Upload
others
View
17
Download
0
Embed Size (px)
Citation preview
Numerical simulation on the multiple dipolarization fronts in the magnetotail
Haoyu Lu,1,2,a) Yun Li,1 Jinbin Cao,1 Yasong Ge,3 Tielong Zhang,4 and Yiqun Yu1
1School of Space and Environment, Beihang University, Beijing, China2Lunar and Planetary Science Laboratory, Macau University of Science and Technology–Partner Laboratoryof Key Laboratory of Lunar and Deep Space Exploration, Chinese Academy of Sciences, Macau, China3Institute of Geology and Geophysics, Chinese Academy of Sciences, Beijing, China4Space Research Institute, Austrian Academy of Sciences, Graz, Austria
(Received 13 July 2017; accepted 19 September 2017; published online 13 October 2017)
Using an extended MHD model including the Hall effect and finite Larmor radius effect, we
reproduce multiple dipolarization fronts (DFs) associated with the interchange instability in the
braking region of bursty bulk flow in the plasma sheet. Our simulations reveal that the multiple
DFs produced by the interchange instability are “growing” type DFs because the maximum plasma
flow speeds are behind the fronts. Both the earthward and tailward moving DFs can be produced by
interchange instability in the near-Earth region. The Hall electric field is the dominant electric field
component in the dip region and the DF layer. The convective and the electron pressure gradient
electric field components are smaller. The sharp Bz changes in both the dip region and DF layer cor-
respond to the oppositely directed currents that are primarily associated with electrons. The ion dia-
magnetic current due to the strong ion pressure gradient causes an intense downward current in the
dip region, which can produce the dip ahead of the front. The energy dissipations in the dip region
and DF layer are dominated by ions through the work done by the Lorentz force. Our simulation
results indicate that the magnetic energy can be converted to plasmas on the DF layer, and viceversa in the dip region. Published by AIP Publishing. https://doi.org/10.1063/1.4996039
I. INTRODUCTION
Busty bulk flows (BBFs) are usually considered to be a
consequence of magnetic reconnection in the middle magne-
totail and closely associated with substorms.1–5 As BBFs
approach the Earth, they are decelerated by the dominant
dipole magnetic field,1,6 exciting current wedge, and geo-
magnetic pulsation Pi2.7,8 A typical phenomenon character-
ized by a sharp increase in Bz at the leading edge of fast flow
is referred to as the dipolarization front (DF), which is a thin,
vertical current sheet layer that separates tenuous plasma
flow from ambient dense plasma in the plasma sheet. In
many cases, the Bz component exhibits an asymmetric bipo-
lar feature, i.e., a small dip arises ahead of the sharp increase
in Bz.9–12
A typical thickness of a DF is comparable to an ion iner-
tial length and the key physical processes at DFs occur on
ion inertial-13,14 and gyro-scales.15–17 Therefore, the Hall
effect due to ion and electron decoupling is to be considered.
Simulations and observations show that the Hall effect not
only increases the current along the tangent plane of the DF,
but also makes the DF structure asymmetric.16–18 Another
precursor signature of DFs is a transient decrease in Bz
(referred to as a Bz dip), which can be explained based on the
models of earthward moving plasmoids19,20 or nightside flux
transfer events.21 Satellite observations show that three quar-
ters of the DFs propagate earthward and one quarter
tailward.22
Numerous simulations and observations have been
implemented to study the generation mechanism of DF. Till
date, however, it is still poorly understood how DFs are
formed. Ohtani et al.10 suggested the asymmetric Bz bipolar
structure of DF is due to the passage of a magnetic island
through comparison of observations with two-fluid simula-
tion. MHD simulation indicated that jet braking occurring
primarily in the near-Earth magnetotail is a possible forma-
tion mechanism of DFs.23 Another possible mechanism of
the generation of DFs is near-Earth reconnection that creates
a magnetic pileup region earthward of the reconnection
site.24–28 Recurrence of the bursty patchy reconnection may
cause the formation of multiple DFs.15,29 Additionally, inter-
change/ballooning instability can be invoked at the interface
between the reconnection jet and the pre-existing plasma
sheet ahead of it, and related to the formation of the BBFs in
the magnetotail.9,30,31 Thus, due to the strong interaction
between the fast flow and the ambient plasma, interchange/
ballooning instability may be another candidate for the gen-
eration mechanism of multiple DFs.9,32–35
A rough comparison of multiple DFs was conducted by
Guzdar et al.32 through ideal MHD simulation. However, the
kinetic features of DFs on the scale of ion inertial length or
ion gyro radius indicate that the ideal MHD model without
Hall and finite Larmor radius (FLR) effects is incapable of
reproducing fully the kinetic features of DFs in the magneto-
tail. In this paper, we performed a two-dimensional extended
MHD simulation, including the Hall effect and the finite
Larmor radius (FRL) effect, to study the kinetic characteris-
tics of multiple DFs on the spatial scale of the ion inertial
length/ion Larmor radius. The multiple DFs are self-
consistently produced by the interchange instability arising
due to the effective buoyant force in the near-Earth region.
