Dissipation in Force-Free Astrophysical Plasmas

1. Dissipation in Force-Free Astrophysical Plasmas • 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 Hui Li (Los Alamos National Lab)

2. Collisionless Reconnection in Lobes Kinetic physics should be includedin 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 >> Dh wpe/Wce ~ 3 (n-61/2/B-6) Plasma b ~ 4x10-3 (n-6 T6/ B-62) 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(t=0) = By2 + Bx2 B2 (tf) = By2 + Bz2 DEB = 1 – (Lz/Lx)2 (Li et al’03)

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 al’02,03 Li et al’03 Li et al’04 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 < a) Helicity transfers to small scale but dissipate subsequently. H (k > 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?