Nonlinear α‐Effect in Dynamo Theory

Abstract

The standard two-scale theory of the dynamo coefficient α in incompressible isotropic helical MHD turbulence is extended to include nonlinear effects of B̄, the large-scale magnetic field. We express α in terms of statistical quantities that can be calculated from numerical simulations of the case B̄ = 0. For large magnetic Reynolds numbers, our formula agrees approximately with that of Kraichnan but disagrees with that of Cattaneo & Hughes.