Specifically, we investigate the instability with a focus on
the electric system and energy conversion at the multiple
DFs.a)[email protected]
1070-664X/2017/24(10)/102903/7/$30.00 Published by AIP Publishing.24, 102903-1
PHYSICS OF PLASMAS 24, 102903 (2017)
II. METHODOLOGY
The evolution of plasmas and field associated with inter-
change instability in the magnetotail discussed in this paper
is restricted to two dimensions. The fundamental model is
the extended MHD equations augmented by terms to include
Hall and FLR effects. Considering the effective gravitational
force,32 we describe the extended MHD equations in a
dimensionless form as follows:
@
@t
q
qV
B
qet
266664
377775þr �
qV
qVV þ PI � BB
lm
VB� BV
ðqet þ PÞV � B
lm
V � Bð Þ
266666664
377777775¼
0
g
0
g � V
266664
377775� dir �
0
pi
0
V � pi
266664
377775þ di
0
0
� 1
l0
r� r� B� B
q
� �
� B
l20
� r � r � B� B
q
� �� �
2666666664
3777777775
þdi
0
01
l0
r� rpe
q
� �
1
l20
B � r � rpe
q
� �� �
2666666664
3777777775; (1)
where P¼ pþB2/2l0, et ¼ V2/2þ p/q(c–1) þ B2/2ql0, g¼ [bqgx/2, 0, 0]T, is the specific heat ratio, b is the plasma
beta, gx is the effective gravitational force in the x direction,
pe is the electron pressure, and di is the dimensionless ion
inertial length. In our study, we take the adiabatic exponent c¼ 5/3. The second and third terms on the right hand side of
Eq. (1) come from the Hall effect and electron pressure gra-
dient (EPG). The gyro-viscosity tension pi is given as
pið Þxx¼ � pið Þyy
¼ �pi@Vy
@xþ @Vx
@y
� �.2B; (2)
pið Þxy¼ pið Þyx
¼ pi@Vx
@x� @Vy
@y
� �.2B; (3)
where pi is the ion pressure, B is the magnitude of magnetic
field, and Vx, Vy are components of velocity.
We adopt the second-order upwind total variation
diminishing scheme36 in conjunction with the Superbee lim-
iter to solve the two-dimensional extended MHD equations.
The computational stability condition requires that the time
step is shorter than the crossing time of the grid cells by the
fastest wave for all grid cells and all directions i¼ 1, 2, i.e.,
�t¼C�xi/cimax, where ci
max is in terms of the largest wave
speed by which information can propagate parallel in the idirection, C is the dimensionless Courant number by which
fluid travelling within one time step is constrained in one
grid cell. Thus, we can get cimax as following expression
cimax ¼ jvij þ ci
fast.
In the process of fast flow in the near-Earth region prop-
agating towards the Earth, a tailward total force arises as a
result from the increase of tailward thermal pressure gradient
and the decrease of the earthward magnetic curvature force.
In conjunction with the tailward gradient of plasma density
due to the flow braking, the total force brings forth inter-
change instability in the braking region, as an analogy for an
effective gravitational force to excite a Rayleigh–Taylor
type instability. We are thus led to consider the theoretical
idealization of interchange instability, occurring in a back-
ground medium that is at rest and at equilibrium. Here, we
adopt the model proposed by Guzdar et al.32 A coordinate
system with the x axis pointed anti-sunward, the y axis points
from dusk to dawn, and the z axis points from south to north
is defined as shown in Fig. 1. The initial quasi-equilibrium is
established in which the plasma pressure balances the mag-
netic field force and effective gravity. The initial profiles of
plasma density and magnetic field component Bz along xdirection can be deduced as follows:
q xð Þ ¼ 0:5 qL þ qRð Þ � qL � qRð Þtanhx
l
� �� �;
BzðxÞ ¼ 0:5 Aþ bgxðqL þ qRÞ þ bðqL � qRÞtanhx
l
� ��
þbgxlðqL � qRÞln coshx
l
� �� ��0:5 ;
where qL and qL are the densities on the left (closer to the
Earth) and on the right, respectively. The parameter A is con-
stant which is used to maintain the magnetic Bz component
positive. The dimensionless ion inertial length di ¼ (mi/
FIG. 1. The setup of the simulation coordinate system with the Earth’s mag-
netotail. The x axis points anti-sunward, the y axis points downward, and the
z axis points from south to north. The purple arrow marked by “g” represents
the effective gravitational force.
