SM23B-2045

The electron-frame dissipation
measure in collisionlessmagnetic reconnection
Seiji Zenitani
National Astronomical Observatory of Japan

Collaborators: Michael Hesse, Alex Klimas,
Masha Kuznetsova, Carrie Black (NASA/GSFC)

Outline• 1. Introduction– Recent debates on the electron diffusion region (EDR)• 2. Theory– Introducing a new measure De• 3. Numerical tests & discussions– 2D kinetic PIC simulations– What’s wrong with the frozen-in and why De works?

• 4. Applications– Closer look at antiparallel symmetric reconnection

Magnetic reconnection
Solar flare
CME

Magnetopause• Explosive topological changeof magnetic field lines• Beyond ideal-MHD

Magnetotail

Our magnetosphere

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

Ion Dissipation Region
Electron Dissipation
Region (EDR)

ZX• We are interested in the innermost EDR– It is traditionally identified by

EDR in 2D kinetic PIC simulations• Large-scale PIC simulations– Daughton+ 2006, Fujimoto 2006, Karimabadi+ 2007, Shay+ 2007

• A two-scale structure– Inner region– Outer region

attached to the reconnection pointelongated in the outflow (X) direction.
A fast electron jet outruns the field lines.

eBZ
Inner EDR : E’y>0

Outer EDR : E’y<0X

Karimabadi+ 2007 GRL

Magnetic field lines are “flipped”
Zp+Ye-X(E+vexB)yInner EDR
Outer EDR

By (Hall field)

From a different angle
Ey’(-vex B)y’Z

Z

Hesse+ 2008 Phys. Plasmas

Y’

Quasi-ideal convection in X’-Z
Is this really EDR?

X’EDR in asymmetric Rx (1/2)-Bz+Bz• “Asymmetric” reconnection• All three components of[E+vexB] are puzzlingsolar wind
dipole field
Magnetopause

Pritchett & Mozer 2009 Phys. Plasmas

EDR in asymmetric Rx (2/2)
Antiparallel

Guide-field

Pritchett & Mozer 2009

• The situation is worse for asymmetric reconnection
with a guide field• Any quantities to characterize the EDR-like region
surrounding the reconnection site?

Something is wrong• The violation of the electron ideal condition(E + vexB ≠ 0) may not identify the critical region.
– The controversial outer EDR– No EDR signature in asymmetric reconnection

SymmetricAsymmetric??
Outer EDR???

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

? ? ? ? ?

• We derive our formula from scratch, considering
three basic requirements.

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

Magneticenergy

Plasma energy
Heat
Bulk flow
Nonthermal
particles• Reconnection consumes the magnetic energy• Magnetic energy consumption or similar quantities should
characterize the reconnection region

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

Outer EDR
Inner EDRX’Y’XY• If we employ a scalar quantity, we don’t need to worry
about the coordinate. The Y direction or the Y’ direction
do not matter.

Desirable conditions for “D” (3/3)
1. Physical meaning
2. Scalar quantity
3. Insensitive toobserver motion
X-line retreat (NENL)• There is always relative motion
between the observer (satellite)
and the reconnection site
Plasma sheet flapping

Earthsatellite

Desirable conditions
1. Physical meaning
2. Scalar quantity
3. Insensitive toobserver motion“The reconnection measure D should bea Lorentz-invariant.”
A. EinsteinMaking a Lorentz invariant• 4-vector quantities• Contracting two, we obtain an invariant scalar.

• We list up all 4-vector quantities in the system.
• We find out a good combination(s) from all possible
patterns.

Our choices : jμ and eμ• Spacelike current• Covariant electric field

Lorentz factor for ve

4-currentElectron fluid 4-velocity

Electromagnetic tensor

... in the moving frame of electrons• Spacelike current
Electric current in this frame• Covariant electric field
Electric field in this frame• Their contraction
Energy transfer fromthe electromagnetic field
to plasmas

The invariant measure• We introduce the electron-frame dissipation measure– The energy transfer in the electron frame

Chargedensity– This has a very good physical meaning.

