激光惯性约束核聚变中直接驱动方式光束排布优化研究
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摘要
激光惯性约束聚变(ICF)有两种常见的驱动方式,分别是多束激光从各个方向直接照射聚变燃料的直接驱动方式,以及激光照射黑腔壁产生X射线来驱动聚变燃料的间接驱动方式。间接驱动方式的一个重要优点是,黑腔辐射有利于均匀辐照,降低了对激光光束的均匀性以及光学系统精度的要求,另一个优点在于间接驱动方式压缩靶丸的物理过程不依赖驱动源的种类,因而可以较为方便地将其扩展到对基于其他驱动源的聚变研究上。直接驱动方式的优势在于其具有较高的能量利用率,对聚变能的实现来说这是至关重要的。
球形内爆物理要求两种驱动方式提供极高的内爆对称性以及稳定性。稳定性问题涉及短波长的扰动,主要来自于辐照光束内部小尺度的不均匀性以及制靶过程中的微小缺陷。而对称性问题涉及长波长扰动,主要来自于有限的光束束数,光束的排布方式,以及光学系统中不可避免的误差如束间功率和能量不均衡,指向误差等。在直接驱动聚变中,一般认为对短波长扰动的控制在脉冲辐照初期至关重要,因为此时等离子体的热匀滑效应并不显著。长波长的扰动由于不能被等离子体的热效应匀滑,会被“印记”在靶上。如果各种扰动的总和超过了一定限度,最终会使绝热压缩无法实现或者直接使靶丸壳层破裂。通过增加光束数目的方法可以改善靶面的辐照均匀性,但是同时会使系统的复杂程度和造价大大增加。如何在给定束数的条件下设计更为合理的光束排布是本文研究的重点。我们对先前的光束排布方案进行了系统研究,并提出了一些新的优化方案。
本文研究内容和取得的成果：
1.系统地研究了直接驱动方式的辐照均匀性。分析了辐照不均匀度的高阶和低阶项对聚变内爆对称性的影响,梳理了辐照不均匀度的主要来源并给出了对应的改善方案。系统地分析了早期光束排布方案的优缺点。
2.对基于电子排斥力模型的光束排布方案进行了详细地分析,对应的光束排布如M20,M24和M48,具有较高的几何对称特性,可以很好的改善靶面辐照均匀性。对基于电子排斥力模型的研究表明,最低的球面电子系统势能对应着所有几何因子项平方和的最小值,因而基于电子排斥力模型的方案可以得到具有高度对称性的排布结构。我们将这个方案推广到了任意势能的粒子系统,并首次证明了最低的靶面辐照不均匀度对应着粒子系统势能的最低值。通过这个对应关系提出了基于构建梯度力的排布优化方案,对于给定的光束强度分布和光束数目,获得的光束排布对应着极小的辐照不均匀度。
3.首次给出了几何因子项G1≤t=0的一般条件：∑Nκ=1Ylm(Ωκ)/N=0,-l≤m≤l;1≤l≤t。该条件在数学上等效于spherical t-design的定义。我们首次将spherical t-design运用于光束排布设计之中,发现了一些排布可以有效地改善靶面的辐照均匀性,这些排布简记为：T724,T732,P732,T948, T954,T106O,T1172.我们系统地这些排布的几何对称特性以及均匀辐照特性进行了研究。
4.系统地研究了基于光纤激光的ICF中光纤非相干组束的问题,首先分析了光纤的模式特性,其次设计了一种基于扩束准直系统的光纤阵列耦合方案,最后讨论了光纤束间距,望远系统放大率,离焦距离等对聚焦平面光束强度轮廓的影响。
5.提出了一种针对甚多光束激光驱动ICF的光束排布方案,我们证明了在光束数目充足的条件下,均匀辐照等效于光束均匀排布。给出了一种基于球面等面积分割的排布优化方案,获得了近似均匀的排布结构。该方案具有简单,计算量小的特点,避免了求解超大规模非线性方程组的困难。
本文创新点包括：
1.给出了基于电子排斥力模型排布优化方案的理论支持,从理论上证明了最低的球面电子系统势能等效于所有几何因子项平方和的最小值。
2.提出了基于粒子构建梯度力的优化排布方案,并首次证明了最低的靶面辐照不均匀度对应着粒子系统势能的最小值。该方案针对给定的光束光强轮廓和光束束数对光束排布进行优化,相比电子排斥力模型,该方案可以将辐照不均匀度降低一个数量级。该方案的意义在于,对光束排布的优化而言,它是一种普适的数值方案。
3.首次给出了获得几何因子项Gl≤t=0的一般条件：∑Nκ=1Ylm(Ωκ)/N=0,-l≤m≤l;1≤l≤t。获得了一系列最佳的光束排布T724,T732,P732, T948,T954,T1060,T1172。这些排布尽最大可能地降低了低阶的几何因子项,很好地改善了辐照不均匀性,对光束强度轮廓的依赖性也较弱。
4.针对甚多激光光束驱动方式,提出了均匀排布的光束优化方案,给出了均匀辐照与均匀排布之间的对应关系。该方案可以避免对大规模非线性方程组的求解。
There exist two possible schemes to achieve the laser fusion. The fusion fuel is irradiated either by the laser directly (Direct drive approach) or by the thermal X-rays emitted from the walls of the Hohlraum (Indirect drive approach). One of the major advantages of the indirect driven scheme is the smoothing effect of the thermal radiation from the Hohlraum, which can relax the requirement of the uniformity of the laser beams and the precision of the optical system. Another important advantage lies in the fact that important results obtained with the indirect-drive ICF can be conveniently applied to other driven sources, as the implosion physics of the indirect-drive ICF is independent on the type of the driven sources. However, compared with the indirect-driven scheme, the direct-driven scheme provides higher energy efficiency, which is significant important to the realization of the Inertial Fusion Energy (IFE).
