The alpha dynamo parameter and measurability of helicities in magnetohydrodynamic turbulence

Abstract

Alpha, an important parameter in dynamo theory, is shown to be proportional to either the kinetic, current, magnetic, or velocity helicities of the fluctuating magnetic field and fluctuating velocity field. The particular helicity to which alpha is proportional depends on the assumptions used in deriving the first‐order smoothed equations that describe the alpha effect. In two cases, viz., when alpha is proportional to either the magnetic helicity or velocity helicity, alpha can be determined experimentally from two‐point measurements of the fluctuating fields in incompressible, homogeneous turbulence with arbitrary rotational symmetry. For the other two possibilities, alpha can be determined if the turbulence is isotropic.