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Momentum Transport

Momentum Transport. Mark Nornberg Hui Li for the CMSO team. CMSO PAC Review, Oct. 17-18, 2011. Angular momentum transport in accretion disks motivates understanding self-organization processes.

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Momentum Transport

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  1. Momentum Transport Mark Nornberg Hui Li for the CMSO team CMSO PAC Review, Oct. 17-18, 2011

  2. Angular momentum transport in accretion disks motivates understanding self-organization processes • Angular momentum must be transported outward efficiently as mass is transported inward at high rates. • Leading mechanism for transport in accretion disks is the Maxwell stress resulting from the magnetorotational instability (MRI). • Magnetically dominated/mediated jet/lobes can transfer energy/momentum to large scales. • Use tools developed both in fusion and astrophysics to address the common physics HST Image of NGC 4261 J. Hawley and Krolik, ApJ 2001

  3. Outline • Midcourse Plans and status • Selected highlights in Momentum Transport • Two-fluid NIMROD simulations of MST • Spontaneous flow in MST • PCX linear stability incorporating Hall-effect & neutral drag • Identification of Shercliff-layer instability in MRI Experiment • Response to PAC comments • Plans and ideas for future work on: • Demonstration of MRI in the lab, 3D simulations • Hydrodynamic stability in rotating shear flow • NIMROD simulations of a jet • Study effect of shear flow on mode suppression • Detailed measurement of two-fluid flows in MST • Compare PCX measurements to 2-fluid NIMROD simulations

  4. Momentum Transport Midcourse Plans • Comparison of 2-fluid effects in NIMROD simulation with MST measurements (part of Jake King’s thesis) • Address the cause of spontaneous flow in MST (measurements of kinetic stress comparable and in right direction, work with NBI and bias probes ongoing) • Comparison of 2-fluid effects in NIMROD simulations with PCX measurements • Pending operation of inner cylinder to drive shear, but established successful model of viscous coupling   • Identification of the spiral mode in the MRI experiment (Shercliff-layer instability) • NIMROD MHD simulation of flux conversion in jets: • Personnel needed: trying to recruit a student to learn to use NIMROD code and PIC codes ✔ ✔ partial ✔ beginning

  5. Relaxation of the Reversed Field Pinch exhibits both spontaneous rotation and sudden rapid momentum transport • Hot plasma confined in a helical magnetic field. • Perpendicular and parallel flows appear spontaneously (without an external momentum source) • Rapid transport due to current-driven tearing instabilities. MHD tearing fluctuation (G) Plasma flow andmode rotation (km/s) Momentum transport Spontaneous flow V ~ 10-50 km/s

  6. 2-fluid NIMROD simulations demonstrate reduction of island widths by drift-tearing effects • The importantBand poloidal curvaturedrifts are captured by ion gyroviscous stress in our fluid model when ions are warm. • These drift-tearing effects reduce saturated island widths, unlike diamagnetic drift-tearing, which is suppressed by energy and particle transport in islands. • The resulting turbulent emf matches measurements in MST

  7. The resulting momentum transport exhibits the same balance between strong stresses as observed in the edge of MST • Maxwell stress is a consequence of two-fluid emf • Significant flows result from relaxation followed by slow diffusion between events • Magnitude of stresses is qualitatively similar to MST measurements, but understanding the cause of the large stresses is a continuing effort

  8. Density fluctuation measurements in quiet periods in MST show that kinetic stress can drive flow

  9. Neutral beam injection on MST creates torque on core, increases flow shear, and suppresses core resonant mode • Core resonant mode may be an internal kink rather than resistive tearing • Mechanism for mode suppressioncould be: • Small current drive removes resonance • Fast particle FLR effects • Flow shear m

  10. MRI stability in PCX plasmas calculated accounting for 2-fluid effects and ion-neutral drag Ion neutral drag Hall term

  11. A liquid metal Taylor-Couette experiment is designed to demonstrate the MRI Flow Driven Momentum Transport: Experiment and Theory Bz < 1T Ga • MRI destabilized with appropriate 1, 2 and Bz in a table-top size. • Identical dispersion relation as in accretion disks in incompressible limit • Centrifugal force balanced by pressure force from the outer wall

  12. Observed Large-amplitude, Coherent Velocity Oscillations When Bz Is Imposed Saturated Modes Exhibit a Spiral Structure • Liquid metal: GaInSn eutectic (Pm ~ 10-6) Residual azimuthal velocity Measurements by Ultrasonic Doppler Velocimetry

  13. Saturated Modes Exhibit a Spiral Structure and Only When Elsasser # Λ > 1 • In both hydro-unstable and (stable) quasi-Keplerian flows Inner cylinder speed (rpm/min)

  14. 3D MHD simulations explain these nonaxisymmetric modes as a Schercliff-layer instability Effect of a strongmagneticfield Rayleigh-stable configuration: Angular velocity : Vphi in the (r,z) plane [400, 200, 66, 53] (Re=4000, Rm=15 ) • Rings efficiently reduce Ekman recirculation in the hydrodynamic case • Strong jump of velocity due to rings near endcaps only =0 B=0 • Velocity jump is extended vertically by magnetic field =1

  15. Mechanism: Destabilization of the free shear layer • Magnetic field helps to set up the strong shear in the flow • Shear is hydrodynamically unstable • Instability develops non-axisymmetric modes as a series of vortices in (r,phi) plane • Nonlinearly these vortices merge to form a large scale m=1 mode Experiment Vphi in (r,phi) plane : Re=4000, Rm=15, Λ=1.5 Simulation

  16. Non-axisymmetric modes in Couette flow: MRI ? Maryland experiment : Cu Na Sisan et al., Phys. Rev. Lett (2004) Numerical code: PaRoDy (Dormy et al) Elsasser =0 magnetic field generates a Shercliff layer Elsasser =2

  17. Simulations of Maryland experiment Re=5000, Rm=50 Upper figures: Our simulations Lower: Experiment (Sisan et al. 2004) Good agreement with experiment Related to Shercliff instability rather than MRI...

