Dissipation in Force-Free Astrophysical Plasmas

Hui Li(Los Alamos National Lab)

Radio lobe formation and relaxation Dynamical magnetic dissipation in force-free plasmas: (with K. Bowers, X. Tang, S. Colgate)

Transport and dissipation of helicity and energy

Collisionless Reconnection in Lobes

Kinetic physics should be included in reconnection:

ion skip depth: di = c/pi ~ 2x1010 cm (n ~10-6 /cc)

filaments: L ~1 kpc, ~ 104 cm2/s, vA ~ 6.6x108 cm/sSweet-Parker width: (L/v)1/2 ~ 2x108 cm

di >>

pe/ce ~ 3 (n-6 1/2/B-6) Plasma ~ 4x10-3 (n-6 T6/ B-6 2)

Max. E: V ~ (v/c) B L (x300) ~ 3x1018 (vol) for L ~ 100 kpc

Q: Is this sheet-pinch configuration stable?Q: If so, how does it convert B2 into plasmas?

An idealized Problem

0)(

sin)(

cos)(

0

0

=

==

zB

zBzBzBzB

z

y

x

αα

Sheet-Pinch:

Sheet-pinch is force-free, with a constant, continuous shear.

Three Configurations

I II III

x x x

x x x

x x x

Harris Equilibrium

Harris + Bguide

Bguide not available for dissipation

Sheet-PinchAll components supported

by internal currents, available for dissipation

Flipping …

Predicting final Bz flux: Bzf = B0 nx (Lz/Lx)Predicting final magnetic Energy: B2(t=0) = By

2 + Bx2

B2 (tf) = By2 + Bz

2

EB = 1 – (Lz/Lx)2

Lx

Lz

Lx

Lz

(Li et al’03)

Resonant Layers in 3D

In 2D, two layers: αz = /2, 3/2In 3D, large number of modes and layers!

⎟⎠

⎞⎜⎝

⎛±±±=

±±=,+⎟⎟⎠

⎞⎜⎜⎝

⎛−=α

=α+α=•

z

yxyx

xy

yx

yx

L

Ln

jjLn

Lnz

zkzk

,,

0

,...,2,1,0

,...2,1,0arctan

0)sin()cos(

0

Bk

A few remarks on PIC

PIC parameters:

Lxx Lyx Lz ~ 8x3x2 di3; grids: 224 x 96 x 64;

mi/me= 100, pe/ce= 2, Te,para/Ti = 1, = 0.2,

vdr = ve, vd = 2-4 vA; ~ 400 particles/cell for 3D runs.

Routinely running ~2003 meshes with ~0.5B particles for ~50K time steps.

Caveats: a. Triply periodic boundary condition;

b. Doubly periodic in {x,y} + conducting on z.

∫∫

•−∝

•−∝

)(/

)2/3

3

JEx : Energy

B(Ex :Helicity

ddtdE

ddtdH

Multiple Layers in 3D

Initial

Final

Conserving helicity

Turbulence/Reconnection

Predicting final state? In 2D, yes.In 3D, sensitive to the initial condition. Helicity conservation gives the least amount of magnetic energy dissipation.

Total Energy Evolution

I II III

I: Linear Stage; II: Layer-Interaction

Stage; III: Saturation Stage

Nishimura et al’02,03 Li et al’03Li et al’04

(1,0)

(0,1)

(1,-1)

(1,1)

Global Evolution (I):Tearing with Island Growth and

Transition to Stochastic Field lines

Global Evolution (II-III): Multi-layer, Turbulence, and Re-Orientation

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Current Filamentation |J|

QuickTime™ and aYUV420 codec decompressor

are needed to see this picture.

Helicity and Energy Dissipation

∫∫ •−∝•−∝ )(/)2/ 33 JEddtdEBEddtdH x (x

Black: dH/dtRed: dE/dt

2 /Lx 2 /Lz 2 /di 2 /de

Inertial Range ? Dissipation Range

Wtot

)Re(

)( 33

∗=

=•∫ ∫kkk

k

BAH

HkdBAxd

Helicity and Energy Evolution

Two Stage:

Total H & W conserved but with significant spectral

transfer, ideal MHD?

Net H and W dissipation.

Htot

Hα

Wα

Htot

Hα

H (k < α)

H (k > α)

Helicity stays at large scale

(though not always)

Helicity transfers to small scale but

dissipate subsequently.

Helicity Spectral Transfer

What is achievable?

How efficiently are electrons accelerated?What mechanism(s) are responsible for acceleration?Are waves/turbulence important? E-S vs. E-M?What are the characteristic scales of current filaments? Are they the primary sites for acceleration?Is there a “universal” reconnection rate in 2D/3D, with/without guide field?

L di di de

Deby

200 10 1 0.2

200 5 1 0.2