The Alpha Effect: The Connection between Cyclonic Events and Current Helicity

In a magnetized plasma, resistive diffusion of large-scale magnetic fields can be suppressed or even overcome by a turbulently generated electromotive force. For a plasma in which the turbulence is homogeneous and isotropic this EMF is characterized by the ensemble average <δv × δb> = αB0, where δv and δb represent the turbulent fields and B0 defines the large-scale field. Determination of the statistical properties of the turbulence that are required to generate a finite alpha effect, as it has become known, is one of the central subjects of dynamo theory. Parker has shown that helical velocity fluctuations possessing a net amount of kinetic helicity are capable of dynamo action. These "cyclonic events" produce electromagnetic fluctuations characterized by their own statistical properties. Within the context of "mean-field electrodynamics" we show that these fluctuations possess a net amount of current helicity, and find that a necessary condition for dynamo action is that the turbulent current helicity and the current helicity in the large-scale field be of opposite sign.