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双流体等离子体模型的动力学可容变分

邹丹旦 杨维紘

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双流体等离子体模型的动力学可容变分

邹丹旦, 杨维紘

Dynamically accessible variations for two-fluid plasma model

Zou Dan-Dan, Yang Wei-Hong
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  • 动力学可容变分方法是一种广义哈密顿系统中的李扰动变换方法,能自动保证卡西米尔函数在相应阶数上的守恒性质. 通过动力学可容方法得到了双流体在欧拉描述中的一组约束变分,而后利用这组变分对双流体哈密顿量取极值得到了平衡方程.
    Dynamically accessible perturbation is a type of Lie perturbation for noncanonical Hamiltonian systems. Firstly, a set of first-order constraint variations that preserve all the Casimir functions is presented based on the two-fluid Poisson bracket. Then the equilibrium equations are given by minimizing the two-fluid Hamiltonian with these variations.
    • 基金项目: 国家自然科学基金(批准号:11375190)资助的课题.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11375190).
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    Arnold V I 1978 Mathematical Method of Classical Mechanics (Springer-Verlag, New York)

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    Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese) [张毅 2012 物理学报 61 214501]

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    Holm D D, Marsden J, Ratiu T, Weinstein A 1985 Physics Reports 123 1

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    Morrison P, Eliezer S 1986 Phys. Rev. A 33 4205

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    Hameiri E 1998 Phys. Plasmas 5 3270

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    Andreussi T, Morrison P, Pegoraro F 2010 Plasma Phys. Control. Fusion 52 055001

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    Arnold V I 1965 Journal of Applied Mathematics and Mechanics 29 5

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    Morrison P, Pfirsch D 1989 Physical Review A 40 7

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    Morrison P, Pfirsch D 1990 Physics of Fluids B 2 1105

    [35]

    Brizard A, Tracy E 2002 Mini-Conference, Bull. Am. Phys. Soc. 47 6

    [36]

    Hirota M, Yoshida Z, Hameiri E 2006 Phys. Plasmas 13 022107

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    Hameiri E 2003 Pysics of Plasmas 10 7

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    Isichenko M B 1998 Phys. Rev. Lett. 80 5

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    Hu X W 2006 Plasma theory foudamentals (Beijing: Beijing University Press) p219 (in Chinese) [(胡希伟 2006 等离子体理论基础 (北京: 北京大学出版社) 第219页]

    [40]

    Wang X, Xiao C, Pu Z, Wang J 2012 Chin. Sci. Bul. 57 12

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    Malyshkin L M 2009 Phys. Rev. Lett. 103 235004

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    Zou D D, Yang W H, Chen Y H, Yoon P H 2010 Phys. Plasmas 17 102102

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    Sahraoui F, Belmont G, Rezeau L 2003 Phys. Plasmas 10 1325

  • [1]

    Lin C C 1961 Proceedings of the International School, Enrico Fermi, Varenna, in Proceedings of the International School of Physics, edited by G.Careri (Academic, New York) XXI p 93

    [2]

    Lamb H 1932 Hydrodynamics (Cambridge Univ. Press, Cambridge) p14

    [3]

    Newcomb W A 1962 Nucl. Fusion Suppl (part 2) p451

    [4]

    Cendra H, Marsden J 1987 Physica D 27 63

    [5]

    Cao X Q, Song J Q, Zhang W M, Zhu X Q, Zhao J 2011 Acta Phys. Sin. 60 080401 (in Chinese) [曹小群, 宋君强, 张卫民, 朱小谦, 赵军 2011 物理学报 60 080401]

    [6]

    Cao X Q, Song J Q, Zhang W M, Zhao J 2011 Chin. Phys. B 20 090401

    [7]

    Marsden J 1994 Introduction to Mechanics and Symmetry (Springer-Verlag New York)

    [8]

    Salmon R 1988 Ann. Rev. Fluid Mech. 20 225

    [9]

    Kambe T 2010 Geometrical theory of dynamical systems and velocity field (World Scientific, Singapore) p1

    [10]

