The Dependence of Dynamo α-Effect on Reynolds Numbers, Magnetic Prandtl Number, and the Statistics of MHD Turbulence

We generalize the derivation of dynamo coefficient α of Field et al. (1999) to include the following two aspects: first, the de-correlation times of velocity field and magnetic field are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity field and magnetic field to the α effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, α-coefficient may not be small if the de-correlation times of velocity field and magnetic field are shorter than the eddy turn-over time of the MHD turbulence. We also show that under certain circumstances, for example if the kinetic helicity and current helicity are comparable, α depends insensitively on magnetic Prandtl number, while if either the kinetic helicity or the current helicity is dominated by the other one, a different magnetic Prandtl number will significantly change the dynamo α effect. Subject headings: Dynamo, MHD turbulence