This paper describes a new method to derive, from soft x-ray (SXR) tomography, robust estimates of the core displacement, growth rate and frequency of a 1/1 sawtooth crash precursor. The method is valid for very peaked SXR profiles and is robust against both the inversion algorithm and the presence of tungsten in a rotating plasma. Three typical ASDEX Upgrade crashes are then analysed. In all cases a postcursor is observed, suggesting incomplete reconnection. Despite different dynamics, in all three cases the growth rate of the core displacement shows similar features. First, it is not constant, supporting the idea of non-linear growth. Second, it can be divided into clearly identified phases with quasi-constant growth rates, suggesting sudden change of growth regime rather than smooth transitions. Third, its evolution is non-monotonic, with phases of accelerated growth followed by damped phases. This damping is interpreted for two cases respectively as an effect of fast ions and of mode coupling, based on the result of a MHD simulation. The mode frequency is observed in all cases to be closely related to the plasma bulk rotation profile, with little or no visible effect of the electron diamagnetic drift frequency. The onset criterion could not be clearly identified and it is shown that the role of the pressure gradient is not as expected from a naive extrapolation of the linear stability theory.
Nonlinear MHD simulations of the gravitational ballooning mode close to marginal stability