102903-2 Lu et al. Phys. Plasmas 24, 102903 (2017)
l0e2Z2L2ni)1/2 is the length below which ion motion is
decoupled from electron motion. It is approximately taken as
di � 0.1. According to the previous observations,37 the pro-
ton and electron temperature ratio Tp/Te is taken as 5, which
leads to pe ¼ p/6 and pi ¼ 5p/6. The boundary condition is
periodic in the y direction and free in the x direction respec-
tively. Initial distributions of plasma density and magnetic
field component Bz along the x direction are plotted in Fig. 2.
III. NUMERICAL RESULTS
Numerical results show that as a result of joint action of
the tailward density gradient (c.f. Fig. 2) and tailward total
force, the interchange instability is triggered to generate an
earthward moving bubble with low ion density. The two
dominant earthward moving flows with lower ion density
and higher Bz are interlaced with tailward flow with higher
density and lower Bz. In the wake and flank of the dominant
flow heads are regions of the reduced field strength. Due to
the fact that the plasma density gradient and total force are
remarkable in the near-Earth flow-braking region, the inter-
laced earthward and tailward moving plasma structures prob-
ably oscillate in the braking region.22,38
The plasma density structure in the equatorial plane is
shown in Fig. 3. The DF features, shown by the snapshots of
Bz at given values of y in Fig. 3, exhibit multiple Bz enhance-
ments in Fig. 4, corresponding to the plasma velocity profiles
in Fig. 5. In this paper, we use the terminology of Pritchett39
that the first DF is referred to as the “primary front” and the
second as the “trailing front.” The Bz dips obviously arise
ahead of the trailing fronts in Fig. 4, which has been con-
firmed by satellite observations.10,11,22,40
It can also be seen that as the multiple DFs in Fig. 4(a)
propagate earthward [cf. Fig. 5(a)], and the maximum ion
flow speeds near both DFs occur behind the fronts, which
represent “growing” DFs in the terminology of Fu
et al.27,41,42 Previous observations from Cluster and magne-
tospheric multiscale mission indicate that there are a signifi-
cant number of tailward moving DFs,22,43–45 which is also
supported by numerical simulations.23 It means that DFs
propagate not only earthward but also tailward. The statisti-
cal analysis of Schmid et al.22 indicated that three quarters
of the DFs propagate earthward and about one quarter tail-
ward. In our simulations, the growing-type of multiple DFs
in Fig. 4(b) propagate tailward, as illustrated by the x compo-
nent of velocity in Fig. 5(b).
In the present extent MHD model with Hall and FLR
effects, the ion velocity is approximately taken as the aver-
age velocity according to the expression V ¼ (miVi þ meVe)/
(mi þ me) � Vi. Thus the velocity of decoupled electron can
FIG. 2. Initial profiles, (a) plasma density, and (b) magnetic field component Bz.
FIG. 3. The plasma density distribution of DF structures on the equatorial
plane in one period of the interchange instability. The colored solid lines
represent the snapshot locations.
FIG. 4. The profile of Bz along the xdirection at given values of y in Fig. 2.
(a) Earthward moving multiple DFs;
(b) tailward moving multiple DFs.
FIG. 5. The profile of x component of
plasma speed along the x direction at
given values of y in Fig. 2. (a)
Earthward moving multiple DFs; (b)
tailward moving multiple DFs.
102903-3 Lu et al. Phys. Plasmas 24, 102903 (2017)
be determined by the electric current density and the ion
velocity, i.e., Ve ¼ Vi � diJ/n. Figure 6 shows the physical
variables along the x direction at y¼ 1.3. It can be seen that
accompanied with the sharp increase in Bz and growing
increase in the x component of bulk ion velocity Vix, the
plasma density and pressure decrease on the multiple DFs.
