Magnetic Filaments: Formation, Stability, and Feedback

As is well known, magnetic fields in space are distributed very inhomogeneously. Sometimes, field distributions have forms of filaments with high magnetic field values. As many observations show, such a filamentation takes place in convective cells in the Sun and other astrophysical objects. This effect is associated with the frozenness of the magnetic field into a medium with high conductivity that leads to the compression of magnetic field lines and formation of magnetic filaments. We analytically show, 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 in magnetic fields play the role of a specific attractor. This analysis was confirmed by numerical simulations of 2D roll-type convective cells. Without dissipation, the magnetic field grows exponentially in time and does not depend on the aspect ratio between the horizontal and vertical scales of the cell. An increase due to compression in the magnetic field of highly conductive plasma is saturated due to the natural limitation associated with dissipative effects when the maximum magnitude of a 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 the mean magnetic energy density for at least two orders of magnitude, which allows one to use the kinematic approximation of the MHD induction equation. In this paper, based on the stability analysis, we explain why downward flows influence magnetic filaments, making them flatter with orientation along the interfaces between convective cells.