Plasma and Fusion Research: Regular Articles

Volume 14, 3401137 (2019)

Horn-Shaped Structure Attached to the Ring-Shaped Ion Velocity
Distribution during Magnetic Reconnection with a Guide Field∗)
Shunsuke USAMI1,2) , Ritoku HORIUCHI1,3) and Hiroaki OHTANI1,3)
1)

National Institute for Fusion Science, National Institutes of Natural Sciences, Toki 509-5292, Japan
2)
University of Tokyo, Tokyo 113-8654, Japan
3)
Sokendai (The Graduate University of Advanced Studies), Toki 509-5292, Japan(Received 9 January 2019 / Accepted 25 June 2019)

The characteristic feature of a “horn-shaped velocity distribution” in magnetic reconnection in the presenceof a guide field is investigated by means of simulation and theory. Particle simulations show that a horn-shaped
velocity structure is formed in the downstream, concomitant with a ring-shaped velocity distribution studied in
the preceding works. The theory which explains the motion of ions responsible for the horn-shaped structure isconstructed as an extension of the basic theory for the ring-shaped structure. In the extended theory, ions areaccelerated in the inflow direction by an electrostatic field in the separatrix, and thus the gyration speed of suchions in the downstream is larger than that for the basic theory. Test particle simulations confirm that some ionsbehave as in the extended theory and form the horn-shaped velocity structure.
c 2019 The Japan Society of Plasma Science and Nuclear Fusion ResearchKeywords: particle simulation, magnetic reconnection, ion heating, PASMO, spherical tokamak
DOI: 10.1585/pfr.14.3401137

1. Introduction
Magnetic reconnection is one of the fundamental processes seen in various plasmas [1], in which magnetic energy is rapidly converted to kinetic and thermal energy ofplasma particles. Fusion plasmas are deeply associatedwith magnetic reconnection processes from both negativeand positive aspects. Sawtooth crash or oscillation, whichis thought to be related to reconnection, in a tokamak device is a negative aspect. When sawtooth crash or oscillation occurs, the stored energy in the core is released tothe periphery region [2]. Hence, the control of sawtoothcrash and oscillation is an important issue for fusion plasmas in tokamaks. On the other hand, magnetic reconnection has a positive aspect for merging plasmas in sphericaltokamaks, in which plasmas with quite high β are createdby plasma heating during magnetic reconnection and are
confined [3, 4]. The mechanism of the heating in sphericaltokamaks, however, remains unsolved.
We explore the heating mechanism during magnetic
reconnection by means of simulation and theory in thiswork. It is a quite useful and commonly used method to observe and analyze velocity distribution functions for magnetic reconnection studies as shown, for example, in Refs.
[5–11]. One can derive where plasma particles are accelerated or heated and what mechanism acts for the plasma
acceleration and heating by analyzing velocity distribution.
In preceding simulation works by Usami et al. [12, 13], on
author’s e-mail: usami.shunsuke@nifs.ac.jp∗) This article is based on the presentation at the 27th International Toki
Conference (ITC27) & the 13th Asia Pacific Plasma Theory Conference(APPTC2018).

the basis of analyzing ion velocity distribution, an eﬀective heating mechanism during magnetic reconnection in
the presence of a guide field was proposed. The essential
point of the mechanism is that ions behave as nonadiabaticupon crossing the separatrix, and ring-shaped ion velocity
distributions are formed in the downstream of reconnection.
In this paper, an additional anomalous structure,
which is observed in the velocity space and is attached toa ring-shaped velocity distribution, is discussed. The organization of this paper is as follows. In Sec. 2, we highlight particle simulation results and review the formation
process of a ring-shaped structure of an ion velocity distribution. In Sec. 3, an additional structure, called a “hornshaped structure,” found in particle simulations is shown.
We extend the theory for the ring-shaped distribution to
explain the formation process of the horn-shaped structure. In addition, we investigate the motion of ions forming
the horn-shaped structure by means of test particle simulations. Lastly, section 4 provides a summary of this work.

