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)lvhy@buaa.edu.cn

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)