The Structure of Thin Current Sheets Associated with Reconnection X-lines

Marc Swisdak

The Second Workshop on Thin Current Sheets

April 20, 2004

Collaborators

• J. Drake• M. Shay

• J. McIlhargey

• B. Rogers

• A. Zeiler

U. of Maryland

Dartmouth College

MPP-Garching

UMBC

BguideJ

Breconn

xy

zSimulation:

Reconnecting field: xInflow velocity: yGuide field/Current: z

p3d Details

• Relativistic PIC code• Boris algorithm for particles• Trapezoidal leapfrog for fields

• Multigrid for Poisson’s equation• MPI parallelization• Biggest runs:

• 512x256x256• 2048 processors• ~109 particles

• How we cheat:• me/mi large• c/cA small

• Also:• Double Harris sheet• Periodic BCs

The Point

Q: At what strength does the guide field become important?

A: Bg 0.1 B0

zJx

y

y

No Guide Field: Overview

0

0

Box size: 6.4 6.4 / 20

Guide field: 0 / 100

Grid: 1024 1024 / 10

Background Density: 0.2

2D Simulation

i A

i e

i e

d c c

B m m

T T

n

zJ

x

y

Development of Bifurcation

1Total time: 4.5 ci

Temperature

y

y

y

y

x

x

x

xxT yyT

zzT

Velocity Distributions

yv

zv

@ x-line: Beams are due to Speiser figure-8 orbits

@ bifurcation: Multiple peaks from two beams

Balancing the Reconnection Electric Field

,,

1(

)

)

)

1

(

( e y

z ex

e ez e

ze

y e

xz

y

z eex ey

x

zm v v vv

PP

E v B

ne z

ve t

Bc

z

y

v

x

Ideal MHD

Pressure tensor

Electron Inertia

1( )ex y ey xv B v B

c

e ezm v

e t

,,1( )e yze xz PP

ne z z

* zE

( )e ez ezex ey

m v vv v

e x y

Balancing the Reconnection Electric Field

zJx

y

y

Guide Field: Bg=1B0

• Current sheet not bifurcated• Electrons magnetized at the x-line

• Canted separtrices• E|| interacting with Bg

T T

yv

Temperature, Bg=1

1( )ex y ey xv B v B

c

e ezm v

e t

,,1( )e yze xz PP

ne z z

* zE

( )e ez ezex ey

m v vv v

e x y

Balancing the Reconnection Electric Field

Guide Field Criterion

• What is the minimum Bg so that the e- excursions are less than de?

in0

0

0.1vv 0.1

( / )Ae

L gce ce g pe

cB B

B B

edid Aec Ac

0.1 Aec

0.1 AcReconnection Rate:

0

z

A

cE

t c B

ExBv

~ 0.1Ac

X-line Structure: Bg = 0, 0.2, 1

Temperature, Bg=0.2T T

yv

Off-Diagonal Pressure Tensor, Pyz

Why is this important? Development of x-line turbulence.Why does it happen? Bg means longer acceleration times.

1gB

0gB

Ions

0.2gB

X-line Distribution Functions

zv

Conclusions

• Bg ~ 0.1B0 is enough to influence the structure of x-lines.– Affects: Flow geometries, separatrices, particle

orbits (temperatures), particle energization, development of turbulence (?)

– Doesn’t affect: Reconnection rate, breaking of frozen-in condition

• Implication: Anti-parallel reconnection is rare in real systems. Most reconnection is component reconnection

xxT

yyT

zzT

Cut Through the X-line

Reconnection Rate & Guide FieldR

econ

nect

ed F

lux

Time

1gB

0gB

Anti-parallel reconnection

Guide field reconnection

Why the difference?

Within the diffusion region electrons are unmagnetized & execute wandering orbits.

Electrons are always magnetized and are not heated.

Tfinal

Tinit

1( )ex y ey xv B v B

c

,,1( )e yze xz PP

ne z z

( )e ez ez ezex ey

m v v vv v

e t x y

zE

Generalized Ohm’s Law

The final three terms become important at different scales:

i c/pi s, ei e

What terms does MHD neglect?

1 1 e eie

nec

m d

e dtc ne + J B

vE B J P

v��

Ideal MHD

Pressure tensorResistive MHD

Hall term Electron Inertia

3D Reconnection with Guide Field

zJy

x0

9

Box size: 4 2 1 / 20

Guide field: 5 / 100

Number of Particles: (10 )

i A

i e

d c c

B m m

O

z

zJ

zE

z

y

vez

Buneman Instability

• Electron-ion two-stream instability. If the distribution functions do not (roughly) overlap then the system is unstable.

1/3 ( / )e i pem m

d/vpek IonsElectrons

~J

3D Reconnection w/o Guide Field

vez

• Initial turbulence (LHDI) disappears as reconnection strengthens.• X-line shows no sign of instability at late times.

zJ

early

late

Temperature

y

y

y

y

x

x

x

xxT yyT

zzT

Temperature, Bg=0.2T T

T T

yv

Temperature, Bg=1

Dissipation mechanism• What balances Ep during guide field reconnection?

• Scaling with electron Larmor scale suggests the non-gyrotropic pressure can balance Ep (Hesse, et al, 2002).

4 pe

2

dJz

dtE z

1

c(v e

B )z

1

ne(

p e )z

Bz=0 Bz=1.0

y y

Transition from anti-parallel to guide field reconnection

• Structure of non-gyrotropic part of the pressure tensor, Pyz

– Remove gyrotropic portion– Significant changes for Bz0=0.1

Bz0=0 Bz0=1.0Bz0=0.1