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Large-scale dynamos at low magnetic Prandtl numbers

Large-scale dynamos at low magnetic Prandtl numbers. above, below, and inside the lab: Pr M = n/h ~ 10 -5. Small-scale dynamos Progressively harder to excite at low Pr M But may level off … Large-scale dynamos Independent of PrM Low PrM can be used to “filter” out SS dynamo

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Large-scale dynamos at low magnetic Prandtl numbers

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  1. Large-scale dynamos at low magnetic Prandtl numbers above, below, and inside the lab: PrM=n/h~10-5 • Small-scale dynamos • Progressively harder to excite at low PrM • But may level off … • Large-scale dynamos • Independent of PrM • Low PrM can be used to “filter” out SS dynamo • Most of energy dissipated Ohmically • Can decrease n even further Axel Brandenburg (Nordita, Stockholm)

  2. Winter School 11-22 January

  3. Small-scale vs large-scale dynamo

  4. Low PrM results • Small-scale dynamo: Rm.crit=35-70 for PrM=1 (Novikov, Ruzmaikin, Sokoloff 1983) • Leorat et al (1981): independent of PrM (EDQNM) • Rogachevskii & Kleeorin (1997): Rm,crit=412 • Boldyrev & Cattaneo (2004): relation to roughness • Ponty et al.: (2005): levels off at PrM=0.2

  5. Maybe no small scale “surface” dynamo? Small PrM=n/h: stars and discs around NSs and YSOs Schekochihin et al (2005) k Boldyrev & Cattaneo (2004)

  6. Levels off for Taylor-Green flow • Confirmation for finite Rm for SS dynamo? • Or effect of LS dynamo?

  7. Hyperviscous, Smagorinsky, normal height of bottleneck increased Haugen & Brandenburg (PRE, astro-ph/0402301) onset of bottleneck at same position Inertial range unaffected by artificial diffusion

  8. Re-appearence at low PrM Gap between 0.05 and 0.2 ? Iskakov et al (2005)

  9. Fully helical turbulence Here: Rm=urmsl/h Brandenburg (2001, ApJ)

  10. ABC flow dynamo • Rm,crit varies still by factor 2 • Spectral magnetic energy peaks at k=1 Mininni et al. (2007, PRE)

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

  12. Growth rate • Growth rate scaling for large Rm as for SS dynamo • Helical dynamo still excited for low Rm

  13. Kinematic regime

  14. Kinematic vs saturated regime

  15. Spectra in kinematic regime • Kazantsev scaling for PrM=1 • Progressively more energy at large scale

  16. Compensated spectra kinematic saturated

  17. Low PrM dynamoswith helicity do work • Energy dissipation via Joule • Viscous dissipation weak • Can increase Re substantially!

  18. PrM=1, saturated case

  19. U and B fields: minor changes

  20. Conclusions 1) low PrM helps to distinguish LS and SS dynamos • LS dynamo must be excited • SS dynamo too dominant, swamps LS field • Dominant SS dynamo: artifact of large PrM=n/h Brun, Miesch, & Toomre (2004, ApJ 614, 1073) 2) Important also for accretion disc dynamos

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