非平衡等离子体碰撞项和输运系数的理论研究
摘要
在以前对于库仑碰撞的研究中,通常是将场粒子的状态设定为热平衡状态从而用麦克斯韦速度分布函数来描述,而真实的等离子体状态往往是偏离平衡的,需要用非麦克斯韦速度分布函数(Non-Maxwellian)来描述。为了简化计算,麦氏分布被应用在各种状况下,并且用热平衡速度取代了场粒子的真实速度。在本文中,我们设计了一种易于控制的非麦氏分布函数来描述等离子体,并且用它取代了原来Fokker-Planck系数计算中所用的错误的场粒子速度分布,使用了以前论文中[1,2]介绍的更加符合原始定义的避免了积分发散的三阶积分和新的德拜截断参数,从而用一种新的方法得出了更加符合物理真相的转移概率函数以及Fokker-Planck系数,进而用它来研究了弱耦合以及中度耦合等离子体中的弛豫过程和输运过程,得出了全新的各项系数。
Usually the states of the field particles were assumed in the motion equilibrium and the Maxwellian approximation substituted for the non-Maxwellian velocity distribution function in despite of the states were mostly in the nonequilibrium.Then the Maxwellian velocity distribution was applied in any condition and the thermal velocity replaced the real velocity of the field particles.In this paper,the new method is introduced to derive the Fokker-Planck coefficients with a non-Maxwellian velocity distribution function for the field particles.The three-fold integral and the new Debye cutoff parameter,which were introduced in previous papers[1,2],have been applied so that the divergence difficulties can be avoided.The probability function P(v,△v)for non-Maxwellian scatters is derived which helps to calculate the Fokker-Planck coefficients.The friction and diffusion coefficients of Fokker-Planck equation are modified and are exerted to investigate the relaxation and transport processes for weakly and moderately coupled plasma.
Usually the states of the field particles were assumed in the motion equilibrium and the Maxwellian approximation substituted for the non-Maxwellian velocity distribution function in despite of the states were mostly in the nonequilibrium.Then the Maxwellian velocity distribution was applied in any condition and the thermal velocity replaced the real velocity of the field particles.In this paper,the new method is introduced to derive the Fokker-Planck coefficients with a non-Maxwellian velocity distribution function for the field particles.The three-fold integral and the new Debye cutoff parameter,which were introduced in previous papers[1,2],have been applied so that the divergence difficulties can be avoided.The probability function P(v,△v)for non-Maxwellian scatters is derived which helps to calculate the Fokker-Planck coefficients.The friction and diffusion coefficients of Fokker-Planck equation are modified and are exerted to investigate the relaxation and transport processes for weakly and moderately coupled plasma.
引文
[1] Y. B. Chang and Ding Li, Phys. Rev. E. 53, 3999 (1996).
[2] Y. B. Chang, Phys. Fluids B 4, 313 (1992).
[3] I. Langmuir, Phys. Rev. 26, 585 (1925).
[4] A. Brue Langdon, Phys. Rev. Lett. 44. 575 (1980).
[5] J. M. Liu etc, Phys. Rev. Lett. 72, 2717 (1994).
[6] L . H . B race, Measurement Techniques in Space Plasmas: Particles, edited by R. F. Pfaff, J. E. Borovsky, and D. F. Young (Am. Geophys. Union, Washington, DC, 1998)
[7] Walter R. Hoegy and Larry H. Brace, Rev. Sci. Ins. 70, 3015 (1999).
[8] B.J. Wets and W. Deering, Phys. Rep. 246, 1 (1994).
[9] D. C. Montgomery and D. A. Tidman, Plasma Kinetic Theory (McGraw-Hill, New York, 1964), Chap. 2.
[10] S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
[11] S. Chandrasekhar, Astrophys. J. 97, 255 (1943).
[12] L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1962), Chap. 5.
[13] M. N. Rosenbluth, W. MacDonald, and D. Judd, Phys. Rev. 107, 1 (1957).
[14] H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984)
[15] D. R. Nicholson, Introduction to Plasma Theory (Wiley,New York, 1983), p. 11.
[16] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Function with Formulas, Graphs, and Mathematical Tables (U.S. Government Printing Office, Washington, DC, 1966).
[17] F. L. Hinton, in Handbook of Plasma Physics, edited by A. A. Galeev and R. N. Sudan (McGraw-Hill, New York, 1983), Vol. 1, Chap.1.5,p.147.
[18]D.L.Book,NRL Plasma Formulary(U.S.Naval Research Laboratory,Washington,DC,1990).
