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
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Abstract dynamo theory
– Conditions for dynamo action
– Structure of resulting fields
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Laboratory dynamos
– Dynamo events in RFP
– Liquid metal experiments
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Astrophysical dynamos
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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=/ ?
Rm =550, Re=1100
Rm =550, Re=550
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Pm = 1/8
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.
Neither satisfied in astrophysical situations.
Exact sol.
MFT
solve
filter
solve
MHD
filter
???
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Does this diagram commute?
What happens to  (mean induction) in
the nonlinear regime?
If turbulent induction is suppressed,
how are large scale fields generated?
Madison 2006
Large scale generation
Finite helicity
Kinematic
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Nonlinear
Non rotating
Rotating
x
MFT
Under suitable conditions it is possible
to transform dynamo problem into QM
System has both extended modes (MFT)
and bound states (fastest growing)
Unstable extended modes
Unstable localized modes
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At high Rm fluctuations
dominate.
Either -effect is collisional.
Or -effect is turbulent but
strongly nonlinearly suppressed.
Madison 2006
Non MF dynamos
What generates strong, large-scale fields?
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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
Toroidal flux (Wb)
MST
Dynamo event
Time (ms)
E
Energy source
 j
instability
B
 v˜ , B˜ 
dynamo
and magnetic field fluctuations.
Tearing mode instabilities generate velocity
 interactions (-effect) regenerate toroidal field.
Fluctuation-fluctuation
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Madison 2006
Dynamo action in the laboratory
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Evidence for strong mean induction
effects
Evidence for non MHD effects at some
locations

˜   j   E 
 v˜  B

Volts/m
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What non MHD physics is important?
– Hall effect
– Diamagnetic
Incorporate two fluid effects in
simulation codes (Nimrod).
Time (ms)
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Why is the -effect strong in the RFP
and weak in numerical simulations?
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Turbulence not strong in RFP.
Similarities to buoyancy driven dynamo.

jB
Hall
ne
pe
Diamagneti c
ne
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.
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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?
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.
Poloidal
Toroidal
Madison 2006
• Abstract dynamo theory
– Mechanisms for large scale generation
• Shear
• Flux pumping
• Essentially nonlinear
Sim. By N. Brummell
Future directions
• 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
Madison 2006
THE END
Madison 2006