超短强激光在等离子体隧道中传输的理论研究
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摘要
本文从理论上研究了超短强激光在等离子体隧道中的传输。文中用哈密顿-雅可比方程方法和源展开方法分别对激光在等离子体隧道中传输所涉及的衍射效应、等离子体散焦效应、三阶强度非线性、相对论自聚焦、等离子体隧道的聚焦和散焦效应、碰撞等离子体中的吸收效应、有限脉宽效应等等做了基本的阐述。本文分四章，第一章为前言，第二、三章介绍作者硕士研究生期间做的部分工作，第四章为总结和展望。
第一章：本章介绍了超短强激光在等离子体隧道中传输研究的背景，并回顾了激光和等离子体相互作用物理。
第二章：本章阐述了超强激光光束在抛物型部分电离的预等离子体(聚焦和散焦)隧道中的传输特性。研究了相对论自聚焦效应和等离子体波引起的密度扰动对传输的影响。从Maxwell方程出发我们得到了两个包含衍射、三阶强度非线性、等离子体散焦、等离子体隧道聚焦和散焦以及相对论自聚焦等效应在内的激光场演化方程，即折射率方程和哈密顿-雅可比方程。在此基础上得到了激光在等离子体隧道中传输的包络方程以及光斑半径与传输距离、隧道宽度等初始参量的关系。
第三章：本章介绍了求解有非线性源项的傍轴方程的有效方法-源展开方法，并给出了两个具体的例子，即考虑等离子体电子间碰撞的隧道传输的求解和考虑激光脉冲的有限脉宽效应的隧道传输求解。源展开方法的解是电场的四个参数的演化方程，即关于波前曲率、光斑半径、振幅和相位的四个偏微分方程。
第四章：本章主要是在总结了两种方法的基础上提出进一步可以做的工作，介绍了等离子体动力论中的Vlasov方程及它的三个矩方程(连续性方程、力方程和压强方程)，以及强激光在介质中传输涉及到的电离和复合机制。
In the thesis, the propagation of the ultrashort intense laser beam in the plasma channel was investigated theoretically. The thesis analyzed the effects, associated with the propagation of laser in plasma channel, such as diffraction, plasma defocusing, the third-order intensity-dependent nonlinearity, the relativistic self-focusing, the focusing and defocusing of the plasma channel, and the absorbtion in the collision plasma and the finite pulse length effect. The thesis is composed of 4 chapters, among which are, Chapter 1 is a survey, Chapter 2, 3 are the introductions of our own work, Chapter 4 is a conclusion and prospect.
Chapter 1: The background of the study of propagation of ultrashort intense laser in plasma channel and a survey of the interaction of laser with plasma were introduced.
Chapter 2: Characteristics of propagation of ultra-intense laser beam in a partially stripped preformed plasma channel is discussed, in which the relativistic self-focusing effects, together with the perturbed plasma density, is discussed. From Maxwell equations the refractive index equation and Hamilton-Jacobi equation, which describe the evolution of the electric field, are derived including the effects of the diffraction, the third-order intensity-dependent nonlinearity, plasma defocusing, the focusing and defocusing of the plasma channel, and the relativistic self-focusing. The envelope equation of laser propagating in the plasma channel, and the general expression related the laser spot size with the propagation distance and the width of the plasma channel etc., are derived based on
the Hamilton-Jacobi equation and the refractive index equation.
Chapter 3: The source-dependent expansion (SDE) method for analyzing the wave
equation is introduced, which is an effective method for solving the paraxial wave equation with nonlinear source terms. Two examples have been given to explain this method, which are the propagation of the ultrashort intense laser pulses propagation in the partially stripped plasma in which the collisions of plasma electrons are taken into account, and the propagation including the finite pulse length effect. The solutions are derived through SDE method introduced in the chapter, which are four differential equations of the electric field parameters, i.e., the wave curvature as, the spot size rs, the laser power p and the phase s.
Chapter 4: There are a summary of two methods used in this thesis, together with
the further work, a introduction of Vlasov equation and its moment equations, i.e., the
continuity equation, the force equation and the pressure equation, and the ionization and
recombination associated with the laser propagation in media.
第一章：本章介绍了超短强激光在等离子体隧道中传输研究的背景，并回顾了激光和等离子体相互作用物理。
第二章：本章阐述了超强激光光束在抛物型部分电离的预等离子体(聚焦和散焦)隧道中的传输特性。研究了相对论自聚焦效应和等离子体波引起的密度扰动对传输的影响。从Maxwell方程出发我们得到了两个包含衍射、三阶强度非线性、等离子体散焦、等离子体隧道聚焦和散焦以及相对论自聚焦等效应在内的激光场演化方程，即折射率方程和哈密顿-雅可比方程。在此基础上得到了激光在等离子体隧道中传输的包络方程以及光斑半径与传输距离、隧道宽度等初始参量的关系。
第三章：本章介绍了求解有非线性源项的傍轴方程的有效方法-源展开方法，并给出了两个具体的例子，即考虑等离子体电子间碰撞的隧道传输的求解和考虑激光脉冲的有限脉宽效应的隧道传输求解。源展开方法的解是电场的四个参数的演化方程，即关于波前曲率、光斑半径、振幅和相位的四个偏微分方程。
第四章：本章主要是在总结了两种方法的基础上提出进一步可以做的工作，介绍了等离子体动力论中的Vlasov方程及它的三个矩方程(连续性方程、力方程和压强方程)，以及强激光在介质中传输涉及到的电离和复合机制。
In the thesis, the propagation of the ultrashort intense laser beam in the plasma channel was investigated theoretically. The thesis analyzed the effects, associated with the propagation of laser in plasma channel, such as diffraction, plasma defocusing, the third-order intensity-dependent nonlinearity, the relativistic self-focusing, the focusing and defocusing of the plasma channel, and the absorbtion in the collision plasma and the finite pulse length effect. The thesis is composed of 4 chapters, among which are, Chapter 1 is a survey, Chapter 2, 3 are the introductions of our own work, Chapter 4 is a conclusion and prospect.
Chapter 1: The background of the study of propagation of ultrashort intense laser in plasma channel and a survey of the interaction of laser with plasma were introduced.
Chapter 2: Characteristics of propagation of ultra-intense laser beam in a partially stripped preformed plasma channel is discussed, in which the relativistic self-focusing effects, together with the perturbed plasma density, is discussed. From Maxwell equations the refractive index equation and Hamilton-Jacobi equation, which describe the evolution of the electric field, are derived including the effects of the diffraction, the third-order intensity-dependent nonlinearity, plasma defocusing, the focusing and defocusing of the plasma channel, and the relativistic self-focusing. The envelope equation of laser propagating in the plasma channel, and the general expression related the laser spot size with the propagation distance and the width of the plasma channel etc., are derived based on
the Hamilton-Jacobi equation and the refractive index equation.
Chapter 3: The source-dependent expansion (SDE) method for analyzing the wave
equation is introduced, which is an effective method for solving the paraxial wave equation with nonlinear source terms. Two examples have been given to explain this method, which are the propagation of the ultrashort intense laser pulses propagation in the partially stripped plasma in which the collisions of plasma electrons are taken into account, and the propagation including the finite pulse length effect. The solutions are derived through SDE method introduced in the chapter, which are four differential equations of the electric field parameters, i.e., the wave curvature as, the spot size rs, the laser power p and the phase s.
Chapter 4: There are a summary of two methods used in this thesis, together with
the further work, a introduction of Vlasov equation and its moment equations, i.e., the
continuity equation, the force equation and the pressure equation, and the ionization and
recombination associated with the laser propagation in media.
引文
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[17] R. Snavely et al., Phys. Roy. Lctt. 85, 2945 (2000).
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[40] P. Sprangle, B. Hafizi, and J. R. Peano, Phys. Rev. E 61, 4381 (2000).
[41] Z. M. Sheng, K. Nishihara, T. Honda, Y. Sentoku, and K. Mima. Phys. Rev. E 64, 066409 (2001).
[42] P. Sprangle, E. Esarey, and B. Hafizi, Phys. Rev. Lett. 79, 1046 (1997).
[43] P. Sprangle, B. Hafizi, and P. Serafim, Phys. Rev. E 59, 3614 (1999).
[44] C. D. Decker, W. B. Mon, K. C. Tzeng, and T. Katsouleas, Phys. Plasma. 3, 2047 (1996).
[45] Govind P. Agrawal, Nonlinear Fiber Optics. (Academic Press, New york, 1995)
[46] W. B. Mori, IEEE J. Quant. Electron. 33, 1942 (1997).
[47] B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, Phys. Rev. E 62, 4120 (2000).
[48] Nicholas H. Matlis, Phys. Plasma. 9, 391 (2002).
[49] J. D. Jackson, Classical Electrodynamics (2nd ed.), (Wiley, New York, 1975).
[50] Y. R. Shen, The Principles of Nonlinear Optics. (Wiley, New York, 1984).
[51] P. Sprangle, A. Ting, and C.M. Tang, Phys. Rev. A 36, 2773 (1987).
[52] E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 24, 907 (1972).
[53] B. La Fontaine et al., Phys. Plasmas 6, 1615 (1999).
[54] W. P. Leemans, Phys. Rev. A 46, 1091 (1992).
[55] 马腾才，等离子体物理原理，中国科学技术出版社(1988)．
[2] M. Born and E. Wolf, Principles of Optics. (Cambridge university Press 7th, 1999).
[3] A. Yariv, Quantum Electronics. (2nd ed.), (John Wiley & Sons, New York, 1975).
[4] A. E. Siegman, Lasers. (University Science Books, Mill Valley, California, 1986).
[5] M. Tabak et al., Phys. Plasmas. 1, 1624 (1994).
[6] M. D. Perry and G. Mourou, Science 264, 917 (1994).
[7] K. B. Wharton et al., Phys. Rev. Lett. 81,822 (1998).
[8] A. Pukhov and J. Meyer-ter-Vehn, Phys. Rev. Lett. 79, 2686 (1997).
