  The small-scale turbulent dynamo in the high Prandtl number regime is
described in terms of the one-point Fourier space correlators. The second order
correlator of this kind is the energy spectrum and it has been previously
studied in detail. We examine the higher order k-space correlators which
contain important information about the phases of the magnetic wavepackets and
about the dominant structures of the magnetic turbulence which cause
intermittency. In particular, the fourth-order correlators contain information
about the mean-square phase difference between any two components of the
magnetic field in a plane transverse to the wavevector. This can be viewed as a
measure of the magnetic field's polarization. Examining this new quantity, the
magnetic field is shown to become plane polarized in the Kazantsev-Kraichnan
model at large time, corresponding to a strong deviation from Gaussianity. We
derive a closed equation for the generating function of the Fourier correlators
and find the large-time asymptotic solutions of these correlators at all
orders. The time scaling of these solutions implies the magnetic field has
log-normal statistics, whereas the wavenumber scaling indicates that the field
is dominated by intermittent fluctuations at high k.