2. Review of the Ring-Shaped Structure in Velocity Distribution
2.1 Particle simulation method and result
In order to investigate the ion heating mechanism during magnetic reconnection in the presence of a guide magnetic field, we carry out two-dimensional particle simulations, since nongyrotropic motions of plasma electrons
and ions, which can not be computed by fluid models, playessential roles in magnetic reconnection, in particular, for3401137-1

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plasma heating during magnetic reconnection.
For particle simulations, we use the PASMO code
[14,15], in which an open boundary condition is employed.
Plasmas are pushed by a driving electric field Ed imposedon the upstream boundary. The driving field Ed supplies
particles satisfying a shifted Maxwellian velocity distribution so that plasmas flow into the simulation domainfrom the upstream boundary. The field Edz is set to zeroat the initial time, begins to grow first near the center ofthe upstream boundary, and eventually has a constant value
E0 in the entire upstream boundary, where Edz is the zcomponent of Ed . On the other hand, through the downstream boundary, plasma particles can enter and exit freely.
As the initial condition, we take a one-dimensional
Harris-type equilibrium with a uniform guide field as Horiuchi and Sato first applied [16]. That is, we set Bx (y) =Bx0 tanh(y/L) and Bz (y) = Bz0 for the magnetic field andP(y) = P0 + B2x0 /(8π)sech2 (y/L) for the plasma pressure,
where Bx0 , Bz0 , and P0 are constants and L is a spatial scale. The temperature is uniform, and the ion temperature is taken to be equal to the electron temperature:
T i0 /T e0 = 1.0.
The simulation parameters are denoted as follows.
The simulation domain size is 10.54(c/ω pi ) × 2.63(c/ω pi ),where c is the speed of light and ω pi is the ion plasma frequency. The initial numbers of electrons and of ions are
14,090,240, respectively. The ion-to-electron mass ratio istaken to be mi /me = 100. The ratio of the electron plasma
frequency to the electron gyrofrequency is ω pe /ωce = 6.0,
where ωce = eBx0 /(me c) is defined. Thus, the Alfvén speed
is expressed
as vA /c = 0.037 for the total magnetic field
B0 = B2x0 + B2z0 . The time step is ω pi Δt = 0.0052, andthe grid spacing is Δg /(c/ω pi ) = 0.010.
We demonstrate results of a simulation run under thefollowing parameter values: Bz0 /Bx0 = 2, L/(c/ω pi ) =0.66, P0 /(B2x0 /8π) = 0.35, and E0 /Bx0 = −0.04. This
simulation run is the same as a run which has been performed in Refs. [12, 13]. Figure 1 (a) shows the spatial
profile of the ion temperature perpendicular to the local
magnetic field as color contours and the magnetic fieldlines at ω pi t = 775. Magnetic reconnection is driven by
inflow plasmas supplied from the upstream boundary, andthe reconnection point (the X-point) is located at the center of the simulation domain (x, y)  (0, 0). An ambipolar reconnection outflow emanates from the X-point. We
can clearly see that the ion temperature rises mainly in thedownstream. Figures 2 (a) - (d) display ion velocity distributions at the local areas (A) - (D) represented in Fig. 1,
respectively. As Refs. [12] and [13] demonstrated, ringshaped velocity distributions are formed, which means thatthe velocity distributions are expanded and ions are eﬀectively heated in the downstream.

2.2

Basic theory
The formation process of the ring-shaped velocity dis-Fig. 1 (a) Spatial profiles of the ion temperature perpendicular
to the local magnetic field as the color contours and themagnetic field lines. (b) Spatial profile of the electric field
Ey . The local areas (A) - (D) indicated in the panels (a)and (b) are in the downstream, primarily where the ion
temperature is increased. In the lower-side separatrix for
x > 0 and in the upper-side separatrix for x < 0, a strong
Ey exists.

