Asymptotic solution of the α2-dynamo problem

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Abstract
The turbulent dynamo equation with non-uniform mean helicity is solved in an approximation, which is similar to the quasi-classical approximation of quantum mechanics. We evaluate the rate of growth of the magnetic field and obtain a condition for dynamo action. The generated magnetic field is concentrated in the vicinity of an extremum of mean helicity, but in general vanishes at the point of extremum itself. The field is asymptotically force-free. The results obtained here clarify the fact, known from numerical calculations, that the threshold values of the dynamo-number for excitation of dipole and quadrupole modes are very close to each other.

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