ICF固体驱动器中的小尺度自聚焦效应研究
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摘要
惯性约束聚变(ICF)固体驱动器由于其在能源、科研、军事等方面的巨大作用，目前越来越受到各个国家的广泛重视。在这种高功率激光系统中，非线性自聚焦效应是其主要的限制因素，其中尤其以小尺度自聚焦效应最为严重。由于小尺度自聚焦会造成系统的成丝破坏，因而限制系统的输出功率，导致系统运行成本增高。由此可见，对它进行研究就是十分重要的了。为了弄清小尺度自聚焦的物理机制，以便于指导我们更加优化地设计驱动器，本文对这一问题进行了相应的探讨。
我们首先从非线性近轴波方程出发，基于B-T理论的思想，在考虑了介质的增益(损耗)特性的情况下，推导得出了小尺度自聚焦所满足的微分方程，并通过近似方法分析了最大增长频率、截止空间频率及积分指数增益等的变化规律。研究表明，对于增益介质，当光束传输到某个最小距离之后，小尺度调制才会增长；而对于损耗介质，当光束传输到某个最大距离之后，小尺度调制就停止增长。我们初步估算了增益和损耗对于小尺度调制的成丝距离的影响，认为适当地提高增益系数，能够从一定程度上抑制小尺度自聚焦效应。
同时，在本文中我们还对所谓的“热像”(hot image)的形成规律进行了实验研究及数值模拟计算，得出了“热像”点的位置以及强度随各个参数的变化规律。研究表明，成像距离基本上与输入光束的强度和调制平面到介质入射面的距离没有关系，但是与介质的增益系数及调制细丝的尺寸有关；“热像”的强度与调制细丝的尺寸和调制平面到介质入射面的距离基本上没有关系，但是与输入光束的强度和增益系数有关。
Nowadays, more and more attention has been paid to the Inerlial Confined Fusion (ICF) solid drivers because of its tremendous functions in energy sources, scientific research, military affairs and so on. In this high power laser system, nonlinear self-focusing effect especially the small-scale self-focusing is the main limiting factor. The system's output power has been limited and its cost of operation has been enhanced because of filament destroy caused by small-scale self-focusing. So it is vital important to study the small-scale self-focusing problems. In order to fully understand the physical mechanism governing the small-scale self-focusing and extract a guide line to the optimization of drivers, in this work, we discuss some problems about it.
Based on the nonlinear paraxial equation and B-T theory, a differential equation, which describes the small-scale self-focusing in gain (loss) media has been derived. The change rule of the maximal gain frequency, cutoff frequency and integral exponential gain have been analyzed approximately. The results indicate that after the beam has propagated for a minimal distance in gain media the modulation begin to increase and after the beam has propagated for a maximal distance in loss media the modulation stop increasing. We have calculated the effects which gain and loss impose on the formation distances of filaments of small-scale modulations, the results indicate that properly increasing the gain coefficient can counteract the small-scale self-focusing in certain degree.
In addition, the formation of the so called "hot image" has been studied experimentally and theoretically. We have calculated the position and intensity of the "hot image". Studies indicated that image distance is independent of input intensity above a certain threshold and distance between modulate plane and input plane of media, but dependent on the gain coefficient and modulation size; The intensity of the "hot image" is independent of modulation size and distance between modulate plane and input plane of media, but dependent on the intensity of input beam and the gain coefficient.
