The dependence of dynamo α-effect on Reynolds numbers, magnetic Prandtl number, and the statistics of magnetohydrodynamic turbulence

We generalize the derivation of the dynamo coefficient alpha of Field et al. to include the following two aspects: first, the decorrelation 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 alpha -effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds number and large magnetic Reynolds number, alpha -coefficient may not be small if the decorrelation times of velocity field and magnetic field are shorter than the eddy turnover time of the MHD turbulence. We also show that under certain circumstances, for example if the kinetic helicity and current helicity are comparable, alpha 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 alpha -effect.