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

• 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

• 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

The Sun

• Helioseismology shows complex rotation pattern in the Sun

• Very anisotropic angular momentum transport in some regions

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 VelocityCore Velocity (km/s)

Time (ms)

5 10 15 20 25 30

10

20

30

km/s

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

• 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

Simulations and experiments in water indicate

desired Couette flow profiles are achievable

Hydro Simulation for MRI Experiment

radial flux of axialangular momentum

3D mesh withsplit endcaps

• 3D nonlinear simulation in same geometry as experiement

• MRI-relevant flow profiles are stable (without magnetic field)

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 Re’s

• 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

MHD Computation for MRI ExperimentShows 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

fl_+0.10.mov

• 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 AngularMomentum Transport?

Maxwell Stress from Current-Driven Instabilities

• Fluctuating B from tearing modes can make a net force, <JkBk>

• If multiple k’s present, can have added contribution from couplinge.g. Jk ~ Bk’Bk-k’ & <JkBk> ~ BkBk’Bk-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 <JkBk> in experiment

3. Assess relevance for astrophysical jets

Core Velocity Profile Flattens DuringRelaxation Events in MHD Computation

)F(vBJvvv

rSSt

2

• Use 3-D resistive nonlinear MHD code (DEBS)• Put ad-hoc force term in momentum equation

Direct Measurements of <JB> DuringRelaxation Events in MST

• FIR Faraday rotation measures <JB> 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

100

80

60

40

20

0

N/m

3

-1.5 -1.0 -0.5 0.0 0.5 1.0 1.5Time [ms]

<JxB>// dV/dt >//

- <JkBk>||

- dv/dt

Computational Jet

Radius0 2.5

Bz

B

RFP Profiles Computational Jet Profiles

Astrophysical Jets Could Be CloseMagnetic 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?

Is There a General Connection BetweenReconnection and Momentum Transport?

• Hall term in Ohm’s 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

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)