The electron velocity and current density in the duskward
direction reach maximum values at the DFs. It indicates that
the current density is mainly associated with the electron
flow, which is confirmed by the comparison between current
densities in Fig. 6(f). It can also be seen in Fig. 6 that the
electron flow dominates the current density in the dip region
of the trailing front, which is mainly dawnward.
As seen in Fig. 6(e), an intense dawnward directed elec-
tron flow occurs at the primary front, whereas an intense
duskward-to-dawnward bi-directed electron flow appears at
the trailing front. Pritchett39 interpreted that it is a localized
E�B drift caused by the electric field normal to the DF. On
both fronts, the current densities are duskward and carried by
the dawnward drifting electrons. In the Bz dip region ahead
of the trailing front, the duskward drifting electron flow con-
tributes to the dawnward current density, which is responsi-
ble for the Bz dip. These results are consistent with the
particle in cell (PIC) results of Pritchett.39
The strong plasma pressure gradient on the front sug-
gests that there is a diamagnetic current in the narrow DF
current sheet. Figure 7 shows the diamagnetic current pro-
duced by the pressure gradients of ions and electrons, i.e.,
jdi¼ (B/B2)��pi, jde¼ (B/B2)��pe. It can be seen that the
current in the DF current sheet is mainly contributed by the
ion pressure gradient drift. The reason is that the ion pressure
changes more sharply than the electron pressure.40
Therefore, the diamagnetic current due to the ion pressure
sharp gradient is the main part of the dawnward current in
the dip region, which generates the Bz dip ahead of the DF.
The carrier of intense current in the dip region is an electron.
Figure 8 shows the profiles of electric field and its ingre-
dients along the x direction at y ¼ 1.3. The magnetic frozen-
in condition is satisfied well in the region where DFs are
absent. In the DF region, the Hall effect plays an important
role in the generation of the electric field. The x and y com-
ponents of the electric field are mainly from positive contri-
bution by Hall and negative by electron pressure gradient
electric fields. The convective electric field also contributes
to the total electric field. However, since the Hall electric
field is much larger than the convective and electron pressure
gradient electric field, the dominant part of electric field is
FIG. 6. Physical variables along the x direction at y¼ 1.3.
FIG. 7. Diamagnetic current produced by the pressure gradient of ions and
electrons.
FIG. 8. Electric field and its components, including convection, Hall, and
electron pressure gradient electric fields, along the x direction at y¼ 1.3.
102903-4 Lu et al. Phys. Plasmas 24, 102903 (2017)
the Hall electric field. The results agree well with each other
in both the dip region and at the DF layer.
J�E describes the conversion between the electromag-
netic energy and plasma kinetic (including thermal and bulk
flow) energy. Positive J�E corresponds to a load, i.e., the
transport of electromagnetic energy to plasma energy, and
negative J�E corresponds to a generator, i.e., the transport of
plasma energy to electromagnetic energy.34,45–47 In our sim-
ulation, positive values of J�E are seen on DFs at both lead-
ing and trailing fronts, while J�E is negative in the dip region
ahead of the trailing front, as shown in Fig. 9. Therefore, in
the presence of Bz dip, the energy transfers from plasmas to
the fields. However, as for the DFs without the precursor sig-
nature of the Bz dip, they only play roles of transferring elec-
tromagnetic field energy into plasma kinetic energy.
IV. DISCUSSION AND CONCLUSIONS
We performed a two-dimensional extended MHD simu-
lation augmented with Hall and finite Larmor radius (FLR)
effects to study the multiple dipolarization fronts (DFs) pro-
duced by the interchange instability in the braking region of
BBF, which is attributed to the joint interaction by the tail-
ward imbalanced total force and the plasma density gradient
toward the magnetotail. It has been proved that the DF is
mostly characterized in the spatial scale of the ion inertial
length/ion gyro radius. Accordingly, the model proposed in
this paper is self-consistent and thus can reproduce the physi-
cal features of the DFs in the kinetic scale.
Multiple DFs reported in the present study can be classi-
fied into two categories according to the plasma flow direc-
tion, i.e., earthward moving DF and tailward moving DF.
