e: roduction, background, and examples of momentum tra mentum transport physics topics being addressed by Physics, Plans, and Progress Momentum Transport D. Craig General Meeting of the Center for Magnetic Self-Organization In Laboratory and Astrophysical Plasmas August 4-6, 2004 in Madison, WI
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Outline: I. Introduction, background, and examples of momentum transport II. Momentum transport physics topics being addressed by CMSO - Physics, Plans,
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Outline:
I. Introduction, background, and examples of momentum transport
II. Momentum transport physics topics being addressed by CMSO
- Physics, Plans, and Progress
Momentum Transport
D. CraigGeneral Meeting of the Center for Magnetic Self-Organization
In Laboratory and Astrophysical Plasmas
August 4-6, 2004 in Madison, WI
Why Study Momentum Transport?• Momentum transport is an important issue in:
• Collisional viscosity fails to explain transport of momentum in all of the above cases
• Magnetic fluctuations can have a large, often dominant effect on the system in all of these situations
• A theme of Center research in this area is to significantly further our understanding of when and how magnetic fluctuations contribute to momentum transport
• Thin disk of material orbits a compact object and slowly falls onto it
• Angular momentum must be
removed from accreting material:
• Leading explanation for this
is torque associated with magnetic
fluctuations
GMRMRTorque )(
Protostellar disk+jet (Hubble Space Telescope)
Accretion Disks
• Associated with disks of protostars, Xray binaries, Active Galactic Nuclei.– Synchrotron radiation
reveals B field in AGN & AGN jets
• Probably rotationally driven and magnetically confined– Helical field pinch
• Axial flow decelerates by transfer of momentum toward edge of jet– Analogous to lab?
Optical jetin galaxy M87(NASA/HST)
Cartoon ofmagneticallycollimated jet
Astrophysical Jets
Internal Rotation Profile of the Sun
• Helioseismology shows the internal structure of the Sun.• Surface differential rotation is maintained throughout the convection zone• Solid body rotation in the radiative interior• Thin matching zone of shear known as the tachocline at the base of the solar convection zone• How does this come about?
Momentum sources + transport
MST (Wisc) Experiment and ToolsR = 1.5 ma = 0.52 mB ~ 0.2 T
n ~ 1019 m-3
Te,i ~ 0.1-1 keV ~ 10 %
Tools:• FIR Interferometer / Polarimeter• Doppler Spectroscopy - Passive - chord averaged flow - Active Charge Exchange Recombination Spectroscopy (CHERS) - 1 cm resolution (in development)• Coil arrays - magnetic fluctuation spectrum• Insertable probes - Langmuir, Mach, magnetic, spectroscopic• Auxiliary flow drivers - biased probes in edge - neutral beam in core (in development)
v toro
idal
r
vmax ~ 30 km/s
v polo
idal
r
vmax ~ 10 km/s
Helical Flows Are Naturally Present in MST Plasmas
• In core, v mostly parallel to B
• In edge, have vparallel and vperp
• Origin of flows unclear
(sketches based on incompleteflow profile measurements)
Plasma Momentum Changes Spontaneously in MST with Bursts of Magnetic Activity
m=1,n=6m=1,n=7
m=0,n=1
20
30
40
10 15 2050
50B (
Gau
ss) 150
100
0
20B (
Gau
ss)
40
0
10v
(k
m/s
)n=
6
25 30Time (ms)
sawteethcore modes
edge mode
~~
• Plasma rotation slows in ~ 100 s
• Not classical - 100 times too fast - n, T, ... do not change enough on this timescale• Leading explanation involves coupled magnetic fluctutaions
v toro
idal (
km/s
)
z
R
• Two kinds of flows:
1. v associated with reconnection 2. toroidal (azimuthal) flows• Momentum transport not examined yet
Spontaneous Flows Also Measured in MRX
Toroidal (out of reconnection plane) flows
null helicity
separatrix
co-helicity(guiding B)
separatrix
v (
km/s
)
v (
km/s
)n = 1-20 x 1019 m-3
T = 4-30 eV
B = 0.05 T
= 0.1-10
Momentum Transport Physics and Plans
1. Momentum transport by stochastic magnetic fields
2. Momentum transport by Maxwell stress from current-driven instabilities
3. Momentum transport by Maxwell stress from magnetorotational instability
4. Generation and relaxation of momentum as part of a 2-fluid form of magnetic relaxation
5. Momentum transport in the sun
We have chosen to focus our efforts on 5 physics topics:
Transport by Stochastic Magnetic Fields
• Mechanism:B field lines wander in spaceParticles or waves follow field lines
Momentum carried in space
• Stochastic fields often found
in lab and space- All Center devices + other lab plasmas- Accretion disks (in MHD computation)- Likely in jets and in sun
• Stochastic fields NOT often invoked for momentum transport
Tor
oida
l Ang
le /
r/a
Puncture Plot of B Field in MST
Plans: Momentum Transport in Stochastic B
1. Measure in MST, a direct measure of this effectRequires diagnostic development (~ 1-2 yrs)
