Abstract
Abstract In this paper, the turbulent diffusion of a magnetic field in the kinematic approximation, i.e., kinematic dynamo theory, is studied in the context of spectral densities rather than mean fields. In particular, we derive the evolution equations for the magnetic energy and helicity spectra, given the corresponding kinetic energy and helicity spectra. We verify that for the kinematic turbulent diffusion problem, the total magnetic helicity remains an exact invariant—as it must for ideal magnetohydrodynamics; and that with the use of inequalities connecting the magnetic energy and helicity spectra, one can place bounds on the magnetic energy spectrum which depend on the field topology.
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