Since the highest ion flow speeds near both kinds of DFs
occur behind the fronts, the DFs are “growing” type in the
terminology of Fu et al.27,41,42 Tailward moving DFs accom-
panied with tailward fast flow have been frequently observed
in the near-Earth region,22,43–45 which cannot be produced
by the tailward outflow of tail magnetic reconnection since
the occurring site is too close to the Earth and the z compo-
nent of magnetic field Bz is positive. The tailward propagat-
ing flow can be referred as a result of a DF rebound at the
magnetic dipole-dominated near-Earth plasma sheet.23 The
fast tailward moving DFs are recorded directly after the
rebound of the fast earthward moving DFs.22 In our study,
we proposed another generation mechanism of the tailward
moving DFs, i.e., interchange instability in the near-Earth
region.
The simulation results indicate that the sharp Bz
increases on the DFs are associated primarily with the elec-
trons, the current densities in the dip region and DF layer are
mainly contributed by the electron flow, which is consistent
with the simulation results.39 It is interesting that all of the
trailing fronts exhibit Bz dips, where the current density is
considerable and dawnward. In previous studies, several
models including BBF-type flux ropes and night side flux
transfer events48–50 have been proposed to explain the physi-
cal property of Bz dip. The present results indicate that it can
also be explained based on the interchange instability. Since
electrons are frozen in the magnetic field on DFs and the
electric field is normal to the tangent plane of DFs, the
intense current density in the dip region is mainly contrib-
uted by the E�B drifting of electron flows. A test particle
model51 showed that the carrier of the dawnward current
ahead of DF is ions that have been reflected and accelerated
by earthward propagating DFs. Although being incapable of
treating ions and electrons as particles, our extended self-
consistent MHD model including Hall and FLR effects can
truly decouple the electron and ion motions, which makes it
get the accordant result with PIC simulation35 that the elec-
trons dominantly contribute to the dawnward current in the
Bz dip region.
The strong plasma pressure gradient on the front moti-
vates us to investigate the diamagnetic current for ions and
electrons. It is found that the main contribution to the current
on the front is the ion pressure gradient drift, same as in the
dip region, which is consistent with the results from observa-
tions and simulations.40,50,51 In some cases,52 the electron
pressure may decrease at the front, and the current resulting
from �pe may dominate. Therefore, although the electrons
are carrier of the intense current in the dip region, the ion
diamagnetic current due to the sharp ion pressure gradient
causes the increase of current there.
DFs are narrow current sheets where Hall physics domi-
nates and the electrons are frozen-in. The comparison
between the components of electric field on the multiple DFs
indicate that at both primary and trailing fronts, the Hall
electric field provides dominant contribution to the total elec-
tric field whereas the contributions from convective and elec-
tron pressure gradient electric fields are very small. This
result is in a good agreement with previous observations16,40
and simulations.18,35 In the present Hall MHD model, since
the electron flow is frozen-in to the magnetic field, the elec-
tric field on the xy plane is E? ¼ �Ve? � B. In addition, the
Hall model assumes jVe?j � jVi?j,53 which means that the
electric current is dominated by the electron current. Thus,
jE?j ¼ jVe? � Bj � jVi?�Bj, i.e., the convective electric
field is very small compared to the total electric field, mean-
ing that the total electric field is substantially provided by
the Hall effect.
Although the electric current is actually contributed by
the electron flow on the multiple DFs, the energy dissipation
at the DFs is dominated by ions, which has been confirmed
by observations and simulations.34,39,45,54 The explanation
can be based on the fact that the energy dissipation is
FIG. 9. Energy conversions around multiple DFs along the x direction at
y¼ 1.3.
102903-5 Lu et al. Phys. Plasmas 24, 102903 (2017)
essentially provided by the work done by the Lorentz force
under the assumption of ideal conductive plasma, i.e.,
J�E¼V�(J�B). In the Hall physics, the bulk ion flow is
generally the same as the MHD flow, i.e., V ¼Vi þ (me/
Mi)Ve � Vi. Therefore, the ions play a dominant role in the
energy dissipation through the work done by the Lorentz
force.
In the present study, two categories of DFs are found in
the simulation results, one is the DF without Bz dip, and
another is the DF with Bz dip, corresponding to the primary
and trailing fronts respectively. The energy of electromag-
netic field on the primary front is transferred to the plasma at
the DF (J�E> 0), which means that the primary one is
energy load region. It is interesting that J�E is negative in the
dip region ahead of the trailing front, which indicates that
the energy of plasma is transferred to the electromagnetic
field. On the trailing front, the energy of electromagnetic
field is transferred to the plasma. Therefore, the energy
exchange between the fields and plasma on the trailing front
alters from load to generator regions.
