Particle dynamics and nongyrotropic
velocity distribution functions
in magnetic reconnection

Seiji ZENITANI
Kobe University
Acknowledgement: T. Nagai, I. Shinohara (JAXA/ISAS)
T. Wada (NAOJ)

Magnetic reconnection in near-Earth space

Burch+ 2016 Space Sci. Rev.

Velocity distribution functions (VDFs)
In order to understand comlicated VDFs,
we need to understand particle motion.

Magnetopause

Magnetotail
Torbert+ 2018 Science

Burch+ 2016 ScienceToday's agenda
1. Particle motion in a reconnected geometry
2. Ion motion and VDF in the outflow exhaust
3. Electron motion around the reconnection site

1. Particle motion in a reconnected geometry
2. Ion motion and VDF in the outflow exhaust
3. Electron motion around the reconnection site

Notes• I employ the GSM-like coordinates• Signs are sometimes opposite, because
figures/equations are taken from my ion/electron papers

YB• Simulation coordinates

XZ
ZX

YB

• GSM/GSE-like coordinates• MagnetotailN• LMN coordinates

ML• Magnetopause, foreshockMeandering motion• Partial gyration about +B0• Partial gyration about -B0
Front view

Side viewBB

BZZYXXEYMeandering ions

• Meandering ions are confirmed in Geotail
observations of magnetotail reconnection
Nagai+ 2015 JGR

Speiser motion• Meandering motion + slow gyration about Bn
ZB0YBnEX

Speiser 1965 JGR

Speiser motion in a moving frame• Consider a moving frame, in which E is transformed away
• In the velocity space, particle goes through a half ring
during the meandering phase.

Speiser 1965 JGRParticle motion in a parabolic field• Model field
Buchner & Zelenyi
1989 JGR• Equation of motion• can be simplified into:

where
Turning frequency by Bz (Bn)
Meandering frequency

Curvature parameter• Ratio of the two frequencies• Ratio of the magnetic curvature radius to the maximum Larmor radius

Buchner & Zelenyi 1989 JGR

B

B

B??
Another adiabaticregime (Meanderingdominated)

Nonadiabatic/Chaotic regime
Two oscillations interferewith each other

Adiabatic regime(Bn-gyration)

Poincaré map• One way to categorize
particle orbits

Chen & Palmadesso 1986

Buchner & Zelenyi 1989

by T. Wada (NAOJ)

Confined on ahyper-surface

https://sci.nao.ac.jp/MEMBER/zenitani/files/regular_orbits.mp4

by T. Wada (NAOJ)

Speiser motion in Poincaré map• Empty regions correspondto Speiser motion• The particle goes far away

Chen & Palmadesso 1986

1. Particle motion in a reconnected geometry
2. Ion motion and VDF in the outflow exhaust
3. Electron motion around the reconnection site

2-D PIC simulation• 2.5D• mi/me=100• 76.8 x 38.4 [di]Z• Harris sheet• nbg/ncs = 0.2• 2 x 109 particles

XVzVyVy

VxIon velocitydistribution function

Vx

Ion velocity distribution function (VDF)

Vy

ZX

Vx

Z

Vy
X

Vx

Ion velocity distribution function (VDF)

Vy

ZX

Vx

Z

Vy
X

Vx

Ion velocity distribution function (VDF)

Vy

ZX

Vx

Z

Vy
X

Vx

Poincaré map vs 2-D VDF
Mapping of two parameters from 5 (x, y, Vx, Vy, Vz)
Similar systems — two degrees of freedom

By
Z

Vy
X

Vx

Poincaré map vs 2-D VDF
Mapping of two parameters from 5 (x, y, Vx, Vy, Vz)
Similar systems — two degrees of freedomByZ8VyXVx

8-shaped orbit

ZX-lineSpeiser orbit (known)
Speiser orbit (known)
Speiser orbit (known)

YX

Ion orbits in PIC simulation

8-shaped orbit in a rotated,moving (outflow) frame
We have discovered figure-8-shaped ion orbits in reconnection

Signatures of 8-shaped-orbit ions
• Occasionally found in the near-exhaust(a) Ion velocity distribution

viyZenitani+ 2013 PoP

vixvx
Arzner & Scholer 2001 JGRSignatures of Speiser motion• A half ring corresponds toSpeiser motion in the outflow frame

