
waves. Therefore, foreshock cavitons do not correspond to these kinds of solitary waves.
ev
rR
Fo
Among the four foreshock cavitons in our study, three cavitons are stable and one is con-
306
tracting, indicating these are mature or near mature structures. The mature foreshock cavitons
307
are structures with a high correlation between the decrements in density and magnetic field
308
magnitude [20]. Due to the enhancement of the pressure of suprathermal ions, the total pressure
309
inside and outside foreshock cavitons is very similar, [16] [19] and the cavitons can maintain
310
equilibrium. However, when the cavitons are steepening and evolving, their sizes evaluated
311
from the density profile become larger as the structures will expand. These cavitons cannot be
312
selected using rigorous criteria [20] and we are still unable to diagnose their evolution from
313
generation to maturity using spacecraft data.
iew
Ac
ce
305
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
314
We find that there is no clear correlation between the size of foreshock cavitons and their
315
distance from the bow shock, which may be due to the origin of foreshock cavitons and their
316
evolution properties. The bow shock model presented in [54] [55] [56] under the corresponding
317
IMF and solar wind conditions is used to calculate the distance from the cavitons to the bow
318
shock. Hybrid simulations have shown that foreshock cavitons can appear in a broad area of
319
the ion foreshock [16] and be carried by the solar wind toward the bow shock. The foreshock
320
region is populated by the weakly compressive waves generated by field-aligned ions [63]. Fast,
321
linearly polarized, oblique waves will grow significantly on the condition that the backstream-
322
ing ions are cold. The density striations in the perpendicular direction caused by waves are
323
essential for the formation of foreshock cavitons. The nonlinear interaction of the two kinds of
324
waves generates foreshock cavitons. The process does not need a trigger and can be generated
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
self-consistently around the bow shock, which is an intrinsic process in foreshock region. Fore-
326
shock cavitons will not disappear on the way to the bow shock. The evolution properties in our
327
study show that cavitons will not expand or contract, instead, caviton width will change only
328
slightly when they are carried toward the bow shock. The width of cavitons depends on their
329
initial size. Therefore, the relationship between the size of cavitons and their distance from the
330
bow shock is not clear. On the other hand, even if foreshock cavitons will expand or contract
331
during their travel toward the bow shock, we cannot obtain the correlation between the size of
332
foreshock cavitons and their distance from the bow shock, as cavitons can be observed on their
333
way to the bow shock and their evolution stages are different from one-another.
pt
ed
325
334
As hybrid simulations performed by Omidi et al. [10] suggested that SHFAs form due to the
335
interaction between foreshock cavitons and the bow shock, more work is required to understand
336
the relation between foreshock cavitons and SHFAs. Using high-resolution plasma data from
337
the Magnetospheric Multiscale (MMS) mission, the particles properties inside foreshock cavi-
338
tons can be analyzed.
339
Acknowledgments We acknowledge the Cluster Team for providing data. All Cluster data is
340
obtained from the Cluster Science Archive (http://www.cosmos.esa.int/web/csa/). We also
341
acknowledge NASA's Space Physics Data Facility (SPDF) for providing OMNI data
342
(https://omniweb.gsfc.nasa.gov/). This work was supported by the National Natural Science
343
Foundation of China (grants 41574157, 41628402, and 41774153), and Hui Zhang is partially
344
supported by NSF AGS-1352669. We are grateful to the International Space Science Institute-
345
Beijing for supporting the international team “Dayside Transient Phenomena and Their Impact
346
on the Magnetosphere-Ionosphere”. The project was also supported by the specialized research
347
fund for State Key Laboratories.
348
Reference
351
2.
3.
4.
Hao Y F, Gao X L, Lu Q M, et al. Reformation of rippled quasi-parallel shocks:2-D
hybrid simulations, J Geophys Res Space Physics, 2017, 122, 6385-6396
356
357
Hao Y F, Lu Q M, Gao X L, et al. Ion dynamics at a rippled quasi-parallel shock: 2D
hybrid simulations, Astrophys J, 2016, 823, 7-18
354
355
J P Eastwood, E A Lucek, C Mazelle, et al. The foreshock. Space Science Reviews,
2005,118: 41–94
352
353
Balogh A, Schwartz S J, Bale S D, et al. Cluster at the Earth’s Bow Shock: Introduction.
