托卡马克中低模态到高模态转迁模型的混沌运动

Chaotic Motions for the Model of the L-Mode to H-Mode in Tokamak

利用Melnikov方法详细研究了在托卡马克(Tokamaks)中,等离子区边缘附近低模态到高模态转迁方程的混沌动力学.该转迁方程是一个含外激励和参数激励的系统.对含周期外激励和线性参数激励、三次参数激励的系统分别绘出了用来划分混沌区和非混沌区的临界曲线.得到的结果表明,含有线性或三次参数激励的系统存在不可控区域,在该区域中异宿轨分岔总是导致混沌发生.特别地,三次参数激励系统存在一个"可控频率",施以该频率的激励,不论激励的振幅多大,同宿轨分岔总是不会导致混沌发生.得到了这类系统的一些复杂的动力学行为.

The chaotic dynamics of the transport equation for the L-mode to H-mode near plasma in Tokamak is studied in detail with Melnilov method. The transport equations represent a system with external and parametric excitation. The critical curves separating the chaotic regions and non-chaotic regions were 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 takes place via heteroclinic bifurcation for the system with linear or cubic parametric excitation. Especially, there exists a ＂. controllable frequency＂ excited at which chaos doesn＇t occur via homoclinic bffurcation no matter how large the excitation amplitude is for the system with cubic parametric excitation. Some complicated dynamical behaviors were obtained for this class of systems.