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Looking for a new light source, especially short-wavelength coherent light source has attracted much attention. A possibility and basic conditions are discussed by using crystalline undulator field radiation as a short-wavelength laser; it is pointed out that the short-wavelength laser has not yet been available so far which is due to not only technical reasons, but also physical reasons. In this paper, the physical problem is analyzed by using parametric excitation method. Introducing the sine-squared potential, the particle motion equation is reduced to a pendulum equation with a damping term and parameter excitation term in the framework of classical mechanics and the dipole approximation. A stability of the system is discussed using Melnikov method, and the critical condition of the system is also analyzed. The results show that the stability of the system relates to its parameters. By adjusting these parameters appropriately, the stability of the system can be ensured in principle.
[1] Kumakhov M A 1976 Phys. Lett. A 57 17
[2] Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Methods Phys. Res. B 266 1173
[3] Korol A V, Solovyov A V, Greiner W 2006 Spontaneous and Stimulated Photon Emission in Crystalline Undulators (Natherlands: Springer) pp165–189
[4] Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[5] Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[6] Sushko G B, Korol A V, Greiner W, Solov’yov A V 2013 J. Phys.: Conf. Ser. 438 012018
[7] Korol A V, Solov’yov A V, Greiner W 2013 Channeling and Radiation in Periodically Bent Crystals (Berlin: Springer) pp195–226
[8] Gennady B S, Bezchastnov V G, Solov’yov I A, Korol A V, Greiner W, Solovyov A V 2013 J. Computat. Phys. 252 404
[9] Luo S Y, Shao M Z 2009 Chin. Laser 36 1378 (in Chinese) [罗诗裕, 邵明珠 2009 中国激光 36 1378]
[10] 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]
[11] 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]
[12] Zhang M, Luo X H, Luo S Y, Shao M Z 2010 Chin. J. Lumines. 31 454 (in Chinise) [张梅, 罗晓华, 罗诗裕, 邵明珠 2010 发光学报 31 454]
[13] Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[14] Liu H Z, Luo S Y, Shao M Z 2013 Chin. Phys. B 22 047807
[15] Luo S Y, Shao M Z, Luo X H 2010 Sci. China: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学 40 207]
[16] Shao M Z, Luo S Y, Wang H C 2009 Chin. Lasers 36 2888 (in Chinese) [邵明珠, 罗诗裕, 王红成 2009 中国激光 36 2888]
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[1] Kumakhov M A 1976 Phys. Lett. A 57 17
[2] Korol A V, Solovyov A V, Greiner W 2008 Nucl. Inst. Methods Phys. Res. B 266 1173
[3] Korol A V, Solovyov A V, Greiner W 2006 Spontaneous and Stimulated Photon Emission in Crystalline Undulators (Natherlands: Springer) pp165–189
[4] Tabrizi M, Korol A V, Solovyov A V 2007 Phys. Rev. Lett. 98 164801
[5] Korol A V, Solovyov A V, Greiner W 2004 Int. J. Mod. Phys. E 13 867
[6] Sushko G B, Korol A V, Greiner W, Solov’yov A V 2013 J. Phys.: Conf. Ser. 438 012018
[7] Korol A V, Solov’yov A V, Greiner W 2013 Channeling and Radiation in Periodically Bent Crystals (Berlin: Springer) pp195–226
[8] Gennady B S, Bezchastnov V G, Solov’yov I A, Korol A V, Greiner W, Solovyov A V 2013 J. Computat. Phys. 252 404
[9] Luo S Y, Shao M Z 2009 Chin. Laser 36 1378 (in Chinese) [罗诗裕, 邵明珠 2009 中国激光 36 1378]
[10] 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]
[11] 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]
[12] Zhang M, Luo X H, Luo S Y, Shao M Z 2010 Chin. J. Lumines. 31 454 (in Chinise) [张梅, 罗晓华, 罗诗裕, 邵明珠 2010 发光学报 31 454]
[13] Luo X H, He W, Wu M Y, Shao M Z, Luo S Y 2013 Chin. Phys. B 22 064210
[14] Liu H Z, Luo S Y, Shao M Z 2013 Chin. Phys. B 22 047807
[15] Luo S Y, Shao M Z, Luo X H 2010 Sci. China: Phys. Mech. Astron. 40 207 (in Chinese) [罗诗裕, 邵明珠, 罗晓华 2010 中国科学 40 207]
[16] Shao M Z, Luo S Y, Wang H C 2009 Chin. Lasers 36 2888 (in Chinese) [邵明珠, 罗诗裕, 王红成 2009 中国激光 36 2888]
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