1. Outline: I. Introduction and examples of momentum transport II. Momentum transport physics topics being addressed by CMSO III. Selected highlights and current status Momentum Transport Topical Leaders: D. Craig (U Wisc) and H. Li (LANL) NSF Site Review for the Center for Magnetic Self-Organization In Laboratory and Astrophysical Plasmas May 1-2, 2006 Madison, WI

2. Angular momentum must be transported outward as mass is transported inward Leading mechanism for this is the Maxwell Stress resulting from the magnetorotational instability (MRI) Accretion Disks J. Hawley and Krolik, ApJ 2001 top view cut away side view z r

3. Produced by a combination of rotation and magnetic fields Possibly collimated by magnetic fields Axial flow decelerates by transfer of momentum toward edge of jet Optical jet in galaxy M87 (NASA/HST) Cartoon of magnetically collimated jet Astrophysical Jets

4. The Sun Helioseismology shows complex rotation pattern in the Sun Very anisotropic angular momentum transport in some regions

5. MST Experiment (U Wisc) Hot plasma confined with helical magnetic fields Plasma flows within nested toroidal surfaces Repeatedly observe sudden momentum transport between different toroidal surfaces Magnetic field fluctuations play a key role Toroidal Velocity 10 20 30 km/s

6. Momentum Transport: Areas of Emphasis 1. Maxwell stress from flow-driven instabilities (MRI) 2. Maxwell stress from current-driven instabilities 3. Two-fluid analogs to Taylor relaxation 4. Momentum transport by stochastic magnetic fields We are focusing our efforts on 4 physics topics: In all 4 topics, momentum transport is mediated by magnetic fluctuations All 4 topics have experiment, theory, computation and lab-astro components

7. Liquid gallium Couette flow Differentially rotating inner and outer cylinders Split end caps to reduce Eckman circulation MRI destabilized with appropriate differential rotation and Bz in a table-top size. Flow profiles measured with laser Doppler velocimetry (in water) The Princeton MRI Experiment

8. Simulations and experiments in water indicate desired Couette flow profiles are achievable Hydro Simulation for MRI Experiment radial flux of axial angular momentum 3D mesh with split endcaps 3D nonlinear simulation in same geometry as experiement MRI-relevant flow profiles are stable (without magnetic field)

9. Subcritical Hydro Shear Instability Proposed values (Richard & Zhan 1999) A proposed alternate of MRI, especially for cold disks Very few relevant experiments and 3D simulations at large Res Directly measured Reynolds stress in Keplerian-like flows is indistinguishable from solid-body flows Pure hydro instabilities very unlikely to be important for cold disks --> MHD/MRI is probably required to explain accretion disks Experiment Reynolds Stress

10. MHD Computation for MRI Experiment Shows Turbulent MRI Initiate with vertical B MRI grows and develops into nonlinear regime Model torque on inner and outer cylinders - To be compared with experiment

11. Corona dominates dissipation in some disks (esp. near black holes) –nonthermal X-ray spectra –outflows and jets from disks Corona may also dominate angular momentum transport Exploring this possibility by combining simulation and semi-analytic models –exploit existing codes for low- MHD in solar corona –anchor field in a differentially rotating disk Simulations underway –Next step: include feedback of twisted field on the disk rotation initial state: flux dipole...after a few rotations Do Disk Coronae Contribute to Angular Momentum Transport?

12. Maxwell Stress from Current-Driven Instabilities Fluctuating B from tearing modes can make a net force, If multiple ks present, can have added contribution from coupling e.g. J k ~ B k B k-k & ~ B k B k B k-k Earlier measurements suggested coupling was most important effect in MST CMSO Strategy: 1.Develop models for these forces in MHD & two-fluid 2.Directly measure in experiment 3.Assess relevance for astrophysical jets

13. Core Velocity Profile Flattens During Relaxation Events in MHD Computation Use 3-D resistive nonlinear MHD code (DEBS) Put ad-hoc force term in momentum equation

14. Direct Measurements of During Relaxation Events in MST FIR Faraday rotation measures in the core Magnetic forces are large (too large) - Force is in opposite direction to flow change - Implies other large term(s) in momentum equation - || - dv/dt

15. Computational Jet Radius 02.5 Bz B RFP Profiles Computational Jet Profiles Astrophysical Jets Could Be Close Magnetic Analog of RFP MHD computation used to investigate evolution of a magnetically dominated jet Profiles with similar magnetic structure to RFP lab plasmas can arise Do current-driven instabilities lead to momentum transport?

16. Is There a General Connection Between Reconnection and Momentum Transport? Hall term in Ohms law Parallel force in momentum equation Broken magnetic surfaces non-ambipolar particle fluxes (evidence for this in MST) buildup of electric fields new sources of flows Current driven reconnection may always produce momentum transport - Emerging topic for CMSO - Should consider the consequences of this in space and astrophysical plasmas

17. Summary Momentum transport due to magnetic fluctuations is an important process in the lab and in astrophysics CMSO Impact MRI experiment & computational support (UC + Princeton) Solar codes used to simulate accretion disks (SAIC + Princeton) Current driven reconnection is accompanied by momentum transport (UW) Analogs of current-driven Maxwell Stress in astrophysical jets?(UW+LANL+Torino)