Based on the requirement of the spherical implosion, the symmetry and stability of the implosion should be kept in a very high level for both drive schemes. The instability issue concerns the turbulence of the short wavelength, and mainly comes from the nonuniformities of small scales inside a single beam as well as tiny defects of the fusion target during its productive process. The symmetry issue concerns the turbulence of the long wavelength, and mainly derives from the finite beam number, the beam configuration or the system imperfection such as the power and energy imbalance and the pointing error. In direct-drive ICF, it is generally considered that the short wavelength turbulence plays an important role in the initial stage of the pulse irradiation, as the smoothing effects of the plasma is not enough. The long wavelength turbulences will be "imprinted" on the fusion target as they cannot be effectively smoothed by the thermal plasma. If the fusion target cannot be compressed uniformly due to the excessive turbulences, the adiabatic compression cannot be achieved and even a break-up can arise in the fusion shell. It is possible to improve the irradiation uniformity by increasing the beam number, however at the cost of a fast increasing in both the complexity and the cost of the system. The present dissertation focuses on a more reasonable beam configuration with a given number of beams. The optimaization of the beam configuration is systematically studied, and some novel optimization strategies are proposed for the first time.
The main research work and results are as follows:
1. The irradiation uniformity in direct-dirve ICF is systematically studied. The influences of low and high modes of the irradiation nonuniformtiy to the implosion of the fusion are studied respectively. The origins of the two types of nonuniformities are also discussed. The optimization schemes of beam configuration are discussed and analyzed systematically.
2. The beam configuration scheme based on the electron dynamic-system is studied systematically. The geometrical characteristics and the irradiation uniformity of the beam configurations M20, M24and M48are analyzed. It is demonstrated that the lowest potential of the electron system corresponds to the minimum of the square sum of all the geometrical factors, which indicates that with the scheme of electron dynamic-system, beam configurations with high degree of geometrical symmetry can be obtained. We have generalized this scheme to a particle system with any type of potential profile. It is firstly demonstrated that the lowest irradiation nonuniformity corresponds the minimum of the total potential energy of the particle system, and a constructed gradient force method is developed accordingly to optimize the beam configuration. This method can provide a beam configuration with the best irradiation uniformity in the condition that the beam number and the beam intensity profile are provided.
3. The general conditions of the beam configuration with Gl≤t=0are firstly provided as:∑k=1NYlm(Ωk)/N=0,-l≤m≤l;1≤l≤t,which are fortunately the same as the definition the spherical t-design in mathematics. The spherical t-design is firstly introduced to the optimization of the beam configurations for the first time. Some of these sphetical t-designs are found to improve the on-target irradiation uniformity efficiently, and denoted as T724, T732, P732, T948, T954, T1060, T1172. The geometrical characteristics and the irradiation uniformity of these beam configurations are studied.