ACKNOWLEDGMENTS
Our work was supported by the National Natural
Science Foundation of China (NSFC) under Grant Nos.
41674176, 41474124, 40931054, 41474144, and 11372028
and the fund of the Lunar and Planetary Science Laboratory,
Macau University of Science and Technology–Partner
Laboratory of Key Laboratory of Lunar and Deep Space
Exploration and the Chinese Academy of Sciences (FDCT
No. 039/2013/A2). The simulation data will be made
available upon request by contacting Haoyu Lu.
1K. Shiokawa, W. Baumjohann, and G. Haerendel, Geophys. Res. Lett.
24(10), 1179–1182, doi:10.1029/97GL01062 (1997).2T. Nagai, M. Fujimoto, R. Nakamura, Y. Saito, T. Mukai, T. Yamamoto,
A. Nishida, S. Kokubun, G. D. Reeves, and R. P. Lepping, J. Geophys.
Res. 103(A10), 23543–23550, doi:10.1029/98JA02246 (1998).3J. B. Cao, Y. D. Ma, G. Parks, H. Reme, I. Dandouras, R. Nakamura, T. L.
Zhang, Q. Zong, E. Lucek, C. M. Carr, Z. X. Liu, and G. C. Zhou,
J. Geophys. Res. 111, A04206, doi:10.1029/2005JA011322 (2006).4J. B. Cao, Y. D. Ma, G. Parks, H. Reme, I. Dandouras, and T. L. Zhang,
J. Geophys. Res. 118, 313–320, doi:10.1029/2012JA018351 (2013).5T. Wang, J. Cao, H. Fu, X. Meng, and M. Dunlop, Geophys. Res. Lett. 43,
1854–1861, doi:10.1002/2016GL068147 (2016).6M. Hesse and J. Birn, J. Geophys. Res. 96, 19417–19426, doi:10.1029/
91JA01953 (1991).7L. Kepko, M. Kivelson, and K. Yumoto, J. Geophys. Res. 106, 1903,
doi:10.1029/2000JA000158 (2001).8J. Cao, J. Duan, A. Du, Y. Ma, Z. Liu, G. C. Zhou, and D. Yang,
J. Geophys. Res. 113, 521–532, doi:10.1029/2007JA012629 (2008).9M. S. Nakamura, H. Matsumoto, and M. Fujimoto, Geophys. Res. Lett.
29(8), 88-1–88-4, doi:10.1029/2001GL013780 (2002).10S. I. Ohtani, M. A. Shay, and T. Mukai, J. Geophys. Res. 109, A03210,
doi:10.1029/2003JA010002 (2004).11H. Fu, Y. V. Khotyaintsev, A. Vaivads, M. Andre, and S. Y. Huang,
Geophys. Res. Lett. 39, L10101, doi:10.1029/2012GL051784 (2012).12Y. S. Ge, J. Raeder, V. Angelopoulos, M. L. Gilson, and A. Runov,
J. Geophys. Res. 116, A00I23, doi:10.1029/2010JA015758 (2011).13A. Runov, V. Angelopoulos, M. I. Sitnov, V. A. Sergeev, J. Bonnell, J. P.
McFadden, D. Larson, K.-H. Glassmeier, and U. Auster, Geophys. Res.
Lett. 36, L14106, doi:10.1029/2009GL038980 (2009).14S. Y. Huang, M. Zhou, X. H. Deng, Z. G. Yuan, Y. Pang, Q. Wei, W. Su,
H. M. Li, and Q. Q. Wang, Ann. Geophys. 30, 97–107 (2012).15K.-J. Hwang, M. L. Goldstein, E. Lee, and J. S. Pickett, J. Geophys. Res.
116, A00I32, doi:10.1029/2010JA015742 (2011).
16H. S. Fu, Y. V. Khotyaintsev, A. Vaivads, M. Andr�e, and S. Y. Huang,
Geophys. Res. Lett. 39, L06105, doi:10.1029/2012GL051274 (2012).17W.-J. Sun, S. Fu, G. K. Parks, Z. Pu, Q.-G. Zong, J. Liu, Z. Yao, H. Fu,
and Q. Shi, J. Geophys. Res. Space Phys. 119, 5272–5278, doi:10.1002/
2014JA020045 (2014).18H. Y. Lu, J. B. Cao, Y. S. Ge, T. L. Zhang, R. Nakamura, and M. W.
