1997 Fiscal Year Final Research Report Summary
Study on measurement of disturbed magnetic surfaces of stellarators ant its robustness
| Project/Area Number |
07680543
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Nuclear fusion studies
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| Research Institution | Science University of Tokyo |
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Principal Investigator |
KOGOSHI Sumio Science University of Tokyo, Science and Technology, Professor, 理工学部, 教授 (60134459)
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| Project Period (FY) |
1995 – 1997
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| Keywords | magnetic surface / fractal dimension / rotational transform / Lyapunov exponent / stellarator / circle mapping / chaos / magnetic island |
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| Research Abstract |
The purpose of this study is to devise the ways to measure disturbances of magnetic surfaces of stellarators and to discuss their robustness. It is said that for stellarators magnetic islands grow at rational surfaces when helical symmetry is destroyed by toroidicity. Then magnetic surfaces are disturbed. When magnetic islands grow so that adjacent islands overlap, the behavior of the magnetic field lines is chaotic.
Commonly, the degrees of the disturbance of magnetic surfaces are estimated with the width of magnetic islands. However, this method needs extensive calculation time. In addition, it can not estimate chaotic magnetic field lines. To improve these points, we propose new methods. One is (1) a fractal dimension method and others are (2) a rotational transformation method and (3) a circle mapping method. We compared these three methods with the common method. Then the followings are confirmed. These methods are all available to estimate the degree of disturbed magnetic surfaces. The method (1), however, can only evaluate chaotic magnetic field lines and the method (2) needs the least calculation time. Also we show at first that Poincare maps of chaotic magnetic field lines have non-integer fractal dimensions and positive Lyapunov exponents.These indicate strongly the behaviors of chaotic magnetic field lines are really chaos.
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