[19]常永斌,等离子体碰撞项之研究,1996博士论文
[20]徐家鸾,金尚宪;等离子体物理(原子能出版社,1981)
[21]Cohen,Spitzer,and Routly,Phys.Rev.80,230(1950).
[22]S.Chandrasekhar,Principles of Stellar Dynamics(University of Chicago Press,Chicago,Illinois,1942),Chap.2
[23]K.Huang,Statistical Mechanics(Wiley,New York,1967),Chap.6
[24]S.I.Braginskii,Transport Processes in a Plasma,Review of Plasma Physics,M.A.Leontovich Ed.(Consultants Bureau,New York,1965)
[25]L.Spitzer,Jr.and R.Harm,Phys.Rev.89,977(1953)
[26]S.Chapman and T.G.Cowling,The Mathematical Theory of Non-Uniform Gases(Cambridge University Press,London,1939).
[27]B.A.Trubnikov,Particle Interactions in a Fully Ionized Plasma,Reviews of Plasma Physics,Vol.1(Consultants Bureau,New York,1965),p.105.
[28]C.K.Li and R.D.Petrasso,Phys.Rev.Lett.70,3059(1993)
[29]C.K.Li and R.D.Petrasso,Phys.Rev.Lett.70,3063(1993)
[2] Y. B. Chang, Phys. Fluids B 4, 313 (1992).
[3] I. Langmuir, Phys. Rev. 26, 585 (1925).
[4] A. Brue Langdon, Phys. Rev. Lett. 44. 575 (1980).
[5] J. M. Liu etc, Phys. Rev. Lett. 72, 2717 (1994).
[6] L . H . B race, Measurement Techniques in Space Plasmas: Particles, edited by R. F. Pfaff, J. E. Borovsky, and D. F. Young (Am. Geophys. Union, Washington, DC, 1998)
[7] Walter R. Hoegy and Larry H. Brace, Rev. Sci. Ins. 70, 3015 (1999).
[8] B.J. Wets and W. Deering, Phys. Rep. 246, 1 (1994).
[9] D. C. Montgomery and D. A. Tidman, Plasma Kinetic Theory (McGraw-Hill, New York, 1964), Chap. 2.
[10] S. Chandrasekhar, Rev. Mod. Phys. 15, 1 (1943).
[11] S. Chandrasekhar, Astrophys. J. 97, 255 (1943).
[12] L. Spitzer, Physics of Fully Ionized Gases (Interscience, New York, 1962), Chap. 5.
[13] M. N. Rosenbluth, W. MacDonald, and D. Judd, Phys. Rev. 107, 1 (1957).
[14] H. Risken, The Fokker-Planck Equation (Springer-Verlag, Berlin, 1984)
[15] D. R. Nicholson, Introduction to Plasma Theory (Wiley,New York, 1983), p. 11.
[16] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Function with Formulas, Graphs, and Mathematical Tables (U.S. Government Printing Office, Washington, DC, 1966).
[17] F. L. Hinton, in Handbook of Plasma Physics, edited by A. A. Galeev and R. N. Sudan (McGraw-Hill, New York, 1983), Vol. 1, Chap.1.5,p.147.
[18]D.L.Book,NRL Plasma Formulary(U.S.Naval Research Laboratory,Washington,DC,1990).
[19]常永斌,等离子体碰撞项之研究,1996博士论文
[20]徐家鸾,金尚宪;等离子体物理(原子能出版社,1981)
[21]Cohen,Spitzer,and Routly,Phys.Rev.80,230(1950).
[22]S.Chandrasekhar,Principles of Stellar Dynamics(University of Chicago Press,Chicago,Illinois,1942),Chap.2
[23]K.Huang,Statistical Mechanics(Wiley,New York,1967),Chap.6
[24]S.I.Braginskii,Transport Processes in a Plasma,Review of Plasma Physics,M.A.Leontovich Ed.(Consultants Bureau,New York,1965)
[25]L.Spitzer,Jr.and R.Harm,Phys.Rev.89,977(1953)
[26]S.Chapman and T.G.Cowling,The Mathematical Theory of Non-Uniform Gases(Cambridge University Press,London,1939).
[27]B.A.Trubnikov,Particle Interactions in a Fully Ionized Plasma,Reviews of Plasma Physics,Vol.1(Consultants Bureau,New York,1965),p.105.
[28]C.K.Li and R.D.Petrasso,Phys.Rev.Lett.70,3059(1993)
[29]C.K.Li and R.D.Petrasso,Phys.Rev.Lett.70,3063(1993)
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