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The Test-field Method

The Test-field Method. Output so far. Simulations showing large-scale fields. Helical turbulence ( B y ). Helical shear flow turb. Convection with shear. Magneto-rotational Inst. K äpyla et al (2008). Low Pr M dynamos. Sun Pr M = n/h =10 -5. Schekochihin et al (2005).

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The Test-field Method

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  1. The Test-field Method

  2. Output so far

  3. Simulations showing large-scale fields Helical turbulence (By) Helical shear flow turb. Convection with shear Magneto-rotational Inst. Käpyla et al (2008)

  4. Low PrM dynamos Sun PrM=n/h=10-5 Schekochihin et al (2005) Here: non-helically forced turbulence k Helical turbulence

  5. Upcoming dynamo effort in Stockholm Soon hiring: • 4 students • 3 post-docs • 1 assistant professor • Long-term visitors

  6. Calculate full aij and hij tensors turbulent emf • Correlation method • MRI accretion discs (Brandenburg & Sokoloff 2002) • Galactic turbulence (Kowal et al. 2005, 2006) • Test field method • Stationary geodynamo (Schrinner et al. 2005, 2007) • Shear flow turbulence (Brandenburg 2005) a effect and turbulent aagnetic diffusivity

  7. Calculate full aij and hij tensors Original equation (uncurled) Mean-field equation fluctuations Response to arbitrary mean fields

  8. Test fields Example:

  9. Validation: Roberts flow SOCA SOCA result normalize

  10. Kinematic a and ht independent of Rm (2…200) Sur et al. (2008, MNRAS)

  11. Non-helical with rotation Rotational quenching, finite d>0 for W>0

  12. Shear turbulence Growth rate Use S<0, so need negative h*21 for dynamo

  13. Dependence on Sh and Rm

  14. Direct simulations

  15. Fluctuations of aij and hij Incoherent a effect (Vishniac & Brandenburg 1997, Sokoloff 1997, Silantev 2000, Proctor 2007)

  16. From linear to nonlinear Use vector potential Mean and fluctuating U enter separately

  17. Nonlinear aij and hij tensors Consistency check: consider steady state to avoid da/dt terms Expect: l=0 (within error bars)  consistency check!

  18. Rm dependence for B~Beq • l is small  consistency • a1 and a2 tend to cancel • making a small • h2 small

  19. Earlier results on ht quenching Yousef et al. (2003, A&A)

  20. Nonlinear aij and hij tensors Another consistency check: passive vector equation

  21. Solar paradigm shifts • 1980: magnetic buoyancy (Spiegel & Weiss) overshoot layer dynamos • 1985: helioseismology: dW/dr > 0  dynamo dilema, flux transport dynamos • 1992: catastrophic a-quenching a~Rm-1(Vainshtein & Cattaneo) Parker’s interface dynamo  Backcock-Leighton mechanism

  22. (i) Is magnetic buoyancy a problem? Stratified dynamo simulation in 1990 Expected strong buoyancy losses, but no: downward pumping Tobias et al. (2001)

  23. (ii) Before helioseismology • Angular velocity (at 4o latitude): • very young spots: 473 nHz • oldest spots: 462 nHz • Surface plasma: 452 nHz • Conclusion back then: • Sun spins faster in deaper convection zone • Solar dynamo works with dW/dr<0: equatorward migr Benevolenskaya et al. (1998) Thompson et al. (2003) Yoshimura (1975)

  24. Revisit paradigm shifts • 1980: magnetic buoyancy  counteracted by pumping • 1985: helioseismology: dW/dr > 0  negative gradient in near-surface shear layer • 1992: catastrophic a-quenching  overcome by helicity fluxes  in the Sun: by coronal mass ejections

  25. Conclusion • 11 yr cycle • Dyamo (SS vs LS) • Problems • a-quenching • slow saturation • Solution • Modern a-effect theory • j.b contribution • Magnetic helicity fluxes • Location of dynamo • Distrubtion, shaped by • near-surface shear 1046 Mx2/cycle

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