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

3

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

4

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

8

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

9

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

12

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)

13

15

Hydrodynamic StabilityAt Large Re’s

17

Guess #0

Guess #1

Guess #2

Guess #3

Guess #4

Guess #5

Guess #6

Fine Profile Controls by Rings

18

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…

19

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

20

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):

22

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

25

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

26

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)]

27

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)

28

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– …

30

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)

31

A Helicon Plasma Device

Spiral AntennaPowered by 13.56MHzRF source up to 2kW

33

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…