Concentration of magnetic energy in magnetohydrodynamic flows

Several modelings of kinematic dynamos predict concentration of the magnetic energy at some regions of the domain, notably in the vicinity of certain stagnation points of the flow. This phenomenon of concentration is also observed in real astrophysical plasmas, such as magnetic flux tubes in the solar atmosphere. By analyzing the behavior of regions where the size of the Elsنsser variables is larger than a fixed amount, we show that the energy of these regions typically decreases at the same rate as their volume. This means that small domains where the magnetic energy is very large must be in contact with regions with high velocity. This is caused by the advection of the magnitudes and it is independent in a large measure of the plasma diffusivity.