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Cosmic ray current-driven turbulence and mean-field dynamo effect. I. Rogachevskii, N. Kleeorin, A. Brandenburg , & D. Eichler (ApJ, submitted). MHD plasma with CRs. To be solved with induction equation and continuity equation, isothermal EOS. Introduces pseudoscalar.

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## Cosmic ray current-driven turbulence and mean-field dynamo effect

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**Cosmic ray current-driven turbulence and mean-field dynamo**effect I. Rogachevskii, N. Kleeorin, A. Brandenburg, & D. Eichler (ApJ, submitted)**MHD plasma with CRs**To be solved with induction equation and continuity equation, isothermal EOS**Introduces pseudoscalar**a effect important for large-scale field in the Sun**Comparison: alpha effect & inverse cascade in MHD (no CRs)**decaying turbulence forced turbulence Here: magnetic helicity of opposite signs at small and large scale!**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)**Bell instability**Bell (2004): J=2 Zirakashvili et al (2008): J=16 Continued growth in both cases! a effect important?**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)**Power spectra**• Bell mode ~25k1 • k4 spectrum • k-5/3 at late time turbulence**3 stages**• Bell instability,small scale, k/k1=40 • Accelerated large-scale growth • Slow growth after initial saturation**Alpha tensor (test-field method)**parallel perp**Normalized alpha effect**Scales with kinetic helicity, prefactor ~0.5**Dynamo number, turb diff**Critical value 1, turb diff >> microscopic value**J and resolution dependence**Larger resolution runs longer, can scale to higher J**Instantaneous growth rate**• Agrees with non-ideal theory • Amplification by many orders of magnitude • Box Reynolds number ~ 1000**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**Inverse cascade of magnetic helicity**argument due to Frisch et al. (1975) and Initial components fully helical: and k is forced to the left

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