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

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.