Presentation on theme: "Outline Dynamo: theoretical General considerations and plans Progress report Dynamo action associated with astrophysical jets Progress report Dynamo: experiment."— Presentation transcript:
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
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 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 o Small scale dynamo Generation on scales o Competition between line stretching and enhanced diffusion Dynamo generates B 2 but not B 2 Large scale dynamo Generation on scales o 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 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? /o/o 1 B 2 kinematic models nonlinear models Large-scale dynamos Small-scale dynamos
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?
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 Computations Hughes & Cattaneo Dynamo action in rotating convecting layer Rotating convection with Ra>>1, 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?
Dynamo action in rough velocities Computations Tobias & Cattaneo Kinematic dynamo action in rough velocities Extend analytical results (see Boldyrevs presentation) to more general cases 1.Finite correlation time flows 2.Non Gaussian statistics 3.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? streamfunction B-field streamfunctionB-field
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 Re>>Rm (Rm smallish) Potentially great opportunity to develop turbulence models Get back to solar dynamo problem---continue with MRIdo both