1. Extragalactic Magnetic Fields and Dynamo Hui Li with K. Bowers, X. Tang, and S. Colgate (Los Alamos National Lab) Extragalactic magnetic fields and Magnetized Universe Project Implications on Dynamo: a) Kinematic dynamo in AGN accretion disks b) Magnetic Relaxation (Flux conversion dynamo?): Dynamical magnetic relaxation in force-free plasmas Helicity and energy transport and dissipation Astrophysical Implications

2. Radio Galaxies

3. Estimating Magnetic Energy Total magnetic energy: ~ 10 60 ergs Total volume: ~ 10 72 cm 3 Typical size: 30 kpc wide, 300 kpc long Electron energy: 10 GeV – 10 TeV ( min unknown) Magnetic fields: 0.5 – 5 Gauss Density: ~10 -6 cm -3 (thermal), < 10 -7 cm -3 (relativi) Total current: I ~ 5 B R ~ 10 18 – 10 19 A. drift velocity: ~10 m/sec ! to relativistic ~ c Radio luminosity, spectral index Estimating the volume, filling factor (~0.1) Use equipartition/minimum energy assumption Estimate the total particle and magnetic field energy in the lobes.

4. High z sources Giants Cluster sources Kronberg, Dufton, Li, Colgate02 Magnetic Energy of Radio Lobes

5. Faraday Rotation Measure (Taylor & Perley93; Colgate & Li00) Very high FRM, giving mean B fields ~ 30 G, over size L ~ 50 kpc implying total magnetic energy 4x10 59 ergs, and coherent flux of 8x10 41 G cm2. Only supermassive black holes can perhaps provide such energy and flux.

6. Galaxy Cluster: Perseus A in X-ray 300 Kpc

7. Perseus A: X-ray + Radio

8. Ubiquity of Supermassive Black Holes (Kormendy et al. 2001) SMBH = 5h 2 x 10 5 M sun / Mpc 3

9. Rationale: Energy, Energy, and Energy Black Hole Mass Growth Magnetic Energy Growth

10. The Magnetized Universe Project Energy Transport: (1) how do jets/helix collimate? (2) how do radio lobes form? Energy Production: (1) how to form SMBH? (2) Accretion disk physics? Energy Conversion: Gravitational Magnetic, dynamo Energy Dissipation: (1) how do magnetic fields dissipate? (2) how to accelerate particles? Astrophys. implications: (1) will lobes expand? (2) how do they impact structure formation? (3) how to prove the existence of B fields?

11. Implications on Dynamo Magnetic energy and flux of radio lobes and their impact to the general IGM really emphasize the need of understanding: (1) kinematic dynamo in accretion disk around SMBHs: How to convert gravitational energy to magnetic energy? * seed field perhaps a non-issue due to large number of rotations * this dynamo seems to saturate at the limit of extracting a significant fraction of the available energy during the SMBH formation Colgate et al.: star-disk collision model for dynamo and liquid sodium experiment at NM-Tech (2) magnetic relaxation (flux-conversion dynamo): How would these lobes evolve in the IGM? ---- Similar to Spheromak and RFP? * degree of magnetization of the IGM, impact on galaxy formation? * ultimate fate of the magnetic energy --- extra-galactic cosmic rays? Li et al.: kinetic simulation of collisionless force-free plasmas

12. AGN Disk Dynamo:Star-Disk Collisions ( Colgate et al; Pariev & Colgate03 ) -phase: disk rotation – toroidal fields -phase (helicity injection): rotation of the rising plumes made by star-disk collisions

13. Liquid Sodium Experiment (Colgate et al.)

14. Magnetic Lobe Relaxation Particles are continuously accelerated in-situ, implying continuous energy conversion. Lobes made in relatively short time (10 7 -10 8 yrs), in a finite volume, with a finite amount of energy and helicity. Since it is over-pressured compared to its surrounding, it should evolve (by relaxation?). Kinetic physics should be included in reconnection in lobes: Kinetic scales: c/ pi ~ 10 11 cm (n ~10 -6 /cc) Sweet-Parker layer width: (L /v) 1/2 ~ 10 9 cm (filaments: L ~10 kpc, eta ~ 10 3, v ~ 10 8 cm/s)