Fig. 2 Ion velocity distributions in the local areas (A) - (D) ofFig. 1. The regions surrounded by the dotted lines denotehorn-shaped structures. In all the panels (a) - (d), ringshaped and horn-shaped structures are shown.

tribution has been elucidated as the following basic theory [12]. A large percentage of ions move from the upstream across the separatrix into the downstream, and theseions are responsible for the formation of the ring-shaped
distribution. The separatrix width is quite thin for ions.
Hence, ions behave as nonadiabatic upon crossing the separatrix [7, 12, 13]. In the basic theory, when ions enter thedownstream across the separatrix, their entry speed is suf-

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Fig. 3 Ion velocity distributions (a) at an earlier phase for thesame run of simulations as in Fig. 2, and (b) for a different run of simulations under a diﬀerent value of thedriving electric field. The regions surrounded by the dotted lines denote horn-shaped structures. Horn-shaped andring-shaped structures are seen in both panels.

ficiently small so that we regard it as zero for the ideal
case. Here it is assumed for simplification that in the downstream, the reconnection outflow is in the x direction andits speed is uout , and the guide magnetic field in the z direction and the convective electric field in the y direction
are uniform. The other components of the electromagnetic field can be ignored because they are much smaller.
The ions move in the x direction owing to the E × B drift
while in gyromotion around the guide magnetic field in thedownstream. It is characteristic that the drift speed is equal
to uout , and the gyration speed is also equal to uout . The
ring-shaped velocity distribution consists of such ions. The
eﬀective temperature of the ions forming the ring-shaped
distribution is simply given as T i = 1/2 mi u2out .

3. Horn-Shaped Structure in Velocity
Distribution
3.1

Particle simulation result

In the velocity distribution of Fig. 2, we can observe
another characteristic structure surrounded by dotted lines,
in addition to the ring-shaped structure. We call this a“horn-shaped structure or distribution.” Such horn-shaped
structures are seen not only for this run of simulations, butalso for various runs of simulations. We further show ion
velocity distributions in Fig. 3. The panel (a) is an ion velocity distribution at an earlier phase (ω pi t = 258) for thesame run of the simulations as in Fig. 2, and the panel (b)is an ion velocity distribution for a diﬀerent run of simulations with a diﬀerent value of the driving electric field
E0 /Bx0 = −0.06. Horn-shaped structures can be seen inboth cases.

3.2

Extended theory

We extend the basic theory in order to explain the formation mechanism of a horn-shaped structure. If someions are accelerated in the y direction by an electrostatic
field Ey in the separatrix, they have a finite speed vy when
they enter the downstream [8, 17, 18]. Actually, Fig. 1 (b)shows that Ey is strong in the lower-side separatrix for
x > 0 and in the upper-side separatrix for x < 0. In someobservational studies in the geomagnetosphere, it has beenreported that ions are accelerated by an electric field in theseparatrix [19, 20].
Let the entry velocity of the ions be (0, vy0 ), where it
is noted that the value of vy0 can be diﬀerent for each ion.
For the electromagnetic field in the downstream, we employ the same assumption as the basic theory. In the downstream, the motion of the ions is the E × B drift while ingyromotion as described in the basic theory. The gyration
speed, however, is diﬀerent from the gyration speed
in thebasic theory. The gyration speed is given as u2out + v2y0 ,which is larger than uout . In the velocity space, the ions arelocated outside a circle whose radius is uout (a ring-shaped
structure). Under the above situation, let us observe a velocity distribution in a local area. Assuming that gyromotion phases of the ions are limited within a narrow range,
the velocity distribution formed by the ions is not a ringshape, but a horn-shape.
In the extended theory, it is essential that ions are not
suﬃciently accelerated in the x direction in the separatrix. If an ion is accelerated in the x and y directions inthe separatrix, it has a finite entry velocity (v x0 , vy0 ). Thegyration speed is expressed as (uout − v x0 )2 + v2y0 . The
large v x0 makes the gyration speed of the ion decrease.
Consequently, a horn-shaped structure would not be seen,
because a structure formed by such ions whose gyration
speed is smaller would overlap the ring-shaped distribution.

