ne: troduction and examples of momentum transport omentum transport physics topics being addressed by Selected highlights and current status Momentum Transport ical Leaders: D. Craig (U Wisc) and H. Li (L NSF Site Review for the Center for Magnetic Self-Organization In Laboratory and Astrophysical Plasmas May 1-2, 2006 Madison, WI
17
Embed
Outline: I. Introduction and examples of momentum transport II. Momentum transport physics topics being addressed by CMSO III. Selected highlights and.
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
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?
• 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