Space Sci Rev, 2005, 118: 155–160
350
ly
1.
On
349
iew
Ac
ce
ev
rR
Fo
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
5.
Hoppe M, Russell C T, Frank L A, et al. Upstream Hydromagnetic Waves and Their
358
Association with Backstreaming Ion Populations ISEE 1 and 2 Observations. J Geophys
359
Res, 1981, 86: 4471-4492
360
361
Page 34 of 41
6.
Greenstadt E W, Le G, Strangeway R J. ULF waves in the foreshock. Adv Space Res,
1995, 15: 71-84
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 35 of 41
362
7.
Su Y Q, Lu Q M, Huang C, et al. Particle acceleration and generation of diffuse super-
363
thermal ions at a quasi-parallel collisionless shock: hybrid simulations, J Geophys Res
364
Space Physics, 2012, 117, A08107
365
8.
Wu M Y, Hao Y F, Lu Q M, et al. The role of large amplitude upstream low-frequency
366
waves in the generation of superthermal ions at a quasi-parallel collisionless shock:
367
CLUSTER observations, Astrophys J, 2015, 808, 2-8
369
9.
Schwartz S J. Hot Flow Anomalies near the Earth’s bow shock. Adv Space Res, 1995,
15: 107-116
pt
ed
368
370
10. Omidi N, Zhang H, Sibeck D, Turner D. Spontaneous hot flow anomalies at quasi-par-
371
allel shocks: 2. Hybrid simulations. J Geophys Res Space Physics, 2013, 118: 173–180
372
11. Zhang H, Sibeck D G, Zong Q G, et al. Spontaneous hot flow anomalies at quasi-parallel
373
374
376
377
12. Sibeck D G, Phan T D, Lin R, et al. Wind observations of foreshock cavities: A case
study. J Geophys Res, 2002, 07: 1271-1272
rR
375
shocks: 1. Observations, J Geophys Res Space Physics, 2013, 118: 3357–3363
Fo
13. Schwartz S J, Sibeck D, Wilber M, et al. Kinetic aspects of foreshock cavities. Geophys
Res Lett, 2006, 33: L12103
ev
14. Omidi N. Formation of cavities in the foreshock. AIP Conf Proc, 2007, 932: 181-190
379
15. Blanco-Cano X, Omidi N, and Russell C T. Global hybrid simulations: Foreshock waves
380
and cavitons under radial interplanetary magnetic field geometry. J Geophys Res, 2009,
381
114: A01216
iew
Ac
ce
378
382
16. Blanco-Cano X, Kajdič P, Omidi N, et al. Foreshock cavitons for different interplanetary
383
magnetic field geometries: Simulations and observations. J Geophys Res, 2011, 116:
384
A09101
On
385
17. Shi Q Q, Zong Q -G, Zhang H, et al. Cluster observations of the entry layer equatorward
386
of the cusp under northward interplanetary magnetic field. J Geophys Res Space Physics,
