Chaotic advection in quiet discharges in tokamaks

Horton et al. (1987) have developed a guiding centre model for turbulent electron diffusion in 'quiet' discharges in tokamaks. They have argued that the electron diffusion in this regime may be due to a spectrum of electromagnetic drift fluctuations. They have studied by numerical means the dependence of the corresponding diffusion coefficient on amplitude and steepness of the spectrum as well as on other parameters of the model. The authors discuss the statistical significance of the results obtained with the type of computation used by Horton et al. They show that when the dependence of the computed diffusivity on computer, model and integrator parameters is taken into account, the corresponding estimation errors may be larger than the 'convergence error bars' calculated in Horton et al. The error bars in question have been designed to show only how well the running diffusivity had settled down to a constant for a particular choice of the parameter set. The authors study how these parameters might influence the value of the constant itself, and as a consequence propose a half-way time-reversing procedure to assess the possible deviation, often referred to as 'numerical diffusion'. They demonstrate, by the way, that an implicit version of the Runge-Kutta integrator that leads to the same numerical diffusion as its explicit counterpart is 10 to 20 times faster.