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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.
[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 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 56 3049]
[11] Shi L F, Mo J Q 2013 Acta Phys. Sin. 62 040203 (in Chinese) [石兰芳, 莫嘉琪. 2013 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 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 59 3642]
[26] Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese) [张毅 2012 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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[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 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 56 3049]
[11] Shi L F, Mo J Q 2013 Acta Phys. Sin. 62 040203 (in Chinese) [石兰芳, 莫嘉琪. 2013 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 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 59 3642]
[26] Zhang Y 2012 Acta Phys. Sin. 61 214501 (in Chinese) [张毅 2012 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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