Magnetic diffusion andion nonlinear dynamics
in magnetic reconnection

Seiji ZENITANI
National Astronomical Observatory of Japan

In collaboration with I. Shinohara, T. Nagai, T. Wada, and T. Umeda

Outline• 1. Introduction• 2. Dissipation region & diffusion regions– Updates on the dissipation measure De– My view on the magnetic diffusion• 3. Ion distribution function– Compositions of the distribution function– Nonlinear dynamics• 4. Summary

Structure of reconnection site (1/2)“Ion Diffusion Region”“Ion Dissipation Region”

Drake & Shay 2007

• The ideal condition should beviolated near the RX site

“Electron Diffusion Region”“Electron Dissipation Region”• We ambiguously call the nonideal site
“diffusion region” or “dissipation region” (DR)• In early 2000‘s, we expected two-scale DRs

Structure of reconnection site (2/2)(e) [E+Vi x B]yZz

xX

Shay+ 2007

SZ+ 2013• In late 2000’s, we became aware that non-idealness is
not a good marker.
• How to define DRs?
– Many quantities are proposed (E//, agyrotropy, etc...)– DR should involve diffusion or dissipation.
We need to understand these notions.
– If you overpush a non-diffusive region as a “diffusion region,”
you will violate the mispresentation act.（不当表示防止法）

Our proposal (1) - dissipation region(E+vi xB)yDe• Energy transfer in the electron frame (SZ+ 2011)• Non-ideal energy transfer in MHD (Birn & Hesse 2005).
This is an irreversible energy dissipation.

• Not clear whether De is irreversible in a kinetic plasma.

Relevance to entropy• MHD entropy evolution (Rossi & Olbert 1970)

LHS ( t=0)

Dmhd

• At the X-line (stagnation point)・qobsMagnetic diffusion

Frozen-in condition(Flux preservation)

Additional compression
or expansion

SZ & Umeda 2014

Magnetic tilt
Line disconnection

Newcomb 1958
Stern 1966

Newcomb 1958

Our proposal (2) - diffusion regions
Electron Diffusion
Regionb・

Ion Diffusion Region

2D PIC simulations

Ion velocity distribution function(E+vi xB)yZX• Non-idealViVyxx
VExB• Almost frozen-inBz
Vx

Ion velocity distribution function• (1) global Speiser ions
• (2) local Speiser ions
• (3) trapped ions

Vz

Vy

Vy

Bz

Vx
Vx(Local-type) Speiser orbit

Z

Bz

Vz

Bz
Lyons & Speiser 1985
Speiser 1965

Vy

Vx
Lottermoser et al. 1998
Nakamura et al. 1998

Ion distribution function• (1) global Speiser ions
• (2) local Speiser ions
• (3) trapped ions

Vz

Vy

Vy

Bz

Vx
Vx

Trapped ions

Local reflection

Trapped ionsZ

X-lineYX

Particle-orbit theory
Nonlinear system

Curvature radius of B

~ Larmor radius
Büchner & Zelenyi 1986, 1989

BB

B??
Bounce motion(I-adiabatic)

Chaotic motion

Gyro motion(μ-adiabatic)

Particle-orbit theoryChen & Palmadesso 1986

BB

B??
Bounce motion(I-adiabatic)

Chaotic motion

Gyro motion(μ-adiabatic)

Ion distribution function
By
Vy

ZX

Vx

By
Z

Vy
XVx

Ion distribution function
By
Vy

ZX

Vx

By
Z

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

Vx

Distribution function ⇔ Poincaré map.
. .
• (x, x) ⇔ (-y, x)

Regular orbits

Speiser orbits(Transient orbits)

Chen & Palmadesso 1986

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

Trapped ions - 3D orbit

8-shaped regular orbit
in an appropriately rotated, moving frame• Thin current sheet (TCS) models (Zelenyi+ 2002)• The first self-consistent one

Nongyrotropic regime!!
ViVyxxVExB• Since particles no longer gyrate,
we do not expect the idealness
in theregime.

Vx

B

Bounce motion(I-adiabatic)

B

B

Gyro motion(μ-adiabatic)

Distribution function

Electron Diffusion Region
Dissipation Region

Nongyrotropic layersIon Diffusion Region
Magnetic dissipation(Zenitani+ 2011 PRL)

Magnetic diffusion

Poincaré map(Zenitani & Umeda 2014 PoP)

Nongyrotropic motion(Zenitani+ 2013 PoP)

• We have reorganized the kinetic
structure of the reconnection site

Successful byproductregular orbit

NONLINEAR PARTICLE DYNAMICS

SummaryChaos in reconnection

Reconnection in chaos
Magnetic reconnection isa fascinating multi-scale process!