  A weak fluctuating magnetic field embedded into a turbulent conducting medium
grows exponentially while its characteristic scale decays. In the ISM and
protogalactic plasmas, the magnetic Pr is very large, so a broad spectrum of
growing magnetic fluctuations is excited at subviscous scales. 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 rapid transverse field direction reversals, while the scale
of the field variation along itself stays approximately constant. Specifically,
we find that the field strength and the field-line curvature are
anticorrelated, and the curvature 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 tail extending to
large values of curvature. The regions of large curvature, therefore, occupy
only a small fraction of the total volume of the system. Our theoretical
results are corroborated by direct numerical simulations. 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. Our
results also directly apply to the problem of statistical geometry of the
material lines in a random flow.