  18. PAC Comments on Momentum Transport Research PAC: “There is still a concern that these very interesting results [on the MRI expt] do not affect the thinking of the practicing astrophysicists...” The MRI experiment is dealing with critical issues involving the influence of boundary conditions, including whether other experimental work properly accounts for them. This has great import for the fundamental question of hydrodynamic stability of disks. • Not to simulate accretion disks directly, but to study basic physics • 2) Provides a validation case between experiment and theory/simulation • 3) Provides insights on nonlinear development of MRI

  19. Possible connection between astro jet/lobe and RFP/Spheromak • Flux injection by disk and volume filling of magnetic fields via generalized Ohm’s law • Collimation and stability in jets • Line-tied system vs. periodic systems? • How will reconnection occur? • Does multi-layer reconnection exist? • Particle acceleration in such magnetic field configuration • Flux conversion in lobes? Colgate, Fowler, HL 2011

  20. PAC Comments on Momentum Transport Research PAC: “The relation between momentum transport in RFPs and astrophysical jets needs to be refined & more clearly articulated. ...the planned NIMROD simulations of jets to study momentum transport by multiple reconnections...should be a high priority item.” • Current-driven instability in disks has been developed further at CMSO (published in ApJ and PoP). • We are currently trying to identify a new student who will use NIMROD code for jet and lobe simulations.

  21. Plan #1: First Serious Attempt of “Standard MRI” in the Lab prediction • Detailed comparisons underway • Faster runs planned, simulations indicate that at the present rotation speed • (60% of max as designed), the threshold of MRI is at hand

  22. Plan #2: 3D MRI Simulation Residual Azimuthal velocity • 3D simulations using Spectral Element Method • High accuracy – can resolve boundary layers • High parallel efficiency • Predicts experimental torque measurements Inner cylinder radius Bright: azimuthally faster Dark: azimuthally slower

  23. Plan #3: Hydrodynamic Turbulence eXperiment (HTX) look for a possible subcritical transition to turbulence Goal: Why quasi-Keplerian flows are stable to nonlinear perturbations? solid body rotation is susceptible to nonlinear perturbations shear is greatly stabilizing

  24. Plant #4: NIMROD simulations of jet stability and lobe • Accretion disk flow winds up a coronal magnetic field • Jet flow is unstable to the kink instability • The kink instability is stabilized by the coriolis effect for sufficient jet rotation Three types of simulations envisioned: • 1) Jet: two-fluid study of current-driven instability • 2) Lobe: flux conversion from toroidal to poloidal fields • 3) Relativistic reconnection in force-free configurations

  25. Plan #5: Complete momentum confinement measurements with NBI and test shear flow stabilization of core mode

  26. Plan #6: Feasibility study of measuring flow pattern predicted by two-fluid NIMROD simulations using CHERS

  27. Plan #7: Complete installation of bias probes to create differential flow in PCX to look for MRI

  28. 3D Rel. Reconnection Current Sheet Reconnection inflow outflow Diffusion Region (X-line) Magnetic Islands

  29. Explaining momentum transport in astrophysical objects requires understanding flow and current driven instabilities t > 0 θ Magnetic Field Line t = 0 • Angular momentum must be transported outward efficiently as mass is transported inward at high rates. • Leading mechanism for transport in accretion disks is the Maxwell stress resulting from the magnetorotational instability (MRI). • Astrophysical jets/lobes could be a current-dominated system in which current-driven instability might strongly influence transport (as in the RFP) • We can use tools developed both in fusion and astrophysics to address the common physics J. Hawley and Krolik, ApJ 2001

  30. Two-fluid effects in momentum transport • Relaxation process • Direct experimental measurements of turbulent transport • Neutral Beam Injection as a tool to conduct momentum transport experiments • Validation of NIMROD simulations incorporating 2-fluid effects • NIMROD simulations to address astrophysical problems • Current-driven reconnection in a magnetized disk • Stabilization of the kink instability by shear flow in extragalactic jets Current-driven instabilities

  31. Thrust #6: Momentum transport via multiple reconnection layers in jets? (motivated by MST results) Herc A Current? Using NIMROD to study possible multiple layer reconnection – Impact on momentum transport in jet/lobe system

  32. Some possible related physics/configurations between MST and astrophysical disks and jets Cylindrical Approximation NIMROD Simulation of Jets

  33. Thrust #1: Liquid metal MRI Experiment and Simulation • Completing experiments in the regime for the axisymmetric MRI with new velocity diagnostics will provide a platform to study saturation of the instability in resistive regime • 3D MHD simulations in cylindrical geometry will help identify observed non-axisymmetric instabilities in the Princeton MRI experiment • 3D Spherical Couette MHD simulations are being used to understand reported results from Maryland MRI Experiment

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