Fast crash and dependence of sawteeth on transport coefficients from reduced-MHD simulations

Sawtooth oscillations of the central temperature occur in practically all tokamaks under a variety of experimental conditions. A theoretical model for the sawteeth was first proposed by Kadomtsev. His model is based on the resistive reconnection of an m=1/n=1 kink deformation which occurs when the safety factor in the centre qo falls below unity. Numerical simulations of sawteeth, generally consistent with the Kadomtsev model, have been performed by several different groups. However, all computations carried out so far have been made with plasma parameters far from those characteristic of current experiments. In this paper, we present self-consistent simulations over a wide range of plasma parameters to obtain the dependence of characteristic features of the sawteeth on the transport coefficients. The simulations are based on the standard, straight cylinder, low-β, reduced-MHD equations with self-consistent evolution of the electron temperature, including a highly anisotropic, thermal diffusivity and ohmic heating. Comparison of the simulation results concerning, e.g., period, growth-time of the instability and collapse time, with experimental data shows excellent agreement for Lundquist numbers up to about 107 (corresponding to machines of the size of Frascati Tokamak, FT). An important effect found in these self-consistent simulations is that the current profile is significantly modified by the sawteeth, leading to a very flat distribution in a central region accompanied by a sharp drop outside the reconnection layer. This profile makes it possible to turn on the resistive kink instability with a large growth-rate by a minute change in central q. Thus, the Kadomtsev model, with some modification of the current profile, appears to describe the sawtoothing in, at least, small and medium sized tokamaks very well. (author) 7 refs., 2 figs