387
2009, 114: A12219
ly
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
388
18. Pu Z Y, Zong Q G, Fritz T A, et al. Multiple flux rope events at the high-latitude mag-
389
netopause: cluster/rapid observation on 26 January, 2001. SURVEYS IN
390
GEOPHYSICS, 2005, 26: 193-214
391
392
393
394
395
396
397
398
19. Kajdič P, Blanco-Cano X, Omidi N, et al. Multispacecraft study of foreshock cavitons
upstream of the quasi-parallel bow shock. Planet Space Sci, 2011, 59: 705–714
20. Kajdič P, Blanco-Cano X, Omidi N, et al. Statistical study of foreshock cavitons. Ann
Geophys, 2013, 31: 2163–2178
21. Kajdič P, Blanco-Cano X, Omidi N, et al. Traveling foreshocks and transient foreshock
phenomena. J Geophys Res: Space Physics, 2017, 122: 9148–9168
22. Lin Y, Global-scale simulation of foreshock structures at the quasi-parallel bow shock.
J Geophys Res, 2003, 108: 1390
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
399
23. Lin Y, and Wang X, Three-dimensional global hybrid simulation of dayside dynamics
400
associated with the quasi-parallel bow shock. J Geophys Res, 2005, 110: A12216
401
24. Shi Q Q, Zong Q G, Fu S Y, et al. Solar wind entry into the high-latitude terrestrial
402
magnetosphere during geomagnetically quiet times. Nat Commun, 2013, 4:1466-1472
403
25. Zhou, X. -Z.; Ge, Y. S.; Angelopoulos, V.; et al. Dipolarization fronts and associated
404
auroral activities: 2. Acceleration of ions and their subsequent behavior. J Geophys Res,
405
2012, 117: A10227
26. Eastwood J P, Sibeck D G, Angelopouloset V et al. THEMIS observations of a hot flow
407
anomaly: Solar wind, magnetosheath, and ground-based measurements, Geophys Res
408
Lett, 2008, 35: L17S03
pt
ed
406
409
27. Eastwood J P, Schwartz S J, Horbury T S et al. Transient Pc3 wave activity generated
410
by a hot flow anomaly: Cluster, Rosetta, and ground‐based observations. J Geophys
411
Res, 2011, 116: A08224
413
414
28. Zhao L L, Zhang H, and Zong Q G. Global ULF waves generated by a hot flow anomaly.
rR
412
Fo
Geophys Res Lett, 2017, 44: 5283–5291
29. Zhang X Y, Zong Q G, Wang Y F et al. ULF waves excited by negative/positive solar
ev
wind dynamic pressure impulses at geosynchronous orbit. J Geophys Res Space Physics,
416
2010, 115: A10221
iew
Ac
ce
415
417
30. Shen X C, Shi Q Q, Zong Q G, et al. Dayside magnetospheric ULF wave frequency
418
modulated by a solar wind dynamic pressure negative impulse. J Geophys Res Space
419
Physics, 2017, 122: 1658–1669
420
31. Shen X C, Zong Q G, Shi Q Q, et al. Magnetospheric ULF waves with increasing am-
421
plitude related to solar wind dynamic pressure changes: The Time History of Events and
422
Macroscale Interactions during Substorms (THEMIS) observations. J Geophys Res
423
Space Physics, 2015, 120: 7179–7190
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 36 of 41
424
32. Shi Q Q, Hartinger H, Angelopoulos V et al. THEMIS observations of ULF wave exci-
425
tation in the nightside plasma sheet during sudden impulse events. J Geophys Res Space
426
Physics, 2013, 118: 284–298
427
33. Shi Q Q, Hartinger H, Angelopoulos V et al. Solar wind pressure pulse-driven magne-
428
tospheric vortices and their global consequences, J Geophys Res Space Physics, 2014,
429
119: 4274–4280
430
34. Hao Y, Lembege B, Lu Q M, et al. Formation of downstream high-speed jets by a rippled
431
nonstationary quasi-parallel shock: 2-D hybrid simulations, J Geophys Res Space Phys-
432
ics, 2016, 121, 2080-2094
433
35. Hao Y F, Lu Q M, Gao X L, et al. Two-dimensional hybrid simulations of filamentary
434
structures and kinetic slow waves downstream of a quasi-parallel shock, Ap J, 2018,
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 37 of 41
435
436
437
438
861, 57-65
36. Omidi N, Zhang H, Chu C, et al. Parametric dependencies of spontaneous hot flow
anomalies. J Geophys Res Space Physics, 2014, 119: 9823–9833
37. Omidi N, Berchem J, Sibeck D, and Zhang H. Impacts of spontaneous hot flow anom-
439
alies on the magnetosheath and magnetopause, J Geophys Res Space Physics, 2016, 121:
440
3155–3169
38. Zong Q G, Wang Y F, Zhang H, et al. Fast acceleration of inner magnetospheric hydro-
442
gen and oxygen ions by shock induced ULF waves. J Geophys Res Space Physics, 2012,
