Structure of Small-Scale Magnetic Fields in the Kinematic Dynamo Theory
Abstract
In the interstellar medium and protogalactic plasmas, the magnetic Prandtl number is very large, and the kinematic dynamo therefore produces a broad spectrum of growing magnetic fluctuations at small (subviscous) scales. The condition for the onset of nonlinear effects depends on the structure of the field lines. We study the statistical correlations that are set up in the field pattern and show that the magnetic-field lines possess a folding structure, where most of the scale decrease is due to the field variation across itself, while the scale of the field variation along itself stays approximately constant. Specifically, we find that, though both the magnetic energy and the mean square curvature of the field lines grow exponentially, the field strength and the field-line curvature are anticorrelated, i.e. the curved field is relatively weak, while the growing field is relatively flat. The detailed analysis of the statistics of the curvature shows that it possesses a stationary limiting distribution with the bulk located at the values of curvature comparable to the characteristic wave number of the velocity field and a power-like tail extending to large values of curvature where it is cut off by the resistive regularization. The growth of the curvature occurs in a small fraction of the total volume of the system, is due to the intermittent nature of the curvature distribution, and is limited only by the resistive cut-off. The implication of the folding effect is that the advent of the Lorentz back reaction occurs when the magnetic energy approaches that of the smallest turbulent eddies.Keywords
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