Dunlop, Geophys. Res. Lett. 42, 10099–10105, doi:10.1002/
2015GL066556 (2015).19Q. Zong, T. A. Fritz, Z. Pu, S. Fu, D. N. Baker, H. Zhang, A. T. Lui, I.
Vogiatzis, K.-H. Glassmeier, A. Korth, P. W. Daly, and A. Balogh,
Geophys. Res. Lett. 31, L18803, doi:10.1029/2004GL020692 (2004).20J. Wang, J. B. Cao, H. S. Fu, W. L. Liu, and S. Lu, J. Geophys. Res. Space
Phys. 122, 185–193, doi:10.1002/2016JA023019 (2017).21V. A. Sergeev, V. Angelopoulos, J. T. Gosling, C. A. Cattell, and C. T.
Russell, J. Geophys. Res. 101, 10817–10826, doi:10.1029/96JA00460 (1996).22D. Schmid, R. Nakamura, M. Volwerk, F. Plaschke, Y. Narita, W.
Baumjohann, W. Magnes, D. Fischer, H. U. Eichelberger, R. B. Torbert
et al., Geophys. Res. Lett. 43, 6012–6019, doi:10.1002/2016GL069520
(2016).23J. Birn, R. Nakamura, E. V. Panov, and M. Hesse, J. Geophys. Res. 116,
A01210, doi:10.1029/2010JA016083 (2011).24A. Runov, V. Angelopoulos, and X.-Z. Zhou, J. Geophys. Res. 117,
A05230, doi:10.1029/2011JA017361 (2012).25M. I. Sitnov, V. G. Merkin, M. Swisdak, T. Motoba, N. Buzulukova, T. E.
Moore, B. H. Mauk, and S. Ohtani, J. Geophys. Res. 119, 7151–7168,
doi:10.1002/2014JA020205 (2014).26M. I. Sitnov and M. Swisdak, J. Geophys. Res. 116(A12), A12216,
doi:10.1029/2011JA016920 (2011).27H. S. Fu, Y. V. Khotyaintsev, A. Vaivads, A. Retin�o, and M. Andr�e, Nat.
Phys. 9, 426–430 (2013).28R. Nakamura, A. Retin�o, W. Baumjohann, M. Volwerk, N. Erkaev, B.
Klecker, E. A. Lucek, I. Dandouras, M. Andr�e, and Y. Khotyaintsev, Ann.
Geophys. 27, 1743–1754 (2009).29M. Zhou, M. Ashour-Abdalla, X. Deng, D. Schriver, M. El-Alaoui, and Y.
Pang, Geophys. Res. Lett. 36, L20107, doi:10.1029/2009GL040663 (2009).30P. L. Pritchett, F. V. Coroniti, and R. Pellat, Geophys. Res. Lett. 24,
873–876, doi:10.1029/97GL00672 (1997).31C. X. Chen and R. A. Wolf, J. Geophys. Res. 98, 21409–21419,
doi:10.1029/93JA02080 (1993).32P. N. Guzdar, A. B. Hassam, M. Swisdak, and M. I. Sitnov, Geophys. Res.
Lett. 37, L20102, doi:10.1029/2010GL045017 (2010).33P. L. Pritchett, F. V. Coroniti, and Y. Nishimura, J. Geophys. Res. Space
Phys. 119, 4723–4739, doi:10.1002/2014JA019890 (2014).34G. Lapenta and L. Bettarini, Geophys. Res. Lett. 38, L11102, doi:10.1029/
2011GL047742 (2011).35H. Y. Lu, J. B. Cao, M. Zhou, H. S. Fu, R. Nakamura, T. L. Zhang, Y. V.
Khotyaintsev, Y. D. Ma, and D. Tao, J. Geophys. Res. 118, 6019–6025,
doi:10.1002/jgra.50571 (2013).36A. Harten, J. Comput. Phys. 49, 357–393 (1983).37W. Baumjohann, G. Paschmann, and C. A. Cattell, J. Geophys. Res. 94,
6597–6606, doi:10.1029/JA094iA06p06597 (1989).38E. V. Panov, R. Nakamura, W. Baumjohann, V. Angelopoulos, A. A.