    Jing H X, Li Y C, Xia L L 2007 Acta Phys. Sin. 56 3049 (in Chinese) [荆宏星, 李元成, 夏丽莉 2007 物理学报 56 3049]

    [11]

    Shi L F, Mo J Q 2013 Acta Phys. Sin. 62 040203 (in Chinese) [石兰芳, 莫嘉琪. 2013 物理学报 62 040203]

    [12]

    Morrison P, Greene J 1980 Phys. Rev. Lett. 45 790

    [13]

    Morrison P 1998 Rev. Mod. Phys. 70 467

    [14]

    Marsden J, Weinstein A 1982 Physica D 4 394

    [15]

    Spencer R, Kaufman A N 1982 Phys. Rev. A 25 2437

    [16]

    Spencer R 1984 J. Math. Phys. 25 2390

    [17]

    Kaufman A N 1984 Physics Letters A 100 8

    [18]

    Morrison P 1986 Physica D 18 1

    [19]

    Guha P 2007 Journal of Mathematical Analysis and Applications 326

    [20]

    Goldstein H 2002 Classical Mechanics. Prentice Hall, 3rd edition

    [21]

    Arnold V I 1978 Mathematical Method of Classical Mechanics (Springer-Verlag, New York)

    [22]

    Li J B, Zhao X H, Liu Z R 1994 Theory and Application of Generalized Hamilton Systems (Beijing: Science Press) (in Chinese) [李继彬, 赵晓华, 刘正荣 2007 广义哈密顿系统理论及其应用(北京: 科学出版社)]

    [23]

    Jiang W A, Luo S K 2011 Acta Phys. Sin. 60 060201 (in Chinese) [姜文安, 罗绍凯 2011 物理学报 60 060201]

    [24]

    LI Y M 2010 Chin. Phys. Lett. 27 1

    [25]

    Li Y C, Xia L L, Wang X M, Liu X W 2010 Acta Phys. Sin. 59 3639 (in Chinese) [李元成, 夏丽莉, 王小明, 刘晓巍 2010 物理学报 59 3642]

    [26]

    Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese) [张毅 2012 物理学报 61 214501]

    [27]

    Arnold V 1963 Usp. Mat. Nauk (Sov. Math. Usp.) 18 85

    [28]

    Holm D D, Marsden J, Ratiu T, Weinstein A 1985 Physics Reports 123 1

    [29]

    Morrison P, Eliezer S 1986 Phys. Rev. A 33 4205

    [30]

    Hameiri E 1998 Phys. Plasmas 5 3270

    [31]

    Andreussi T, Morrison P, Pegoraro F 2010 Plasma Phys. Control. Fusion 52 055001

    [32]

    Arnold V I 1965 Journal of Applied Mathematics and Mechanics 29 5

    [33]

    Morrison P, Pfirsch D 1989 Physical Review A 40 7

    [34]

    Morrison P, Pfirsch D 1990 Physics of Fluids B 2 1105

    [35]

    Brizard A, Tracy E 2002 Mini-Conference, Bull. Am. Phys. Soc. 47 6

    [36]

    Hirota M, Yoshida Z, Hameiri E 2006 Phys. Plasmas 13 022107

    [37]

    Hameiri E 2003 Pysics of Plasmas 10 7

    [38]

    Isichenko M B 1998 Phys. Rev. Lett. 80 5

    [39]

    Hu X W 2006 Plasma theory foudamentals (Beijing: Beijing University Press) p219 (in Chinese) [(胡希伟 2006 等离子体理论基础 (北京: 北京大学出版社) 第219页]

    [40]

    Wang X, Xiao C, Pu Z, Wang J 2012 Chin. Sci. Bul. 57 12

    [41]

    Malyshkin L M 2009 Phys. Rev. Lett. 103 235004

    [42]

    Zou D D, Yang W H, Chen Y H, Yoon P H 2010 Phys. Plasmas 17 102102

    [43]

    Sahraoui F, Belmont G, Rezeau L 2003 Phys. Plasmas 10 1325

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出版历程
  • 收稿日期:  2013-09-19
  • 修回日期:  2013-10-18
  • 刊出日期:  2014-02-05

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