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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (7): 811-820.doi: https://doi.org/10.1007/s10483-009-0701-z

• Articles •    下一篇

Chaotic motions of the L-mode to H-mode transition model in tokamak

陈芳启1,3 周良强2,3 王霞1 陈予恕2,3   

  1. 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, P. R. China;
    2. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
    3. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control,Tianjin 300072, P. R. China
  • 收稿日期:2008-10-17 修回日期:2009-06-12 出版日期:2009-07-01 发布日期:2009-07-01

Chaotic motions of the L-mode to H-mode transition model in tokamak

 CHEN Fang-Qi1,3, ZHOU Liang-Qiang2,3, WANG Xia1, CHEN Yu-Shu2,3   

  1. 1. Department of Mathematics, Nanjing University of Aeronautics and Astronautics,Nanjing 210016, P. R. China;
    2. Department of Mechanics, Tianjin University, Tianjin 300072, P. R. China;
    3. Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control,Tianjin 300072, P. R. China
  • Received:2008-10-17 Revised:2009-06-12 Online:2009-07-01 Published:2009-07-01

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摘要： The chaotic dynamics of the transport equation for the L-mode to H-mode near the plasma in a tokamak is studied in detail with the Melnikov method. The transport equations represent a system with external and parametric excitation. The critical curves separating the chaotic regions and nonchaotic regions are presented for the system with periodically external excitation and linear parametric excitation, or cubic parametric excitation, respectively. The results obtained here show that there exist uncontrollable regions in which chaos always take place via heteroclinic bifurcation for the system with linear or cubic parametric excitation. Especially, there exists a controllable frequency, excited at which chaos does not occur via homoclinic bifurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation. Some complicated dynamical behaviors are obtained for this class of systems.

关键词: transitions in tokamak, chaos, Melnikov method, uncontrollable regions, controllable frequency

Abstract: The chaotic dynamics of the transport equation for the L-mode to H-mode near the plasma in a tokamak is studied in detail with the Melnikov method. The transport equations represent a system with external and parametric excitation. The critical curves separating the chaotic regions and nonchaotic regions are presented for the system with periodically external excitation and linear parametric excitation, or cubic parametric excitation, respectively. The results obtained here show that there exist uncontrollable regions in which chaos always take place via heteroclinic bifurcation for the system with linear or cubic parametric excitation. Especially, there exists a controllable frequency, excited at which chaos does not occur via homoclinic bifurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation. Some complicated dynamical behaviors are obtained for this class of systems.

Key words: transitions in tokamak, chaos, Melnikov method, uncontrollable regions, controllable frequency

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