论文部分内容阅读
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。
Using the phenomenological theory model, the control problem of the chaos in the light field of the storage ring type free electron laser is discussed. A method to control chaos in non-autonomous ordinary differential equations is proposed, which is called “shot method”. Theoretical analysis and numerical results show that when a weak periodic control light field is introduced into the laser cavity, the laser intensity changes with time as the amplitude and period of the control light field change from chaos to periodicity. The corresponding maximum Lyapunov characteristic exponent changes from positive to negative. Further research also found that the light field chaos can be controlled only when the period of the control light field is an integral multiple of the original gain modulation period in the cavity. In other words, this control method of chaos adding a “beat function” is actually a non-feedback resonance method. In addition, by introducing the concept of “evolved operator eigenvalue”, a method of determining the optimal “slap” position is given.