The structure of the diffusion regionin collisionless reconnection:
Theory, simulation, and observation

Seiji ZENITANI
National Astronomical Observatory of Japan
Collaborators: M. Hesse, A. Klimas,
M. Kuznetsova, C. Black (NASA/GSFC), I. Shinohara (JAXA/ISAS),T. Nagai (Titech), T. Wada (NAOJ), T. Umeda (Nagoya U)

Outline• 0. Introduction• 1. Dissipation region– Magnetic energy dissipation• 2. Diffusion regions– Magnetic diffusion• 3. Ion nongyrotropic layer– Chaotic particle dynamics• 4. Geotail observation• 5. SummaryMagnetic reconnectionSun• The ideal MHD condition is violatedaround the so-called diffusion region.
• We expect a similar picture in acollisionless kinetic plasma.

Earth’s MagnetosphereJetJet

Kinetic structure of the reconnection site•“Diffusion” or “dissipation” regions are undefinedionelectron“Electron Diffusion Region”“Electron Dissipation Region”(E+ve xB)y?

ZX“Ion Diffusion Region”“Ion Dissipation Region”(E+vi xB)y?
X

2D PIC simulations

Traditional picture
Electron Diffusion Region?
Electron Dissipation Region?

Ion Diffusion Region?
Ion Dissipation Region?

New picture
Electron Diffusion Region

Dissipation Region

Ion Diffusion Region

Magnetic dissipation

Nonidealnessrelax

Magnetic diffusion

1. Dissipation region
The dissipation region should be a place,where magnetic dissipation takes place.

What is Dissipation?

What is Dissipation?
• Irreversible process• Something that never comesback

Magnetic [energy] dissipation
Total energy transfer

irreversible in MHD

Work by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

Magnetic [energy] dissipation
Total energy transfer

Neutral two-fluid plasma
Electric current inthe observer frame

Electric field in the electron frame

irreversible in MHD

Work by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

Electron-frame dissipation measure
Total energy
transfer
Frame-independent
formulaLorentz factor
Electric current in theelectron frame

Electric field in theelectron frame

Charge density

Zenitani+ 2011 PRL
irreversible in MHD

Work by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

Dissipation region

AntiparallelZ

Guide-field

Symmetric Rx

Z

Asymmetric Rx

Dissipation Region

XXDissipation region: always in electron-scale• De: j . E in the electron’s frame• Di: j . E in the ion’s frame• Dmhd : j . E in the MHD frameDeDi

2. Diffusion regions
The diffusion region should be a place,where magnetic diffusion takes place.

Magnetic diffusion• Arbitrary Ohm’s law

Frozen-in condition(Flux preservation)

Magnetic diffusion

Bv• Relaxation to the frozen-in state

Newcomb 1958

Stern 1966, Vasyliunus 1972,
Scudder 1997, Hornig 2001

Relative concepts that depend
on a reference velocity field v

Effective magnetic diffusivity

Zenitani & Umeda 2014

Electron diffusion region

Ion diffusion region
2D PIC simulationsElectron diffusion region• Vlasov simulation by T. Umeda• Electron diffusion region is similar to the dissipation region
Diffusive loss of mag. flux: b・(∇x Re)

Nonideal part of Poynting flux

De: Nonideal energy conversion

Zenitani & Umeda 2014

3. Ion nongyrotropic layer

Ion velocity distribution function(E+vi xB)yZ
Ion diffusion region
X• Non-ideal, but outside
the ion diffusion region

Vy• Non-MaxwellianBz
Vx

Ion distribution function
By
Vy

ZX

Vx

By
Z

Vy
X

Vx

Ion distribution function
By
Vy

ZX

Vx

By
ZVy
X
• Two of 5 variables (x, y, Vx, Vy, Vz) at z=0

Vx

Nonlinear dynamics in 1980’s• The night before
kinetic PIC simulations• Poincarémap:.
(x, x) at z=0

Empty islands

Sea of chaos
Great onion

One can visuallyclassify particle orbits.
Büchner & Zelenyi 1989 JGRChen & Palmadesso 1986 JGRDistribution function ⇔ Poincaré map.
. .
• (x, x) ⇔ (-y, x)

Regular orbits

Speiser orbits(Transient orbits)

Chen & Palmadesso 1986 JGRConfined on a
hyper-surface

by T. Wada @ NAOJ

http://th.nao.ac.jp/MEMBER/zenitani/research-e.html
http://th.nao.ac.jp/MEMBER/zenitani/files/regular_orbits.mp4

Particle orbits

Phase diagram @x=51

3 orbitRegularZ 2
Main
population

10

Vy’
3.5

3

3

2.5

Z 2
Figure-8 orbit in an
appropriately-rotated,moving frame2

Orbit theory

1.5

1

10.5

00-2-10Vy’

12(Local-type) Speiser orbit

ZBz

VzBzLyons & Speiser 1985 JGRSpeiser 1965 JGR

VyVx
Lottermoser et al. 1998 JGRNakamura et al. 1998 JGRIdeal condition & flow speed

ViVyxxVExB

BzVx• Speiser motion explains
the violation of the idealcondition (Speiser 1970 PS&S)• Average ion speed (Vi) is
substantially slower than theupstream Alfvén speed CA,in(e.g., Karimabadi+ 2007 GRL,
Wu & Shay 2011 PoP)

4. Observation

2003-05-15 event [Nagai+ 2011]
Energy Dissipation

Dissipation [pWm-3]

Plasma velocity [km/s]

6040203000De*V⊥x (ion)V⊥x (electron)

2000
1000

00-20-1000-40-2000

-60
1053

1054

1055
1056
1057
Time [UT] - 15 May 2003

+vix+vex
Zenitani+ 2012 GRL

1058

Dissipation Region-3000-vix-vex

Summary• Magnetic dissipation & dissipation region– Nonideal energy transfer, usually irreversible• Magnetic diffusion & diffusion regions– Relaxation to the frozen-in staterelax– EDR and dissipation regions are similar• Ion nonideal layer– Poincaré map ⇔ Velocity distribution function– Chaotic particle motion• Geotail observation– First direct detection of the dissipation region• Better understanding of the kinetic reconnection
structure, based on MHD&orbit theories, simulations,and observations

Visual Summary
Electron Diffusion Region
60-3
pWm

40

Dissipation Region

De*W

20
0-20
-40
1053

1054

1055

1056

1057

1058

Observational support

Nongyrotropic layers

Ion Diffusion Region
Magnetic dissipation
relax

Magnetic diffusion
Nongyrotropic motion• Better understanding of the kinetic reconnection structure,from MHD&orbit theories, simulations, and observations

Thank you for your attention!

Zenitani, Hesse, Klimas, & Kuznetsova, Phys. Rev. Lett., 106, 195003 (2011)
Zenitani, Shinohara, & Nagai, Geophys. Res. Lett., 39, L11102 (2012)
Zenitani, Shinohara, Nagai, & Wada, Phys. Plasmas, 20, 092120 (2013)
Zenitani & Umeda, Phys. Plasmas, 21, 034503 (2014)