Electron particle dynamics incollisionless magnetic reconnection
Seiji ZENITANI
Kyoto UniversityOutline• 1. Electron orbits in antiparallel reconnection• 2. Electron-physics signatures in asymmetric reconnection• 3. New measure of electron mixing

1. Antiparallel reconnection

Magnetic reconnection in near-Earth space

Burch+ 2016 Space Sci. Rev.

Magnetospheric Multiscale (MMS) mission
20152017 MMS observation in magnetotail>>> It is important to understandelectron physics with particle-incell (PIC) simulations.

2016

Burch+ 2016 ScienceElectron velocity distribution functions (VDFs)
in PIC simulation

Chen+ 2008 JGR• Many PIC studies on electron-physics signatures in symmetric MRX• Hoshino+ 2001, Pritchett 2006, Chen+ 2008, 2009, Ng+ 2011, 2012, Hesse+ 2011, Bessho+ 2014,
Shuster+ 2014, 2015, Cheng+ 2015

Electron VDFs vs electron orbits
VDFs

Orbits-By

B
Egedal orbit
ne-aligdlew
Fi
inflodDissipation
regionLocal
Speiser orbitzyGlobal Speiser
orbit+Byx-B• In addition to VDFs,
we have to understandelectron orbits, too.

Do we really
understandelectron orbits?

Orbit theories

19651980’sSpeiser 1965

Chen & Palmadesso 1986, Buchner & Zelenyi 1989

Ion orbits

1990’sNakamura+ 1998

2000’sDrake+ 2009

Do we really understand electron orbits?
IonsElectrons• Gyration• Opposite gyration• Large gyroradius• Small gyroradius• (Response to E field)
Previous expectation-By

B
Egedal orbit
igne
d-alleiw
F
inflodDissipation
regionLocal
Speiser orbitzyGlobal Speiser
orbit+Byx-B

Trajectory analysis in PIC simulations

MemoryPOka et al. 2010 ApJBessho et al. 2014 GRLICTrajectory analysis in PIC simulations

MemoryPP
Oka et al. 2010 ApJ

Bessho et al. 2014 GRLICTrajectory analysis in PIC simulations

MemoryPP
Oka et al. 2010 ApJ

Bessho et al. 2014 GRLPICTrajectory analysis in PIC simulations

MemoryPP
Oka et al. 2010 ApJ

Bessho et al. 2014 GRLPPICTrajectory analysis in PIC simulations

MemoryPP
Oka et al. 2010 ApJ

Bessho et al. 2014 GRLPPIPC

Trajectory analysis in PIC simulations

MemoryPP
Oka et al. 2010 ApJ

Bessho et al. 2014 GRLPPIPPCTrajectory analysis in PIC simulations
The number of self-consistent
trajectories is limited

MemoryPPOka et al. 2010 ApJ

Bessho et al. 2014 GRLPPIPPCOur simple solution
Hard drive
PI

CMemoryPIC

Our simple solution
Hard drive
IPP

MemoryCI

CPICOur simple solution
Hard drive
I

PI

PP

MemoryCCIC

PIC

Our simple solution
Hard drive
IPI

P

MemoryCCIPPPCICICOur simple solution
Hard drive
IPCIPPPCMemoryCIPIPCICICPIC simulation & full Lagrange analysis• 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 DES (dual-eyeballspectrometers; a.k.a.
naked eyes)Electron Speiser VDFs in PIC simulation
Vex : electron jets

“Global Speiser”
via X-line region“Local Speiser”
of reflection type

Z321

Z

0-1-2-3
3540

3540

4550

4550

0Vey-5

Y -10-15-20Vex

32.5123X

Electron regular orbits(b) VexZz

Trapped in a figure-8
shaped orbit (κ~0.2)

2.5
21.5
10.5

Z0-0.5-1-1.5-2

36

38

40

42

20-2-4X

44

46

48

Chen & Palmadesso 1986 JGRZenitani+ 2013 PoP

Noncrossing electrons
3Orbits
2.52Zz

(d)

(a)

6

1.5

4

120.5

Midplanevey 00-0.5

35

40

10

Traditional orbits -1(b)X45

50-2-4

Electrostatic field Ez-6-2y -3
Midplane

1-4-5-6-7-8

ε0.35
0.3

0.8

1230.635404550

z 0.4
0.2-2

Noncrossing electrons
3Orbits
2.52Zz

(d)

(a)

61.5

41-eEz0.5

Midplanevey 00-0.5354010

Traditional orbits -12(b)X

4550-2-4

Electrostatic field Ez

-6-2

y -3
Midplane

1-Ez-4-5-6-7-8

ε0.35
0.3

0.8

12
30.6Ez35404550

z 0.4
0.2-2

Noncrossing electrons
3Orbits
2.52Zz

(d)

(a)

