experimental attempts to study mri and related...
TRANSCRIPT
Hantao Ji
June 17, 2008 @ MRI WorkshopInstitute of Advanced Study
Center for Magnetic Self-Organization in Laboratory & Astrophysical PlasmasPrinceton Plasma Physics Laboratory, Princeton University, USA
Experimental Attempts to Study MRI andRelated Instabilities in the Laboratory
Experimental:Michael Burin*Mark NornbergAustin Roach
Ethan Schartman
Theory/Simulation:Fausto Cattaneo
Akira Kageyama**Jeremy Goodman
Wei Liu***Alex ObabkoJames StoneAcknowledgement:
S. Balbus, P. Longaretti
Thus far, there is no conclusiveevidence that “the MRI” has been
realized in laboratory
But we have learned (and will learn) alot about rotating flows from laboratory
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Experiments, and What Can Be Studied
• Hydrodynamic experiments– Electrically non-conducting fluids (e.g. water)– Stability of rotating shear flows at large Re’s
• Magnetohydrodynamic experiments– Electrically conducting fluids (e.g. liquid metal)– Stability of rotating shear flows at large Re’s but moderate Rm’s
• Plasma experiments– Electron-ion plasma with varying degrees of neutral particles– Physics beyond dissipative MHD in rotating shear flows
Not to simulate accretion disks, but to study basic physics
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Laboratory Contributions to Two CompetingMechanisms of Angular Momentum Transport
β<3.4×10-6 (98% conf.)(improved from our Nature paper)
MHD exp started;Plasma exp prototyping
Princeton MRIexp’ts
β=(1-2)×10-5 based on Wendt(‘33),Taylor (‘36); qualitative exp’ts by
Richard (‘01), Beckley (‘02)
[Sisan et al (‘04);Stefani et al. (‘06)]
Other labexp’ts
None-existing for Keplerian flows10-3-10-1Simulations
Inward transport if any (β<0)**No predictions?Theoreticalarguments
e.g.2×10-5-4×10-4
e.g.10-3-10-1
Observationalrequirements*
Nonlinear HydroMRIMechanism(parameter)
!
" turb =#CsH
!
"turb
= #R3 $% /$R
The Basic Idea
6
Magnetized Taylor-Couette Flow ofLiquid Gallium
• Centrifugal force balancedby pressure force from theouter wall
• MRI destabilized withappropriate Ω1, Ω2 and Bzin a table-top size.
• Identical dispersion relationas in accretion disks inincompressible limit
Ga
!
" + #k 2( ) " +$k 2( ) + kzVA( )
2[ ]2 k
2
kz
2+% 2 " +$k 2( )
2
+&'2
& ln rkzVA( )
2
= 0
7
Taylor-Couette Flows
• Maurice Couetteconceived first device tomeasure water viscosity(1890)
• Lord Rayleigh’scriterion (1916): stable ifangular momentumincreases with radius
• G.I. Taylor (1923)included viscosity,leading to quantitativeagreements
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Taylor-Couette Flows (Cont’d)
• Most modern work focused on nonlinear dynamics: bifurcationsand transition to turbulence
16th International Couette-Taylor Workshop will be heldon Sep 9-11, 2009 at Princeton University
http://mri.pppl.gov/ICTW.html
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Stability Diagram of MagnetizedTaylor-Couette Flow
Past experiments focused onstabilization by magneticfield
Stable but can bedestabilized by B: MRI
Ji, Goodman, and Kageyama, MNRAS (2001)
Unstable but canbe stabilized by B
Always stable
Experimental Adventure
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Importance of Controlling Ekman Effect
Solution: multiple driven rings ateach end
Final design: 2-rings, R1=7.1cm,R2=20.3cm, H=27.9cm
Vagn Ekman (1905)
Kageyama et al. (2004)
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Hydrodynamic StabilityAt Large Re’s
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Guess #0
Guess #1
Guess #2
Guess #3
Guess #4
Guess #5
Guess #6
Fine Profile Controls by Rings
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Nonlinear Transition to Turbulence Observed in CyclonicFlows, and Also in Quasi-Keplerian Flows?
