【摘要】 用唯象理论模型讨论了储存环型自由电子激光器光场混沌的控制问题。提出了一种控制非自治常微分方程系统混沌的方法,即“拍方法”。理论分析和数值计算结果都表明:当在激光共振腔内引入一个弱周期控制光场时,随着控制光场振幅和周期的改变,激光强度随时间的变化可以由混沌的变为周期的。相应的最大Lyapunov特征指数由正数变为负数。进一步的研究还发现:只有当控制光场的周期是腔内原有增益调制周期的整数倍时,光场混沌才能被控制住。也就是说,这种加一个“拍函数”的控制混沌方法实际上是一种无反馈的共振方法。另外,通过引入“演化算符本征值”的概念,给出了确定最佳“拍击”位置的方法。更多还原

【Abstract】 The controlling of optical field chaos in a storage ring free-electron laser oscil-lator is discussed by using a phenomenal model. A novel method (which is called the "beating method") of controlling chaos in a nonlinear dynamical system descri-bed by nonautonomous ordinary differential equations was developed. The result of theoretical analysis and numerical simulation shows that the optical field chaos in a storage ring free-electron laser oscillator can be suppressed and a periodic laser inten-sity can be obtained when a weak periodic control field is added to the optical cavity. The validity of this method of eliminating chaos is confirmed by the fact that the leading Lyapunov characteristic exponent of the system changes from a positive real number to a negative one. A further research is carried out, and it is found that only when the period of the control field equals to an integral multiple of that of the gain modulation in the optical cavity can the optical field chaos be suppressed. This means that the "beating method" of controlling chaos is a kind of resonant method. A way to determine the "best beating position" in the phase tra-jectory has also been obtained.更多还原