Initial Hydrodynamic Results from the Princeton MRI Experiment

1. Initial Hydrodynamic Results from the Princeton MRI Experiment M.J. Burin1,3, H. Ji2,3, J. Goodman1,3, E. Schartman2, W. Liu2,3 1. Princeton University Department of Astrophysical Sciences 2. Princeton Plasma Physics Laboratory 3. Center for Magnetic Self-Organization (CMSO) CMSO general meeting Oct. 5-7 2005

2. Outline Motivation and background Brief description of apparatus Result I. obtaining a Keplerian-like* flow Result II. on subcritical hydrodynamic shear instability Progress report on Gallium use (towards MRI)

3. Motivation: The Cause of Turbulence in Astrophysical Accretion Disks: What Instability(s) are Relevant? • If sufficiently ionized and magnetized MRI probably responsible, but perhaps not solely • If not? (e.g. some protostellar disks). The presence and relevance of various hydrodynamic instabilities is uncertain; subcriticalshear instabilities are possible, but simulations and experiments so far appear to disagree. • Hope: that a laboratory experiment which can create suitable velocity/shear profiles with sufficient Re/Rm can simulate accretion disk type instabilities in a controlled and repeatable environment. Taylor-Couette Flow ?

4. Experimental Apparatus: Overview Roller Bearing Teflon seal (1/5) Phenolic gear (1/6) connects to motor via belt Inter-nested stainless steel shaftsaligned by cam followers. Shafts are co-supported with roller/thrust collars Rotating vessel components are of cast acrylic except for inner cylinder. (Tie-rods are used to reinforce the outer cylinder) Roller/Thrust Bearing Note: this is mechanically nontrivial

5. Experimental Apparatus: Detail of Rotating Vessel Inner cylinder: R1=7cm, 1 < 4000rpm Outer cylinder: R2=21cm, 2 < 500rpm Chamber height: H=28cm; Aspect Ratio ~ 2; ‘wide-gap’ Unique: Independently-Driven Intermediate Rings as End-Caps Fluids: water, Gallium alloy (soon) When we operate at full speeds: Max Re ~ 107 Max Rem ~ 10-100

6. Rotating Apparatus Design: Use of Intermediary Rings to Reduce Ekman Circulation In most experiments the end caps rotate as a solid body with the outer cylinder. A resulting pressure imbalance drives a circulation, which efficiently (and undesirably) transports angular momentum radially. ideal (pure radial flux) data (from prototype) It was found numerically that just a couple intermediary rings, rotating at intermediary speeds, can significantly reduce the Ekman effect. (Kageyama et al. 2004)

7. Use of Intermediary Rings to Reduce Ekman Circulation: Initial Results Low-Speed “PIV” Data: Re ~ 2 x 105 2D simulation: Re ~3600 by W. Liu w/ differential end-caps w/ solid end-caps Use of differentially rotating end rings successfully reduces Ekman circulation, allowing the ideal profile to be approached, which in turn allows for Keplerian-like profiles to be realized. Results submitted to Experiments in Fluids, August 2005

8. Subcritical Shear Instability: Background Comments • Being able to establish a high-Re Keplerian-like shear flow, we ask: • * what instabilities/fluctuations may now be observed? • * what sort/amount of transport results from them? • in the absence of magnetic, kinetic, and stratification effects. This is a very reduced but fundamental question, with a sparse and debatable history… It needs to be addressed first. Because: * The question is relevant for (at least) cool unmagnetized disks * The question is relevant to a laboratory study of MRI: E.g., Is the background state is already turbulent?

9. Subcritical Shear Instability: Recent Observations (?) Centrifugally Unstable -1 < R  < 0 Also relevant: Rotation Number R R = -4/3 Keplerian w/ shear ? Rayleigh stability boundary R > 0 Cyclonic Case “?” grey areas of subcritical instability ? Example point  Richard & Zhan 1999, Richard 2001

10. Subcritical Shear Instability: what does the data mean?I.e.,What makes for an instability signature (“x”)? The stability boundary data given (“x”s) do not appear to represent a sudden subcritical transition to relatively high fluctuation levels Not exactly sudden 8 % Not exactly increasing Unconvincing. Boundary flows (e.g. Ekman circulation) are suspect Re0

11. Subcritical Shear Instability: Simulations • ‘Shearing-box’ simulations by Balbus, Hawley, and Stone/Winters (1996/1999) conclude hydrodynamic stability even for slightly centrifugally stable flows. (Re ~ 104) • New numerical work by Lesur & Longaretti (2005) give a similar claim. • New work also ongoing by J. Stone and collaborators … Rg = Critical Re for transition Lesur & Longaretti (2005)

12. Subcritical Shear Instability: An Experimental Test From Keplerian-like conditions to a centrifugally-unstable regime … and back again (check for hysteresis). Rayleigh stability boundary Note: actual Re #’s used are about two orders of magnitude higher

13. Initial Result: No Significant Fluctuation Power for high Re Keplerian-like Flow data from midplane Re ~ 1e6 R ~ -1.05 V • Fluctuations start and return to near-quiescent levels (~1%) • Initial evidence for subcritical stability • No evidence • for hysteresis

14. Conclusions • Ekman circulation can be significantly reduced in a wide-gap rotating flow, allowing for Keplerian-like profiles to be obtained. • There is no significant hydrodynamic turbulence in a Keplerian-like flow up to Re ~ 1e6. This is in accord with simulations and in tentative disagreement with the experimental data of Richard & Zahn. More thorough experiments are planned. And then onto MHD and MRI …

15. Addendum: Plans for MRI study • Replacement of vessel with stainless steel version to withstand large rotation pressures (~25 atm.) • Creation of axial B field (~ 6000 G) via 6 electromagnets • Diagnostics: pickup coils for magnetic fluctuations and motor torque (via load cells) for gross radial angular momentum transport. Possible use of ultrasound and acoustics to assess the interior flow state. An invasive fin featuring pressure and Hall probes may be used as well. • Some initial Gallium data may be seen later this month at APS-DPP. ** Go on Lab Tour ** See Poster by E. Schartman **