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