Magnetic diffusion andion nonlinear dynamics inmagnetic reconnection

Seiji ZENITANI
National Astronomical
Observatory of Japan

In collaboration with I. Shinohara (JAXA/ISAS),T. Nagai (Titech), T. Wada (NAOJ)

Outline•1. Introduction– Kinetic structure of the reconnection site

•2. Magnetic diffusion– Magnetic diffusion in a kinetic plasma•3. Ion velocity distribution function– Composition of the VDF– Chaotic particle motion•4. Discussion & Summary– Outflow speed problem– Up-to-date picture of reconnection site

1. Introduction

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 reconnection siteionelectron“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Electron-scale structure(A) Quadrupole
magnetic field

(B)

-ByH

rreucallnt(F) Pedestal+By(D) Dissipation regionzy(C) Electron current layerx

Zenitani et al. 2011 PoP(E) Super-Alfvénic electron jetElectron-scale
structure
Ion-scalestructure(E+vi xB)yZ(A) Quadrupole
magnetic field

(B)

-By

Hal

nturrelc(F) Pedestal+By(D) Dissipation regionzy(C) Electron current layerx

Zenitani et al. 2011 PoPX(E) Super-Alfvénic electron jet

HybridLottermoser et al. 1998 JGRArzner & Scholer 2001 JGRHigashimori & Hoshino 2012 JGRKinetic
Drake et al. 2009 JGR
Liu et al. 2011--2012 PoPElectron-scale
structure
Ion-scalestructure(E+vi xB)yZ(A) Quadrupole
magnetic field(B)-ByHalnturrelc(F) Pedestal+By(D) Dissipation regionzy(C) Electron current layerxX(E) Super-Alfvénic electron jetHybridLottermoser et al. 1998 JGRArzner & Scholer 2001 JGRHigashimori & Hoshino 2012 JGRKinetic
Drake et al. 2009 JGR
Liu et al. 2011--2012 PoP•Q1. Is this a “(ion) diffusion region”?
•Q2. Why is the ion ideal condition violated?
•Q3. Why is the ion flow sub-Alfvénic?

Zenitani et al. 2011 PoP

2. Magnetic diffusionDiffusion• Something spreads out• Can be combined with convection• Relaxation to a reference stateMagnetic diffusion• Ohm’s law, with respect toa reference velocity field v

Frozen-in condition(Flux preservation)

Magnetic diffusion• Violation of the frozen-in (in a diffusion-like manner

B• Relaxation to a reference statev

Newcomb 1958 Ann. Phys
Stern 1966 SSR

Ideal condition)

Magnetic diffusion• Ohm’s law, with respect toa reference velocity field v

Frozen-in condition(Flux preservation)

B

Magnetic diffusion• Violation of the frozen-in (in a diffusion-like manner• Relaxation to a reference statev

Newcomb 1958 Ann. Phys
Stern 1966 SSR

Ideal condition)

Effective diffusion coefficient

Preliminary

Nonideal(E+vi xB)yZXElectron diffusion region
based on its original meaning

Ideal &Frozen-in

Ion diffusion region
based on its original meaning

Frozen-in
2D PIC simulations

3. Ion velocity distributionfunction

Ion velocity distribution function(E+vi xB)y• 2D PIC simulation• mi/me=100Z• 76.8 x 38.4 [di]• 109 particles

X• Non-Maxwellian• Non-gyrotropicViVy• Non-idealxx
VExB

Bz
Vx

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

Vz

VyVy

Bz

Vx
Vx

(Local-type) Speiser orbit

Zx
VExB
Bz

Vz

Bz
Lyons & Speiser 1985 JGRSpeiser 1965 JGR

Vy

Vx
Lottermoser et al. 1998 JGRNakamura et al. 1998 JGRArzner & Scholer 2001 JGRHall effect• Magnetic field lines are draggedout of the page (Sonnerup 1979,Mandt et al. 1994)(c) T. Wada

