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Non-Helical MHD Dynamics in Astrophysical Plasma Systems

Exploring the inverse cascade of magnetic helicity and its conservation in non-helical MHD systems, with emphasis on slow saturation and magnetic buoyancy effects. Investigate turbulent dynamo processes in convective systems with shear and rotation. Implications of magnetic helicity flux and two-scale assumptions in nonlinear dynamo theory.

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Non-Helical MHD Dynamics in Astrophysical Plasma Systems

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  1. Non-helical MHD at 10243 Haugen, Brandenburg, & Dobler (2003, ApJ)

  2. Inverse cascade of magnetic helicity argument due to Frisch et al. (1975) and Initial components fully helical: and  k is forced to the left

  3. Magnetic helicity Maxwell eqns Vector potential Uncurled induction eqn

  4. Magnetic helicity

  5. Slow saturation Brandenburg (2001, ApJ 550, 824)

  6. Periodic box, no shear: resistively limited saturation Brandenburg & Subramanian Phys. Rep. (2005, 417, 1-209) Significant field already after kinematic growth phase followed by slow resistive adjustment Blackman & Brandenburg (2002, ApJ 579, 397)

  7. Magnetic helicity conservation Steady state, closed box Early times

  8. Slow-down explained by magnetic helicity conservation molecular value!!

  9. Slow-down explained by magnetic helicity conservation

  10. With hyperdiffusivity Brandenburg & Sarson (2002, PRL) for ordinary hyperdiffusion

  11. Evidence from different simulations:strong fields only with helicity flux 3-D simulations, no mean-field modeling Forced turbulence in domain with solar-like shear Brandenburg (2005, ApJ 625, 539) Convective dynamo in a box with shear and rotation Käpylä, Korpi, Brandenburg (2008, A&A 491, 353) Only weak field if boxis closed

  12. Nonlinear stage: consistent with … Brandenburg (2005, ApJ)

  13. Best if W contours ^ to surface Example: convection with shear  need small-scale helical exhaust out of the domain, not back in on the other side Magnetic Buoyancy? Tobias et al. (2008, ApJ) Käpylä et al. (2008, A&A)

  14. To prove the point: convection with vertical shear and open b.c.s Magnetic helicity flux Käpylä, Korpi, Brandenburg (2008, A&A) Käpylä, Korpi, & myself (2008, A&A 491, 353) Effects of b.c.s only in nonlinear regime

  15. Implications of tau approximation • MTA does not a priori break down at large Rm. (Strong fluctuations of b are possible!) • Extra time derivative of emf •  hyperbolic eqn, oscillatory behavior possible! • t is not correlation time, but relaxation time with

  16. Kinetic and magnetic contributions

  17. Connection with a effect: writhe with internal twist as by-product a effect produces helical field W clockwise tilt (right handed)  left handed internal twist both for thermal/magnetic buoyancy

  18. … the same thing mathematically Two-scale assumption Production of large scale helicity comes at the price of producing also small scale magnetic helicity

  19. Revised nonlinear dynamo theory(originally due to Kleeorin & Ruzmaikin 1982) Two-scale assumption Dynamical quenching Kleeorin & Ruzmaikin (1982) ( selective decay) Steady limit  algebraic quenching:

  20. General formula with magnetic helicity flux Rm also in the numerator

  21. Mean field theory is predictive • Open domain with shear • Helicity is driven out of domain (Vishniac & Cho) • Mean flow contours perpendicular to surface! • Excitation conditions • Dependence on angular velocity • Dependence on b.c.: symmetric vs antisymmetric

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

  23. Test fields Example:

  24. Validation: Roberts flow SOCA SOCA result Brandenburg, Rädler, Schrinner (2009, A&A) normalize

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

  26. Scale-dependence: nonlocality cf talk by Alexander Nepomnyashchy

  27. Time-dependent case Hubbard & Brandenburg (2009, ApJ)

  28. Importance of time-dependence

  29. From linear to nonlinear Brandenburg et al. (2008, ApJ) Use vector potential Mean and fluctuating U enter separately

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

  31. ht(Rm) dependence for B~Beq • l is small  consistency • a1 and a2 tend to cancel • to decrease a • h2 is small

  32. Application to passive vector eqn cf. Cattaneo & Tobias (2009) Verified by test-field method Tilgner & Brandenburg (2008)

  33. Is the field in the Sun fibril? Käpylä et al (2008) with rotation without rotation

  34. Takes many turnover times Rm=121, By, 512^3 LS dynamo not always excited

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