3.3 Test particle simulation
In order to show that a horn-shaped structure is formedby ions expressed by the extended theory, we perform test
particle simulations. The method for test particle simulations is as follows. Before test particle simulations, we
perform a particle simulation by using the PASMO codeand obtain the electromagnetic field data under a steadystate of magnetic reconnection. The equations of motion
for test ion particles are calculated in the given electromagnetic field.
We trace the motions of 60,000 test ion particles, anddemonstrate the positions of the ion particles at various
times (a) ω pi τ = 0, (b) 60, (c) 120, and (d) 240 in Fig. 4.
For distinguishing the time in the test particle simulationfrom the time in the particle simulations by the PASMO
code, we use τ as the time in the test particle simulation. The panel (a) shows that the initial positions of
the test ions are set on the upper-side upstream boundaryy/(c/ω pi ) = 1.31 and on the lower-side upstream boundaryy/(c/ω pi ) = −1.31. The x-coordinate of the initial positionis uniformly distributed within −4.0 < x/(c/ω pi ) < 4.0.
The number of the test ions which initially are set on eachside of the upstream boundary is 30,000. The black andblue points correspond to the test ions whose initial posi-

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Fig. 4 Positions of the ion particles calculated by a test particle
simulation at various times. The black and blue points
denote the ions coming from the upper-side and lowerside upstream boundaries, respectively.

tions are on the upper- and lower-side upstream boundary,respectively. Each test ion has an initial velocity equal tothe ion fluid velocity, which has been obtained by the particle simulation, at each local position. At ω pi τ = 60 (thepanel (b)), the ions from the upper-side upstream move inthe −y direction, and the ions from the lower-side upstream
move in the y direction. At ω pi τ = 120 (the panel (c)), theblack and blue points mix. Hence, we can find that theions coming from both sides converge and co-exist in thesame region. At ω pi τ = 240 (the panel (d)), which is thetermination time of the test particle simulation, a large partof ions already escaped from the simulation domain acrossthe downstream boundary.
We would like to explain that the formation of a hornshaped structure is responsible for ions coming from thelower-side upstream. We plot the orbit, velocity, and kinetic energy of a typical ion particle in Fig. 5. Here, wecall an ion particle described by the extended theory “EXion,” while we call an ion expressed within the basic theory“BS-ion.” The solid lines denote a typical EX-ion, and thedashed lines represent a BS-ion, which was introduced inRef. [13], for comparison.
Figure 5 (a) shows the orbits of the ion particles,
where the color contours indicate the electric field Ey . Let
us concentrate on the half region x > 0. We find that thelower-side separatrix is wider than the upper-side separatrix, and a large Ey exists in the lower-side separatrix. The
EX-ion is accelerated in the y direction across the lowerside separatrix. In the downstream, the EX-ion moves inthe x direction with oscillating owing to the E × B drift andthe gyromotion. The amplitude of the gyration is larger

Fig. 5 Motion of an ion particle calculated by a test particle simulation. The panels (a), (b), (c), (d), and (e) plot the orbit
in the (x, y) plane, the orbit in the (v x , vy ) plane, the time
evolution of v x , vy , and the kinetic energy, respectively.
The solid and dashed lines denote ions based on the basic
and extended theories, respectively. The color contours
in the panel (a) indicate the electric field Ey .

