SELF-CONSISTENT THEORY OF MEAN-FIELD ELECTRODYNAMICS

Mean-field electrodynamics, including both a and beta effects while accounting for the effects of small-scale magnetic fields, is derived for incompressible magnetohydrodynamics. The principal result is alpha = (alpha(0) + beta0R . del x R)/(1 + R2), beta = beta0; where alpha0,beta0 are conventional kinematic dynamo parameters, the reduction factor is proportional to the mean magnetic field R + R(m)1/2B/(rhoV2)1/2, R(m) 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.