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Magnetic helicity: why is it so important and how to get rid of it

Magnetic helicity: why is it so important and how to get rid of it. Axel Brandenburg (Nordita, Copenhagen) Kandaswamy Subramanian (Pune). Brandenburg (2001, ApJ 550, 824; 2005, ApJ 625, 539) Brandenburg & Subramanian (2005, Phys. Rep., astro-ph/0405052). Magnetic helicity.

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Magnetic helicity: why is it so important and how to get rid of it

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  1. Magnetic helicity:why is it so important and how to get rid of it Axel Brandenburg (Nordita, Copenhagen) Kandaswamy Subramanian (Pune) Brandenburg (2001, ApJ 550, 824; 2005, ApJ 625, 539) Brandenburg & Subramanian (2005, Phys. Rep., astro-ph/0405052)

  2. Magnetic helicity

  3. Magnetic helicity conservation How J diverges as h0 Ideal limit and ideal case similar!

  4. Inverse cascade of magnetic helicity Pouquet, Frisch, & Leorat (1976) and Initial components fully helical: and  k is forced to the left

  5. Production of LS helicity forcing produces and But no net helicity production therefore:  alpha effect Yousef & Brandenburg A&A 407, 7 (2003)

  6. LS dynamos • Difference to SS dynamos • Field at scale of turbulence • The small PrM problem • Mechanisms for producing LS fields • Field at scale larger than that of turbulence • Alpha effect (requires helicity) • Shear-current of WxJ effect • Others: incoherent alpha, Vishniac-Cho effect, + perhaps other effects

  7. Cartesian box MHD equations Magn. Vector potential Induction Equation: Momentum and Continuity eqns Viscous force forcing function (eigenfunction of curl)

  8. (i) Small scale dynamos Small PrM: stars and discs around NSs and YSOs Schekochihin et al (2005) ApJ 625, 115L k Here: non-helically forced turbulence

  9. 256 processor run at 10243 at PrM=1 -3/2 slope? Haugen et al. (2003, ApJ 597, L141) Result: not peaked at resistive scale  Kolmogov scaling! instead: kpeak~Rm,crit1/2kf ~ 6kf

  10. (ii) Large scale dynamos: 2 different geometries (a) Periodic box, no shear (b) open box, w/ shear • Helically forced turbulence (cyclonic events) • Small & large scale field grows exponentially • Past saturation: slow evolution  Explained by magnetic helicity equation

  11. Scale separation: inverse cascade Position of the peak compatible with Decomposition in terms of Chandrasekhar-Kendall-Waleffe functions No inverse cascade in kinematic regime LS field: force-free Beltrami

  12. Time dependence: slow saturation Brandenburg (2001, ApJ 550, 824) Position of the peak compatible with

  13. 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

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

  15. Dynamo growth & saturation Significant field already after kinematic growth phase followed by slow resistive adjustment

  16. Large scale vs small scale losses Diffusive large scale losses:  lower saturation level Brandenburg & Dobler (2001 A&A 369, 329) Periodic box with LS losses Small scale losses (artificial)  higher saturation level  still slow time scale Numerical experiment: remove field for k>4 every 1-3 turnover times (Brandenburg et al. 2002, AN 323 99)

  17. Current helicity flux • Advantage over magnetic helicity • <j.b> is what enters a effect • Can define helicity density Rm also in the numerator

  18. Significance of shear • a transport of helicity in k-space • Shear  transport of helicity in x-space • Mediating helicity escape ( plasmoids) • Mediating turbulent helicity flux Expression for current helicity flux (first order smoothing, tau approximation) Schnack et al. Vishniac & Cho (2001, ApJ 550, 752) Subramanian & Brandenburg (2004, PRL 93, 20500) Expected to be finite on when there is shear Arlt & Brandenburg (2001, A&A 380, 359)

  19. (ii) Forced LS dynamo with no stratification azimuthally averaged no helicity, e.g. Rogachevskii & Kleeorin (2003, 2004) geometry here relevant to the sun neg helicity (northern hem.)

  20. Conclusions • Shearflow turbulence: likely to produce LS field • even w/o stratification (WxJ effect, similar to Rädler’s WxJ effect) • Stratification: can lead to a effect • modify WxJeffect • but also instability of its own • SS dynamo not obvious at small Pm • Application to the sun? • distributed dynamo  can produce bipolar regions • a perhaps not so important? • solution to quenching problem? No: aM even from WxJ effect 1046 Mx2/cycle

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