Making Large Scale Magnetic Fields Steve Cowley UK Atomic Energy Authority and Imperial College.
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Transcript of Making Large Scale Magnetic Fields 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?
Russell Kulsrud
Academic Genealogy
Jeremiah Ostriker
Bengt Strongren Subrahmanyan Chandrasekhar
Arthur Stanley EddingtonRalph Fowler
Isaac Newton?
Why bother?Russell Kulsrud
Begat1965 Thomas J. Birmingham (w/J. Dawson)1970 Robert L. Dewar1971 Catherine Cesarsky (not 1st advisor)1974 Russell S. Johnston1975 Scott Tremaine (not 1st advisor)1977 Ellen Zweibel (not 1st advisor)1978 Edward Allen Adler Adilnawaz B.S. Hassam1982 Carl Goran Schultz1985 Steven C. Cowley Darwin D.-M. Ho1986 Carl Richard DeVore1991 Steven W, Anderson1995 Armando Howard1996 Victoria Dormand1997 Benjamin D.G. Chandran1998 Dmitri A. Uzdensky2000 Gianmarco Felice2001 Alexander Schekochihin2001 Leonid Malyshkin2001 Troy Carter2010 Yansong Wang
Amitava Bhattacharjee
Chris Hegna
Eric Held
John James
SIX GENERATIONS!
• 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
Magnetogenesis.On the Origin of Cosmic Magnetic Fields Russell Kulsrud and Ellen ZweibelReports on Progress in Physics, Volume 71, Issue 4, pp. 046901 (2008).
• “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.
Maxwell Prize .
M51Spiral galaxy M 51 with magnetic field data. Credit: MPIfR Bonn
Rosse’s M51 Sketch in 1845
Cluster Turbulence
The Coma Cluster: pressure map[Schuecker et al. 2004, A&A 426, 387]
L ~ 102…103 kpcU ~ 102…103 km/s (subsonic)L/U ~ 108…109yr
• Mergers• AGNs• Wakes
Cluster MHD Turbulence
Turbulence scale is around here
TURBULENCEComa cluster
[Schuecker et al. 2004, A&A 426, 387]
MAGNETIC FIELDSHydra A Cluster
[Vogt & Enßlin 2005, A&A 434, 67]
•Magnetic Reynolds #, Rm ~ 10Magnetic Reynolds #, Rm ~ 102929..
Many Questions1. Seed Field: making the first field .. Particle physics, Weibel instability, stars.
-- typical assumption SEED few times 10-10 gauss
2. How fast can field be amplified-- <B2> just magnetic energy. Small-scale-dynamo. SSD
-- mean <B> -- structured flow – what structure? Helicity, sheared flow, ..?
2. 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 --
2. Instability:-- Providing the stirring flow – MRI, convection etc. Large scale?
-- Small scale instability – plasma instability – firehose, mirror, heat flow etc.
Cluster Turbulence Scales and Times
forcing
1/L102 kpc
k ~ Re3/4/L10 kpc
1/mfp ~ Re/LM1…10 kpc
M=U/vthi Mach No.
Viscous Turnover time1/0 ~ Re–1/2L/U ~ 107…108 yr
Kinetic energy
k-5/3
kk ~ Pm1/2 k
~1000 km
[Schekochihin et al., ApJ 612, 276 (2004)]
Turnover timeL/U ~ 109 yr TOO SLOW
MAGNETO-FLUID PHYSICS | PLASMA PHYSICS
ICM is Magnetised
forcing
1/L k 1/mfp
Turnover time1/0 ~ Re–1/2L/U ~ 107…108 yr
Magneticenergy
Kinetic energy
k-5/3
kk
l
SSD
Smaller is quickerSeed could be small scale, Stars: ReesPlasma Instabilities; Medvedev
ICM is Magnetised
forcing
1/L k 1/mfp
Turnover time1/0 ~ Re–1/2L/U ~ 107…108 yr
Magneticenergy
Kinetic energy
k-5/3
kk
SSDk3/2
Kulsrud and Anderson 1992
Homogeneous dynamo
Bending and Stretching.
Weak B
Strong B
Bend Stretch
Compress
Curvature and |B|anti-correlated.
Amplification without generating smaller scales.
Bend Stretch
Compress
Compress in the directionalong which B doesn’t change.Only some of the random motions do this.
Folded Structure Visualised
[see Schekochihin et al. 2004, ApJ 612, 276; Schekochihin & Cowley, astro-ph/0507686
for an account of theory and simulations]
Fold thickness is resistive scale k~ k
Fold length is size of stretching eddy k|| ~ k.
Intermediate Nonlinear Growth
forcing
k-5/3
k0
Kinetic energy
kks(t)
Define stretching scale ls(t) :
[Schekochihin et al. 2002, NJP 4, 84]
k ~ Pm1/2 kk ~ Re3/4 k0
Saturation
forcing
k0 k ~ Re–1/2 k0 k ~ Re3/4 k0
Kinetic energy
k
Magnetic energy saturates 109 years
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]
?How do we destroy the small scale field? Unwinding?
Current Sheets Go Unstable?
[Alexey Iskakov]
|u| |B|
Pm = 50, Re ~ 300
Reconnection of folds
Alfven waves forming cascade?Goldreich-Sridhar
Unwinding – what is the viscosity in the field?
Plasma Turbulence: 1995 Santa Barbara
Conservation of adiabatic invariantIf the motion is magnetized (when larmorRadius is smaller than turbulent scale):
Even at low field – if we double field we double perpendicular energy.
Magnetized Viscosity --Anisotropic Pressure
Anisotropic pressure tensor in magnetized plasma. Because of fast motion around the field the tensor must be of the form:
DEFINITION OF PRESSURETENSOR.
Chew, Goldberger and Low 1956 – Kulsrud 1963 Varenna notes.
Magnetized Viscosity.
B
Collisionless particle motion restricted tobeing close to field line and conserving .
Compressing Field
Collisionless.Relaxed by Collisions.
P
Collisionless Micro-Instability.
What does it do to the macroscopic behaviour.
Firehose.
Parallel pressure forcessqueeze tube out.
Rosenbluth 1956Southwood and Kivelson 1993P|| P||
Tighter bend grows faster.
Unstable when
Growth rate at negligible B VERY FAST
Marginal Instability
0.1
• MORE COLLISIONS? – mode scatters particles.effective collision rate
• FOLD FIELD TO ENFORCE
HOW DO WE ENFORCE MARGINAL INSTABILITY?
Sharma, Hammett and Quataert 2006 Schekochihin and Cowley 2006
Reduces viscosity – creates smaller velocity scales
Schekochihin,Cowley, Kulsrud, Rosin, Heineman PRL 2006
• MORE COLLISIONS? – mode scatters particles.effective collision rate
• FOLD FIELD TO ENFORCE
Explosive Growth
Sharma, Hammett and Quataert 2006 Schekochihin and Cowley 2006
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