Mean-field electrodynamics, including both α and β effects while accounting for the effects of small-scale magnetic fields, is derived for incompressible magnetohydrodynamics. The principal result is α=(α0+β0R×R)/(1+R2), β=β0; where α0,β0 are conventional kinematic dynamo parameters, the reduction factor is proportional to the mean magnetic field R=Rm1/2B/(ρV2)1/2, Rm is the magnetic Reynolds number, and V is the characteristic turbulent velocity. This result follows from a generalization of the Zeldovich theorem to three dimensions, exploiting magnetic helicity balance.
ASJC Scopus subject areas
- Physics and Astronomy(all)