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晶体摆动场辐射系统的全局分叉与混沌行为

罗诗裕 邵明珠 罗晓华

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晶体摆动场辐射系统的全局分叉与混沌行为

罗诗裕, 邵明珠, 罗晓华

The global bifurcation and chaotic behaviours for the crystalline undulator radiation

Luo Shi-Yu, Shao Ming-Zhu, Luo Xiao-Hua
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  • 引入正弦平方势,在经典力学框架内和偶极近似下,考虑到运动阻尼和非线性影响,把粒子在晶体摆动场中的运动方程化为具有阻尼项和受迫项的广义摆方程.利用Jacob椭圆函数和椭圆积分分析了无扰动系统的相平面特征,并解析地给出了系统的解和粒子振动周期; 进一步利用Melnikov方法分析相平面上三类轨道的分叉性质和进入Smale马蹄意义下的混沌行为,找到系统的全局分叉与系统进入混沌的临界条件.结果表明,系统的临界条件与它的物理参数有关,只需适当调节这些参数就可以原则上避免、抑制分叉或混沌的出现.
    Introducing sine-squared potential,the particle motion equation in the crystalline undulator field is reduced to the generalized pendulum equation with a dampping and a force terms in the classical mechanics frame in the dipole approximation. The properties of the phase plane are ananysed for a non-peturbated system by means of Jacobian elliptic function and the elliptic integral,and the solution of the equation and the period of the particle motion for this system are expressed exactly. The global bifurcation and a chaotic behaviour with the Smale horseshoe for the 3 kinds of orbits in a phase plane are analysed by Melnikov method. The critical condition of the system entering into a bifurcation or a chaoc is found. The result shows that critical condition is related to the parameters of the system,by suitably regulating the parameters of the system,the bifurcation or the chaos can be avoided or controlled in principle.
    • 基金项目: 广东省自然科学基金(批准号: 8151170003000010)资助的课题.
    [1]

    [1]Kumakhov M A 1976 Phys. Lett. A 57 17

    [2]

    [2]Shao M Z,Luo S Y 1986 Chin. Laser 13 607 (in Chinese) [邵明珠、罗诗裕 1986 中国激光 13 607]

    [3]

    [3]Korol A,Solovyov A V,Greiner W 1998 J. Phys. G 24 L45

    [4]

    [4]Korol A,Solovyov A V,Greiner W 1999 Int. J. Mod. Phys. E 8 49

    [5]

    [5]Gevorging L A,Hovsepyan L A 2007 J. Contemp. Phys. 42 87

    [6]

    [6]Luo S Y,Shao M Z 2005 High Energ. Phys. Nucl. Phys. 29 193 (in Chinese) [罗诗裕、邵明珠 2005 高能物理与核物理 29 193

    [7]

    [7]Korol A V,Solovyov A V,Greiner W 2008 Nucl. Inst. Method. Phys. Rese. B 266 1173

    [8]

    [8]Wiedemann H 2006 Advance Radiation Sources and Application (Natherlands: Springer) p165

    [9]

    [9]Tabrizi M,Korol A V,Solovyov A V 2007 Phys. Rev. Lett. 98 164801

    [10]

    ]Korol A V,Solovyov A V,Greiner W 2004 Int. J. Mod. Phys. E 13 867

    [11]

    ]Wiedemann H 2006 Advance Radiation Sources and Application (Natherlands: Springer) p191

    [12]

    ]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]

    [13]

    ]Luo S Y,Shao M Z 2003 Chin. J. Semiconductors 24 485 (in Chinese) [罗诗裕、邵明珠 2003 半导体学报 24 485 ]

    [14]

    ]Luo S Y,Shao M Z 1984 Chin. Phys. 4 670

    [15]

    ]Luo S Y,Shao M Z 2005 Chin. J. Semiconductors 26 294 (in Chinese) [罗诗裕、邵明珠 2005 半导体学报 26 294]

    [16]

    ]Luo S Y,Shao M Z 2006 Acta Phys. Sin. 55 1324 (in Chinese) [罗诗裕、邵明珠 2006 物理学报 55 1324]

    [17]

    ]Deng C L,Shao M Z,Luo S Y 2006 Acta Phys. Sin. 55 1721 (inChinese) [邓成良、邵明珠、罗诗裕 2006 物理学报 55 1721]

