1. Madison 2006 Dynamo Fausto Cattaneo ANL - University of Chicago Stewart Prager University of Wisconsin

2. 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. 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.

3. 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

4. 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-vorticityB field

5. 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 =550, Re=550 Rm =550, Re=1100

6. 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 solve 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.

7. 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 rotatingRotating Nonlinear

8. 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). B y - B y +

9. Madison 2006 Dynamo action in the laboratory Dynamo event MST Toroidal flux (Wb) Time (ms) Energy source instability dynamo Tearing mode instabilities generate velocity and magnetic field fluctuations. Fluctuation-fluctuation interactions ( - effect) regenerate toroidal field.

10. Madison 2006 Dynamo action in the laboratory Evidence for strong mean induction effects Evidence for non MHD effects at some locations Time (ms) Volts/m What non MHD physics is important? –Hall effect –Diamagnetic Incorporate two fluid effects in simulation codes (Nimrod). Why is the -effect strong in the RFP and weak in numerical simulations? Turbulence not strong in RFP. Similarities to buoyancy driven dynamo.

11. 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

12. 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. Brummell

13. Madison 2006 THE END