Petrukovich, A. Retin�o, M. Volwerk, T. Takada, K. H. Glassmeier, J. P.
McFadden, and D. Larson, Geophys. Res. Lett. 37, L08103, doi:10.1029/
2009GL041971 (2010).39P. L. Pritchett, J. Geophys. Res. Space Phys. 121, 214–226, doi:10.1002/
2015JA022053 (2016).40A. Runov, V. Angelopoulos, X.-Z. Zhou, X.-J. Zhang, S. Li, F. Plaschke,
and J. Bonnell, J. Geophys. Res. 116, A05216, doi:10.1029/
2010JA016316 (2011).41H. S. Fu, Y. V. Khotyaintsev, M. Andr�e, and A. Vaivads, Geophys. Res.
Lett. 38, L16104, doi:10.1029/2011GL048528 (2011).42H. S. Fu, Y. V. Khotyaintsev, A. Vaivads, M. Andr�e, V. A. Sergeev, S. Y.
Huang, E. A. Kronberg, and P. W. Daly, J. Geophys. Res. 117, A12221,
doi:10.1029/2012JA018141 (2012).43M. Zhou, S. Y. Huang, X. H. Deng, and Y. Pang, Chin. Phys. Lett. 28(10),
109402 (2011).44R. Nakamura, W. Baumjohann, E. Panov, A. A. Petrukovich, V.
Angelopoulos, M. Volwerk, W. Magnes, Y. Nishimura, A. Runov, C. T.
Russell, J. M. Weygand, O. Amm, H.-U. Auster, J. Bonnell, H. Frey, and
D. Larson, J. Geophys. Res. Space Phys. 118, 2055–2072, doi:10.1002/
jgra.50134 (2013).45S. Y. Huang, H. S. Fu, Z. G. Yuan, M. Zhou, S. Fu, X. H. Deng, W. J.
Sun, Y. Pang, D. D. Wang, H. M. Li, and X. D. J. Yu, Geophys. Res.
Space Phys. 120, 4496–4502, doi:10.1002/ 2015JA021083 (2015).
102903-6 Lu et al. Phys. Plasmas 24, 102903 (2017)
46H. S. Fu, A. Vaivads, Y. V. Khotyaintsev, M. Andr�e, J. B. Cao, V.
Olshevsky, J. P. Eastwood, and A. Retin�o, Geophys. Res. Lett. 44, 37–43,
doi:10.1002/2016GL071787 (2017).47V. Angelopoulos, A. Runov, X.-Z. Zhou, D. L. Turner, S. A. Kiehas, S.-S.
Li, and I. Shinohara, Science 341, 1478–1482 (2013).48Z. Yao, W. J. Sun, S. Y. Fu, Z. Y. Pu, J. Liu, V. Angelopoulos, X.-J.
Zhang, X. N. Chu, Q. Q. Shi, R. L. Guo, and Q.-G. Zong, J. Geophys.
Res. Space Phys. 118, 6980–6985, doi:10.1002/2013JA019290
(2015).49V. Sergeev, V. Angelopoulos, S. Apatenkov, J. Bonnell, R. Ergun, R.
Nakamura, J. McFadden, D. Larson, and A. Runov, Geophys. Res. Lett.
36, L21105, doi:10.1029/2009GL040658 (2009).
50D.-X. Pan, X.-Z. Zhou, Q.-Q. Shi, J. Liu, V. Angelopoulos, A. Runov,
Q.-G. Zong, and S.-Y. Fu, Geophys. Res. Lett. 42, 4256–4262,
doi:10.1002/2015GL064369 (2015).51X.-Z. Zhou, V. Angelopoulos, J. Liu, A. Runov, and S.-S. Li, J. Geophys.
Res. 119, 211–220, doi:10.1002/2013JA019394 (2014).52X.-J. Zhang, V. Angelopoulos, A. Runov, X.-Z. Zhou, J. Bonnell, J. P.
McFadden, D. Larson, and U. Auster, J. Geophys. Res. 116, A00I20,
doi:10.1029/2010JA016287 (2011).53M. V. Goldman, D. L. Newman, and G. Lapenta, Space Sci. Rev. 199(1),
651 (2016).54J. F. Drake, M. Swisdak, P. A. Cassak, and T. D. Phan, Geophys. Res.
Lett. 41, 3710–3716, doi:10.1002/2014GL060249 (2014).
102903-7 Lu et al. Phys. Plasmas 24, 102903 (2017)