Title: Observation of magnetocoriolis waves in the Princeton MRI Experiment
1Observation of magnetocoriolis waves in the
Princeton MRI Experiment
Princeton Plasma Physics Lab
Contributors E. Schartman, H. Ji, A. Roach, W.
Liu, and Jeremy GoodmanPST Seminar 18 December
2008
2Outline
- Motivation for studying magnetorotational
instability (MRI) - Experiment to study magnetically induced
turbulence in rotating shear flow - Theory from linear stability analysis
- Observations of propagating waves in
hydrodynamically turbulent liquid metal flow - Conclusions
- Possible discussion of free surface MHD
3What is an accretion disk?
- Gas, dust, and plasma accumulated by massive
stars and black holes - Accretion of material onto the central object
releases energy which is radiated away producing
the measured luminosity of the object - Accretion is responsible for many important
astrophysical processes - Star and planet formation
- Mass transfer in binary systems
- Huge amounts of radiation from quasars and active
galactic nuclei (1015 times luminosity of the sun)
4What is the cause of turbulence in accretion
disks?
- Accretion rate limited by angular momentum
transport - Accretion disks have faster inflow than predicted
by classical viscous transport, so flow is likely
turbulent - Disk flows are linearly stable in hydrodynamics
- Possibilities for instability leading to disk
turbulence - Nonlinear hydrodynamic instability
- MHD instability
- The magnetorotational instability (MRI) is the
destabilization of rotating shear flow by a
magnetic field - We wish to demonstrate the MRI and study angular
momentum transport in the laboratory
5The MRI mechanism
- Magnetic tension can lead to a runaway
instability creating effective radial flux of
angular momentum. - Free energy flow shear
- Only requires dO/dr lt 0
- Purely growing mode
- Resistively limited (minimum Rm required)
- Accretion disk flow follows
- Keplerian orbits
- O(r) (GM)1/2 / r3/2
- dO/dr lt 0
- Centrifugally stable d(r2 O)/dr gt 0
- Re gt 1012
Balbus and Hawley, APJ (1991) Rev. Mod. Phys.
(1998)
6Novel Couette-Taylor experiment
Maryland Spherical Couette
Sisan, PRL, 2004
Stefani, PRL, 2006
- High Reynolds number flows
- Control secondary flow due to boundary layers
Ji et al., Nature, 2006 Burin et al., Exp.
Fluids, 2006
7Linear MHD stability analysis
- Assume ideal Couette profile
- MHD equations
- Flow shear is quantified by vorticity parameter
- Dispersion relation from local (WKB) stability
analysis
8Basic waves in rotating incompressible conducting
fluids
- Dispersion relation for ideal fluid
- Assume no rotation, recover shear Alfvén waves
- Transverse polarization
- Restoring force caused by Lorentz force
- Flow becomes uniform along field
- Assume no field and no flow shear, obtain
inertial waves - Transverse polarization
- Restoring force caused by Coriolis force
- Generated by deviations from uniform rotation
along rotation axis(Taylor-Proudman Theorem
flow becomes uniform along axis of rotation)
9Basic waves in rotating incompressible conducting
fluids
- Magnetocoriolis waves result as a combination of
- Coriolis Lorentz forces
- In phase Fast MC wave
- Out of phase Slow MC wave
- Split Alfvén frequency
- Add resistivity
- Add sufficient shear
- Slow wave becomesunstable (MRI)
Alfvén waves
and Inertial waves
10Couette-Taylor experiment well suited to study
the MRI
Re based on inner cylinder
Re based on outer cylinder
Ji, Goodman, and Kageyama, MNRAS (2001) Ji, et
al., Exp. Models (2004)
11Liquid metal experiments
- Inner cylinder r17cm, ?1 lt 4000 rpm
- Outer cylinder r221cm, ?2 lt 500 rpm
- Chamber height H28cm (aspect ratio 2.1)
- Re 107 and Rm 10
- Liquid metal GaInSn eutectic (Pm 10-6)
- Six coils provide 5 kG axial field (S 0.3 -
3.0) - External magnetic field measured by array of
pickup coils and Hall sensors
E. Schartman (thesis 2008)
12Experimental procedure
- Establish flow in liquid metal by starting motors
- Flow develops over several Eckman times ?200 s
- Apply axial magnetic field (up to 5 kG, ??10 ms)
- Observe external magnetic fluctuations on array
of radial Hall probes (1 Gauss resolution) and
pickup coils (0.5 G/sec sensitivity) - Compare results for different rotation speeds,
shear, and magnetic field strength
13Non-axisymmetric modes observed
Z (cm)
Toroidal angle (radians)
Br (Gauss) measurements at surface show azimuthal
(m1) mode
B0 3.30 kG
14Fourier decomposition of modes
(0,1)
(1,1)
(axial mode, azimuthal mode)
- Two nonaxisymmetric modes with different phase
