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

12
Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment General considerations and plans Progress report

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

Page 1: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

Outline

• Dynamo: theoretical General considerations and plansProgress report

• Dynamo action associated with astrophysical jets

Progress report

• Dynamo: experimentGeneral considerations and plansProgress report

Page 2: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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

Page 3: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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

Page 4: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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 α-effect• Average diffusion β-effect• Average advection γ-effect

Page 5: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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 small---stars 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

elsLarge-scale dynamos

Small-scale dynamos

Page 6: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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?

Page 7: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

Research Plan

• Develop a self-consistent computational model for the “solar dynamo”.

• Build a code that integrates multiple physical processes in spherical and cylindrical geometry.

• Focus understanding origin of the large-scale magnetic field.

• Compare with solar observations, and with available liquid metal experiments.

Page 8: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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 non-MHD dynamo effects are significant?

Page 9: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

Research Plan

Detailed description of • Research tasks

• Approximate timeline

• People involved

Can be found at the CMSO web-page

http://cmso.info/html/dynamoplan.htm

Page 10: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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 anti-symmetric about the midplane

anti-symmetric -effect• System is a “turbulent” small-scale dynamo• No evidence for large-scale field generation• Results consistent with a laminar -effect• What is going on?

Page 11: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

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

B-fi

eld

streamfunction B-field

Page 12: Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment.

Computational MRI: preliminary results

Com

pu

tati

on

s F

isch

er,

Ob

ab

ko &

Catt

an

eo

Nonlinear development of Magneto-Rotational Instability• Cylindrical geometry similar to Goodman-Ji experiment

• Hydrodynamically stable rotation profile• Weak vertical field

• Use newly developed spectral finite-elements 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 problem---continue with MRI—do both