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