Small-scale kG strong magnetic field elements in the solar photosphere are often identified as so-called magnetic bright points (MBPs). In principle these MBPs represent the cross-section of a vertical, strong, magnetic flux tube which is expanding with height in the solar atmosphere. As these magnetic elements represent possible MHD wave guides, a significant interest has been already paid to them from the viewpoint of observations and simulations. In this work we would like to shed more light on a possible scenario for the creation of such strong magnetic field concentrations. The accepted standard scenario involves the convective collapse process. In this ongoing work we will show indications that this convective collapse process may become triggered by sufficiently strong pressure disturbances. However, it is highly unlikely that p-mode waves can be of such a strength.

The combined action of the subadiabatic ambient stratification in the overshoot region below the convection zone and the inertial forces associated with the solar rotation is shown to lead to the suppression of the escape of magnetic flux in the form of toroidal flux tubes both toward the surface and toward higher latitudes. We show that a flux ring initially in thermal equilibrium with its environment and rotating with the ambient angular velocity moves radially and latitudinally towards an equilibrium configuration of lower internal temperature and larger internal rotation rate with respect to the surrounding, field-free gas. We conclude that flux rings with B≲ 105 G can be kept within the overshoot region if the superadiabaticity is sufficiently negative, i.e. δ = ▿ – ▿ad ≲–10−5; below that field strength the poleward drift is also reduced to a latitudinal oscillation of moderate amplitude, δθ ≲ 20 deg. Flux rings with significantly larger field strength cannot be kept in the equatorial parts of the overshoot region: their equilibrium configuration is located at high latitudes far outside the solar activity belts and, at any rate, requires unrealistic values of δ.

We consider the linear stability of a toroidal flux tube lying in the equatorial plane of a differentially rotating star and investigate its dependence on superadiabaticity, magnetic field strength, and gradient of angular velocity.