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Steve Cowley UK Atomic Energy Authority and Imperial College

Making Large Scale Magnetic Fields. Steve Cowley UK Atomic Energy Authority and Imperial College. For Russell at 85. Why bother?. Academic Genealogy. Isaac Newton?. Ralph Fowler. Arthur Stanley Eddington. Bengt Strongren. Subrahmanyan Chandrasekhar. Jeremiah Ostriker. Russell Kulsrud.

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Steve Cowley UK Atomic Energy Authority and Imperial College

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  1. Making Large Scale Magnetic Fields Steve Cowley UK Atomic Energy Authority and Imperial College

  2. For Russell at 85

  3. Why bother? Academic Genealogy Isaac Newton? Ralph Fowler Arthur Stanley Eddington Bengt Strongren Subrahmanyan Chandrasekhar Jeremiah Ostriker Russell Kulsrud

  4. Why bother? Begat • 1965  Thomas J. Birmingham (w/J. Dawson) • 1970  Robert L. Dewar • 1971 Catherine Cesarsky (not 1st advisor) • 1974  Russell S. Johnston • Scott Tremaine (not 1st advisor) • 1977 Ellen Zweibel (not 1st advisor) • 1978  Edward Allen Adler •           Adilnawaz B.S. Hassam • 1982  Carl Goran Schultz • 1985  Steven C. Cowley •           Darwin D.-M. Ho • 1986  Carl Richard DeVore • 1991  Steven W, Anderson • Armando Howard • Victoria Dormand • 1997  Benjamin D.G. Chandran • 1998  Dmitri A. Uzdensky • 2000  Gianmarco Felice • 2001  Alexander Schekochihin • 2001 Leonid Malyshkin • 2001 Troy Carter • 2010  Yansong Wang Amitava Bhattacharjee Chris Hegna Eric Held John James SIX GENERATIONS! Russell Kulsrud

  5. Magnetogenesis. On the Origin of Cosmic Magnetic Fields Russell Kulsrud and Ellen Zweibel Reports on Progress in Physics, Volume 71, Issue 4, pp. 046901 (2008). • When was the first significant field? Before, during or after structure? • Top down or bottom up? Is field made/amplified at small scale then “cascaded” to large scale or does it just grow at large scale? • Is the seed relevant? Does subsequent amplification and processing by turbulence wash out any relic? SKA -- Understanding cosmic magnetism

  6. Maxwell Prize . • “The author will attempt to describe one of the more important of these plasma-astrophysical problems, and discuss why its resolution is so important to astrophysics. This significant example is fast, magnetic reconnection. Another significant example is the large-magnetic-Reynolds number magnetohydrodynamics (MHD) dynamo.” Kulsrud 1994 Maxwell prize address Both problems are unfinished.

  7. M51 Spiral galaxy M 51 with magnetic field data. Credit: MPIfR Bonn Rosse’s M51 Sketch in 1845

  8. Cluster Turbulence • Mergers • AGNs • Wakes L ~ 102…103 kpc U ~ 102…103 km/s (subsonic) L/U ~ 108…109yr The Coma Cluster: pressure map [Schuecker et al. 2004, A&A 426, 387]

  9. Cluster MHD Turbulence TURBULENCE Coma cluster [Schuecker et al. 2004, A&A 426, 387] MAGNETIC FIELDS Hydra A Cluster [Vogt & Enßlin 2005, A&A 434, 67] Turbulence scale is around here • Magnetic Reynolds #, Rm ~ 1029.

  10. Many Questions • Seed Field: making the first field .. Particle physics, Weibel instability, stars. -- typical assumption SEED few times 10-10 gauss • How fast can field be amplified -- <B2> just magnetic energy. Small-scale-dynamo. SSD -- mean <B> -- structured flow – what structure? Helicity, sheared flow, ..? • What is the structure of the Saturated field? few times 10-6 gauss -- folds, plasmoids, Alfven waves, -- <B>2/<B2> • Universality – do the transport properties of the medium matter. -- PM the magnetic Prandtl number (viscosity/resistivity) -- plasma versus rock, neutrals, cosmic rays -- • Instability: -- Providing the stirring flow – MRI, convection etc. Large scale? -- Small scale instability – plasma instability – firehose, mirror, heat flow etc.

