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⋅/B∇×R)/(1+R2), where α0, β0 are the standard kinematic dynamo parameters, and R is proportional to the mean magnetic field B0, R=B0/(4πρV2/Rm)1/2, ρ is the fluid density, V is the characteristic turbulent velocity, and Rm is the magnetic Reynolds number. The derivation of this formula is illustrated using a simple model—the turbulent dynamo for an asymmetrical top.