outline: i. introduction and examples of momentum transport ii. momentum transport physics topics...
TRANSCRIPT
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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
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• 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
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• 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
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The Sun
• Helioseismology shows complex rotation pattern in the Sun
• Very anisotropic angular momentum transport in some regions
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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
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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
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• 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
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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)
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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
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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
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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?
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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
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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
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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
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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?
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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
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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)