4. The incoherent beam combination of the fiber lasers in the context of the fiber-based laser fusion is systematically studied. The modal characteristics of fiber lasers are analyzed. A simple scheme based on an expanding-collimating system is proposed to couple the fiber lasers to the fusion target. The dependences of the combination beams intensity profile on the distance between fibers, the expanding ratio of the telescope system and the defocusing distance are discussed.
5. A beam configuration scheme based on numerous laser beam ICF program is proposed. We demonstrated that with sufficient laser beams, the uniform irradiation is equivalent to the uniform distribution of the laser beams on sphere. A simple method based on the equal areal spherical subdivision is proposed to provide a nearly uniform beam placement. With this method, the effort for the solution of large scale nonlinear equations can be avoided.
Highlights of the dissertation are listed as:
1. The theoretical supports are provided to the beam configuration scheme which is based on the electron dynamic-system. It is demonstrated that the lowest potential of the electron system corresponds to the minimum of the square sum of all the geometrical factors.
2. A beam configuration optimization scheme based on the constructed gradient force of a particle system is provided. It is firstly demonstrated that the lowest irradiation nonuniformity corresponds the minimum of the total potential energy of the particle system.
3. The general conditions of the beam configuration with Gl≤t=0are firstly provided as:∑k=1NYlm(Ωk)/N=0,-l≤m≤l;1≤l≤t.T724,T732,P732, T948, T954, T106O, T1172are considered as the best beam configuration.
4. In the condition that numerous laser beams are provided, a simple beam configuration scheme based on the uniform distribution is proposed. The effort for the solution of large scale nonlinear equations can be avoided.
球形内爆物理要求两种驱动方式提供极高的内爆对称性以及稳定性。稳定性问题涉及短波长的扰动,主要来自于辐照光束内部小尺度的不均匀性以及制靶过程中的微小缺陷。而对称性问题涉及长波长扰动,主要来自于有限的光束束数,光束的排布方式,以及光学系统中不可避免的误差如束间功率和能量不均衡,指向误差等。在直接驱动聚变中,一般认为对短波长扰动的控制在脉冲辐照初期至关重要,因为此时等离子体的热匀滑效应并不显著。长波长的扰动由于不能被等离子体的热效应匀滑,会被“印记”在靶上。如果各种扰动的总和超过了一定限度,最终会使绝热压缩无法实现或者直接使靶丸壳层破裂。通过增加光束数目的方法可以改善靶面的辐照均匀性,但是同时会使系统的复杂程度和造价大大增加。如何在给定束数的条件下设计更为合理的光束排布是本文研究的重点。我们对先前的光束排布方案进行了系统研究,并提出了一些新的优化方案。
本文研究内容和取得的成果：
1.系统地研究了直接驱动方式的辐照均匀性。分析了辐照不均匀度的高阶和低阶项对聚变内爆对称性的影响,梳理了辐照不均匀度的主要来源并给出了对应的改善方案。系统地分析了早期光束排布方案的优缺点。
2.对基于电子排斥力模型的光束排布方案进行了详细地分析,对应的光束排布如M20,M24和M48,具有较高的几何对称特性,可以很好的改善靶面辐照均匀性。对基于电子排斥力模型的研究表明,最低的球面电子系统势能对应着所有几何因子项平方和的最小值,因而基于电子排斥力模型的方案可以得到具有高度对称性的排布结构。我们将这个方案推广到了任意势能的粒子系统,并首次证明了最低的靶面辐照不均匀度对应着粒子系统势能的最低值。通过这个对应关系提出了基于构建梯度力的排布优化方案,对于给定的光束强度分布和光束数目,获得的光束排布对应着极小的辐照不均匀度。
3.首次给出了几何因子项G1≤t=0的一般条件：∑Nκ=1Ylm(Ωκ)/N=0,-l≤m≤l;1≤l≤t。该条件在数学上等效于spherical t-design的定义。我们首次将spherical t-design运用于光束排布设计之中,发现了一些排布可以有效地改善靶面的辐照均匀性,这些排布简记为：T724,T732,P732,T948, T954,T106O,T1172.我们系统地这些排布的几何对称特性以及均匀辐照特性进行了研究。
4.系统地研究了基于光纤激光的ICF中光纤非相干组束的问题,首先分析了光纤的模式特性,其次设计了一种基于扩束准直系统的光纤阵列耦合方案,最后讨论了光纤束间距,望远系统放大率,离焦距离等对聚焦平面光束强度轮廓的影响。
5.提出了一种针对甚多光束激光驱动ICF的光束排布方案,我们证明了在光束数目充足的条件下,均匀辐照等效于光束均匀排布。给出了一种基于球面等面积分割的排布优化方案,获得了近似均匀的排布结构。该方案具有简单,计算量小的特点,避免了求解超大规模非线性方程组的困难。
本文创新点包括：
1.给出了基于电子排斥力模型排布优化方案的理论支持,从理论上证明了最低的球面电子系统势能等效于所有几何因子项平方和的最小值。
