Turbulent Dynamo Theory and its Possible Applications to Reversed Field Pinches.

Turbulent transport effects due to small-scale fluctuations in large-scale structures in MHD systems are very important both in space-plasma situations and fusion plasma situations. However, the original turbulent "alpha" dynamo theory is insufficient when applied to the latter. In this thesis, a generalization of the "alpha" dynamo theory is attempted. We first complete some multiple-scale perturbation calculations of turbulent MHD transport coefficients begun in our earlier papers. These generalize the original dynamo -effect coefficient calculations by treating the velocity field and magnetic fields on the same footing. Then we address the problem of rendering such calculations self -consistent, generalizing an eddy-viscosity hypothesis similar to that of Heisenberg for the Navier-Stokes case. The method also borrows from Kraichnan's direct-interaction approximation. The output is a set of integral equations relating the spectra and the turbulent transport coefficients. Previous "alpha effect" and "beta effect" coefficients emerge as limiting cases. The new approach thus underpins, to an extent, the turbulent dynamo theory as applied to toroidal flux generation in reversed-field pinch effect experiments. A treatment of the inertial range using the new method can also be given, consistent with a - 5/3 energy spectrum power law. In the Navier-Stokes limit, a value of 1.72 is extracted for the Kolmogorov constant. Further applications to MHD are possible.