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 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 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

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 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.

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?

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

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?

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

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