Dissipation in Force-Free Astrophysical Plasmas

1
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

2
Collisionless Reconnection in Lobes

• Kinetic physics should be included in
  reconnection
• ion skip depth di c/wpi 2x1010 cm (n
  10-6 /cc)
• filaments L 1 kpc, h 104 cm2/s, vA 6.6x108
  cm/s
• Sweet-Parker width (Lh/v)1/2 2x108 cm
• di gtgt Dh
• wpe/Wce 3 (n-6 1/2/B-6)
• Plasma b 4x10-3 (n-6 T6/ B-6 2)
• Max. E V (v/c) B L (x300)
• 3x1018
  (vol) for L 100 kpc

3
An idealized Problem
Sheet-Pinch
Sheet-pinch is force-free, with a constant,
continuous shear.
Q Is this sheet-pinch configuration stable? Q
If so, how does it convert B2 into plasmas?
4
Three Configurations
x
x
x
x
x
x
x
x
x
III
I
II
Harris Equilibrium
Harris Bguide Bguide not available for
dissipation
Sheet-Pinch All components supported by internal
currents, available for dissipation
5
Flipping
Lz
Lz
Lx
Lx

• Predicting final Bz flux
• Bzf B0 nx (Lz/Lx)
• Predicting final magnetic
• Energy
• B2(t0) By2 Bx2
• B2 (tf) By2 Bz2
• DEB 1 (Lz/Lx)2

(Li et al03)
6
Resonant Layers in 3D

• In 2D, two layers az p/2, 3p/2
• In 3D, large number of
• modes and layers!

7
A few remarks on PIC

• PIC parameters
• Lxx Lyx Lz 8x3x2 di3 grids 224 x 96 x
  64
• mi/me 100, wpe/Wce 2, Te,para/Ti 1, b
  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.

8
Multiple Layers in 3D
Initial
Turbulence/ Reconnection
Conserving helicity
Final

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

9
Total Energy Evolution
Nishimura et al02,03 Li et al03 Li et al04
I II III
I Linear Stage II Layer-Interaction Stage
III Saturation Stage
10
Global Evolution (I)
Tearing with Island Growth and Transition to
Stochastic Field lines
(1,0)
(0,1)
(1,-1)
(1,1)
11
Global Evolution (II-III)
Multi-layer, Turbulence, and Re-Orientation
12
Current Filamentation J
13
Helicity and Energy Dissipation
Black dH/dt Red dE/dt
14
Inertial Range ?
Dissipation Range
2p/Lx
2p/Lz
2p/di
2p/de
15

• Helicity and Energy Evolution
• Two Stage
• Total H W conserved but with significant
  spectral transfer, ideal MHD?
• Net H and W dissipation.

Htot
Wtot
Ha
Wa
16
Helicity Spectral Transfer
Htot
Ha
Helicity stays at large scale (though not
always)
H (k lt a)
Helicity transfers to small scale but dissipate
subsequently.
H (k gt a)
17
What is achievable?
200 10 1 0.2
200 5 1 0.2
L di di de
Deby

• 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?