The low MN map for single-null divertor tokamaks

Abstract

The low MN map is derived from the general theory of maps and the generating function for the low mn perturbation. The unperturbed magnetic topology of a single-null divertor tokamak is represented by the symmetric simple map. The perturbed topology is represented by the low MN map. The method of maps is applied to calculate the effects of low mn perturbation on the stochastic layer and the magnetic footprint. The low mn perturbation organizes the stochastic layer into large scale spatial structures. This is reflected in the phase portraits, safety factor, Liapunov exponents, magnetic footprints, and the semiconnection length. For the expected range of the amplitude of the low mn perturbation, the fraction of magnetic flux escaping the stochastic layer, the width of stochastic layer, the area of the magnetic footprints increase, while the number of hot spots and the fraction of flux going into the hot spots both decrease. The key features of the complex patterns in the heat deposition on the collector plates in divertor tokamaks are quite well recovered from the results of the low MN map.