Effect of Weak Dissipation on a Drift Orbit Mapping

Abstract

The discontinuity at the boundary between an area preserving system and dissipative system has been studied by investigating the effect of weak dissipation on drift orbits making use of a simple mapping model in a helical magnetic field. It is found that, after many mapping iterations, any orbit even chaotic one tends to an attractor forming a vortex line with a very small dissipation. The number of iteration to converge within a certain distance from the attractor is inversely proportional to the amount of the dissipation. Although the behavior of orbits completely change, the basic stability characteristics of the system does not change, i.e., the coordinate of the attractors are determined by the stable fixed points in the area preserving system. Since wide range of orbits are concentrated around the attractors after many toroidal rotations, a pinch effect is created by a small dissipation. Application of this pinch effect to fusion plasmas is discussed.