1. Comparing classical and lab plasma dynamos S. Prager University of Wisconsin useful discussions with D. Craig, H. Ji, J. Sarff, E. Zweibel

2. The classical dynamo well-posed problem(s) The lab plasma dynamo well-posed The astrophysical field generation problem maybe less clear

3. The classical dynamo problem V velocity-driven energy source fluctuationsmean, large-scale (with seed B)

4. Poynting flux Poynting flux is outward from plasma volume 0, source term V P > 0

5. Magnetic helicity flux Magnetic helicity flux direction is unclear using Ohms law < 0 in sodium expts < 0 in Taylor state unclear in astrophysics > 0 in all lab cases

6. V P HmHm or V P HmHm The classical dynamo

7. The lab plasma dynamo B Magnetically-driven energy source fluctuations mean, large-scale two cases: Free relaxation (no energy or helicity injected) Driven relaxation (energy and helicity injected)

8. Free relaxation Poynting flux = 0 = helicity injection large-scale field,, transported by fluctuations ( in MHD) magnetic energy (kJ) Helicity (Wb) Time (ms)

9. Driven relaxation Poynting flux 0 helicity injection PHmHm Magnetic field grows and redistributes

10. Experimental examples in a torus (e.g. reversed field pinch) helicity injection through surface = toroidal flux ~ = toroidal loop voltage dc injection of helicity fluctuations

11. experimental result MST McCollam, Blair, Sarff

12. another experimental example spheromak

13. One physics link between the classical and lab dynamos In both cases, can be driven by instability or nonlinear coupling lab dynamo shows alpha effect can be large, Indicates that dynamo quenching predictions are not universal

14. The astrophysical field generation problem B fields are observed or deduced to Grow from a seed field (Earth, ISM…) Oscillate in time (Earth, Sun….) Be transported in spatial scale or wavenumber (ISM….) Be transported through space (Extragalactic jets…) What are the most important problems in the generation of magnetic fields in astrophysics? Lab relaxation processes can contribute to the latter three

15. Coupling of two dynamo processes e.g., discussed by Blackman velocity-driven dynamo magnetic-driven dynamo (relaxation) P HmHm velocity-driven dynamo on LHS drives relaxation or field growth on RHS

16. Coupling of two dynamo processes e.g., discussed by Blackman velocity-driven dynamo magnetic-driven dynamo (relaxation) P HmHm velocity-driven dynamo on LHS drives relaxation or field growth on RHS HmHm

17. Solar fields V dynamo P

18. Disk/Jet/lobe system velocity-driven dynamo magnetic-driven dynamo (relaxation) P disk engine Jet/lobe

19. Disk/Jet/lobe system magnetic-driven dynamo P Jet/lobe relaxation, transport of B over over space, transport of B from high to low k

20. Magnetic energy in the universe jets/lobes other

21. Magnetic energy in the universe jets/lobes other is this correct? so, magnetic transport and consequent creation of large- scale field may be important (the lab plasma dynamo or magnetic dynamo)

22. Summary Two B generation mechanisms can work together velocity-driven engine (dynamo) internal energy source in flow contains little magnetic energy (?) occupies small space (?) magnetically-driven relaxation driven by boundary condition produces large-scale field via transport contains large magnetic energy (?) occupies large space (?)

23. Summary Two B generation mechanisms can work together velocity-driven engine (dynamo) internal energy source in flow contains little magnetic energy (?) occupies small space (?) magnetically-driven relaxation driven by boundary condition produces large-scale field via transport contains large magnetic energy (?) occupies large space (?) Should the astrophysical dynamo problem be broadened to include both effects about equally?