443
117: A11206
pt
ed
441
444
39. Yang B, Zong Q G, Wang Y F et al. Cluster observations of simultaneous resonant in-
445
teractions of ULF waves with energetic electrons and thermal ion species in the inner
446
magnetosphere. J Geophys Res Space Physics, 2010, 115: A02214
Fo
447
40. Zong Q G, Zhou X Z, Wang Y F, et al. Energetic electron response to ULF waves in-
448
duced by interplanetary shocks in the outer radiation belt. J Geophys Res Space Physics,
449
2009, 114: A10204
450
41. Zong Q G, Zhou X Z, Li X, et al. Ultralow frequency modulation of energetic particles
ev
451
rR
in the dayside magnetosphere. Geophys Res Lett, 2007, 34: L12105
42. Russell C T, Mellott M M, Smith E J, et al. Multiple spacecraft observations of inter-
453
planetary shocks: Four spacecraft determination of shock normal. J Geophys Res, 1983,
454
88(A6): 4739–4748
iew
Ac
ce
452
455
43. Shi Q Q, Shen C, Pu Z Y, et al. Dimensional analysis of observed structures using mul-
456
tipoint magnetic field measurements: Application to Cluster. Geophys Res Lett, 2005,
457
32: L12105
On
458
44. Shi Q Q, Shen C, Dunlop M W, et al. Motion of observed structures calculated from
459
multi-point magnetic field measurements: Application to Cluster. Geophys Res Lett,
460
2006, 33: L08109
461
462
463
464
465
466
ly
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
45. Balogh A, Carr C M, Acuña M H, et al. The Cluster Magnetic Field Investigation: overview of in-flight performance and initial results. Ann Geophys, 2001, 19:1207-1217
46. Zong Q G, Fritz T A, Pu Z Y, et al. Cluster observations of earthward flowing plasmoid
in the tail. Geophys Res Lett, 2004, 31: L18803
47. Zong Q G, Fritz T A, Zhang H, et al. Triple cusps observed by Cluster - Temporal or
spatial effect? Geophys Res Lett, 2004, 31: L09810
467
48. Rème H, Aoustin C, Bosqued J M. et al. First multispacecraft ion measurements in and
468
near the Earth’s magnetosphere with the identical Cluster ion spectrometry (CIS) exper-
469
iment. Ann Geophys, 2001, 19: 1303-1354
470
49. Schwartz S J. Shock and discontinuity normals, Mach numbers, and related parameters.
471
In Analysis Methods for Multi-Spacecraft Data, Report, edited by G Paschmann and P
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
472
473
474
475
476
477
478
W Daly, Bern, International Space Science Institute ISSI, 1998, 249–270,
50. Yao S T, Shi Q Q, Li Z Y et al. Propagation of small size magnetic holes in the magnetospheric plasma sheet. J Geophys Res Space Physics, 2016, 121: 5510–5519
51. Yao S T, Wang X G, Shi Q Q, et al. Observations of kinetic-size magnetic holes in the
magnetosheath. J Geophys Res Space Physics, 2017, 122: 1990–2000
52. Yao S T, Shi Q Q, Guo R L, et al. MMS observations of electron scale magnetic peak.
Geophys Res Lett, 2017, 45: 527-537
53. Xiao T, Zhang H, Shi Q Q, et al. Propagation characteristics of young hot flow anoma-
480
lies near the bow shock: Cluster observations. J Geophys Res Space Physics, 2015, 120:
481
4142–4154
pt
ed
479
482
54. Knetter T. A new perspective of the solar wind micro-structure due to multi-point ob-
483
servations of discontinuities. Doctoral Dissertation, Köln: Univ. zu Köln, 2005, 88-108,
484
185-241
Fo
485
55. Knetter T, Neubauer F M, Horbury T et al. Four-point discontinuity observations using
486
Cluster magnetic field data: A statistical survey. J Geophys Res, 2004, 109: A06102
487
56. Sun W J, Shi Q Q, Fu S Y, et al. Cluster and TC-1 observation of magnetic holes in the
ev
488
rR
plasma sheet. Ann Geophys, 2012, 30: 583-595
57. Sun W J, Slavin J A, Fu S Y, et al. MESSENGER observations of Alfvénic and com-
490
pressional waves during Mercury’s substorms. Geophys. Res. Lett., 2015, 42: 6189–
491
6198
492
493
494
495
497
498
499
500
501
502
503
58. Eastwood J P, Balogh A, Mazelle C, et al. Oblique propagation of 30 s period fast magnetosonic foreshock waves: A Cluster case study. Geophys Res Lett, 2004,31, L04804
59. Ji X F, Wang X G, Sun W J, et al. EMHD theory and observations of electron solitary
waves in magnetotail plasmas. J Geophys Res Space Physics, 2014, 119: 4281–4289
ly
496
iew
Ac
ce
489
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 38 of 41
