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Searching for new light source, especially short wave-length coherence light source has attracted extensive attention. The using of the crystalline undulator radiation as a short wave-length coherence light source is most likely to be one of the options. From the viewpoints of potential and field, the centrifugal force generated by periodic bent crystal is regarded as centrifugal potential, the particle motion equation is reduced to Mathieu equation with Duffing-type, and from the energy viewpoint the stability of the system is discussed. The behaviors of particles in the vicinity of the resonance are analyzed by perturbation method; the jump phenomena and instable behavior are revealed. The results show that the stability of the system is related to its parameters, and only properly adjusting these parameters, the bifurcation and instability for the system can be avoided in principle.
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Keywords:
- crystalline undulator radiation /
- parametric excitation /
- short-wavelength laser /
- nonlinearity
[1] Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Methods Phys. Res. B 266 1173
[2] Korol A, Solovyov A V, Greiner W 2006 Advanced Radiation Sources and Applications (Natherlands: Undulators, Springer) pp165-189
[3] Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[4] Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[5] Korol A V Solov’yov A V Greiner W 2013 Springer Series on Atomic, Optical, and Plasma Physics (Berlin: Splinger) p473
[6] Luo S Y, Shao M Z 2009 Chin. J. Laser 36 1378 (in Chinese) [罗诗裕, 邵明珠 2009 中国激光 36 1378]
[7] Wang S J, Wu M Y, Luo S Y, Zhang W F, Luo X H, Shao M Z 2010 Acta Opt. Sin. 30 180 (in Chinese) [王善进, 吴木营, 罗诗裕, 张伟风, 罗晓华, 邵明珠 2010 光学学报 30 180]
[8] Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin. 59 2685 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 59 2685]
[9] Luo S Y, Shao M Z, Luo X H 2010 Sci. China G: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学 G: 物理学, 力学, 天文学 40 207]
[10] Shao M Z, Luo S Y, Wang H C 2009 Chin. J. Lasers 36 2888 (in Chinese) [邵明珠, 罗诗裕, 王红成 2009 中国激光 36 2888]
[11] Li X P, Wang S J, Chen Q, Luo S Y 2013 Acta Phys. Sin. 62 224102 (in Chinese) [李秀平, 王善进, 陈琼, 罗诗裕 2013 62 224102]
[12] Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[13] Nayfeh A H 1981 Introduction to Peturbation Techniques (New York: John Wiley & Sons.) p182
[14] Luo X H, He W, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[15] Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[16] Nayfeh A H, Mook D T 1979 Nonlinear Oscillations (New York: John Wiley & Sons.) p216
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[1] Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Methods Phys. Res. B 266 1173
[2] Korol A, Solovyov A V, Greiner W 2006 Advanced Radiation Sources and Applications (Natherlands: Undulators, Springer) pp165-189
[3] Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[4] Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[5] Korol A V Solov’yov A V Greiner W 2013 Springer Series on Atomic, Optical, and Plasma Physics (Berlin: Splinger) p473
[6] Luo S Y, Shao M Z 2009 Chin. J. Laser 36 1378 (in Chinese) [罗诗裕, 邵明珠 2009 中国激光 36 1378]
[7] Wang S J, Wu M Y, Luo S Y, Zhang W F, Luo X H, Shao M Z 2010 Acta Opt. Sin. 30 180 (in Chinese) [王善进, 吴木营, 罗诗裕, 张伟风, 罗晓华, 邵明珠 2010 光学学报 30 180]
[8] Luo S Y, Shao M Z, Luo X H 2010 Acta Phys. Sin. 59 2685 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 59 2685]
[9] Luo S Y, Shao M Z, Luo X H 2010 Sci. China G: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学 G: 物理学, 力学, 天文学 40 207]
[10] Shao M Z, Luo S Y, Wang H C 2009 Chin. J. Lasers 36 2888 (in Chinese) [邵明珠, 罗诗裕, 王红成 2009 中国激光 36 2888]
[11] Li X P, Wang S J, Chen Q, Luo S Y 2013 Acta Phys. Sin. 62 224102 (in Chinese) [李秀平, 王善进, 陈琼, 罗诗裕 2013 62 224102]
[12] Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[13] Nayfeh A H 1981 Introduction to Peturbation Techniques (New York: John Wiley & Sons.) p182
[14] Luo X H, He W, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[15] Liu H Z, Luo S Y Shao M Z 2013 Chin. Phys. B 22 047807
[16] Nayfeh A H, Mook D T 1979 Nonlinear Oscillations (New York: John Wiley & Sons.) p216
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