我们首先从非线性近轴波方程出发，基于B-T理论的思想，在考虑了介质的增益(损耗)特性的情况下，推导得出了小尺度自聚焦所满足的微分方程，并通过近似方法分析了最大增长频率、截止空间频率及积分指数增益等的变化规律。研究表明，对于增益介质，当光束传输到某个最小距离之后，小尺度调制才会增长；而对于损耗介质，当光束传输到某个最大距离之后，小尺度调制就停止增长。我们初步估算了增益和损耗对于小尺度调制的成丝距离的影响，认为适当地提高增益系数，能够从一定程度上抑制小尺度自聚焦效应。
同时，在本文中我们还对所谓的“热像”(hot image)的形成规律进行了实验研究及数值模拟计算，得出了“热像”点的位置以及强度随各个参数的变化规律。研究表明，成像距离基本上与输入光束的强度和调制平面到介质入射面的距离没有关系，但是与介质的增益系数及调制细丝的尺寸有关；“热像”的强度与调制细丝的尺寸和调制平面到介质入射面的距离基本上没有关系，但是与输入光束的强度和增益系数有关。
Nowadays, more and more attention has been paid to the Inerlial Confined Fusion (ICF) solid drivers because of its tremendous functions in energy sources, scientific research, military affairs and so on. In this high power laser system, nonlinear self-focusing effect especially the small-scale self-focusing is the main limiting factor. The system's output power has been limited and its cost of operation has been enhanced because of filament destroy caused by small-scale self-focusing. So it is vital important to study the small-scale self-focusing problems. In order to fully understand the physical mechanism governing the small-scale self-focusing and extract a guide line to the optimization of drivers, in this work, we discuss some problems about it.
Based on the nonlinear paraxial equation and B-T theory, a differential equation, which describes the small-scale self-focusing in gain (loss) media has been derived. The change rule of the maximal gain frequency, cutoff frequency and integral exponential gain have been analyzed approximately. The results indicate that after the beam has propagated for a minimal distance in gain media the modulation begin to increase and after the beam has propagated for a maximal distance in loss media the modulation stop increasing. We have calculated the effects which gain and loss impose on the formation distances of filaments of small-scale modulations, the results indicate that properly increasing the gain coefficient can counteract the small-scale self-focusing in certain degree.
In addition, the formation of the so called "hot image" has been studied experimentally and theoretically. We have calculated the position and intensity of the "hot image". Studies indicated that image distance is independent of input intensity above a certain threshold and distance between modulate plane and input plane of media, but dependent on the gain coefficient and modulation size; The intensity of the "hot image" is independent of modulation size and distance between modulate plane and input plane of media, but dependent on the intensity of input beam and the gain coefficient.
引文
1 Wang GC, "Suggestion of Neutron Generation with Powerful lasers", Chinese J of Lasers, 14-11(1987): 641
2 H.F.巴索夫等，《稠密等离子体诊断学》，《强激光与粒子束》杂志社，1992年12月第一版
3 J.H.Nuckolls , L.Wood,A.Thiessen , and G.B.Zimmermam,Laser compression of matter to super-high densities: thermonuclear(CTR) application. Nature 239,129(1972)
4 郑志坚，“ICF基本概念”，《惯性约束聚变与强激光技术》，(内部资料)，1990年
5 J.A. Paisner, National Ignition Facility Conceptual Design Report, Lawrence Livermore ROP-117093(1994)
6 J.A. Paisner, Utility of the National Ignition Facility , Lawrence Livermore National Laboratory, Livermore,CA,NIF-LLNL-94- 240, UCRL-PROP- 117384(1994)
8 中物院核化所强激光技术室，惯性约束聚变——驱动源技术译文集(1)，1996
9 W.H. Lowdermilk, "Status of the National Ignition Facility project", SPIE vol.3047:16
10 Michel L. Andre, Status of the LMJ project, SPIE Vol.3047:38
11 J.A.McMordie et al., "Conceptual Design of 100TW Solid State Laser System", SPIE Vol.2633(1995)
12 Gennadi A. Kirillov, "Development of a high-power 300-kJ neodymium laser", SPIE Vol.3047:43
13 Yujun Zhao, "Development of ICF laser driver technology in China", SPIE, Vol.3047:54
14 Peng H S, Zhang X M, Wei X F, et al., Status of the SG-Ⅲ solid state laser project, SPIE, Vol. 3492(1992): 25
15 国家高技术惯性约束聚变委员会，863-416-5专题专家组，神光—Ⅲ原型装置(TIL)概念设计报告，第三版，2000
16 Y. R. SHEN, The Principles of NONLINEAR OPTICS (John Willy & sons, Inc., New York, 1984) .Chap. 17
17 B.M. Van Wonterghem, et al, System description and initial performance results for Beamlet, LLNL ICF Quarterly Report, Vol. 5(1994)
18 景峰，钕玻璃激光多程放大技术研究，博士学位论文，1998
19 E.S.Bliss,Nonlinear propagation studies, Lawrence Livermore National Laboratory, Livermore, UCRL-25752(1974)
20 E.S. Bliss, G. E. Sommargren, Loss of Focusing Energy Due To Small-scale Nonlinear Effects, Lawrence Livermore National Laboratory,Livermore, UCRL-76322 (1974)
21 J.A. Fleck, J. R. Morris, and E. S. Bliss, Small-scale self-focusing effects in a high power glass laser amplifier, IEEE J. Quantum Electron, Vol. QE-14-5(1978): 353
22 J.H. Marburger, Self-focusing theory, Progr. Quantum Electron. ,Vol. 4(1975)
23 唐永林，陈建国，李大义，强激光圆对称超高斯光束的自聚焦环，强激光与离子束，Vol．12(2000)
24 Wade H. Williams,Jerome M.Auerbach,and et al.,Modeling characterization of the National Ignition Facility focal spot ,SPIE Vol. 3264(1998)
25 V. I. Bespanlov, V. I. Tanalov, Filamentary structure of light beams in nonlinear liquids, JETP Lett., 3(1966): 307
26 A.J.Campillo, S.L.Shapiro, and B.R.Suydam. Periodic breakup of optical beams due to self-focusing. Appi. Phys. Lett., 23-11(1973): 628
27 E.S.Bliss,D.R.Speck,J.F.Holzrichter et al..Propagation of a high-intensity laser pulse with small-scale intensity modulation. Appl.Phys.Lett., 25-8(1974) :448
28 W. W. Simmons, J. T. Hunt, and W. E. Warren. Light Propagation Through Large Laser Systems. IEEE Journal of Quantum electronics, 17-9(1981) : 1727
29 R. A. Sacks, M. A. Henesian, The Prop92 Fourier beam propagation code, UCRL-LR, 105821(1997)
30 A. Sacks, M. A. Henesian, Propagation modeling in two transverse dimensions of the NIF baseline performance,UCRL-LR,105821(1996) : 207
31 J. A. Glaze, Opt. Engineering, 15-2(1976) : 136
32 WEN Sluiangchun, FAN Dianyuan. Small-Scale Self-Focusing of Intense Laser Beams in Nonlinear Media with Loss. CHINESE JOURNAL OF LASERS, B9-4(2000) :356
33 J. A. Fleck, C. layne, Study of self-focusing damage in a high-power Nd:31 glass-rod amplifier, APPL. phys. Lett. , Vol. 22(1973)
34 J. Merle Elson and Jean M. Bennett, Calculation of the power spectral density from surface profile data, APPLL. OPTICS Vol. 1(1995)
35 栗敬钦，魏晓锋，马驰，激光束低频畸变波前模型的计算模拟，强激光 与粒子束，Vol．12(2000)
2 H.F.巴索夫等，《稠密等离子体诊断学》，《强激光与粒子束》杂志社，1992年12月第一版
3 J.H.Nuckolls , L.Wood,A.Thiessen , and G.B.Zimmermam,Laser compression of matter to super-high densities: thermonuclear(CTR) application. Nature 239,129(1972)
4 郑志坚，“ICF基本概念”，《惯性约束聚变与强激光技术》，(内部资料)，1990年
