  The amplification of magnetic fields in a highly conducting fluid is studied
numerically. During growth, the magnetic field is spatially intermittent: it
does not uniformly fill the volume, but is concentrated in long thin folded
structures. Contrary to a commonly held view, intermittency of the folded field
does not increase indefinitely throughout the growth stage if diffusion is
present. Instead, as we show, the probability-density function (PDF) of the
field strength becomes self-similar. The normalized moments increase with
magnetic Prandtl number in a powerlike fashion. We argue that the
self-similarity is to be expected with a finite flow scale and system size. In
the nonlinear saturated state, intermittency is reduced and the PDF is
exponential. Parallels are noted with self-similar behavior recently observed
for passive-scalar mixing and for map dynamos.
