受迫摆方程与准沟道辐射的稳定性
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摘要
从受迫摆方程出发导出了系统的频率响应,并从Mathieu方程的稳定区和不稳定区讨论了系统的稳定性。指出了粒子的准沟道运动可以用周期转动解来描述,并利用系统的周期倍分叉、跳跃现象和弛豫行为讨论了准沟道粒子运动的稳定性。结果表明,适当选择参数,系统的稳定性是可以保证的。
The frequency response of the system was derived from the forced pendulum equation,and the stability of the system was discussed from the stability and instability of Mathieu equation.It is pointed out that the quasi-channel motion of particles can be described by the rotational periodic solution,and the stability of quasi-channel particle motion is discussed by using the periodic bifurcation,jumping phenomenon and relaxation behavior of the system.The results show that the stability of the system can be ensured by choosing the parameters properly.
The frequency response of the system was derived from the forced pendulum equation,and the stability of the system was discussed from the stability and instability of Mathieu equation.It is pointed out that the quasi-channel motion of particles can be described by the rotational periodic solution,and the stability of quasi-channel particle motion is discussed by using the periodic bifurcation,jumping phenomenon and relaxation behavior of the system.The results show that the stability of the system can be ensured by choosing the parameters properly.
引文
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[17]罗诗裕,吴木营,邵明珠,等.应变超晶格的共振行为与动力学稳定性[J].物理学报,2010,59(8):5766-5771.Luo Shiyu,Wu Muying,Shao Mingzhu,et al.The resonance behaviour and dynamic stabilities of strained superlattice[J].Acta Phys.Sin.,2010,59(8):5766-5771.
[2]Brau C A,Choi B K,Jarvis J D,et al.Channeling radiation as a source of hard X-rays with high spectral brilliance[J].Synchrotron Radiation News,2012,25(1):20-24.
[3]Epp V,Sosedova M A.Coherent radiation from atoms and a channeled particle[J].Nuclear Instruments&Methods in Phys.Research,2013,301(301):1-6.
[4]Sushko G B,Bezchastnov V G,Solov’yov I A,et al.Simulation of ultra-relativistic electrons and positrons channeling in crystals with MBN explorer[J].J.of Computational Phys.,2013,252:404-410.
[5]Kostyuk A.Monte-Carlo simulations of electron channeling:Abent(110)channel in silicon[J].European Phys.J.D,2013,67(5):1-7.
[6]Backe H,Krambrich D,Lauth W,et al.Channeling and radiation of electrons in silicon single crystals and Si1-xGex crystalline undulators[J].J.of Phys.Conf.Series,2013,438(1):012017-8.
[7]Backe H,Krambrich D,Lauth W,et al.Radiation emission at channeling of electrons in a strained layer Si1-xGex undulator crystal[J].Nuclear Instruments and Methods in Phys.Research,Section B:Beam Interactions with Mater.and Atoms,2013,309:37-44.
[8]Luo Xiaohua,He Wei,Shao Mingzhu,et al.Crystalline undulator radiation and possibility as short wavelength laser[J].Chin.Phys.B,2013,22(6):401-404.
[9]邵明珠,罗诗裕,王红成.周期弯晶摆动场辐射的混沌振荡[J].中国激光,2009,36(11):2888-2892.Shao Mingzhu,Luo Shiyu,Wang Hongcheng.Chaotic oscillation of undulator radiation in a periodically bent crystal[J].Chinese J.of Lasers,2009,36(11):2888-2892.
[10]罗晓华,杨杰,李秀平,等.晶体摆动场辐射及其共振线附近粒子的运动行为[J].物理学报,2014,63(8):224102-224105.Luo Xiaohua,Yang Jie,Li Xiuping,et al.Crystalline undulator radiation and motion behavior in the vicinity of the resonance line[J].Acta Phys.Sin.,2014,63(8):224102-224105.
[11]Nayfeh A H,Mook D T.Nonliniear Oscillations[M].New York:John Wiley&Sons,Inc.,1979.
[12]Nayfeh A H.Introduction to Perturbation Techniques[M].New York:John Wiley&Sons,Inc.,1981.
[13]王娜,罗诗裕.应变超晶格中粒子运动的混沌不稳定性[J].半导体光电,2018,39(3):381-384.Wang Na,Luo Shiyu.Chaos instability of particle motion in strained superlattices[J].Semiconductor Optoelectronics,2018,39(3):381-384.
[14]李广明.倒置摆的有效势与晶体摆动场辐射的稳定性[J].半导体光电,2015,36(5):741-745.Li Guangming.Effective potential of inverted pendulum and stability of crystalline undulator radiation[J].Semiconductor Optoelectronics,2015,36(5):741-745.
[15]罗晓华,何为,吴木营,等.准周期激励与应变超晶格的动力学稳定性[J].物理学报,2013,62(24):247301-247306.Luo Xiaohua,He Wei,Wu Muying,et al.Quasi-periodic excitation and dynamic stability for strained superlattice[J].Acta Phys.Sin.,2013,62(24):247301-247306.
[16]李秀平,王善进,陈琼,等.参数激励与晶体摆动场辐射的稳定性[J].物理学报,2013,62(22):224102-224105.Li Xiuping,Wang Shanjin,Chen Qiong,et al.Parametric excitation and stability of crystalline undulator radiation[J].Acta Phys.Sin.,2013,62(22):224102-224105.
[17]罗诗裕,吴木营,邵明珠,等.应变超晶格的共振行为与动力学稳定性[J].物理学报,2010,59(8):5766-5771.Luo Shiyu,Wu Muying,Shao Mingzhu,et al.The resonance behaviour and dynamic stabilities of strained superlattice[J].Acta Phys.Sin.,2010,59(8):5766-5771.