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Inverse magnetic cascade as a paradigm for Early Universe MHD

Inverse magnetic cascade as a paradigm for Early Universe MHD. A. Brandenburg, K. Enqvist, P. Olesen: 1996, PRD 54, 1291 A. Brandenburg, K. Enqvist, P. Olesen: 1997, PLB 392, 395 M. Christensson, M. Hindmarsh, A. Bramdemburg: 2001, PRE 64, 056405

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Inverse magnetic cascade as a paradigm for Early Universe MHD

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  1. Inverse magnetic cascadeas a paradigm forEarly Universe MHD A. Brandenburg, K. Enqvist, P. Olesen: 1996, PRD 54, 1291 A. Brandenburg, K. Enqvist, P. Olesen: 1997, PLB 392, 395 M. Christensson, M. Hindmarsh, A. Bramdemburg: 2001, PRE 64, 056405 M. Christensson, M. Hindmarsh, A. Bramdemburg: 2002, astro-ph/0209119 2005, AN (in press)

  2. Decay of field – growth of scale • Starting point: EW phase transition t=10-10 s, B=1024 G • Horizon scale very short: ~ 3 cm • With cosmological expansion: ~ 1 AU • Can field grow to larger scales?

  3. Connection withordinary MHD • Fully relativistic equations in 2-D • 64x64 or 128x128 • Larger scales form

  4. Cartesian box MHD equations Induction Equation: Momentum and Continuity eqns Viscous force

  5. Shell model ofEarly Universe

  6. Silk damping large Pm (n>>h)

  7. Inverse cascade;helicity conservation and Initial components fully helical and

  8. 3-D simulations Initial slope E~k4 Christensson et al. (2001)

  9. Comparison with forced turbulence Injection at wavenumber kf  non-local energy transfer, Not a local cascade with const flux kf =5 kf =30 Brandenburg (2001, ApJ 550, 824)

  10. Helical vs nonhelical

  11. Helical decay law:Biskamp & Müller (1999)

  12. Helical decay law:Christensson (20022005) H not exactly constant Assume power law H follows power law iff r=1/2; then

  13. All length scales scale similarly

  14. Check scaling of s should be s should be ½+2s

  15. s is correction for finite Rm

  16. Again: comparison with forced

  17. Structure function exponents agrees with She-Leveque third moment

  18. 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

  19. Relation to ‘laboratory’ 1D spectra

  20. Bottleneck effect: 1D vs 3D spectra Compensated spectra (1D vs 3D)

  21. Decay run with hyperviscosity Decay rate just as in ordinary turbulence Correction now compatible with She-Leveque

  22. Conclusions • Hyperviscosity allows for a reasonable guess of what one might see a decade later using direct simulation

  23. Magnetisation from quasars??

  24. Application: magnetic contamination of galaxy cluster 10,000 galaxies for 1 Gyr, 1044 erg/s each Similar figure also for outflows from protostellar disc

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