2.提出了基于粒子构建梯度力的优化排布方案,并首次证明了最低的靶面辐照不均匀度对应着粒子系统势能的最小值。该方案针对给定的光束光强轮廓和光束束数对光束排布进行优化,相比电子排斥力模型,该方案可以将辐照不均匀度降低一个数量级。该方案的意义在于,对光束排布的优化而言,它是一种普适的数值方案。
3.首次给出了获得几何因子项Gl≤t=0的一般条件：∑Nκ=1Ylm(Ωκ)/N=0,-l≤m≤l;1≤l≤t。获得了一系列最佳的光束排布T724,T732,P732, T948,T954,T1060,T1172。这些排布尽最大可能地降低了低阶的几何因子项,很好地改善了辐照不均匀性,对光束强度轮廓的依赖性也较弱。
4.针对甚多激光光束驱动方式,提出了均匀排布的光束优化方案,给出了均匀辐照与均匀排布之间的对应关系。该方案可以避免对大规模非线性方程组的求解。
There exist two possible schemes to achieve the laser fusion. The fusion fuel is irradiated either by the laser directly (Direct drive approach) or by the thermal X-rays emitted from the walls of the Hohlraum (Indirect drive approach). One of the major advantages of the indirect driven scheme is the smoothing effect of the thermal radiation from the Hohlraum, which can relax the requirement of the uniformity of the laser beams and the precision of the optical system. Another important advantage lies in the fact that important results obtained with the indirect-drive ICF can be conveniently applied to other driven sources, as the implosion physics of the indirect-drive ICF is independent on the type of the driven sources. However, compared with the indirect-driven scheme, the direct-driven scheme provides higher energy efficiency, which is significant important to the realization of the Inertial Fusion Energy (IFE).
Based on the requirement of the spherical implosion, the symmetry and stability of the implosion should be kept in a very high level for both drive schemes. The instability issue concerns the turbulence of the short wavelength, and mainly comes from the nonuniformities of small scales inside a single beam as well as tiny defects of the fusion target during its productive process. The symmetry issue concerns the turbulence of the long wavelength, and mainly derives from the finite beam number, the beam configuration or the system imperfection such as the power and energy imbalance and the pointing error. In direct-drive ICF, it is generally considered that the short wavelength turbulence plays an important role in the initial stage of the pulse irradiation, as the smoothing effects of the plasma is not enough. The long wavelength turbulences will be "imprinted" on the fusion target as they cannot be effectively smoothed by the thermal plasma. If the fusion target cannot be compressed uniformly due to the excessive turbulences, the adiabatic compression cannot be achieved and even a break-up can arise in the fusion shell. It is possible to improve the irradiation uniformity by increasing the beam number, however at the cost of a fast increasing in both the complexity and the cost of the system. The present dissertation focuses on a more reasonable beam configuration with a given number of beams. The optimaization of the beam configuration is systematically studied, and some novel optimization strategies are proposed for the first time.
The main research work and results are as follows:
1. The irradiation uniformity in direct-dirve ICF is systematically studied. The influences of low and high modes of the irradiation nonuniformtiy to the implosion of the fusion are studied respectively. The origins of the two types of nonuniformities are also discussed. The optimization schemes of beam configuration are discussed and analyzed systematically.