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

Vz

Vy

Vy

Bz

Vx
Vx

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

Empty islands
Sea of chaos
Mystery onion

One can visuallyclassify particle orbits.
Chen & Palmadesso 1986 JGRIon velocity distribution function
By
Vy

ZX

Vx

By
Z

Vy
X

Vx

Ion velocity distribution function
By
Vy

ZX

Vx

By
Z

Vy
XVx

Ion velocity distribution function
By
Vy

ZXVx

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

with a factor of 1/vz

Vx

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

Chen & 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

Vy’Simulation vs Theory

3PIC simulation

Z 2ZZ

10X

Vy’
Chaos model

3.5

332.5

Z 2

2

1.5

1

10.500-2

Regular motion in a moving, rotated frame
-1

0

Vy’

12

Vy’

Simulation vs Theory

3PIC simulation

Z 2ZZ

10

X

Vy’
Chaos model

3.5

3

3

2.5

Z 2

2

1.5

1

1

0.5

00-2

Regular motion in a moving, rotated frame
-1

0

Vy’

12

4. Discussion

Particle-orbit theory
Curvature radius of BLarmor radius

Büchner & Zelenyi 1989 JGR

B

Bounce motion

B

Chaotic motion

B

Gyro motion(μ-adiabatic)

Macroscopic properties
Nonidealness← Nongyrotropic motionVixZX
Inflow Alfvén speed (cA,in)

ViVyxx
VExB

VExB

Bz
Sub-Alfvénic flow
= apparent effect|Vi -VExB| sinαVx

Electron-scale
structure
Ion-scalestructure(E+vi xB)yZ(A) Quadrupole
magnetic field-By

H(B)allencurr

Xt(F) Pedestal

HERE
+By

(D) Dissipation regionzy(C) Electron current layerx(E) Super-Alfvénic electron jetHybridLottermoser et al. 1998 JGRArzner & Scholer 2001 JGRHigashimori & Hoshino 2012 JGR•Q1. Is this a “diffusion region”? A. No!
•Q2. Why is the ion ideal condition violated?
•Q3. Why is the ion flow sub-Alfvénic?
A. Nongyrotropic ion motion is responsible.

Zenitani et al. 2011 PoP

Kinetic
Drake et al. 2009 JGR
Liu et al. 2011--2012 PoP

Traditional picture
Electron Diffusion Region
Electron Dissipation Region

Ion Diffusion Region
Ion Dissipation Region
Daughton et al. 2006 PoP
Karimabadi et al. 2007 GRL
Shay et al. 2007 PRL

New picture

Dissipation Region

ElectronDiffusion
RegionIon Diffusion Region
in a diffusion-like manner
Nonideal energy
dissipation
Zenitani et al. 2011 PRL
Zenitani et al. 2013 PoP
Zenitani & Umeda in prepTraditional picture
Electron Diffusion Region
Electron Dissipation Region

Ion Diffusion Region
Ion Dissipation Region
Daughton et al. 2006 PoP
Karimabadi et al. 2007 GRL
Shay et al. 2007 PRL

New picture

Dissipation Region

ElectronDiffusion
RegionNongyrotropiclayers

Ion Diffusion Region
in a diffusion-like manner
Nonideal energy
dissipation
Zenitani et al. 2011 PRL
Zenitani et al. 2013 PoPZenitani & Umeda in prep

Summary• Basic concepts– Nonidealness– Violation of flux frozen-in– Magnetic diffusion

special case of• Poincaré map ⇔ Ion velocity distribution function– (1) Global Speiser ions
– (2) Local Speiser ions
• Violation of the ideal condition• Sub-Alfvénic ion flow

– (3) Trapped ions
• Regular orbits in the chaos theory• First demonstration in PIC simulation– Chaotic particle motion is important• Better understanding of the reconnection outflow region,
both from the macroscopic and microscopic viewpoints

Thank you for your attention!