Self-consistent mean field electrodynamics of turbulent dynamos

A turbulent dynamo in a conducting fluid is accompanied by the generation of small-scale magnetic fields, which are much stronger than the mean dynamo-generated magnetic field. These small-scale fields modify the α effect in such a way as to stabilize the dynamo process, α= (α₀+β₀R·▽xR)/(1+R²), where α₀, β₀ are the standard kinematic dynamo parameters, and R is proportional to the mean magnetic field B₀, R=B₀/(4πρV²/R_m)^1/2, ρ is the fluid density, V is the characteristic turbulent velocity, and R_m is the magnetic Reynolds number. The derivation of this formula is illustrated using a simple model - the turbulent dynamo for an asymmetrical top.