2. The beam configuration scheme based on the electron dynamic-system is studied systematically. The geometrical characteristics and the irradiation uniformity of the beam configurations M20, M24and M48are analyzed. It is demonstrated that the lowest potential of the electron system corresponds to the minimum of the square sum of all the geometrical factors, which indicates that with the scheme of electron dynamic-system, beam configurations with high degree of geometrical symmetry can be obtained. We have generalized this scheme to a particle system with any type of potential profile. It is firstly demonstrated that the lowest irradiation nonuniformity corresponds the minimum of the total potential energy of the particle system, and a constructed gradient force method is developed accordingly to optimize the beam configuration. This method can provide a beam configuration with the best irradiation uniformity in the condition that the beam number and the beam intensity profile are provided.
3. The general conditions of the beam configuration with Gl≤t=0are firstly provided as:∑k=1NYlm(Ωk)/N=0,-l≤m≤l;1≤l≤t,which are fortunately the same as the definition the spherical t-design in mathematics. The spherical t-design is firstly introduced to the optimization of the beam configurations for the first time. Some of these sphetical t-designs are found to improve the on-target irradiation uniformity efficiently, and denoted as T724, T732, P732, T948, T954, T1060, T1172. The geometrical characteristics and the irradiation uniformity of these beam configurations are studied.
4. The incoherent beam combination of the fiber lasers in the context of the fiber-based laser fusion is systematically studied. The modal characteristics of fiber lasers are analyzed. A simple scheme based on an expanding-collimating system is proposed to couple the fiber lasers to the fusion target. The dependences of the combination beams intensity profile on the distance between fibers, the expanding ratio of the telescope system and the defocusing distance are discussed.
5. A beam configuration scheme based on numerous laser beam ICF program is proposed. We demonstrated that with sufficient laser beams, the uniform irradiation is equivalent to the uniform distribution of the laser beams on sphere. A simple method based on the equal areal spherical subdivision is proposed to provide a nearly uniform beam placement. With this method, the effort for the solution of large scale nonlinear equations can be avoided.
Highlights of the dissertation are listed as:
1. The theoretical supports are provided to the beam configuration scheme which is based on the electron dynamic-system. It is demonstrated that the lowest potential of the electron system corresponds to the minimum of the square sum of all the geometrical factors.
2. A beam configuration optimization scheme based on the constructed gradient force of a particle system is provided. It is firstly demonstrated that the lowest irradiation nonuniformity corresponds the minimum of the total potential energy of the particle system.
3. The general conditions of the beam configuration with Gl≤t=0are firstly provided as:∑k=1NYlm(Ωk)/N=0,-l≤m≤l;1≤l≤t.T724,T732,P732, T948, T954, T106O, T1172are considered as the best beam configuration.
4. In the condition that numerous laser beams are provided, a simple beam configuration scheme based on the uniform distribution is proposed. The effort for the solution of large scale nonlinear equations can be avoided.
引文
[1]Dawson JM. On the Production of Plasma by Giant Pulse Lasers[J]. Physics of Fluids (1958-1988),1964,7(7):981-987.
[2]Basov NG, Krokhin ON. CONDITIONS FOR HEATING UP OF A PLASMA BY THE RADIATION FROM AN OPTICAL GENERATOR[J]. Journal Name:Zh Eksperim i Teor Fiz; Journal Volume:Vol:46; Other Information:Orig Receipt Date:31-DEC-64,1964: Medium:X; Size:Pages:171-175.
[3]王淦昌.利用大能量大功率的光激射器产生中子的建议[J].原子能科学技术,1988,(01)：7-12.
[4]Kidder RE. Laser fusion:the first ten years (1962-1972):proceedings of,1998[C].
[5]Nuckolls J, Wood L, Thiessen A, Zimmerman G. Laser Compression of Matter to Super-High Densities:Thermonuclear (CTR) Applications[J]. Nature,1972,239(5368):139-142.
[6]Basov NG, Boiko VA, Zakharov SM, Krokhin ON, Sklizkov GV. Generation of Neutrons in a Laser CD2 Plasma Heated by Pulses of Nanosecond Duration[M].1971.
[7]Speck D, