非线性动力学在磁约束核聚变约束模式转换中的应用  

APPLICATION OF NONLINEAR DYNAMICS TO L-H MODE TRANSITION IN MAGNETIC CONFINEMENT FUSION

作　　者：艾媛媛 朱浩[1,2] AI Yuanyuan;ZHU Hao(Faculty of Science,Beijing University of Technology,Beijing 100124;Beijing-Dublin International College,Beijing University of Technology,Beijing 100124)

机构地区：[1]北京工业大学理学部,北京100124 [2]北京工业大学北京都柏林国际学院,北京100124

出　　处：《物理与工程》2023年第5期95-101,107,共8页Physics and Engineering

基　　金：北京市自然科学基金资助项目(1194020,2232045);北京市教委科技计划一般项目(KM201910005001);国家重点研发计划(2018YFB0703500)。

摘　　要：非线性动力学在诸如双摆和振荡电路等本科物理教学中扮演着积极的角色。雅可比矩阵作为非线性动力学中的重要概念,常被用来分析不动点的性质。本文中我们先推导了一个二维系统中雅可比矩阵的具体形式,并将其应用到磁约束核聚变约束模式转换模型,最后延伸求解出ZCD模型中各不动点的雅可比矩阵本征值。我们随后调整了模型中的外界加热功率,并使用雅可比矩阵观察模型中非线性动力学性质的变化。经研究发现,外界加热功率的改变会使得ZCD模型极限环的大小发生变化,即功率越大极限环半径越大。极限环半径的扩大导致环与鞍点相交为一个同宿轨,诱使系统产生同宿分岔。Nonlinear dynamics plays an active role in university physics such as double pendulum and resonant circuit.As an important concept in nonlinear dynamics,Jacobian matrix is often adopted to analyze the properties of fixed points.In this paper,we derive the specific form of the Jacobian matrix in a classic two-dimensional system,and apply it to the L-H mode transition model of magnetic confinement fusion,then solve the eigenvalues of the Jacobian matrix at each fixed point in the ZCD model.We adjust the external heating power in the model and analyze the nonlinear dynamic properties of the model by the Jacobian matrix.It is found that the variance of external heating power changes the size of limit cycle in ZCD model;and the higher the power is,the larger the limit cycle will be.The expansion of the limit cycle radius leads itself to intersect with the saddle point into a homologous orbit,which induces the system to occur homoclinic bifurcation.

关 键 词：非线性动力学 雅可比矩阵 约束模式转换模型 同宿分岔 

分 类 号：TL62[核科学技术—核技术及应用]