plans for dynamo research presented by f. cattaneo, s. prager
TRANSCRIPT
Plans for Dynamo Research
Presented byF. Cattaneo, S. Prager
Outline
• Evidence for dynamo effectsin astrophysics
in the lab
• Nonlinear Features of the dynamostatus and plans
• Dynamo Effects Beyond MHDstatus and plans
Evidence for dynamo effects in astrophysics
IGM
• Typical size: 30 kpc wide, 300 kpc long• Magnetic fields: 0.5 – 5 Gauss• Dynamo action in disk around central
SMBH
Galaxy
• Typical size: 1020 m. Rotation period 108
years• Magnetic fields: 3 Gauss (horizontal
cmpnt)• Turbulence driven by supernovae
explosions• Classical - dynamo
Evidence for dynamo effects in astrophysics
Accretion disks
• Turbulence driven by MRI• Magnetic field necessary to drive MRI, self
consistently generated by dynamo action
Late-type stars (Sun)
• Magnetic activity extremely well documented
• Turbulence driven by convection. • Activity cycles• “Mounder minima”• Classical - dynamo for large-scale field• Evidence for small scale dynamo action
Evidence for dynamo effects in “astrophysics”
Geodynamo • Example of system where dynamo must
operate• Turbulence driven by (compositional?)
convection. Strong rotation• Moderate Rm
• Dipolar field exhibits reversals
Laboratory experiments• Plasma devices (more about it
presently)• Liquid metal experiments
• Experiments with highly constrained geometries have achieved dynamo action
• Experiments with “open” geometries hopefully will achieve dynamo action soon
The Madison Dynamo Experiment
Dynamo Effects in Laboratory Plasmas
The lab plasma dynamo does• Generate current locally • Convert poloidal magnetic flux to toroidal flux (and the inverse)• Increase toroidal magnetic flux• Conserve magnetic helicity• Act through alpha and other effects• Arise from fluctuations superposed on the mean field• Achieve a nonlinearly saturated state with
(with self-generated )
The lab plasma dynamo does NOT• Generate magnetic field from a small seed field• Increase magnetic energy (it redistributes magnetic field) †
B ˜ B
Evidence of field generation
• Cowling’s Theorem
• Toroidal flux generation
• Ohm’s law
Cowling’s theorem applied to the RFP
A time-independent, cylindrically symmetric plasma cannot contain a reversed magnetic field
Proof: assume Bz is reversed.
at the radius where Bz = 0
E dl E ||rd
J r2 dBz
drr2 0
Thus, magnetic flux decays within reversal surface, in constrast to experiment
Bz
r
Toroidal magnetic flux increases(in discrete dynamo events)
ToroidalMagneticFlux(Wb)
MST
time (ms)
in experiment
-0.5
0.5
1.0
1.5
2.0
V/m
0.0
0.0 0.2 0.4 0.6 0.8 1.0/a
E||
neo J||(Zeff = 2)
E j
E||
j||
radius
additional current drive mechanism (dynamo)
Linear and nonlinear dynamos
1 2
1 2
( )
( Re ) ,
0, 0, .
t
t
Rm
p
B u B B u
u u u
u B J
J F
B
B
Kinematic regime • Weak initial field• Lorentz force negligible • Seek “exponentially” growing solutions of the induction equation • Linear eigenvalue problem
Nonlinear regime• Lorentz force dynamically important• Dynamo saturation and stationary MHD state• Self consistent solution of velocity and magnetic field• Nonlinear initial value problem
Large and small scale dynamos
Assume that velocity is characterized by typical scale ℓ
Small scale dynamo • Generation on scales ℓo• Competition between line stretching and enhanced diffusion
• Dynamo generates B2 but not B2
Large scale dynamo• Generation on scales ℓo• Lack of reflectional symmetry important (helicity)• Inverse cascades (magnetic helicity, energy, etc.)• Mean field theory and transport
• Average induction α-effect• Average diffusion β-effect• Average advection γ-effect
From kinematic to nonlinear dynamosMost astrophysical situations:
• Dynamos operate in nonlinear regime• Magnetic fields are in equipartition with velocity on integral
scales• Rotation is present and important
What are the dynamo saturation mechanisms that leads to observed field stregths?
ℓ/ℓo
1B2
kin
em
ati
c m
od
els
non
linear
mod
elsLarge-scale dynamos
Small-scale dynamos
How do dynamos saturate?Small-scale dynamos
• What happens to lagrangian properties of flow?
• What is the structure of resulting MHD turbulence?
• Dependence of dynamo fields on Pm
Large-scale dynamos
• Saturation of turbulent transport• α-effect (strong-weak)• β-effect (strong-weak)
• Role of shear• Role of boundary conditions
Proposed researchBasic phenomena: SSD
• Study development and properties of stationary MHD turbulence state generated and sustained by dynamo action (Turbulence effort)• Eulerian properties• Lagrangian properties
• Study dependence of final state with magnetic Prandtl number.
