1. Cosmic ray current-driven turbulence and mean-field dynamo effect I. Rogachevskii, N. Kleeorin, A. Brandenburg, & D. Eichler (ApJ, submitted)

2. MHD plasma with CRs To be solved with induction equation and continuity equation, isothermal EOS

3. Introduces pseudoscalar a effect important for large-scale field in the Sun

4. Comparison: alpha effect & inverse cascade in MHD (no CRs) decaying turbulence forced turbulence Here: magnetic helicity of opposite signs at small and large scale!

5. Bi-helical fields from Ulysses • Taylor hypothesis • Broad k bins • Southern latitude with opposite sign • Small/large distances • Positive H at large k • Break point with distance to larger k Brandenburg, Subramanian, Balogh, & Goldstein (2011, ApJ 734, 9)

6. Bell instability Bell (2004): J=2 Zirakashvili et al (2008): J=16 Continued growth in both cases!  a effect important?

7. New simulations • 5123 resolution, non-ideal (Re=Lu < 300) • larger J parameter (80 and 800) • most unstable k /k1= 40 and 400 (unresolved) • measure alpha and turbulent diff. tensor • Related to earlier work by Bykov et al. (2011)

8. Bell instability  turbulence (J=80)

9. Animation

10. Power spectra • Bell mode ~25k1 • k4 spectrum • k-5/3 at late time  turbulence

11. Spectral growth

12. 3 stages • Bell instability,small scale, k/k1=40 • Accelerated large-scale growth • Slow growth after initial saturation

13. Isotropization

14. Growth of length scale

15. Alpha tensor (test-field method) parallel perp

16. Normalized alpha effect Scales with kinetic helicity, prefactor ~0.5

17. Dynamo number, turb diff Critical value 1, turb diff >> microscopic value

18. J and resolution dependence Larger resolution runs longer, can scale to higher J

19. Equipartition ratio: J dependent

20. Instantaneous growth rate • Agrees with non-ideal theory • Amplification by many orders of magnitude • Box Reynolds number ~ 1000

21. Convergence of alpha

22. Conclusions • Growth by many orders of magnitude • a effect and turbulent diffusivity tensors • dynamo number > 1 at late times • k-5/3 spectrum at late times • growth at larger length scales • numerically converged

23. Inverse cascade

24. Animation (poor)

25. Animation5

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