    [18]

    ]Shao M Z,Luo S Y 2005 Acta Phys. Sin. 54 4092 (in Chinese) [邵明珠、罗诗裕 2005 物理学报 54 4092]

    [19]

    ]Luo S Y,Shao M Z 2004 Acta Phys. Sin. 53 1157 (in Chinese) [罗诗裕、邵明珠 2004 物理学报 53 1157]

    [20]

    ]Luo S Y,Shao M Z 2004 Acta Phys. Sin. 53 1940 (in Chinese) [罗诗裕、邵明珠 2004 物理学报 53 1940]

    [21]

    ]Shao M Z,Luo S Y 2007 Acta Phys. Sin. 56 3407 (in Chinese) [邵明珠、罗诗裕 2007 物理学报 56 3407]

  • [1]

    [1]Kumakhov M A 1976 Phys. Lett. A 57 17

    [2]

    [2]Shao M Z,Luo S Y 1986 Chin. Laser 13 607 (in Chinese) [邵明珠、罗诗裕 1986 中国激光 13 607]

    [3]

    [3]Korol A,Solovyov A V,Greiner W 1998 J. Phys. G 24 L45

    [4]

    [4]Korol A,Solovyov A V,Greiner W 1999 Int. J. Mod. Phys. E 8 49

    [5]

    [5]Gevorging L A,Hovsepyan L A 2007 J. Contemp. Phys. 42 87

    [6]

    [6]Luo S Y,Shao M Z 2005 High Energ. Phys. Nucl. Phys. 29 193 (in Chinese) [罗诗裕、邵明珠 2005 高能物理与核物理 29 193

    [7]

    [7]Korol A V,Solovyov A V,Greiner W 2008 Nucl. Inst. Method. Phys. Rese. B 266 1173

    [8]

    [8]Wiedemann H 2006 Advance Radiation Sources and Application (Natherlands: Springer) p165

    [9]

    [9]Tabrizi M,Korol A V,Solovyov A V 2007 Phys. Rev. Lett. 98 164801

    [10]

    ]Korol A V,Solovyov A V,Greiner W 2004 Int. J. Mod. Phys. E 13 867

    [11]

    ]Wiedemann H 2006 Advance Radiation Sources and Application (Natherlands: Springer) p191

    [12]

    ]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]

    [13]

    ]Luo S Y,Shao M Z 2003 Chin. J. Semiconductors 24 485 (in Chinese) [罗诗裕、邵明珠 2003 半导体学报 24 485 ]

    [14]

    ]Luo S Y,Shao M Z 1984 Chin. Phys. 4 670

    [15]

    ]Luo S Y,Shao M Z 2005 Chin. J. Semiconductors 26 294 (in Chinese) [罗诗裕、邵明珠 2005 半导体学报 26 294]

    [16]

    ]Luo S Y,Shao M Z 2006 Acta Phys. Sin. 55 1324 (in Chinese) [罗诗裕、邵明珠 2006 物理学报 55 1324]

    [17]

    ]Deng C L,Shao M Z,Luo S Y 2006 Acta Phys. Sin. 55 1721 (inChinese) [邓成良、邵明珠、罗诗裕 2006 物理学报 55 1721]

    [18]

    ]Shao M Z,Luo S Y 2005 Acta Phys. Sin. 54 4092 (in Chinese) [邵明珠、罗诗裕 2005 物理学报 54 4092]

    [19]

    ]Luo S Y,Shao M Z 2004 Acta Phys. Sin. 53 1157 (in Chinese) [罗诗裕、邵明珠 2004 物理学报 53 1157]

    [20]

    ]Luo S Y,Shao M Z 2004 Acta Phys. Sin. 53 1940 (in Chinese) [罗诗裕、邵明珠 2004 物理学报 53 1940]

    [21]

    ]Shao M Z,Luo S Y 2007 Acta Phys. Sin. 56 3407 (in Chinese) [邵明珠、罗诗裕 2007 物理学报 56 3407]

计量
  • 文章访问数:  7433
  • PDF下载量:  928
  • 被引次数: 0
出版历程
  • 收稿日期:  2009-05-03
  • 修回日期:  2009-07-23
  • 刊出日期:  2010-02-05

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