Requirements:
• Existing codes • Manpower
Proposed researchBasic phenomena: LSD
• Establish existence of inverse cascades in high Rm systems• Establish conditions for strong satruration of α-effect
• Boundary terms (helicity flux)• Time dependence• Relation between DN simulations results and RFP
experiments• Conditions for strong satruration of β-effect• Role of shear • Role of magnetic helicity
Requirements:
• Some modifications of existing codes• Formulation of sensible “model problems”• Manpower
Proposed researchSpecific models:
• The solar dynamo: Develop a self consistent model capable of reproducing basic observed properties• Cyclic activity• Realistic distribution of angular velocity in the CZ• Thin tachocline• Correct migration pattern of magnetic activity
Requirements:
• New code must be developed• Spherical geometry• Incompressible/anelastic• Spatial adaptivity
• Major effort in Sub-Grid-Scale modeling• Better understanding of angular momentum transport (angular
momentum effort)• Manpower
Dynamo Effects Beyond MHD
• In the labstrong indications of importance,a rich, relatively unexplored topic
• In astrophysicsgeneral importance not established,possibly only some “special cases,”depends on scope of “dynamo physics”
Dynamo Effects Beyond MHD
• Hall dynamo
• Diamagnetic dynamo
• Kinetic dynamo (current transport)
time (ms)
r/a = 0.9
˜ v ˜ B
j E
MHD dynamo dominant at some radii, not everywhere
r/a = 0.8
Measurement of MHD dynamo
0
-10
-20
0
-20
-10
Volts m
Volts m
-0.5 0 0.5time (ms)
r/a = 0.9
r/a = 0.8
Hall dynamo: a two-fluid effect
j ˜ v ˜ B ˜ j ˜ B
neMHD
dynamoHall
dynamo
Two fluid effects also alter the <v x B> dynamo
From quasilinear theory for tearing mode dynamo
-1
0
1
2
3
4
5
6
0.001 electron skin depth 0.05 ion Larmor radius 1 3
DISTANCE FROM RESONANCE SURFACE X/L
˜ j ˜ B ||
ne
˜ v ˜ B || 100
distance from resonant surface
de s
Mirnov
100
80
60
40
20
0-2 -1 0 1 2
Time [ms]
Time Evolution of Current Density Fluctuation
Ding et al
-25
-20
-15
-10
-5
0
5
-1 -0.5 0 0.5 1 1.5 2
Hal
l dyn
amo
(V/m
)
Time from crash (ms)
Hall term is significant at r/a = 0.8
time (ms)
V/m
˜ j ˜ B ne
Fiksel, Almagri
The diamagnetic dynamo
j|| E
|| ˜ v ˜ B
||
˜ j ˜ B ||
ne
j E v B j B
ne
pe
ne
j E ˜ E ˜ B
B
˜ p e ˜ B
B
parallel component of mean-fields,
or, writing yields
˜ v ˜ j
ne ˜ E ˜ p e B
B2
MHD dynamo
diamagnetic dynamo
Measurement of diamagnetic dynamo
Ji et al
TPE-1RM20 RFP
Different dynamo mechanisms dominate in different parameter regimes
Kinetic Dynamo
Radial transport of parallel current (electron momentum) by particle motion along stochastic magnetic field
not yet measured
Ready for a comprehensive study via
• Experiment (MST, some SSPX, possibly MRX)
• Analytic theory (quasilinear, early nonlinear stage)
• Computation (NIMROD)
Measure dynamo mechanisms directly
• MHD
• Hall
• Diamagnetic
• Kinetic
• Also measure <E> and <j>
˜ v ˜ B
˜ j ˜ B
˜ B ˜ p e
˜ B || ˜ p e
Measurement Techniques
In the hot core
˜ v passive spectroscopy,
active spectroscopy (charge exchange recombination spectroscopy)
Laser Faraday rotation
Motional Stark effect
˜ B
In the cool edge
Insertable probes: magnetic, Langmuir (E), spectroscopic
Active Spectroscopy
30 keV H Beam
Beam CurrentMonitor
Perpendicular Viewing Chords
22.5° ViewingChordMST Vessel
3-Wave Polarimeter-Interferometer System
MST R0 = 1.50 ma = 0.52 mIp = 400 kAne ~ 1019 m-3
B0 ~ 4 kG
Faraday rotation/interferometer system
Spectroscopic probe
Plannned measurements
MHD DynamoEdge: upgrade spectroscopy probe (6 months)Core: CHERS - operation in 1 year for V fluctuations
physics in 2 years
Hall DynamoEdge: probe measurements in 1 yearCore: improve FIR - 1 year
MSE - design spec for mag fluctuations - 6 months
first operation ~ 1.5 years
Study spectral properties (nonlinear coupling)
Diamagnetic dynamoedge: probes to reversal surface ~ 1.5 yearsCore: need new ideas for pe fluctuations (fast
Thomson)
Kinetic dynamoNeed ideas for pe|| fluctuations
Two-Fluid Dynamo Theory
• Quasilinear theory with p(one year)
• Early nonlinear stage
(1 - 2 years)
Two-Fluid Computation
Nimrod: well-suited to experiment,
two-fluid operation in ~ 1
year,
physics results in 2 - 3 years
In ~ 3 years,expect major advance in understanding two-fluid dynamos in the lab
Flow-driven dynamo
• Drive flow with neutral beam injection orbiased probes (in MST, MRX)
• Establish NBI feasibility for MST (expt) and MRX (calculation) - 6 months
Effects beyond MHD in astrophysics
Important physical parameters:
ion skin depth
ion sound gyroradius
MHD reconnection layer width
di c
pi
s cs
ci
dR L
S 2 / 5
Hall dynamo important if
di >> dR
or s >> dR
satisfied in lab
Venues in astrophysics with Hall effects
•Extra-galactic radio lobes
flux conversion dynamo in relaxing plasmas
•Black hole accretion disks
MRI dynamo, flux conversion
•Protostellar disks
Weakly ionized, charged dust
•Neutron star, white dwarf crusts
ions immobilized
Plans: Computation of disk flux conversion
r
z
0 5 10 15 200
2
4
6
8
10
12
14
16
18
20 (a)
r
z
0 0.25 0.5 0.750
0.3
0.6
0.9
1.2
1.5(b)
disk arcade spheromak
Proceed with Nimrod
Plans:
more completely assess prospects of non-MHD effects in astrophysical dynamo physics
then, construct work plan or de-emphasize (~ 4 months)