Chaotic Approach to Evaluation of Disturbed Magnetic Surfaces

Abstract

A circle mapping can approximately reproduce the cross section of magnetic surfaces and the value of the periodic driving force (K) at a magnetic island varies with the width of the magnetic island, which suggests the value of K is one of measures for the degradation of magnetic surfaces. The profile of a rotational transform has flat regions at the magnetic islands. The width of the flat region is proportional to the width of the magnetic island. Therefore it may be another measure of the degradation of magnetic surfaces. This method requires less data for the estimation than the usual method of calculating the width of magnetic islands. For collapsed magnetic surfaces that are produced by overlapping of two magnetic islands, the fractal dimension can effectively estimate the degradation of them. The fractal dimensions of cross sections of regular magnetic surfaces and clear magnetic islands are nearly 1, while that of a collapsed magnetic surface is about 1.2 in the present study.