The dynamic mutation characteristics of thermonuclear reaction in Tokamak.

Jing Li,Wei Zhang,Wei Deng,Tingting Quan

doi:10.1155/2014/841891

Abstract

The stability and bifurcations of multiple limit cycles for the physical model of thermonuclear reaction in Tokamak are investigated in this paper. The one-dimensional Ginzburg-Landau type perturbed diffusion equations for the density of the plasma and the radial electric field near the plasma edge in Tokamak are established. First, the equations are transformed to the average equations with the method of multiple scales and the average equations turn to be a Z 2-symmetric perturbed polynomial Hamiltonian system of degree 5. Then, with the bifurcations theory and method of detection function, the qualitative behavior of the unperturbed system and the number of the limit cycles of the perturbed system for certain groups of parameter are analyzed. At last, the stability of the limit cycles is studied and the physical meaning of Tokamak equations under these parameter groups is given.

Highlights

Periodic solution theory is mainly about the existence and stability of periodic solution of dynamical systems
Arnol’d [1] examined the problem on equivariant fields and their topologically versal deformations in the functional space of all equivariant fields and these results yield the first approximation for the stability loss problem
This paper focuses on the bifurcations of multiple limit cycles for a Ginzburg-Landau type perturbed transport equation which can describe the low confinement mode (L-mode) to high confinement mode (H-mode) transition near the plasma edge in Tokamak

Summary

Introduction

Periodic solution theory is mainly about the existence and stability of periodic solution of dynamical systems. Armengol and Joan [6] perturb a vector field with a general polynomial perturbation of degree n and study the maximum number of limit cycles that can bifurcate from the period annulus of the origin in terms of k and n Their approach is based on the explicit computation of the Abelian integral that controls the bifurcation and on a new result for bounding the number of zeroes of a certain family of real functions. Using the bifurcation theory and the method of detection function, the number of limit cycles of the average equation under a certain group of parameters is given The stability of these limit cycles is analyzed and the diffusion coefficients of H-mode and L-mode are obtained

Equation of Motion and Perturbation Analysis

The Dynamic Characteristics of Thermonuclear Reaction in Tokamak

The Analysis of Stability

Conclusions