  11. Cluster Turbulence Scales and Times Kinetic energy k-5/3 Viscous Turnover time 1/0 ~Re–1/2L/U ~ 107…108 yr forcing MAGNETO-FLUID PHYSICS | PLASMA PHYSICS 1/L 102 kpc k ~ Re3/4/L 10 kpc k ~ Pm1/2 k ~1000 km k 1/mfp ~ Re/LM 1…10 kpc M=U/vthi Mach No. Turnover time L/U ~ 109yr TOO SLOW [Schekochihin et al., ApJ612, 276 (2004)]

  12. ICM is Magnetised Kinetic energy k-5/3 Turnover time 1/0 ~Re–1/2L/U ~ 107…108 yr SSD forcing Magnetic energy 1/L k k k 1/mfp Smaller is quicker Seed could be small scale, Stars: Rees Plasma Instabilities; Medvedev l 

  13. ICM is Magnetised Kinetic energy k-5/3 Turnover time 1/0 ~Re–1/2L/U ~ 107…108 yr Kulsrud and Anderson 1992 SSD k3/2 forcing Magnetic energy 1/L k k k 1/mfp Batchellor 1950 Saffman 1963 Kazantsev 1968 Menaguzzi and Poquet 1963 Chandran 1997, Schekochihin …… Homogeneous dynamo

  14. Bending and Stretching. Weak B Strong B Bend Stretch Curvature and |B| anti-correlated. Compress

  15. Amplification without generating smaller scales. Bend Stretch Compress in the direction along which B doesn’t change. Only some of the random motions do this. Compress

  16. Folded Structure Visualised Fold thickness is resistive scale k~ k Fold length is size of stretching eddy k|| ~ k. [see Schekochihin et al. 2004, ApJ612, 276; Schekochihin & Cowley, astro-ph/0507686 for an account of theory and simulations]

  17. Intermediate Nonlinear Growth Kinetic energy k-5/3 forcing k0 ks(t) k Define stretching scalels(t) : k ~ Pm1/2 k k ~ Re3/4 k0 [Schekochihin et al. 2002, NJP 4, 84]

  18. Saturation Kinetic energy ? Magnetic energy saturates 109 years How do we destroy the small scale field? Unwinding? forcing k0 k ~ Re3/4 k0 k ~ Re–1/2 k0 k Nonlinear growth/selective decay/fold elongation continue until ls ~ l0 B2 ~ u2 and l ~ Rm–1/2 l0 [Schekochihin et al. 2002, NJP 4, 84]

  19. Current Sheets Go Unstable? Reconnection of folds Alfven waves forming cascade? Goldreich-Sridhar |u| |B| Pm = 50, Re ~ 300 [Alexey Iskakov]

  20. Unwinding – what is the viscosity in the field? Plasma Turbulence: 1995 Santa Barbara Conservation of adiabatic invariant If the motion is magnetized (when larmor Radius is smaller than turbulent scale): Even at low field – if we double field we double perpendicular energy.

  21. Magnetized Viscosity --Anisotropic Pressure Chew, Goldberger and Low 1956 – Kulsrud 1963 Varenna notes. DEFINITION OF PRESSURE TENSOR. Anisotropic pressure tensor in magnetized plasma. Because of fast motion around the field the tensor must be of the form:

  22. Magnetized Viscosity. B Collisionless particle motion restricted to being close to field line and conserving . Collisionless. Relaxed by Collisions. P Compressing Field

  23. Collisionless Micro-Instability. What does it do to the macroscopic behaviour.

  24. Firehose. Unstable when VERY FAST Growth rate at negligible B Parallel pressure forces squeeze tube out. Tighter bend grows faster. Rosenbluth 1956 Southwood and Kivelson 1993 P|| P||

  25. Marginal Instability 0.1

  26. HOW DO WE ENFORCE MARGINAL INSTABILITY? • MORE COLLISIONS? – mode scatters particles. • effective collision rate • FOLD FIELD TO ENFORCE Sharma, Hammett and Quataert 2006 Schekochihin and Cowley 2006 Reduces viscosity – creates smaller velocity scales Schekochihin,Cowley, Kulsrud, Rosin, Heineman PRL 2006

  27. Explosive Growth • MORE COLLISIONS? – mode scatters particles. • effective collision rate • FOLD FIELD TO ENFORCE Sharma, Hammett and Quataert 2006 Schekochihin and Cowley 2006

  28. So where are we? • There is time for plenty of field growth. • The seed field is probably not visible in the data. • I still don’t understand how the field structure • forms – and what it is. • Russell we aren’t finished

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