  As well known, magnetic fields in space are distributed very inhomogeneously.
Some-times field distributions have forms of filaments with high magnetic field
values. As many ob-servations show, such a filamentation takes place in
convective cells in the Sun and other astro-physical objects. This effect is
associated with the frozenness of the magnetic field into a medium with high
conductivity that leads to compression of magnetic field lines and forming
magnetic filaments. We show analytically, based on the general analysis, that
the magnetic field intensifies in the regions of downward flows in both
two-dimensional and three-dimensional convective cells. These regions of the
hyperbolic type for magnetic fields play a role of a specific attractor. This
analysis was confirmed by numerical simulations for 2D convective cells of the
roll-type. Without dissipation the magnetic field grows exponentially in time
and does not depend on the aspect ratio between horizontal and vertical scale
of the cell. An increase due to compression in the magnetic field in the high
conductive plasma is saturated due to the natural limitation associated with
dissipative effects when the maximum magnitude of the magnetic field is of the
order of the root of the magnetic Reynolds number Rem. For the solar convective
zone the mean kinetic energy density exceeds mean magnetic energy density at
least for two orders of magnitude that allows one to use the kinematic
approximation for the MHD induction equation. In this paper based on the
stability analysis we explain why downward flows influence magnetic filaments
from making them more flat with orientation along interfaces between convective
cells.
