The electron-frame dissipation
measure in collisionlessmagnetic reconnection
Seiji Zenitani
NASA Goddard Space Flight CenterCollaborators
Michael Hesse, Alex Klimas,Masha Kuznetsova, Carrie Black

Outline• 1. Review– Recent debates on the electron diffusion region (EDR)• 2. Theory– Introducing a new measure De• 3. Numerical tests (1)– 2D kinetic PIC simulations• 4. Discussion– What’s wrong with the frozen-in and why De works?

• 5. Numerical tests (2)– Revisiting EDRs in antiparallel reconnection

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

Ion Dissipation Region
Electron DissipationRegion (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 et al. 2006, Fujimoto 2006, Karimabadi et al. 2007, Shay et al. 2007

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

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

eBZ
Inner EDR : E’y>0

Outer EDR : E’y<0XKarimabadi et al. 2007 GRL

Magnetic field lines are “flipped”
Z“Quadruple” By
YX(E+vexB)yInner EDR
Outer EDRFrom a different angle
Ey’(-vex B)y’Z

ZHesse et al. 2008 PoP

Y’X’

It looks like “ideal” convection in X’-Z planeWhere is the EDR in asymmetric Rx?
-Bz

+Bz

solar wind

• Magnetopause-likeconfiguration• (E + ve x B) and manyother quantities fail tolocate the X-point

dipole fieldwith a guide field[E+vexB]x[E+vexB]y [E+vexB]z[E+vexB]xBy[E+vexB]y [E+vexB]z

no guide field
Pritchett & Mozer 2009 PoP• 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• We introduce a new reconnection measure “D”(“D” of Dissipation) to identify the critical region.

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

Magneticenergy

Plasma energyHeat
Bulk flow
Nonthermalparticles• 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. Observer 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 possiblepatterns.

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

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• Spacelike current

Desirable conditions• Covariant electric field

1. Physical meaning
2. Scalar quantity
3. Observer motion• We introduce the electron-frame dissipation measure– The energy transfer in the electron frame

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

Inner EDR

Outer EDR

minor fluctuations
no strong dissipation

DeOur Dissipation Region

2D PIC simulation (2/2) : Asymmetric Rx
no guide field(E+vexB)ywith a guide field

By(E+vexB)y

Z

DeX

DeX

ZXX

• 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.

• All other drifts (diamagnetic, grad B, curvature ...)
violates the ideal condition• Example: grad B drift in a stationary B and zero E– Particles don’t consume the field energy
neither in this frame nor in the electron frame: De=0electronsions

Why does De work? (1/2) : Eye test
DeDi : ion-frame measure

In a neutral plasma, De = Di = Dmhd

Why does De work? (2/2) : Energy balance• Resistive MHD (e.g. Birn & Hesse 2005)• Kinetic plasma

work by Lorentz force

Non-idealby Coulomb forceNon-ideal

Non-ideal

De = nonideal energy conversion

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

(E+vexB)y : mi/me = 100

De : mi/me = 100• Electron physics controls the size of the dissipation region• Longer than the inner region of (E+vexB)y > 0.
• DeJ・(E+vexB)Not y but J-aligned component matters

Closer look (2/2) : outer EDR(E+vexB)y : mi/me = 100

Outer EDR

De : mi/me = 100

De<0Dmhd<0• Energy conversion from plasmas to the fields in the MHD frame• It is not appropriate to call it “dissipation” nor “diffusion”

Summary• The ideal frozen-in condition does not always work, but
we kinetic scientists paid a lot of attention to the frozen-in.
• We were frozen-in to the frozen-in condition.
• We have introduced the electron-frame dissipation measure.

– Energy transfer in the electron’s frame– Nonideal energy conversion– Verified by PIC simulations in various configurations• Antiparallel reconnection– The dissipation region is controlled by electron physics– The outer region is non-dissipativeThank you for your attention!!

• Zenitani et al., Phys. Rev. Lett., 106, 195003 (2011)• Zenitani et al., Phys. Plasmas, to be submitted

Frequently asked questions• Does the measure work in 3D?
– We believe so. Our 4D theory should work in 3D.
• The charge density is difficult to probe. How important is it?
– The charge term may be negligible in magnetosphericparameters, but this needs to be verified by simulations.

• Where do the 4-vectors come from?
– LHS and RHS of the covariant Ohm’s law in relativistic resistive
MHD equations.

Covariantelectric field

Spacelike current

Zenitani, Hesse, & Klimas 2010 ApJ[presented in St. Andrews]