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Detection of negative effective magnetic pressure instability in turbulence simulations

Detection of negative effective magnetic pressure instability in turbulence simulations. Instability in stratified turbulence with B -field (here horizontal) Reproduced in mean-field magnetohydrodynamics R m dependence of turbulent transport coefficient.

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Detection of negative effective magnetic pressure instability in turbulence simulations

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  1. Detection of negative effective magnetic pressure instabilityin turbulence simulations • Instability in stratified turbulence with B-field (here horizontal) • Reproduced in mean-field magnetohydrodynamics • Rm dependence of turbulent transport coefficient Axel Brandenburg, Koen Kemel, Nathan Kleeorin, Dhrubaditya Mitra, Igor Rogachevskii

  2. Setup • 3-D box, size (2p)3, isothermal MHD • Random, nonhelical forcing at kf/k1=5, 15 or 30 • Stratified in z, r~exp(-z/H), H=1, Dr=535 • Periodic in x and y • stress-free, perfect conductor in z • Weak imposed field B0 in y • Run for long times: what happens? • Turnover time tto=(urmskf)-1, turb diff ttd=(htk12)-1 • Is longer by factor 3(kf/k1)2 = 3 152 = 675 • Average By over y and Dt=80tto

  3. Negative effective magnetic pressure instability in action (ReM=70, kf/k1=15) Brandenburg et al. (2011, ApJL 740, 50L)

  4. Poorly visible in snapshots (kf/k1=15)

  5. Exponential growth • Several thousand turnover times • Or ½ a turbulent diffusive time • Exponential growth  linear instability of an already turbulent state

  6. Large aspect ratio: more cells • not all cells equally strong • reasonably well seen in just y-averages (top) • Better with additional time averaging (bottom)

  7. Larger scale separation: 30 instead of 15

  8. Better visible in snapshots for kf/k1=30

  9. Seems to work only in certain B range • is expected • B0/Beq~0.15 • Vertical inhomo. for stronger field

  10. But B structure produced deeper down • Here more scale separation (30 instead of 15) • Field strength and growth rate the same for different B0 • Can just reposition z range of the box to get the same growth rate and field strength

  11. Rm dependence Breakdown of quasi-linear theory ReM here based on forcing k Here 15 eddies per box scale ReM=70 means 70x15x2p=7000 based on box scale

  12. Mean-field concept a effect, turbulent diffusivity, Yoshizawa effect, etc Turbulent viscosity and other effects in momentum equation

  13. Earlier results for low Rm • Rädler (1974) computed magnetic suppression (for other reasons) • Rüdiger (1974)  works only for Pm < 8 • Roberts & Soward (1975), Rüdiger et al. (1986) Maxwell tension formally negative for Rm > 1, but invalid • Rüdiger et al. (2012), no negative effective magnetic pressure for Rm < 1. • Kleeorin et a. (1989, 1990, 1996), Kleeorin & Rogachevskii (1994, 2007)

  14. Magnetic contribution to pressure & energy different! Can lead to reversed mean-field buoyancy in stratified system

  15. Formation of flux concentrations Earlier work with Kleeorin & Rogachevskii (2010, AN 331, 5)

  16. Stratified runs isothermal  constant scale height, density contrast, exp(2p)=535, Beq varies, so B/Beq varies, get whole curve in one run

  17. Convection not just for forced turbulence,  result is robust!

  18. Effective magnetic pressure

  19. Fit formula and Rm dependence

  20. Basic mechanism Anelastic: descending structure  compression B amplifies B amplifies Growth rate

  21. Conclusions: new food for thought • Essential ingredient for shallow sunspot acticity identified (ApJL 740, L50) • Effect does not exist below Rm=1 (SOCA) • Becomes stronger with better scale separation (e.g. 30 instead of 15) • Active regions shallow phenomena Hindman et al. (2009, ApJ)

  22. Thanks to the Astrophysics group at Nordita

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