Madison 2006

Dynamo

Fausto Cattaneo

ANL - University of Chicago

Stewart Prager

University of Wisconsin

Madison 2006

Dynamos

Sustained mechanism to convert kinetic energy into magnetic energy within the bulk of an

electrically conducting fluid.

Invoked to explain the origin of magnetic fields in the universe.

The Madison Dynamo Experiment • Abstract dynamo theory

– Conditions for dynamo action

– Structure of resulting fields

• Laboratory dynamos– Dynamo events in RFP

– Liquid metal experiments

• Astrophysical dynamos– Planets

– Stars

– Galaxies

– ICM

– Magnetars

– Etc.

Madison 2006

Active research areas

• Role of turbulence in dynamo action

• Large scale field generation in laboratory and astrophysics

• Flux redistribution in accretion flows and jets

Madison 2006

Dynamos and turbulence

Conditions for dynamo action in a turbulent fluid. Turbulence consists of velocity

fluctuations on different spatial and temporal scales (self similar range) plus coherent

structures (long lived).

Pseudo-vorticity B field

Madison 2006

Turbulent dynamo action

If < dynamo must operate in the inertial range of the turbulence. Reconnection is

mediated by a strongly fluctuating (rough) velocity.

• Linear: Can dynamo operate for arbitrarily small ?

• Nonlinear: Does field amplitude decrease indefinitely with decreasing Pm=/ ?

Pm = 1/8

Rm

=55

0, R

e=55

0

Rm

=55

0, R

e=11

00

Madison 2006

Large scale generation

Equipartition mean fields are often observed in astrophysics.

What are the mechanisms to generate strong, large-scale fields?

Traditionally discussed within framework of Mean Field Theory (introduce

averaging). MFT correct for kinematic fields and small Rm.

MHD filter MFT

solv

e

solv

e

Exact sol. filter ???

• Does this diagram commute?

• What happens to (mean induction) in the nonlinear regime?

• If turbulent induction is suppressed, how are large scale fields generated?

Neither satisfied in astrophysical situations.

Madison 2006

• At high Rm fluctuations dominate.

• Either -effect is collisional.

• Or -effect is turbulent but strongly nonlinearly suppressed.

Large scale generation

Unstable localized modes

x

Finite helicity

Unstable extended modes

MFT• Under suitable conditions it is possible to transform dynamo problem into QM

• System has both extended modes (MFT) and bound states (fastest growing)

Kinematic

Non rotating Rotating

Non

line

ar

Madison 2006

Non MF dynamos

What generates strong, large-scale fields?• Turbulent -effect is rescued by

– Boundary effect (magnetic helicity injection)

– Strong spatial inhomogeneities

• Non MF effect

– Large scale motions

– Magnetically induced instabilities (essentially nonlinear).

By -

By +

Madison 2006

Dynamo action in the laboratory

Dynamo event

MST

Tor

oid

al f

lux

(Wb

)

Time (ms)

E

jB

˜ v , ˜ B Energy source

instability

dynamo

• Tearing mode instabilities generate velocity and magnetic field fluctuations.

• Fluctuation-fluctuation interactions (-effect) regenerate toroidal field.

Madison 2006

Dynamo action in the laboratory

• Evidence for strong mean induction effects

• Evidence for non MHD effects at some locations

˜ v ˜ B

j E

Time (ms)

Vol

ts/m

• What non MHD physics is important?

– Hall effect

– Diamagnetic

• Incorporate two fluid effects in simulation codes (Nimrod).

Hall ne

Bj

cDiamagneti ne

pe

• Why is the -effect strong in the RFP and weak in numerical simulations?

• Turbulence not strong in RFP. Similarities to buoyancy driven dynamo.

Madison 2006

Accretion flows-jets

Radio galaxies show coherent magnetic structures with Kpc scales.

Magnetic field (probably) generated by dynamo action in accretion disk

around compact central object.

Evidence for moderately strong fields in the ICM.

• Both super Alfvénic injection and magnetic pinch help to collimate.

• Finite external pressure (possibly ram pressure as well) can lead to containment of magnetic structure.

• Similarities between spheromaks and disk arcades; kink instability (flux conversion) in jets and reversed field pinch experiments.

• What is the role of magnetic fields in jet dynamics ?

• What is the role of rotation and external pressure in the formation of coherent magnetic structures ?

• Are there analogies between laboratory and astrophysical magnetic structures?

ToroidalPoloidal

Madison 2006

Future directions

• Abstract dynamo theory

– Mechanisms for large scale generation• Shear

• Flux pumping

• Essentially nonlinear

• Laboratory dynamos

– Introduce PIC and two-fluid codes to study dynamo processes

• Astrophysical dynamos

– Magnetized/relativistic jets (Pluto)

– Accretion flows • Jet launching

• Accretion disk dynamos

– Stellar dynamo models

Sim

. By

N. B

rum

mel

l

Madison 2006

THE END