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: d i = c/ pi ~ 2x10 10 cm (n ~10 -6 /cc) filaments: L ~1 kpc, ~ 10 4 cm 2 /s, v A ~ 6.6x10 8 cm/s Sweet-Parker width: (L /v) 1/2 ~ 2x10 8 cm d i >> pe / ce ~ 3 (n -6 1/2 /B -6 ) Plasma ~ 4x10 -3 (n -6 T 6 / B -6 2 ) Max. E: V ~ (v/c) B L (x300) ~ 3x10 18 (vol) for L ~ 100 kpc

Q: Is this sheet-pinch configuration stable? Q: If so, how does it convert B 2 into plasmas? An idealized Problem Sheet-Pinch: Sheet-pinch is force-free, with a constant, continuous shear.

Three Configurations III III xxx xxx xxx Harris Equilibrium Harris + B guide B guide not available for dissipation Sheet-Pinch All components supported by internal currents, available for dissipation

Flipping … Predicting final B z flux: B zf = B 0 n x (L z /L x ) Predicting final magnetic Energy: B 2 (t=0) = B y 2 + B x 2 B 2 (t f ) = B y 2 + B z 2 E B = 1 – (L z /L x ) 2 LxLx LzLz LxLx LzLz (Li et al03)

Resonant Layers in 3D In 2D, two layers: z = /2, 3 /2 In 3D, large number of modes and layers!

A few remarks on PIC PIC parameters: L x x L y x L z ~ 8x3x2 d i 3 ; grids: 224 x 96 x 64; m i /m e = 100, pe / ce = 2, T e,para /T i = 1, = 0.2, v dr = v e, v d = 2-4 v A ; ~ 400 particles/cell for 3D runs. Routinely running ~200 3 meshes with ~0.5B particles for ~50K time steps. Caveats: a. Triply periodic boundary condition; b. Doubly periodic in {x,y} + conducting on z.

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 al02,03 Li et al03 Li et al04

(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

Current Filamentation |J|

Helicity and Energy Dissipation Black: dH/dt Red: dE/dt

2 /L x 2 /L z 2 /di2 /de Inertial Range ?Dissipation Range

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

H H (k < ) H (k > ) 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 d i d i d e Deby