Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action...

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Transcript of Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action...
Outline
• Dynamo: theoretical General considerations and plansProgress report
• Dynamo action associated with astrophysical jets
Progress report
• Dynamo: experimentGeneral considerations and plansProgress report
The Madison Dynamo Experiment
Dynamo action in “astrophysics”
Liquid metal experiments
Geodynamo Solar/stellar dynamos Galactic dynamos
IGM
Dynamo action present in many different physical systems
Range of scales from meters to hundred of Kpc
Basic mechanism very robust
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 (turbulence) 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 ℓo
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 αeffect• Average diffusion βeffect• Average advection γeffect
From kinematic to nonlinear dynamosMost astrophysical situations:• Dynamos operate in nonlinear regime• Magnetic fields are in equipartition with velocity on integral
scales• Rotation is often present and important• Pm (= ) is either
• Huge—interstellar medium• Hugely smallstars and liquid metals
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
elsLargescale dynamos
Smallscale dynamos
Research PlanResearch to target three areas:
• Understand generic properties of nonlinear MHD dynamos.
• What determines the nonlinear saturation?
• What is the structure of dynamo fields at small magnetic Prandtl number?
• How are large scale fields generated by inverse cascades?
• Why is the alpha effect strong in the RFP and weak in numerical simulations aimed at astrophysics?
Research Plan
• Develop a selfconsistent computational model for the “solar dynamo”.
• Build a code that integrates multiple physical processes in spherical and cylindrical geometry.
• Focus understanding origin of the largescale magnetic field.
• Compare with solar observations, and with available liquid metal experiments.
Research Plan
• Understand the dynamics of dynamo effects beyond MHD, and their relevance to astrophysics and experiments.
• Under what conditions are different dynamo effect large? What is the relation of reconnection layer physics to dynamos?
• Which dynamo effects dominates in experiment?
• Are there important astrophysical situations for which nonMHD dynamo effects are significant?
Research Plan
Detailed description of • Research tasks
• Approximate timeline
• People involved
Can be found at the CMSO webpage
http://cmso.info/html/dynamoplan.htm
Helical dynamos and inverse cascades
Com
pu
tati
on
s H
ug
hes &
Catt
an
eo
Dynamo action in rotating convecting layer• Rotating convection with Ra>>1, and strong rotation (TaRa)• (Kinetic) helicity distribution antisymmetric about the midplane
antisymmetric effect• System is a “turbulent” smallscale dynamo• No evidence for largescale field generation• Results consistent with a laminar effect• What is going on?
Dynamo action in rough velocities
Com
pu
tati
on
s T
ob
ias &
Catt
an
eo
Kinematic dynamo action in rough velocities• Extend analytical results (see Boldyrev’s presentation) to more
general cases1. Finite correlation time flows2. Non Gaussian statistics3. Presence of coherent structure
• Preliminary results show • For many systems impact of 1 and 2 is relatively weak• For certain classes of dynamos (quick dynamos) presence of coherent
structures very important• What is important in practice?
str
eam
fun
cti
on
Bfi
eld
streamfunction Bfield
Computational MRI: preliminary results
Com
pu
tati
on
s F
isch
er,
Ob
ab
ko &
Catt
an
eo
Nonlinear development of MagnetoRotational Instability• Cylindrical geometry similar to GoodmanJi experiment
• Hydrodynamically stable rotation profile• Weak vertical field
• Use newly developed spectral finiteelements MHD code• Try to understand differences between experiments and simulations
• Simulations ReRm (moderate). Experiments Re>>Rm (Rm smallish)• Potentially great opportunity to develop turbulence models
• Get back to solar dynamo problemcontinue with MRI—do both