than that for the BS-ion.
Figure 5 (b) shows the ion orbits in the velocity space(v x , vy ). When the EX-ion enters the downstream at ω pi τ 
60, the EX-ion has a large vy . Hence, the velocity circle of
the EX-ion is larger than that of the BS-ion.
Further, we plot the time development of velocity
components v x and vy in Figs. 5 (c) and (d). At ω pi τ  60,
when the EX-ion enters the downstream, the EX-ion has asmall v x and a large vy , which is consistent with the extended theory. After that, v x is increased and vy is decreased because of the transformation from vy to v x owing to the gyromotion. In contrast, at ω pi τ  140, whenthe BS-ion is in the downstream (This is the re-entry. See
Ref. [13] for details.), v x and vy of the BS-ion are small,which is consistent with the basic theory.
Lastly, we plot the time evolution of the kinetic energy
in Fig. 5 (e). At ω pi τ  60 (the entry time of the EX-ion),
the EX-ion has large kinetic energy. In the downstream, the3401137-4

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EX-ion further gains kinetic energy from the convective
electric field, the main component of which is Ey . Compared with the BS-ion at the same time τ, the EX-ion has
much larger kinetic energy. We can explain the larger increase in the kinetic energy of the EX-ion as follows. In
both the basic and the extended theories, the electromagnetic field is assumed to be uniform. However, in particular Ey becomes larger in a deeper downstream (x is larger).
The EX-ion moves to the deeper downstream (stronger Ey
region) earlier than the BS-ion. Hence, at the same time τ,
the kinetic energy of the EX-ion is much larger than that of
the BS-ion.
We discuss not only the behavior of a single particle,
but also motions of many particles. In the following figures, we display not only the particles which are in a local
area at the instance ω pi τ = 240, but the particles whichwere and are in a local area by ω pi τ = 240. In other words,
we record the particle data every ω pi δτ = 3, and treat an
identical particle at a past time as a diﬀerent particle. Thus,
it is noted that some particles are displayed in the following figures multiple times. The reason is as follows. We set
all the ion particles on the upstream boundary at ω pi τ = 0.
We do not supply new particles after the initial time. Undera steady state of reconnection, however, particles should
continuously flow inward from the upstream with a constant flux. Instead of continuous supply of particles fromthe upstream, we accumulate the temporal sequence dataof the particles during ω pi τ = 0 - 240 in order to mimic
continuous inflow plasmas under a steady state.
In Fig. 6, we plot velocities (v x , vy ) of the particles inside the local area whose location is the same as the area(A) of Fig. 1. The panels (a) and (b) show the ions fromthe upper-side upstream and from the lower-side upstream,
respectively. A ring-shaped structure is clearly seen in
the panel (a) and a horn-shaped structure is found in thepanel (b). We can understand that the ions from the upperside upstream dominantly form the ring-shaped structure
and the ions from the lower-side upstream form the hornshaped structure. The panel (c), which is a superimposed
figure of the panels (a) and (b), reproduces the entire structure seen in Fig. 2 (a).
Here, it is noted that horn-shaped structure has a finite width in the direction of the ring center and hence
the horn is attached to the ring. The ion velocity distributions obtained in our particle simulations also indicatethat the horns are attached to the rings. A reason for theattachment of the rings and the horns can be explained asfollows. An electrostatic field in the separatrix is not uniform [11]. Ions from the lower-side upstream pass throughslightly diﬀerent positions in the lower-side separatrix andare accelerated to slightly diﬀerent entry velocities. Thus,
the horn-shaped structure has a finite width in the directionof the ring center and thus is attached to the ring-shaped
structure. Discussed in more detail, the acceleration in thex direction by E x , which decreases the gyration speed, i.e.,the velocity radius in the velocity space as described inFig. 6 Positions of the ions inside the local area (A) in Fig. 1 calculated by a test particle simulation. The panel (a) showsthat the ions from the upper-side upstream form the ringshaped structure, and the panel (b) displays that the ionsfrom the lower-side upstream form the horn-shaped structure. The panel (c) is a superimposed figure of the panels(a) and (b).

