A new picture of the central engineof kinetic magnetic reconnection

Seiji Zenitani
National Astronomical Observatory of Japan

Outline•1. Introduction– Central engine of magnetic reconnection•2. Dissipation– Generalized magnetic dissipation– Dissipation region in reconnection•3. Diffusion– Generalized magnetic diffusion– Diffusion regions in reconnection•4. Nongyrotropic layer– Chaotic particle dynamics•5. Summary

Introduction

Magnetic reconnectionSun• Reconfiguration of field-line topology• Explosive release of magnetic energy• MHD-scale process

Earth’s MagnetosphereJetJetMHD “central engine”
Reconnection point+B0
Symmetry-B0• Localized η is a key for fast evolution.
Localized η → fast evolution

Uniform η → slow evolution

Kinetic “central engine” - two-scale structureionelectron“Electron Diffusion Region”“Electron Dissipation Region”(E+ve xB)y“Ion Diffusion Region”“Ion Dissipation Region”(E+vi xB)yZXX

2D PIC simulations

Kinetic “central engine” - two-scale structure• How to better understand the central engine,“Dissipation” or “Diffusion” regions?
ionelectron“Electron Diffusion Region”“Electron Dissipation Region”(E+ve xB)y?

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

ZXX

2D PIC simulations

Many opinions ...
(ion or electron)

Dissipation
region?

• Plasma nonidealness (s=i,e...)E + vs

B=0• Maximum flow speed, ve,max(Daughton+ 2006, Fujimoto 2006...)• Electric current, J

Diffusion
region?

• Parallel electric field E = 0• Plasma inertial effect (Klimas+ 2010)• Agyrotropy in velocity distribution function
and GCT parameters (Scudder & Daughton 2008)– Ratio of P⊥1 to P⊥2– Ratio of P// to P⊥– Thermal Mach number– Ratio of the forces on the fluid

Dog?

Dog!

Many opinions ...

Dissipationregion?

• Plasma nonidealness (s=i,e...)E + vsB=0• Maximum flow speed, ve,max(Daughton+ 2006, Fujimoto 2006...)• Electric current, JDiffusion
region?

• Parallel electric field E = 0• Plasma inertial effect (Klimas+ 2010)• Agyrotropy in velocity distribution function
and GCT parameters (Scudder & Daughton 2008)– Ratio of P⊥1 to P⊥2– Ratio of P// to P⊥– Thermal Mach number– Ratio of the forces on the fluidDissipation
region?

= The place where
magnetic dissipation occurs.

Diffusion
region?

= The place where
magnetic diffusion occurs.

What are magnetic dissipation andmagnetic diffusion in a fully kinetic plasma?

Dissipation

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

2D PIC simulations

Magnetic [energy] dissipation
Total energy transfer

Neutral two-fluid plasma
Electric current in
the observer frame

Electric field in the electron frame

irreversible in MHD

Work by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

2D PIC simulations

Frame-independent generalization
Total energy
transfer
Electron-frame
dissipation
measureLorentz 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

Typical RX configurations

Guide-fieldAntiparallel

Symmetric Rx

Asymmetric Rx

Generalized dissipation measure: DeAntiparallelZ

Guide-field

Symmetric Rx

Z

Asymmetric Rx

Dissipation Region

XX

2D PIC simulations

On the irreversibility• De: j・E in the electron’s frame• Di: j・E in the ion’s frame• Dmhd : j・E in the MHD frame• Kinetic expansion of the MHD entropy

Rossi & Olbert 1970

• De > 0 usually indicates irreversible processes• For further discussion, we need to generalize plasma entropy.

Diffusion

Magnetic diffusion• Ohm’s law

Frozen-in condition(Flux preservation)

Magnetic diffusion

Bv

Finite frozen-in term
relaxes to zero
Newcomb 1958, Stern 1966

(relaxation to the frozen-in state).
.

Violation of the frozen-in condition

R=0
Frozen-in condition(Flux preservation)

Magnetic loss or gain

SZ & Umeda 2014

Disconnection(Line preservation)

Newcomb 1958

Diffusion region• Ad-hoc diffusion coefficient• Induction equation=b・b·(b·R)
B• Generalized magnetic
diffusion>02D PIC simulations

Again, frozen-in• Arbitrary Ohm’s law

Frozen-in condition(Flux preservation)

Bv

Frozen-in [and all other concepts] arerelative concepts that depend on
a reference velocity field v

Two-scale diffusion regions
Electron Diffusion
Regionb・Ion Diffusion Region

2D PIC simulations

Nongyrotropic layer

Ion velocity distribution function(E+vi xB)yZ
Ion diffusion region
XiVy

Bz
Vx

• Ideal condition is violated
outside the central engine(ion diffusion region)

Orbit theory in a parabolic fieldZ

Nonlinear systemX

Büchner & Zelenyi 1986, 1989

BB

B??
Bounce motion(I-adiabatic)

Chaotic motion

Gyro motion(μ-adiabatic)

Orbit theory in a parabolic field

Chen & Palmadesso 1986

BB

B??
Bounce motion(I-adiabatic)

Chaotic motion

Gyro motion(μ-adiabatic)

Ion velocity distribution function
By
Vy

ZX

Vx

By
Z

Vy
XVx

Ion velocity 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)

Chen & Palmadesso 1986 JGRDistribution function

Poincaré map.
. .
• (x, x) ⇔ (-y, x)

Regular orbits

Speiser orbits(Transient orbits)

Chen & Palmadesso 1986 JGRNongyrotropic ions

ViVyxxVExB• Since particles do not gyrate,
we do not expect the idealness.

Vx

B

Nongyrotropicmotion

B

B

Gyro motion(μ-adiabatic)

Conventional picture“Electron Diffusion Region”“Electron Dissipation Region”

Nonidealness“Ion Diffusion Region”“Ion Dissipation Region”

New picture
Distribution function

Electron Diffusion Region

DissipationRegion

Nongyrotropic layers

Ion Diffusion Region

Magnetic dissipation(Zenitani+ 2011 PRL)
relax

Magnetic diffusion(Zenitani & Umeda 2014 PoP)

Nongyrotropic motion(Zenitani+ 2013 PoP)

Poincaré map

Summary• Magnetic dissipation & dissipation region– Frame-independent, nonideal energy transfer– Usually irreversible• Magnetic diffusion & diffusion regions– Relaxation to the frozen-in state– Relative concept w.r.t. the reference flow

• Nongyrotropic layer– Nongyrotropic particles, such as in regular orbits– Particles don’t satisfy the assumption for the idealness• Dissipation region and diffusion regions in kinetic
magnetic reconnection are better understood,by generalizing basic notions

relax