60. Chao J K, Wu D J, Lin C H, et al. Models for the size and shape of the Earth’s magnetopause and bow shock. Cospar Colloq Ser, 2002, 12: 127–135
61. Liu J, Shi Q Q, Tian A M, et al. Shape and position of Earth’s bow shock near-lunar
orbit based on ARTEMIS data. Science China Earth Sciences, 2016, 59: 1700–1706
62. Zhang H, Khurana K K, Kivelson M G, et al. Three-dimensional lunar wake reconstructed from ARTEMIS data. J. Geophys. Res. Space Physics, 2014, 119: 5220–5243
63. Sun W J, Fu S Y, Parks G K, et al. Field-aligned currents associated with dipolarization
fronts. Geophys. Res. Lett., (2013),40: 4503-4508
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
iew
Ac
ce
ev
rR
Fo
504
On
505
Figure 1 Timing analysis results for one typical foreshock caviton. The left four panels (a-d) are for the
506
leading boundary, and the right four panels (e-h) are for the trailing boundary. Four different magnetic
507
field magnitudes marked by the four colored horizontal lines in Figures 1(a) are used to determine the
508
time when the spacecraft crossed the caviton, corresponding to the different histograms of the same color
509
in Figures 1b-1d. The magnetic field observed by the Cluster spacecraft (Figure 1a). And the black, red,
510
green, and blue curve denotes Cluster 1, 2, 3, 4, respectively. Histograms of the velocities of the boundary
511
in the spacecraft frame (Figure 1b). Histograms of the velocities in the solar wind frame (Figure 1c).
512
Histograms of angles between any two normal vectors of leading boundary (Figure 1d). And the ultimate
513
results of velocity, normal and their uncertainty considering four calculations are written in bold in every
514
subgraph. Figures 1e-1h are results for the trailing boundary of this caviton, and the formats are the same
515
as in Figures 1a-1d.
ly
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
pt
ed
Page 39 of 41
516
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
517
518
ev
rR
Fo
Figure 2 MDD and STD analysis result: (a) magnetic field magnitude in GSE coordinates. (b) eigenvalues 𝜆1 , 𝜆2 , 𝑎𝑛𝑑 𝜆3 . (c) normal along the maximum derivative direction of magnetic field. (d) velocity
520
along the maximum direction. The red shadowed area indicates the leading edge, while the blue shad-
521
owed area is the trailing edge.
522
iew
Ac
ce
519
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 40 of 41
pt
ed
SCIENCE CHINA Technological Sciences
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
Page 41 of 41
pt
ed
523
rR
Fo
524
525
Figure 3 Distribution of foreshock cavitons in GSE XY and XZ plane, with velocity vector in
526
the spacecraft frame (a and b) and in the solar wind frame (c and d). GSE coordinate syste
m is used. The azure arrows denote the timing results, and the pink arrows denote the MDD
Ac
ce
527
ev
and STD results. A bow shock model presented by Chao et al.[60] is used, under typical solar
529
wind condition s (𝐵𝑍 = −0.35𝑛𝑇, 𝐷𝑝 = 2.48𝑛𝑇, 𝑀𝑚𝑠 = 6.96, 𝑎𝑛𝑑 𝛽 = 2.08). The green curve
iew
528
530
denotes the nominal bow shock. The caviton observed on Mar 26, 2005 is marked by a
531
black solid dot.
532
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
SCIENCE CHINA Technological Sciences
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english
SCIENCE CHINA Technological Sciences
pt
ed
533
534
Fo
535
Figure 4 (a) The size of foreshock cavitons versus their propagation velocity of foreshock cavitons in
536
the solar wind frame. The X axis shows the velocity from the timing or the MDD and STD methods in
537
the solar wind frame, and the Y axis denotes the size of foreshock cavitons. The blue horizontal and
538
vertical lines denote error bars. (b) The angle between the normal direction of the boundary of foreshock
539
cavitons and the ambient magnetic field. The caviton observed on Mar 26, 2005 is marked as ’1’.
540
In both plots, the blue thin diamonds denote the timing result, while the pink asterisks denote the MDD
541
542
and STD results.
iew
Ac
ce
ev
rR
ly
On
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Page 42 of 41
Downloaded to IP: 192.168.0.24 On: 2019-03-25 08:44:28 http://engine.scichina.com/doi/10.1007/s11431-018-9450-3
http://tech.scichina.com/english