Measure Doppler shifted and broadened line emission profile Need accurate model for profile shape Need accurate technique for data fitting
2000
0
CHERS: Profile measurement
1000
Beam-driven CHERS emission is localized
View emission resulting from charge exchange between beam neutrals (H) and background impurity ions Intersection volume between beam and fiber views is small localized measurement of impurity Ti, vi (and possibly ni)
30 keV H beam
MST vessel
Fiber bundle views of beam and background
Perpendicular viewing chords
Beam current monitor
Upgraded CHERS system installed on MST(April 2004)
Initial measurements made on CVI line emission (~344 nm)Data exhibit large signal, low signal-to-noise Will allow impurity Ti, vi to be resolved on fast time scale (~ 100 s)Atomic modeling & initial fitting of CVI line shape has been done
12 14 16 18
200
400
600
800
1000
time (ms)
Ti (
eV)
Beam ONBeam off Beam off
Momentum Transport Physics and Plans
1. Momentum transport by stochastic magnetic fields
2. Momentum transport by Maxwell stress from current-driven instabilities
3. Momentum transport by Maxwell stress from magnetorotational instability
4. Generation and relaxation of momentum as part of a 2-fluid form of magnetic relaxation
5. Momentum transport in the sun
Current-Driven Tearing Modes• Perturbations with k·B = 0 do not bend B field lines
Fluctuations with k·B = 0 somewhere are called “resonant”Position (surface) where k·B = 0 called “resonant surface”
• In MST, have helical B helical resonant perturbationsPitch of B field lines changes with radius
Multiple resonances throughout plasma
• Tearing ModesOne class of resonant perturbations
Driven primarily by J(r)
Tear magnetic field to form islands
• Typically see full spectrum of
tearing modes in MST toro
idal
dir
ectio
n
radius
Puncture plot for single mode
• Fluctuating B can make net force, <JkBk>- Can rewrite as (BkBk) magnetic analog of (vkvk)
• Nonlinear mode coupling can give
• Force at resonant location for mode k has the form:
• In MHD, forces localized to resonant positions of coupled modes
• Forces are differential (3 forces at 3 locations all add to 0)
- Momentum transport, no net force
k'-kk'k ~ B~B~J~
)sin(C~F k'-kk'kk'kk'kk'
k'-k,k'k,k BBB
phases ofmodes
Magnetic Maxwell Stress FromNonlinearly Coupled Tearing Modes
coupling coefficient
Coupled Tearing Modes ProduceStrong Torques in MST
<JB>
tvM
2
• Maxwell stress in core estimated from edge measurements of B
• Mode amplitude and coupling increase during relaxation events
• Strong <JB> forces result
Plans: Momentum Transport byMaxwell Stresses from Tearing Modes
1. Measure <JB> directly in MST (~ 1-2 yrs)
2. Calculate <JB> directly in MHD computation (~ 1 yr)
3. Evaluate the role of active disk coronae in angular momentum
transport in accretion disksRequires code development (longer term)
• Liquid gallium Couette flow
• Centrifugal force balanced by pressure force from the outer wall
• MRI destabilized with appropriate 1, 2 and Bz in a table-top size.
• Identical dispersion relation as in accretion disks in incompressible limit
Bz<1T
The Princeton MRI Experiment
Status• Water experiments and hydrodynamic simulations revealed
importance of Ekman effect due to end plates. Paper published.
• Optimized design includes 2 independently driven rings at each end:– Ekman effect minimized, and thus much wider operation regimes
– Much more complex apparatus
• Engineering design completed, reviewed, bid awarded, and the apparatus fabricated and assembled. Testing underway.
• Magnetic coils designed, fabricated. Other components completed or underway. Ready for gallium experiments later in the year.
• Modeling: a new spectral-element code working (Fausto et al.) and the existing ZEUS code being adapted (Liu, Stone, Goodman).
Angular momentum transport in thin disks and coronae
• Schnack & Mikic visited Princeton Jan 04
• Met with Goodman, Yamada, Ji, Kulsrud
• Thin disk tutorial• Formulated
computational plan• Summary notes written
by Goodman
Status
• Princeton to hire post-doc (status?)• Spend fraction of time at SAIC/San Diego to work
on simulations (Schnack & Mikic)• Codes exist, but need modification of BCs
(Goodman notes)• Similar to coronal disruption/flare/CME problem• Model problems (disk flares) done 10 years ago at
SAIC (NASA proposal, not funded!)
Problem Formulation
• Magnetic loops in disk coronae are stressed by differential rotation of disk (similar to solar corona evolution)
• Two consequences:– Disruptions (disk flares)– “Non-local” angular momentum transport between footpoints of loops (feedback
on disk rotation)
• Modify existing code (MAC) to include Goodman model for disk dynamics (thin disk approximation)– MAC developed and extensively used to study formation and disruption of solar
coronal loops
• Initialize with potential field in corona (specified normal field distribution on disk surface)