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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

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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

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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.

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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

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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)

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

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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.

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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.

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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

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(1,0) (0,1) (1,-1) (1,1) Global Evolution (I): Tearing with Island Growth and Transition to Stochastic Field lines

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

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Current Filamentation |J|

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

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

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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

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H H (k < ) H (k > ) Helicity stays at large scale (though not always) Helicity transfers to small scale but dissipate subsequently. Helicity Spectral Transfer

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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

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