The dependence of dynamo alpha-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 v elocity field and magnetic held are different; second, the magnetic Prandtl number can be arbitrary. We find that the contributions of velocity held a nd magnetic held to the alpha -effect are not equal, but affected by their different statistical properties. In the limit of large kinetic Reynolds nu mber and large magnetic Reynolds number, alpha -coefficient may not be smal l if the decorrelation times of velocity held and magnetic field are shorte r than the eddy turnover time of the MHD turbulence. We also show that unde r certain circumstances, for example if the kinetic helicity and current he licity are comparable, alpha depends insensitively on magnetic Prandtl numb er, while if either the kinetic helicity or the current helicity is dominat ed by the other one, a different magnetic Prandtl number will significantly change the dynamo alpha -effect.