61.5

41-eEz0.5

Midplanevey 00-0.5

3540

10

Traditional orbits -12(b)X45-250-4

Electrostatic field Ez

-6-2

y -3
Midplane-4

electron-5-6-7-8

ε0.35
0.31-Ez

ion

1230.80.6Ez
3540

4550z 0.40.2-2

Orbit theories

1965

1980’sSpeiser 1965

Chen & Palmadesso 1986, Buchner & Zelenyi 1989

2016

Zenitani & Nagai 2016

Noncrossing electrons: majority in number

MRXzzvz

vz

Observational signatures: ET diagram
PIC simulation(a) z=0.0• Speiser-accelerated electrons• Low-energy noncrossing
electrons are absent

log10ε• Midplane (super-Alfvénic e jet)x
Noncrossing electrons-Ez

keV

Ez

Geotail observationtime

2007-05-05 (Nagai+ 2013 JGR)State-of-art 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• Many new orbits are found• Noncrossing electrons are MAJORITY in number density• This will lead to the revision of theoretical models

2. Asymmetric reconnection

Asymmetric reconnection at the magnetopause
20152017 MMS observation in magnetotail>>> It is important to understandelectron physics with particle-incell (PIC) simulations.

2016

Burch+ 2016 ScienceElectron-physics signatures near the X line
(E + v e ⇥ B)y > 0(c) E’
Ey0 = [E + V e ⇥ B]y

1. Magnetosphere
1zX
3

2. Magnetosheath2x(E + v e ⇥ B)y < 0Same as in Pritchett 2008, Hesse+ 2013 PoP, 2014 GRL

Sphere-side: Crescent-shaped VDF
Electron velocity distribution function

MMS observation (Burch+ 2016 Science)(c) E’y

1See also
Hesse+ 2014 GRLBessho+ 2016 GRL
Shay+ 2016 GRLz
32x

Sheath-side: Nonadiabatic electrons(c) E’
Eyy0 = [E + V e ⇥ B]y1z
32x(E + v e ⇥ B)y < 0

Typical orbit through Region 2• Chaotic orbitz• No longer a gyration + ExB drift

xZenitani+ 2017 JGR

E + v e ⇥ B 6= 0

Sheath-side: Nonadiabatic electrons(c) E’Eyy0 = [E + V e ⇥ B]y• Curvature parameter1(Buchner & Zelenyi 1989 JGR)

z32x

(E + v e ⇥ B)y < 0⌘sRc⇢

Magneticcurvature radiusElectronLarmor radius(g) Box 2parameters- curv. parameter
Curvaturein Region 2

Weakly nonadiabatic (1<k<2.5)• ρ ~ Rc
• Chaotic motion• No longer a gyration + ExB driftE + v e ⇥ B 6= 0

Sheath-side: Nonadiabatic electrons(c) E’
Eyy0 = [E + V e ⇥ B]y• Curvature parameter

1(Buchner & Zelenyi 1989 JGR)

z32x(E + v e ⇥ B)y < 0⌘sRc⇢

Magnetic
curvature radiusElectronLarmor radius

Sharp magnetic
curvature in 3D

Electron jet in symmetric reconnection
Vex : electron jets

ZNonadiabatic (k << 1)• Speiser motion• No longer a gyration + ExB drift

E + v e ⇥ B 6= 0

• Non-idealness (Shay+ 2007 PRL,Karimabadi+ 2007 GRL)• ⇒ Electron-physics signatures
can be better organized byadiabaticity (Le+ 2013 PRL)

3. Electron mixing

Quantifying electron mixing (1/3)
Mf (t0 , t)

+ t

“Forward” mixing01

Quantifying electron mixing (2/3)

Quantifying electron mixing (3/3)+ tQuantifying electron mixing (3/3)

t1“Backward” mixing

Mb (t0 ,0t)

Finite-time mixing fraction (FTMF)
MR (t0 ,t) ⌘ M
Mff(t(t00,, t)t) ⇥ Mb (t0 , t)t0 : time of interestt : an electron-scale time interval
Mf (t0 ,t)

Mb (t0 ,t)

MR (t0 , t)Mixing measure
Zenitani+ 2017 JGR

MR (t0 , t)

vsEnergy dissipation

Asymmetric RX

Zenitani+ 2011 PRL

De ' j · (E + v e ⇥ B)

Asymmetric RX with a guide-field

BySummary• 1. Antiparallel reconnection– Many new electron orbits are found– Noncrossing electrons due to electrostatic field– Noncrossing electrons are majority in number density• 2. Asymmetric reconnection– Nonadiabatic electrons, due to steep curvature in 3D• ⇒ Electron orbits & signatures: more research needed• 3. Electron mixing– We have introduced finite-time mixing fraction (FTMF)– FTMF marks the energy-dissipation region• References– Zenitani & Nagai, Phys. Plasmas 23, 102102 (2016)– Zenitani, Hasegawa, & Nagai, J. Geophys. Res. 122, 7396 (2017)

Particle motion in a curved B-field
B

Curvature parameter
Curvature radius of B

=sRmin⇢max~ Larmor radius
Buchner & Zelenyi 1989 JGR

B

B

B??
Nonadiabatic
Meandering motion(I-adiabatic)

.1

Weaklynonadiabatic

1 .  . 2.5

Gyromotion(adiabatic)