15. In astrophysical plasmas, the condition is often assumed and it is nearly force-free. Q: Is this sheet-pinch configuration unstable? Q: If so, how does it convert B 2 into plasmas? An idealized Problem Sheet-Pinch:

16. Why would it evolve? Lz is the longest length scale --- no relaxation Lz < Lx, Ly --- relaxation

17. Flipping … Predicting final Bz 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 Lx Lz Lx

18. Stability For a background B 0 = (B x,B y,0), consider a perturbed B z, with modes k=(k x, k y ), one gets: B z = i(k. B 0 )u z + non-ideal terms At resonant layer, k. B 0 = 0, energy flows into the layer: for > 0. Dissipation dominates in this layer: resistivity: Furth et al63 collisionless: Drake & Lee77, Bobrova et al.01, Li et al.03 x z MHD kinetic dissipation 0 2 L z /2

19. Resonant Layers in 3D In 2D, two layers: z = /2, 3 /2 In 3D, large number of modes and layers! Layer-Layer Interaction in 3D is expected to play an important role.

20. q-Profile of Resonant Surfaces 3D 2D q = By / Bx z

21. Short Wavelength Limit Collisionless Tearing: Linear Growth Rate (Li et al03, PoP) Long Wavelength Limit

22. V4PIC A Particle-in-Cell (PIC) Kinetic Code First principles simulation of the relativistic Maxwell-Vlasov system in three dimensions Does not need an equation-of-state for closure Particles are advanced using fields interpolated from a mesh; fields are advanced using sources accumulated from particles V4PIC was designed from the ground up for ultra-high performance on modern commodity processors

23. V4PIC -- Under the Hood Lagrangian Eulerian

24. V4PIC -- Current Status Sustained 7.1M particles advanced per second per processor (0.14 s per particle) in the common case was demonstrated on a Pentium 4 2.5GHz. –Memory subsystem is at theoretical limits. –Floating point subsystem is near theoretical limits (~60-80%). –Substantially faster (well over an order of magnitude in some cases) than other PIC codes. A simple parallelization of V4PIC has been done. –Tens of processors on particle dominated simulations. –Routinely running ~100 3 meshes with ~0.5B particles for ~50K time steps on 16 to 32 processors (ranging from overnight to a couple of days per run). V4PIC has been ported to several x86 clusters and LANLs Q machine and validated against simple test problems, magnetic reconnection and plasma instabilities simulations.

25. PIC Simulation Parameters

26. Total Energy Evolution 2D3D I II III I: Linear Stage; II: Layer Interaction Stage; III: Saturation Stage (Nishimura et al02,03; Li et al03a; Li et al03b)

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

28. Global Evolution (II-III): Multi-layer Interactions, Transition to Turbulence, Relaxation, and Re-Orientation

29. Helicity and Energy Dissipation Run 9c4Run 9c1

30. 9c4 9c1

31. Total H H at k = H (k < ) H (k > ) Run 9c4 Two Stage: Total H & W conserved but with significant spectral transfer. Net H & W dissipation.

32. Total H H at k = Total W W at k = Run 9c1

34. 2 /L x 2 /L z 2 /di2 /de Inertial Range ?Dissipation Range

36. Relaxation with intermittency t=0-1.6 7.8 9.35 11 14 15.6 (Li et al03) Evolution of |J| in pdf. Its mean is decreasing with time, i.e., relaxing. But with a significant high |J| tail, i.e., localized high |J| filaments where reconnection is occurring. |J||J| f(|J|)

37. t i = 8 Current Filaments

38. Current Filamentation

40. Field-Aligned E Generalized Ohms Law:

49. Summary System evolves by c onstantly choosing more relaxed states within the constraints of the geometry. In so doing, converting the excess magnetic energy to particle heating/acceleration. 3D simulation shows the existence of intermittent regions, with large local shear, current density and magnetic dissipation rates. Needs more dynamic range to cleanly separate inertial and dissipation ranges, might recover the helicity conservation?

50. New Experiments Expanding and relaxing magnetic bubble experiments without external driving.

51. Background (4) and …. Radio Galaxies