中国物理B ›› 2013, Vol. 22 ›› Issue (6): 64210-064210.doi: 10.1088/1674-1056/22/6/064210

• ELECTROMAGNETISM, OPTICS, ACOUSTICS, HEAT TRANSFER, CLASSICAL MECHANICS, AND FLUID DYNAMICS • 上一篇    下一篇

Crystalline undulator radiation and sub-harmonic bifurcation of system

罗晓华a b, 何为a, 吴木营c, 邵明珠c, 罗诗裕c   

  1. a College of Electric Engineering, Chongqing University, Chongqing 400044, China;
    b Library, Chongqing Jiaotong University, Chongqing 400074, China;
    c College of Electronic Engineering, Dongguan University of Technology, Dongguan 523808, China
  • 收稿日期:2012-08-31 修回日期:2012-10-15 出版日期:2013-05-01 发布日期:2013-05-01

Crystalline undulator radiation and sub-harmonic bifurcation of system

Luo Xiao-Hua (罗晓华)a b, He Wei (何为)a, Wu Mu-Ying (吴木营)c, Shao Ming-Zhu (邵明珠)c, Luo Shi-Yu (罗诗裕)c   

  1. a College of Electric Engineering, Chongqing University, Chongqing 400044, China;
    b Library, Chongqing Jiaotong University, Chongqing 400074, China;
    c College of Electronic Engineering, Dongguan University of Technology, Dongguan 523808, China
  • Received:2012-08-31 Revised:2012-10-15 Online:2013-05-01 Published:2013-05-01
  • Contact: He Wei E-mail:hewei@126.com

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摘要： Looking for a new light source, especially short wavelength laser light source has attracted widespread attention. In the paper analytically described is the radiation of crystalline undulator field by the sine-squared potential. In the classical mechanics and the dipole approximation, the motion equation of particle is reduced to a generalized pendulum equation with damping term and forcing term. The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and numerical method, and the stability of the system is discussed. The results show that the stability of the system relates to its parameters, and only by adjusting appropriately these parameters, in principle can the occurrence of bifurcation be avoided or suppressed.

关键词: crystalline undulator radiation, short wavelength laser, Melnikov method, bifurcation, stability

Abstract: Looking for a new light source, especially short wavelength laser light source has attracted widespread attention. In the paper analytically described is the radiation of crystalline undulator field by the sine-squared potential. In the classical mechanics and the dipole approximation, the motion equation of particle is reduced to a generalized pendulum equation with damping term and forcing term. The bifurcation behavior of periodic orbits is analyzed by using the Melnikov method and numerical method, and the stability of the system is discussed. The results show that the stability of the system relates to its parameters, and only by adjusting appropriately these parameters, in principle can the occurrence of bifurcation be avoided or suppressed.

Key words: crystalline undulator radiation, short wavelength laser, Melnikov method, bifurcation, stability

中图分类号:  (X- and γ-ray lasers)

  • 42.55.Vc
78.20.Bh (Theory, models, and numerical simulation) 05.45.Ac (Low-dimensional chaos) 46.40.Ff (Resonance, damping, and dynamic stability)