velocity
15Observation of rotating modes
- (0,1) and (1,1) are dominant nonaxisymmetric
modes - Each show different phase velocity which changes
with field strength
16Observed rotation rates match fast/slow MC-waves
- Phase speeds similar to Alfvén wave
- Match behavior of MC-waves with B0
- Should be damped when ??? so they must be driven
- Positive growth for doubling the rotation speed
17Beginning analysis of rotating shear flow
- Similar separation in phase velocities observed
- Speeds too low to observe significant growth
rates - Excitingly close to marginal stability
183D simulations of experiment
- Collaboration with U. Chicago to simulate
experiment - Nek5000 spectral element code
- Quantitative agreement for quiescent flows
- Examining propagation of nonaxisymmetric modes
-
Obabko, Cattaneo, Fischer, Phys. Scr., 2008
19Conclusions
- Contributing to understanding of astrophysical
MHD processes through laboratory experiments - In magnetized hydrodynamically unstable flows,
we observe several nonaxisymmetric modes - The rotation rates of the two largest
nonaxisymmetric modes match the dispersion
relation for fast and slow magnetocoriolis waves - By mapping the field dependence of the
magnetocoriolis waves we should be able to detect
the threshold for the MRI - Experiments to observe destabilization of a
quiescent flow by an applied magnetic field and
further investigation of magnetized turbulent
flows, both through experiments and simulations,
are ongoing
202D simulation results
- Ekman-Hartman layer development (boundary layer
transitions to Hartmann layer - Steep velocity gradient (Stewartson layer)
becomes unstable to MRI
Liu, PRE (2008)
21Measured profiles for unstable flow
22(No Transcript)
23Study of Free Surface MHD in the Liquid Metal
Experiment
- Mark Nornberg
- Contributors Hantao Ji, John Rhoads, Luc Peterson
24Motivation Astrophysical free surface MHD
- Important in describing dredge up mechanism in
classical novae - Possible explanation for quasi-periodic x-ray
emission from binary star systems
Lattimer Prakash, Science 304, 536 (2005)
25Motivation Liquid Metal PFCs
- Application of liquid metal walls in fusion
reactors - Effective heat transfer
- Protect solid wall
- Reduce recycling
- Possibly improve plasma stability
- Not much is known about the stability of
free-surface liquid metal flow in strong magnetic
fields with electric current
26Design of channel
- Hydrodynamic flows studied to determine best way
to reduce development length - Surface waves due to entrance effects suppressed
using wave damper - Channel enclosed and filled with argon to prevent
oxidization
27Design of magnet
- Up to 3 kG magnetic field provided by cooled
copper wrapped around steel flux core - 2.5 kA from DC Rectifier
28Laser reflection surface wave diagnostic
- Laser beam reflections off surface onto screen
tracked with CCD camera - Wavelength measured from relative phase between
beams
29Determination of dispersion from laser diagnostic
- Laser positions determined by IDL image
recognition routine for each frame - Time series of laser spot positions fitted to
sinusoid packet - Phase determined from fit
- Wave number calculated from linear fit
30Surfactant effect of oxides
- Exposure to oxygen creates oxide film which acts
as surfactant, effectively reducing surface
tension and eliminating capillary waves
Nornberg, Rev. Sci. Instr. (2008)
31Modification of turbulence by magnetic field
- Cross-channel magnetic field has no damping
effect on driven streamwise waves - Yet natural surface fluctuations from turbulent
flow are significantly reduced
Nornberg, Rev. Sci. Instr. (2008)
322D Turbulence
Position Sensitive Device
- We are measuring the power spectrum of surface
fluctuations to study the two-dimensionalization
of surface wave turbulence - Observations indicate scale dependence in damping
- Two sensors are used to obtain k-space spectrum
from cross-correlation analysis
33Measurements of flow profile
- Simulations indicate that Hartmann boundary layer
effect lead to peaking of flow profile - Support from preliminary measurements using
potential probe velocimetry
34Summary
- We have developed a liquid metal channel flow
experiment to study the basic physics of free
surface MHD - We are developing diagnostics to study changes to
both the flow profile and the surface turbulence
due to magnetic fields - Further investigation of stability, heat
transport, and the development of a weak
turbulence theory is underway