Phase mixing of shear Alfven waves in a line-tied X-point geometry

One of the most fundamental question of solar physics is to understand the heating of the corona. Among other mechanisms phase mixing of Alfven waves appears to be a good candidate for explaining the fast energy dissipation. In a nonhomogeneous magnetic structure Alfven waves travel at different speeds thus creating cross-field gradients that are likely to enhance the damping rate of energy. Most phase mixing studies have focused on 1D geometry and none has considered the introduction of a null point. The present analysis thus extend the previous ones in a line-tied X-point geometry. By solving an initial value problem, we show that only the first stage of the decay (10-20 Alfven times) obeys the classical cubic law (Heyvaerts & Priest 1983). Later on a diffusive orchestration of the oscillations leads to an eigenmode behaviour with an almost viscosity-independant dissipation rate.