Outline

1
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

2
Dynamo action in astrophysics

• Dynamo action present in many different physical
  systems
• Range of scales from meters to hundred of Kpc
• Basic mechanism very robust

Liquid metal experiments
IGM
Geodynamo
Galactic dynamos
Solar/stellar dynamos
3
Linear and nonlinear dynamos

• 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

4
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 ?B?2
• 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 a-effect
• Average diffusion ß-effect
• Average advection ?-effect

5
From kinematic to nonlinear dynamos

• Most 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
• Hugeinterstellar medium
• Hugely small---stars and liquid metals

What are the dynamo saturation mechanisms that
leads to observed field stregths?
l/lo
Large-scale dynamos
1
kinematic models
nonlinear models
?B2?
Small-scale dynamos
6
Research Plan

• Research 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?

7
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.

8
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?

9
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

10
Helical dynamos and inverse cascades
Computations Hughes Cattaneo

• Dynamo action in rotating convecting layer
• Rotating convection with Ragtgt1, and strong
  rotation (Ta?Ra)
• (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?

11
Dynamo action in rough velocities
streamfunction
B-field
streamfunction
Computations Tobias Cattaneo
B-field

• Kinematic dynamo action in rough velocities
• Extend analytical results (see Boldyrevs
  presentation) to more general cases
• Finite correlation time flows
• Non Gaussian statistics
• 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?

12
Computational MRI preliminary results
Computations Fischer, Obabko Cattaneo

• 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 Re?Rm (moderate). Experiments RegtgtRm
  (Rm smallish)
• Potentially great opportunity to develop
  turbulence models
• Get back to solar dynamo problem---continue with
  MRIdo both