**AAS Meeting #193 - Austin, Texas, January 1999**

*Session 77. Astrophysical Processes and Computational Techniques*

Display, Friday, January 8, 1999, 9:20am-6:30pm, Exhibit Hall 1
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## [77.01] A New Derivation of Nonlinear \alpha-Effect in Dynamo Theory

*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).

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