Reynolds #
Torq
ue
Taylor (1936), Wendt (1933): Richard & Zahn (1999) Richard (2001)
Kepler
ian
Rayl
eigh
stabi
lity b
ound
ary
Re based on outer cylinder
Re
base
d on
inne
r cyl
inde
r
Transition toturbulence
Transition towavy states?
A surge of theoretical and numerical work onthis subject since 2002…
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Operation Diagram of Taylor-Couette Flows
Re based on outer cylinder
Re
base
d on
inne
r cyl
inde
r
Richard2001
most Taylor-Couette exp’sexplore alongthis line
CyclonicFlows
quasi-Keplerianflows are asquiet assolid bodyflows
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Direct Measurement of Reynolds Stress
• Simultaneous measurement of Vrand Vθ by a dual synchronizedLaser Doppler Velocimetry– Random errors are reduced by large
number statistics– Systematic errors are removed by
comparing with solid-body flows• Benchmarked at hydrodynamically
unstable casesVr measured by a pair of lasers
!
" turb = #R3$%
$R
• Quantifying transport:
!
" #˜ V r
˜ V $
q2
V$
2
!
" = (1# 2) $10#5Richard & Zahn (‘99):
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No Signs of Turbulence up to Re=2×10^6
• Remarkable fromexperience on terrestrialflows
• Large Reynolds stresswhen– Boundary conditions not
optimum, or– At smaller Re’s
• β<3.4×10-6 with 98%confidence
• β unlikely larger at evenlarger Re’s.
H. Ji, M. Burin, E. Schartman, J. Goodman., Nature (2006)E. Schartman, H. Ji, M. Burin, J. Goodman, in prep. (2008)
Non-optimal b.c.
Laminar transport
Liquid Metal Experiments
• Physics within dissipative MHD:– MRI saturation at small Pm– Nonlinear instability in highly resistive
MHD
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Spherical Couette Flow Experimentin Liquid Sodium
Outer sphere at rest
Sisan et al (2004)
• Exhibits signatures resemble to MRI,but with complications with boundaryconditions, nonaxisymmetric modes
• Still not understood
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Cylinderical Experiment with “Helical”Magnetic Field in Liquid Gallium (HMRI)
• Lower critical Re & Rm by 10^3 [Hollerbach & Ruediger (2005)]• Observed traveling wave in liquid gallium [Stefani et al. (2006)]• Destabilized inertial waves, stable in Keplerian flow [Liu et al. (2006)]• Traveling waves launched in Ekman layer [Liu et al. (2006,2007)]
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Initial Runs at Princeton Exp:Imposing Bz on Hydro-unstable Flows
B~2.5kG Br measurements at surface shownon-axisymmetric mode
Z(cm)
Toroidal angle (radians)
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Detailed Characterizations Underway
Magneto-corelis waves?t(sec)
amplitude spectra dispersion relation
Plasma Experiments
• Physics beyond dissipative MHD:– Hall current (two-fluid effects)– ambipolar diffusion (three-fluid effects)– kinetic effects– radiation– general relativity– …
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Two-fluid Effects on Growth Rates
• Te=4eV, Ti=0.5eV, n=3x1012cm-3, plasma radius=10cm, peak biasvoltage=15V. The rotation profile is assumed to be Keplerian
!
" + #k 2( ) " +$k 2( ) + kzVA( )
2[ ]2 k
2
kz
2+% 2 " +$k 2( )
2
+&'2
& ln rkzVA( )
2
+(H
" + #k 2( )2
+% 2kz
2
k2
)
* + +
,
- . .
&'
& ln r+(
H
/
0 1
2
3 4 + 4'+
&'
& ln r
/
0 1
2
3 4 kzVA( )
25 6 7
8 7
9 : 7
; 7 = 0
!
"H # k2 c
" pi
$
% & &
'
( ) )
2
*ci
Ji (2007)
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A Helicon Plasma Device
Spiral AntennaPowered by 13.56MHzRF source up to 2kW
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What We Learned From the Lab…• Never underestimate the nature
• Never underestimate old ideas
• Importance of (global) boundaries
• Pure hydrodynamics unlikely responsible for AMT
• Richness of rotating shear flow physics– Dissipative MHD (Pm dependence)– Multi-fluid effects– Kinetic effects…