5 J.A. Paisner, National Ignition Facility Conceptual Design Report, Lawrence Livermore ROP-117093(1994)
6 J.A. Paisner, Utility of the National Ignition Facility , Lawrence Livermore National Laboratory, Livermore,CA,NIF-LLNL-94- 240, UCRL-PROP- 117384(1994)
8 中物院核化所强激光技术室，惯性约束聚变——驱动源技术译文集(1)，1996
9 W.H. Lowdermilk, "Status of the National Ignition Facility project", SPIE vol.3047:16
10 Michel L. Andre, Status of the LMJ project, SPIE Vol.3047:38
11 J.A.McMordie et al., "Conceptual Design of 100TW Solid State Laser System", SPIE Vol.2633(1995)
12 Gennadi A. Kirillov, "Development of a high-power 300-kJ neodymium laser", SPIE Vol.3047:43
13 Yujun Zhao, "Development of ICF laser driver technology in China", SPIE, Vol.3047:54
14 Peng H S, Zhang X M, Wei X F, et al., Status of the SG-Ⅲ solid state laser project, SPIE, Vol. 3492(1992): 25
15 国家高技术惯性约束聚变委员会，863-416-5专题专家组，神光—Ⅲ原型装置(TIL)概念设计报告，第三版，2000
16 Y. R. SHEN, The Principles of NONLINEAR OPTICS (John Willy & sons, Inc., New York, 1984) .Chap. 17
17 B.M. Van Wonterghem, et al, System description and initial performance results for Beamlet, LLNL ICF Quarterly Report, Vol. 5(1994)
18 景峰，钕玻璃激光多程放大技术研究，博士学位论文，1998
19 E.S.Bliss,Nonlinear propagation studies, Lawrence Livermore National Laboratory, Livermore, UCRL-25752(1974)
20 E.S. Bliss, G. E. Sommargren, Loss of Focusing Energy Due To Small-scale Nonlinear Effects, Lawrence Livermore National Laboratory,Livermore, UCRL-76322 (1974)
21 J.A. Fleck, J. R. Morris, and E. S. Bliss, Small-scale self-focusing effects in a high power glass laser amplifier, IEEE J. Quantum Electron, Vol. QE-14-5(1978): 353
22 J.H. Marburger, Self-focusing theory, Progr. Quantum Electron. ,Vol. 4(1975)
23 唐永林，陈建国，李大义，强激光圆对称超高斯光束的自聚焦环，强激光与离子束，Vol．12(2000)
24 Wade H. Williams,Jerome M.Auerbach,and et al.,Modeling characterization of the National Ignition Facility focal spot ,SPIE Vol. 3264(1998)
25 V. I. Bespanlov, V. I. Tanalov, Filamentary structure of light beams in nonlinear liquids, JETP Lett., 3(1966): 307
26 A.J.Campillo, S.L.Shapiro, and B.R.Suydam. Periodic breakup of optical beams due to self-focusing. Appi. Phys. Lett., 23-11(1973): 628
27 E.S.Bliss,D.R.Speck,J.F.Holzrichter et al..Propagation of a high-intensity laser pulse with small-scale intensity modulation. Appl.Phys.Lett., 25-8(1974) :448
28 W. W. Simmons, J. T. Hunt, and W. E. Warren. Light Propagation Through Large Laser Systems. IEEE Journal of Quantum electronics, 17-9(1981) : 1727
29 R. A. Sacks, M. A. Henesian, The Prop92 Fourier beam propagation code, UCRL-LR, 105821(1997)
30 A. Sacks, M. A. Henesian, Propagation modeling in two transverse dimensions of the NIF baseline performance,UCRL-LR,105821(1996) : 207
31 J. A. Glaze, Opt. Engineering, 15-2(1976) : 136
32 WEN Sluiangchun, FAN Dianyuan. Small-Scale Self-Focusing of Intense Laser Beams in Nonlinear Media with Loss. CHINESE JOURNAL OF LASERS, B9-4(2000) :356
33 J. A. Fleck, C. layne, Study of self-focusing damage in a high-power Nd:31 glass-rod amplifier, APPL. phys. Lett. , Vol. 22(1973)
34 J. Merle Elson and Jean M. Bennett, Calculation of the power spectral density from surface profile data, APPLL. OPTICS Vol. 1(1995)
35 栗敬钦，魏晓锋，马驰，激光束低频畸变波前模型的计算模拟，强激光 与粒子束，Vol．12(2000)