Desirable conditions
1. Physical meaning
2. Scalar quantity
3. Insensitive toobserver motion

Nonrelativistic formula• Electric current in the electron’s frame• Electric field in the electron’s frame• The energy transfer in the electron frame (= a unique frame)– The relativistic formula in the limit of γe → 1

2D PIC simulation (1/2) : Symmetric Rx(E+vexB)y• Mass ratio mi/me=25• 109 particles
Inner EDR

Outer EDR

Our Dissipation Region

The New Measure De

minor fluctuations
no strong dissipation

2D PIC simulation (2/2) : Asymmetric Rx
no guide fieldwith a guide field

By(E+vexB)yZXThe new measure
DeXZXX• De accurately locates the reconnection site
• The field reversal line is located inside the dissipation region

Why (E+vexB) does not work?
• The ideal condition assumes the E x B drift motion.

• Diamagnetic, grad B, curvature ... drifts violate theideal condition• Example: ∇B drift in zero-E– Particles don’t consume the field energy
neither in this frame nor in the electron frame: De=0

∇Belectronsions

Energy budget• Resistive MHD (e.g. Birn & Hesse 2005)

work by Lorentz force

Non-ideal• Kinetic neutral plasma

Non-ideal

De = nonideal energy transfer

Closer look at the dissipation region (1/2)
De : mi/me = 25

De : mi/me = 100• Our dissipation region is controlled by the electron physics• Scales like (me/mi)1/4 [bounce width] ~ (me/mi)1/2 [inertia]

Closer look at the dissipation region (2/2)(E+vexB)y : mi/me = 100

JBzyx

De : mi/me = 100

De0.1
0.05
0
De-0.05
Jx E'xJy E'y-0.1
32

34

36

38

jx E’x40jy E’y 4244

• The dissipation region is usually longer than the classical inner
EDR of (E+vexB)y > 0.
• The x-component is important, too.

Eye test : ion-frame versionDeDi : ion-frame version

In a neutral plasma, De = Di = Dmhd

Closer look at the “outer EDR” (1/3)(E+vexB)y : mi/me = 100vex

Outer EDR

DeDe<0Dmhd<0• The “outer EDR” is anti-dissipative• It is not appropriate to call it “dissipation” nor “diffusion” region

Closer look at the “outer EDR” (2/3)

JJ-aligned componentvexe-• Electron jet– Oblique projection of the electron current sheet(Hesse+ 2008)

Closer look at the “outer EDR” (3/3)
Magnetic cavitiesByDey+3
Electronvelocity vex108

10.8z

60.6

40.4-32038

25.6 Bz
Reconnected
4144

4750

53056

101
“Electron shock”

80.8

638.4

42038

44

47

50

0.6
0.4

t=42
t=40
t=38
t=36

"Flipped" field lines

0.2

x41

Electrontemperature(d)Electrontemperature

0.2

53056

51.2

Quickheating

Summary (1/2)• The ideal frozen-in condition does not always work,
however, we paid too much attention to the ideal condition.
• We were frozen-in to the ideal condition!
• We have introduced the electron-frame dissipation measure.

– Lorentz invariant scalar– Energy transfer in the electron’s frame– Nonideal energy conversion– Verified by PIC simulations in various configurations

We propose to redefine the dissipation region by De

Summary (2/2)• Further analysis– Generic, electron-scale dissipation region– “Outer EDR” is anti-dissipative jet, terminated by a shock– Electron shock-heating is responsible for magnetic cavity
signature• References– Zenitani et al., Phys. Rev. Lett., 106, 195003 (2011)– Zenitani et al., Phys. Plasmas, in press (arXiv:1110.3103)

Previous picture

Antiparallel

Symmetric
Electron DRs
Ion DR??
Inner EDR : E’y>0

Guide-field

Asymmetric

Outer EDR : E’y<0??

??

New picture
Asymmetric

Antiparallel

Symmetric

Guide-field

Dissipation Region