Identification of thedissipation region incollisionless magnetic
reconnection: Theoryand Simulations

Seiji ZENITANI
National AstronomicalObservatory of Japan
with Michael Hesse, Alex Klimas,Carrie Black, Masha Kuznetsova
NASA/GSFC

Invited talk @ AGU Fall Meeting, 5 Dec 2012Outline• 1. Introduction– Recent debates on the electron dissipation region• 2. Theory– Introducing a new measure De• 3. Simulation– Numerical tests with 2D kinetic (PIC) simulations• 4. Discussion– Magnetic topology and energy balance1. Introduction

Magnetic reconnectionSun• Dissipation region around the X-point• Structure and internal physics criticallycontrols the macroscopic evolution

Earth’s MagnetosphereJetJet

Kinetic dissipation regions• The ideal condition• We expected a multi-scale structure

Ion Dissipation Region
Electron Dissipation
Region (EDR)

ZX• We are interested in the innermost EDRElectron nonideal layer• Kinetic PIC simulations[Since Daughton+ 2006]• Narrow nonideal layer unexpectedly stretched– Is the entire layer EDR?

ZNonideal layer

ZXX

Karimabadi+ 2007 GRL

From a different angleEy’(-vex B)y’

[Hesse+ 2008]Nonideal layer[E+vexB]yControversial
outer partZ

Z

Hesse+ 2008 PoP

Y’X’

We may have better understanding
in a rotated coordinate.

EDR in asymmetric Rx-Bz+Bz• All three components of[E+vexB] are puzzling

solar wind
dipole field
Magnetopause

Pritchett & Mozer 2009 PoP

Something is wrong• E + vexB ≠ 0 may not identify the critical region.
– The controversial outer layer– No clear signature in asymmetric reconnection

Symmetric

Asymmetric??
False detection???

Something is wrong• E + vexB ≠ 0 may not identify the critical region.
– The controversial outer layer– No clear signature in asymmetric reconnection

Symmetric

Asymmetric

We need a generic measure
to identify the critical region

2. Theory

A new measure “D”• Let us construct a new measure “D” to identify
the critical region.

Chargedensity• We derive our formula, considering three basic
requirements.

Desirable conditions for “D” (1/3)
1. Energy conversion
2. Scalar quantity
3. Insensitive toobserver motion

Magnetic
energyPlasma energy
Heat
Bulk flow
Nonthermal
particlesDesirable conditions for “D” (2/3)
1. Energy conversion
2. Scalar quantity

Outer EDR
Inner EDR

3. Insensitive toobserver motion

X’Y’XY• A scalar quantity is rotation-free. We don’t need to worry
about the rotation angle.

Desirable conditions for “D” (3/3)
1. Energy conversion
2. Scalar quantity
Violent
3. Insensitive toobserver motion

solar wind

Plasma sheet flapping

satellite• Relative motion between
the observer (satellite) andthe reconnection siteDesirable conditions
1. Energy conversion
2. Scalar quantity
3. Insensitive toobserver motion“The reconnection measure D should bea Lorentz-invariant.”
A. EinsteinMaking a Lorentz invariant• 4-vectors

Lorentz transformation• Contracting two, we obtain an invariant scalar.

• Two 4-vectors from relativistic MHD equations

Covariant electric field

Space-like current

The electron-frame dissipation measure

Chargedensity

Space-like current

4-current

Covariant electric field

Electron bulk 4-velocity

The electron-frame dissipation measure

Ohmic dissipationin the electron’s moving frame

Space-like current

Covariant electric fieldLorentz transformation

Electron bulk 4-velocity

The electron-frame dissipation measure

Ohmic dissipationin the electron’s moving frame

Space-like current

Covariant electric field

Lorentz transformation

Electron bulk 4-velocity
Desirable conditions

1. Energy conversion
2. Scalar quantity
3. Insensitive toobserver motion

3. Simulation

Previous measure: (E + vexB)y

AntiparallelZ

Guide-field

Symmetric Rx

Z

Asymmetric Rx

XX-+New measure: De

Guide-field

Antiparallel

Symmetric Rx

Asymmetric Rx

Z

Dissipation Region

ZXX

Unsteady reconnection [by Alex Klimas]• Accurate tracking of moving X-points• Noises stem from kinetic instabilities -- spatial/timeaveraging further improves the visual appearance

4. Discussion

Why is (E+vexB) insufficient?
• Magnetic topology–Newcomb 1958, Stern 1966, Vasyliunus 1972, Hesse & Schindler 1988,
Hornig & Schindler 1995, Scudder 1997, Dorelli & Bhattacharjee 2008 ...

– (1) Ideal condition– (2) Frozen-in condition– (3) Line connection• Particle drift motion– ExB– Non-ExB (e.g., diamagnetic)• Not always related to energy conversion
Apparent bulk flow∇p
※ barotropic caseWhy does De work? : Energy conversion!
Total energy transfer

Electron-frame dissipation measure

in MHDWork by Lorentz force (Ideal MHD)

Birn & Hesse 2005

Nonideal energy conversion

Nonideal effects in MHD
Topology conditions for arbitrary v

MHD Ohm’s law

ideal condition
flux preservation(flux frozen-in)

MHD equations

line preservation
topology
conservation

Essential for reconnection
nonideal
Poynting flux
nonideal energy
conversion• Line disconnection• Nonideal energy
transferSummary• 1. Theory– A new measure to identify the dissipation region:
the electron-frame dissipation measure.

– Frame-independent (Lorentz invariant)– Nonideal energy conversion– Nonidealness, line-disconnection, and magnetic dissipation
are all different in a kinetic plasma• 2. PIC Simulation– The measure works in various 2D configurations– It detects moving X-lines, too

We can better identify the dissipation region