Post on 27-Mar-2015
transcript
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:
Accretion DisksAstrophysical JetsSolar InteriorLaboratory Experiments
• 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)
2. Drive flows in MST, vary fluctuations, measure momentum transportRequires electrically biased probes and/or neutral beams (~ 0.5-1 yr)
3. Measure mean flow profile and its evolution in MSTRequires diagnostic development (~ 1-2 yrs)
4. Drive flows in MRX and measure momentum transportRequires electrically biased probes and/or neutral beams (mid-long term)
5. Measure flows in SSX (diagnostic development, near term)
6. Include momentum transport in self-consistent theory for transport in stochastic magnetic fields (~ 1 yr)
7. Assess relevance of self-consistent theory to astrophysics (~ 1 yr)
˜ p i|| ˜ B r
Flow Perturbation Experiments
• Insertable biased probes create pulse of edge flow in MST• Core responds with some delay
global momentum transport timescale ~ 1 ms
Pulse
Time (ms)
2.5 ms
0
10
20
30
40
0 10 20 30 40
Bias
No Bias
Tor
oida
l ve
loci
ty (
km/s
)
Core ion flow (Cv)
• Neutral beam injection might be able to make pulsed core flows
Charge Exchange Recombination Spectroscopy (CHERS): Basic principles
)(AHAH 1)-(ZZ0 n,l (1) Charge exchange
hWe observe this!
hlnln ),(A),(A 1)-(Z1)-(Z
(2) Radiative decay
3431 3435Wavelength (Å)
Sign
al l e
vel (
phot
ons)
Doppler shift () gives vimpurity
Doppler width() gives Timpurity
Area givesnimpurity
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. Drive flows in MST, vary fluctuations, measure momentum transportRequires electrically biased probes and/or neutral beams (~ 0.5-1 yr)
4. Measure mean flow profile and its evolution in MST (~ 1-2 yrs)
Look for evidence of localized forces near resonant surfaces
5. Measure flows in SSX (near term)
6. 3D MHD computation in SSX geometry with hybrid code (near term)
7. Assess relevance for astrophysical jet problem (~ 1 yr)
Maxwell Stress in MHD Computation
• Using DEBS code (3D nonlinear resistive MHD in periodic cylinder)
• Generate saturated RFP state with many tearing modes
• Apply ad hoc uniform toroidal momentum force
(On behalf of F. Ebrahimi, by way of S. Prager)
Maxwell Stress in MHD Computation
• Will examine <J B> from tearing fluctuations and v(r) evolution
• First numerical runs now underway
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
• Believed to dominate angular momentum transport in disks
• Exists in ideal MHD for arbitrarily weak fields: >>
• Feeds on differential rotation• Converts toroidal kinetic
energy to magnetic energy + turbulence
• Growth rate shear rate• Saturates at 10 100 (?)• Demonstrated in simulation,
not yet in lab
Topviewalongrotationaxis
Side viewin poloidalplane
Magnetorotational Instability (MRI)
• How far from ideal can the plasma be?– Some are quite resistive: protostellar disks, quiescent cataclysmic
variables, etc.
• Can AMT be explained by hydrodynamic instabilities?
• Can MRI exist only when > 1 ?
• Do simulations get the transport rate right?
• Answer to latter two questions may be “No” if the scale height of the magnetic field is much larger than that of the plasma: a magnetized corona.
Outstanding Issues Concerning MRI
Plans: Momentum Transport by MRI
1. Calculate linear stability of MRI in lab, apply to MST ( ~ 1 yr)
2. Investigate MRI in liquid metal Gallium experimentOperate experiment (near term)
Apply nonlinear MHD theory to experiment (near term)
Develop incompressible MHD computation (near term)
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)
• Apply differential rotationto boundary with “feedback” BC• Analyze ensuing dynamics
Initial Conditions
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
Parallel Momentum Relaxation• Taylor relaxation - single fluid MHD
Global helicity (AB dV) “conserved” Relax to minimum magnetic energy (via vB) Constant JB/B2 profile
• 2-fluid relaxation Generalized helicity for each species (AsBs dV) is “conserved”
where As = A + (ms/qs) vs and Bs = As
Relax to minimum magnetic + flow energy (via vB and JB)
Constant JB/B2 and nvB/B2 profiles
Parallel current and parallel momentum profiles get coupled
(alternatively dynamo and momentum transport coupled)
• Open question whether this actually happens in lab or space
Plans: Two Fluid Relaxation
1. Observe momentum profile relaxation in 2 fluid MHD computation
in MST geometryRequires code development (~ 1 yr)
2. Measure parallel momentum profile relaxation in any or all
Center devices (MST, MRX, SSX, SSPX) (~ 2-3 yrs)
Develop diagnostics for v(r)
Perform flow perturbation and merging experiments
Evaluate changes in magnetic and kinetic helicity
3. 3D MHD computation in SSX geometry with hybrid code (near term)
4. Evaluate 2-fluid relaxation theory for lab (near term)
5. Assess relevance of theory for astrophysical cases
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
Plans: Momentum Transport in the Sun
1. Develop incompressible/anelastic MHD spectral element code (~ 2 yrs)
2. Develop sub-grid-scale models and compare to direct numerical simulation (~ 2 yrs)
3. Incorporate sub-grid-scale models into spectral element code (~ 3 yrs)
4. Investigate physics of integrated solar dynamo model (~ 4 yrs)
Note: Work to be done in conjunction with work on the solar dynamo problem
Observations and Opportunites inMomentum Transport
1. Opportunities for lab - astro coupling
Coronal MRI simulation - good start, waiting for postdoc
Liquid Gallium experiment - good start
MRI calculation for lab - will begin soon
Astrophysical jet lab connection - need more effort
Astrophysical applications for stochastic B transport - need more
2. Experimental and computational components are strong
Would benefit from increased theory effort for several topics