Upload
jed
View
50
Download
2
Embed Size (px)
DESCRIPTION
Plasma Dynamos. UCLA January 5th 2009 Steve Cowley, UKAEA Culham and Imperial Thanks to Alex Schekochihin, Russell Kulsrud, Greg Hammett and Mark Rosin. After re-ionization the universe was probably a reasonably collisionless turbulent high plasma. - PowerPoint PPT Presentation
Citation preview
Plasma DynamosUCLA January 5th 2009
Steve Cowley, UKAEA Culham and Imperial
Thanks to Alex Schekochihin, Russell Kulsrud, Greg Hammett and Mark Rosin.
Early magnetic fields -- what, when and how.
• After re-ionization the universe was probably a reasonably collisionless turbulent high plasma.
• Many large scale plasmas are quite collisionless. • I will argue that (random) magnetic fields grow rapidly
in such a plasma. • I will also argue that we need to know a lot more
about the small scale dynamics of high plasmas. We need an experiment at >> 1!
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 Turbulence
Note: it is not obvious that there isturbulence! [A. Fabian 2003,MNRAS 344, L48]
• Mergers• AGNs• Wakes
L ~ 102…103 kpcU ~ 102…103 km/s (subsonic)L/U ~ 108…109yrmfp ~ 0.1…10 kpc
Re ~ 1…102
The Coma Cluster[Schuecker et al. 2004, A&A 426, 387]
Cluster Magnetic Fields
Abell 400 cluster [Eilek & Owen 2002, ApJ 567, 202]
900 kpc
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..
The Large Prandtl Number Case: Galaxies, Clusters etc.
• Magnetic Prandtl number = Pr = /.
• On the turnover time of the viscous eddies the “seed field” grows. The field develops structure below the viscous scale down to the resistive scale l= Pr -1/2 l
l
l = 10 -30kpcViscous scale
t
= 10 8 yearsViscous eddy Turnover.
Isotropic Homogeneous Dynamo Folded Structure at Resistive Scale
Grayscale is |B|.
ScalarViscosity
Plasma not Fluid
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.
Magnetized Viscosity.
B
Collisionless particle motion restricted tobeing close to field line and conserving .
Compressing Field
Collisionless.Relaxed by Collisions.
P
Incompressible Braginskii MHD.
Coefficients worked out by Braginskii Reviews of Plasma Physics Vol. 2.
Collisional limit
Unit vector along B
Equilibrium -- Decreasing B.
V0 V0
B0
B0
Stretching rate
Firehose Instability.
Look at instabilities that are smaller scale than the field and growing faster than the stretching rate. Treat B0 as quasi-constant during the growth.
We take perturbed velocity to go as:
The condition that the growth rate is faster than stretching rate is:
Firehose Instability.
Linearized:
The x component becomes:
Perturbed field lineCurvature.
Firehose Instability.
Putting this into force equation we get.
Alfven wave when no anisotropy
More Firehose.
Parallel pressure forcessqueeze tube out.
Rosenbluth 1956Southwood and Kivelson 1993P|| P||
Tighter bend grows faster.
Unstable when
Growth rate at negligible B
So What!? -- Nonlinear Firehose.
Nonlinear kinetic theory gives:
Rate of changeof B2 averaged along B.
Instability tries to keep average B constant by bending the field.
DivergingFlow.
Makes finite wiggles
Schekochihin et. al. Phys. Rev. Lett.
Nonlinear Mirror Mode.
When the field increasing the plasma is unstable to the mirrorMode which creates little traps in the plasma.
Converging
Stretching and compressing
Field decreasingP||>P FirehoseUnstable.
Field increasingP||< P Mirror modeUnstable.
Stretched at the turnover rate of theviscous eddies.
Using Braginskii’sExpression we getP||-P ~ Re-1/2P ~ P/6
Scales
ll00~~1-3Mpc1-3Mpc
Viscous Scale l ~l0Re-3/4~10 - 30 kpc
l0 /u0~109
yearsl/ u~108
years
Mean-FreePath. mfp
~ l0Re-1~1-10kpc
kResistive Scale ~ l0Rm-1/2 ~ 104km
Ion LarmorRadiusScale @B = 1G~105km.
EB ?EV
Maximum growth rate
ll00~~1-3Mpc1-3Mpc
Viscous Scale l ~l0Re-3/4~10 - 30 kpc
l0 /u0~109
yearsl/ u~108
years
Mean-FreePath. mfp
~ l0Re-1~1-10kpc
kResistive Scale ~ l0Rm-1/2 ~ 104km
Ion LarmorRadiusScale @B = 1G~105km.
EB ?EV
?
?
Scales
What does small scale field do?
Enhanced particle scattering? Effective collisions increase --i? If so viscosity decreases -- Re gets large and turbulence has faster motions.
Dynamo Growth Time: ~ 0( i/L)(1/2) ~ 1000 years!
MAGNETIC FIELD CAN GROW ON TRIVIAL TIMESCALES.
Sharma, Hammett, Schekochihin, Kulsrud etc.
Conclusions.
• Small scale fast growing instabilities to be expected in weak field magnetized fully ionized plasmas. Make finite wiggles on the scale almost of the ion larmor radius.
• May enhance collisions, dissipation and change the transport properties.