Dynamo ``$\alpha$ effect'' in the MHD plasma due to noise

Response is studied in the long-time and- large-scale limit of a magnetohydrodynamic plasma driven by a noise that depends on a selective direction $\hat s$, which may be due to the rotation about an axis or to the strong magnetic field. The noise is assumed to represent the short-scale turbulence that is often observed in the experiments and the numerical simulations. In addition to enhanced dissipation (that is, the so-called ``$\beta$ effect'') of the magnetic field contributed from the diagonal part of the noise spectrum, it is found that it also yields the so-called ``$\alpha$ effect,'' the curl of the magnetic field in Ohm's law. It is interesting to note that the term is independent of $\hat s$ although $\hat s$ is a necessity to begin with. Comparisons to the gyrotropic noise model will be discussed at the presentation.