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Hongsong Chou (Harvard-Smithsonian Center for Astrophysics), George B. Field (Harvard-Smithsonian Center for Astrophysics), Vincent Fish (Harvard-Smithsonian Center for Astrophysics), Eric G. Blackman (Californian Institute of Technology)
In the frame of standard two-scale turbulence theory, we reconsider the dynamo coefficient \alpha in incompressible isotropic helical MHD turbulence by taking the nonlinear effects of <\bf{B}>, the large-scale magnetic field into account. Contrary to standard kinematic dynamo theory where \alpha has only contribution from the kinetic helicity of turbulence velocity field, we find(Field, Blackman and Chou, 1998) that nonlinear dynamo \alpha effect has contributions from current helicity of turbulen ce magnetic field, too. Our final result of \alpha-effect is expressed in terms of statistical quantities that can be calculated from numerical simulations of the case <\bf{B}>=0. We also show(Chou and Fish, 1998) that non-unit Prandtl number \it{Pr} ={\nu}/{\lambda}, where \nu and \lambda are molecular viscosity and magnetic diffusivity, will affect the non-triviality of \alpha. Our calculation shows that \alpha remains finite in the limit of infinite magnetic Reynolds number, in support of Kraichnan(1979)'s analysis, but contrary to the simulation of Cattaneo and Hughes(1996).