Hybrid simulation

ZDrake+ 2009 JGR

PIC simulations(a) Ion velocity distribution

THEMIS dataviyVyvix

Zenitani+ 2013 PoPVx

Fujimoto+ 2016 PoP
Hietala+ 2015 GRL

Lottermoser+ 1998 JGR

1. Particle motion in a reconnected geometry
2. Ion motion and VDF in the outflow exhaust
3. Electron motion around the reconnection siteElectron orbits in PIC simulation• 2.5D• mi/me=100• 76.8 x 38.4 [di]• Harris sheet• nbg/ncs = 0.2• 2 x 109 particles
X• 20,000,000 electron orbits
from 1250 snapshot data
• 3,000 orbits are inspectedwith human eyesElectron Speiser orbits
Speiser orbit
via X-line region
Another Speiser orbitof reflection type

Z

Front view
321Z

0-1-2-3
35

40

35

40

45

50

45

50

0-5

Y -10-15Speiser 1965 JGR-20
32.5
2

123X

Top view

Electron 8-shaped orbit(b) VexZz

Trapped in an 8-shapedorbit (κ~0.2)

2.5
21.5
10.5

Z

0-0.5-1-1.5-236

38

40

4244

4648

20-2-4-6X

Chen & Palmadesso 1986 JGRSurprise: Noncrossing electrons
3Orbits
2.52Zz

(d)

(a)

6

1.5

4

120.5

Midplanevey 00-0.5354010(b)Traditional Speiser-1orbits

X4550-2-4

Electrostatic field Ez

-6-2

y -3
Midplane

1-4-5-6-7-8

ε0.35
0.3
0.25

0.8

12
30.6

35

40

4550z 0.4
0.2(c)

0-20

Surprise: Noncrossing electrons
3Orbits
2.52Zz

(d)

(a)

6

1.5

4

1-eEz

0.5

Midplanevey 00-0.5

3540

102(b)

Traditional Speiser-1orbits

X45-250-4

Electrostatic field Ez-6-2y -3
Midplane-4electron-5-6-7-8

ε0.35
0.3
0.25

1-Ez

ion1230.8
0.6Ez
35404550z 0.40.2(c)0-20Orbit theories

1965

1980’sSpeiser 1965

Chen & Palmadesso 1986, Buchner & Zelenyi 1989

2016

A related theory
came out recently:
Tsai+ 2017

Zenitani & Nagai 2016

Previous picture of electron orbits-By

B
Egedal orbit
ned
aligdlFie flowinDissipation
regionLocal
Speiser orbitzy

Global Speiser
orbit+Byx-B

New picture of electron orbits
B-By
Super-Alfvénic
electron jet

Field-aliinflo gnedwyNongyrotropic
electrons

Dissipation
regionLocal
Speiser orbit

Noncrossing
regular orbit

GlobalSpeiser orbit+Byx

Noncrossing local
Speiser orbit

Egedal orbit

Crossing
regular orbitzNoncrossing global
Speiser orbit-B

Field-aligned
electron outflow

Zenitani & Nagai 2016 PoP

Noncrossing electrons in VDF(c)vezvexSpatial distribution of VDFs

https://sci.nao.ac.jp/MEMBER/zenitani/images/map_color100i.png

Spatial distribution of Noncrossing electrons

Reconnection site

• Noncrossing electrons occupy a large area(surrounding the electron jets inside the ion diffusion region)• They are majority in number

Noncrossing electrons: Majority in number

Reconnectionzzvz

vzSummary•1. Particle motion in a reconnected geometry– Meandering orbit– Speiser orbit– Figure-8-shaped orbit•2. Ion motion and VDF in the outflow exhaust– Ion 8-shaped orbits•3. Electron motion around the reconnection site
– Electron 8-shaped orbits– Noncrossing electrons -- They are majority•References:– [1] Zenitani, Shinohara, Nagai, & Wada, Phys. Plasmas 20, 092120 (2013)– [2] Zenitani & Nagai, Phys. Plasmas 23, 102102 (2016)– [3] Zenitani, J. Plasma Fusion Res., 97, 47 (2021) [Tutorial article in Japanese]
http://www.jspf.or.jp/Journal/PDF_JSPF/jspf2021_02/jspf2021_02-47.pdf

More research needed!
•1. Orbit theory– Influence of Ez•2. Ion 8-shaped orbit– Spatial distribution and the reason– Signatures of the Ion Diffusion Region (IDR)?

•3. Noncrossing electrons– Signatures in VDFs
– Influence to electron mixing– Two-fluid theory needs to be updated to three-fluid theory?

•Transition to the guide-field cases•Influence of the 3-D structure•...

Thank you for your attention

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