Analytic theory of the period, amplitude and crash time of sawteeth in tokamaks

A recently developed nonlinear dynamical model of turbulence is analysed and shown to result in scaling laws for the period, amplitude and crash time in terms of the sawtooth-averaged quantities characteristic of the q < 1 'core' region to which it applies. These scaling relations involve plasma parameters such as the core plasma beta, confinement time, pressure length-scale and shear parameter at the q = 1 radius. The analytic formulae are compared with numerical simulations for TEXT, TEXTOR and JET conditions and found to be in excellent agreement. The model is therefore able to predict the period, temperature amplitude and crash time given to these core properties from experimental data. It also describes the temporal behaviour (during both ramp and crash) of the core-averaged temperature and turbulence level. (author)