Sec. 3.2, plays a partial role in a finite width of the hornshaped structure. The same holds true for the basic theory. A finite width of the ring also contributes to the attachment between the ring and the horn. In the idealizedcase of the basic theory, the ion entry speed is regarded
as zero. However, the entry velocities of ions are small,but not completely zero. The ions have slightly diﬀerent
entry velocities, because a non-uniform electrostatic field,
which is weaker than in the lower-side separatrix, exists inthe upper-side separatrix. This makes the width of ringshaped structures be finite.
Let us discuss why the ions from the lower-side upstream do not form a ring-shaped structure, but construct ahorn-shaped structure in the local area (A). In other words,
we discuss how the gyromotion phases of the ions from thelower-side upstream are limited within a narrow range. In
Fig. 7, we depict the number of particles vs x0 , the initial

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Fig. 7 The number of ion particles vs the initial positions (a)for the ions from the upper-upstream and (b) for the ionsfrom the lower-upstream, inside the local area (A) of
Fig. 1.

x-positions of ions which are inside the local area, (a) forthe particles from the upper-side upstream and (b) for theparticles from the lower-side upstream. Among the total
number of ions, the ratio of the ions from the upper-side
upstream and from the lower-side upstream are approximately 80% and 20%. Ions whose initial positions arewithin a wide range of −0.013 < x0 /(c/ω pi ) < 2.17 (a standard deviation of 0.52) from the upper-side upstream canenter the local area (A), while ions whose initial positions
are within a narrow range of 0.190 < x0 /(c/ω pi ) < 1.79 (astandard deviation of 0.34) from the lower-side upstream
can enter the local area (A). This result would be one of
the important factors leading to bias of gyromotion phasesof the ions from the lower-side upstream inside the local
area. In other words, it would be inevitable that upon entering the downstream across the lower-side separatrix, almost ions obtain gyromotion phases which will occupy thedotted-line box in Fig. 2 (a) when they later arrive at theposition of the boxed area (A).

4. Summary
By means of particle and test particle simulations andtheory, we have studied a horn-shaped structure of ions in
the velocity space in magnetic reconnection with a guidemagnetic field. In particle simulations, the horn-shaped
structure has been found as an additional structure to aring-shaped velocity distribution. In our previous works,
we have constructed the basic theory explaining the formation process of the ring-shaped structure. In this work, wehave improved the basic theory to construct the extended
theory for the formation mechanism of the horn-shaped
structure. In the basic theory, ions enter the downstream
across the separatrix with zero velocity. In the extended
theory, ions are accelerated perpendicular to the outflow
direction (in the inflow direction) upon crossing the separatrix, and thus enter the downstream with a finite velocity
perpendicular to the outflow. The gyration speed of theions is larger than that for the basic theory. By means oftest particle simulations, it has been confirmed that the motion of ions coming from the lower-side upstream is basedon the extended theory, because a strong electrostatic field
exists in the lower-side separatrix (for the x > 0 region).
Furthermore, test particle simulations have demonstrated
that the ions responsible for the extended theory inside a
local area have gyromotion phases limited within a narrow range, and consequently the horn-shaped structure isformed in the velocity space.
In this work, we have focused on the formation process of anomalous velocity distributions in the downstream
region close to the X-point (within ∼ 5c/ω pi ). A largerscale simulation, for instance, Ref. [21] indicates that theion acceleration mechanism is changed in the far downstream region. In such a far downstream, ion velocity distributions will be changed from the ring-shaped and hornshaped structures.