[9] M. H. Key et al., Phys. Plasmas. 5, 1966 (1998).
[10] R. Kodama et al., Phys. Rev. Lett. 84, 674 (2000).
[11] M. I. K. Santals et al., Phys. Rev. Lett. 84, 1459 (2000).
[12] K. A. Tanaka et al., Phys. Plasmas. 7, 2014 (2000).
[13] P. A. Norreys et al., Phys. Plasmas. 7, 3721 (2000).
[14] R. Kodama, P. A. Norreys, K. Mima et al., Nature 472, 798 (2001).
[15] M. Roth, T. E. Cowan et al., Phys. Rev. Lett. 86, 436 (2001).
[16] M. D. Perry et al., Opt. Lett. 24, 160 (1999).
[17] R. Snavely et al., Phys. Roy. Lctt. 85, 2945 (2000).
[18] William. L. Kruer, Phys. Plasmas. 7, 2270 (2000).
[19] K. A. Tanaka et al., Phys. Plasmas. 7, 2014 (2000).
[20] J. Fuchs, J. C. Adam et al., Phys. Plasma. 6, 2563 (1999).
[21] E. M. Campbell, Phys. Fluid B. 4, 3781 (1992).
[22] 常铁强等，激光等离子体与激光聚变，湖南科学技术出版社(1991)．
[23] William.L. Kurer, The Physics of Laser Plasma Interactions. (Addison-Wesley Press 1988).
[24] J. M. Dawson, Rev. Mod. Phys. 55,403 (1983).
[25] J. M. Dawson, Phys. Plasmas. 2, 2189 (1995).
[26] K. Birdsall and A. B. Langdon, Plasma Physics Via Computer Simulation. (McGraw-Hill Book Company, 1991).
[27] K. Birdsall and D. Fuss, J. Comput. Phys. 3, 494 (1969).
[28] J. C. Adam and A. G. Serveniere, J. Comput. Phys. 47, 229 (1982).
[29] J. M. Wallace, J. Comput. Phys. 63, 434 (1986).
[30] C. D. Decker and W. B. Mori, Phys. Rcv. Lett. 72, 490 (1994).
[31] A. Pukhov and J. Meyer-ter-Vehn, Phys.Plasmas, 5 , 1880 (1998).
[32] A. Pukhov and J. Meyer-ter-Vehn, Phys. Rev. Lett. 76, 3975 (1996).
[33] S. Suckewer and C. H. Skinner, Mol. Phys. 30, 331 (1995).
[34] D. Umstadter, S. Y. Chen, A. Maksimchuk, G. Mourou, and R.. Wagner, Science 273, 472 (1996).
[35] Mykhailo Fomyts'kyi, IEEE J. Quant. Electron. 33, 1915 (1997).
[36] Franklin Grigsby, Phys. Rev. E 65, 016406 (2001).
[37] C. Deutsch, H. Furukawa, K. Mima, M. Murakami, and K. Nishihara, Phys. Rev. Lett. 77, 2483 (1996).
[38] E. Esarey, P. Sprangle, J. Krall, and A. Ting, IEEE J. Quant. Electron. 33, 1879 (1997).
[39] E. Esarey. J. Krali, and P. Sprangle, Phys. Rev. Lett. 72, 2887 (1994).
[40] P. Sprangle, B. Hafizi, and J. R. Peano, Phys. Rev. E 61, 4381 (2000).
[41] Z. M. Sheng, K. Nishihara, T. Honda, Y. Sentoku, and K. Mima. Phys. Rev. E 64, 066409 (2001).
[42] P. Sprangle, E. Esarey, and B. Hafizi, Phys. Rev. Lett. 79, 1046 (1997).
[43] P. Sprangle, B. Hafizi, and P. Serafim, Phys. Rev. E 59, 3614 (1999).
[44] C. D. Decker, W. B. Mon, K. C. Tzeng, and T. Katsouleas, Phys. Plasma. 3, 2047 (1996).
[45] Govind P. Agrawal, Nonlinear Fiber Optics. (Academic Press, New york, 1995)
[46] W. B. Mori, IEEE J. Quant. Electron. 33, 1942 (1997).
[47] B. Hafizi, A. Ting, P. Sprangle, and R. F. Hubbard, Phys. Rev. E 62, 4120 (2000).
[48] Nicholas H. Matlis, Phys. Plasma. 9, 391 (2002).
[49] J. D. Jackson, Classical Electrodynamics (2nd ed.), (Wiley, New York, 1975).
[50] Y. R. Shen, The Principles of Nonlinear Optics. (Wiley, New York, 1984).
[51] P. Sprangle, A. Ting, and C.M. Tang, Phys. Rev. A 36, 2773 (1987).
[52] E. Yablonovitch and N. Bloembergen, Phys. Rev. Lett. 24, 907 (1972).
[53] B. La Fontaine et al., Phys. Plasmas 6, 1615 (1999).
[54] W. P. Leemans, Phys. Rev. A 46, 1091 (1992).
[55] 马腾才，等离子体物理原理，中国科学技术出版社(1988)．