Acknowledgments
This simulation work was performed on “Plasma
Simulator” (FUJITSU FX100) at the National Institutefor Fusion Science.
This work was partially supported by a Grant-in-Aid for Scientific Research fromthe Japan Society for the Promotion of Science (KAKENHI 16K17847), the Research Cooperation Program on“Hierarchy and Holism in Natural Sciences” and “Magnetic Reconnection Studies with Kinetic Simulations” at
the National Institutes of Natural Sciences, the General Coordinated Research at the National Institute for
Fusion Science (NIFS17KNWS003, NIFS18KNTS055,
NIFS17KNSS100), and “Joint Usage/Research Center
for Interdisciplinary Large-scale Information Infrastructures” and “High Performance Computing Infrastructure”
in Japan.
[1] M. Yamada, R. Kulsrud and H. Ji, Rev. Mod. Phys. 82, 603(2010).
[2] H.K. Park, N.C. Lühmann Jr., J.H. Donn, I.G.J. Glassen,
C.W. Domie, E. Mazzucato, T. Munsat, N.J. van de Pol,Z. Xia and TEXTOR team, Phys. Rev. Lett. 96, 195003(2006).
[3] Y. Ono, Y. Hayashi, T. Ii, H. Tanabe, S. Ito, A. Kuwahata,
T. Ito, Y. Kamino, T. Yamada, M. Inomoto and TS-Group,
Phys. Plasmas 18, 112113 (2011).
[4] Y. Ono, H. Tanabe, T. Yamada, M. Inomoto, T. Ii, S.
Inoue, K. Gi, T. Watanabe, M. Gryaznevich, R. Scannell,
C. Michael and C.Z. Cheng, Plasma Phys. Control. Fusion
54, 124039 (2012).
[5] M. Hoshino, T. Mukai, T. Yamamoto and S. Kokubun, J.
Geophys. Res. 103, 4509 (1998).
[6] M. Hesse, M. Kuznetsova and J. Birn, Phys. Plasmas 11,5387 (2004).
[7] J.F. Drake, P.A. Cassak, M.A. Shay, M. Swisdak and E.
Quataert, Astrophys. J. 700, L16 (2009).
[8] C.Z. Cheng, S. Inoue, Y. Ono and R. Horiuchi, Phys. Plasmas 22, 101205 (2015).
[9] S. Zenitani, H. Hasegawa and T. Nagai, J. Geophys. Res.
Space Physics 122, 7396 (2017).
[10] F. Pucci, S. Usami, H. Ji, X. Guo, R. Horiuchi, S. Okamura,
W. Fox, J. Jara-Almonte, M. Yamada and J. Yoo, Phys.

3401137-6

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Volume 14, 3401137 (2019)

Plasmas 25, 122111 (2018).
[11] M. Hesse, C. Norgren, P. Tenfjord, J.L. Burch, Y.-H,
Liu, L.-J. Chen, N. Bessho, S. Wang, R. Nakamura, J.P.
Eastwood, M. Hoshino, R.B. Torbert and R.E. Ergun, Phys.
Plasmas 25, 122902 (2018).
[12] S. Usami, R. Horiuchi and H. Ohtani, Phys. Plasmas 24,
092101 (2017).
[13] S. Usami, R. Horiuchi, H. Ohtani, Y. Ono and H. Tanabe,
Plasma Fusion Res. 13, 3401025 (2018).
[14] W. Pei, R. Horiuchi and T. Sato, Phys. Rev. Lett. 87,
235003 (2001).
[15] H. Ohtani and R. Horiuchi, Plasma Fusion Res. 4, 024(2009).
[16] R. Horiuchi and T. Sato, Phys. Plasmas 4, 277 (1997).

[17] N. Aunai, G. Belmont and R. Smets, J. Geophys. Res. 116,
A09232 (2011).
[18] R. Horiuchi, S. Usami and H. Ohtani, Plasma Fusion Res.
9, 1401092 (2014).
[19] J.R. Wygant, C.A. Cattell, R. Lysak, Y. Song, J. Dombeck,
J. McFadden, F.S. Mozer, C.W. Carlson, G. Parks, E.A.
Lucek, A. Balogh, M. Andre, H. Reme, M. Hesse and C.
Mouikis, J. Geophys. Res. 110, A09206 (2005).
[20] L.-J. Chen, N. Bessho, B. Lefebvre, H. Vaith, A.
Fazakerley, A. Bhattacharjee, P.A. Puhl-Quinn, A. Runov,
Y. Khotyaintsev, A. Vaivads, E. Georgescu and R. Torbert,
J. Geophys. Res. 6, A12213 (2008).
[21] K. Fujimoto, Front. Phys. 6, 119 (2018).

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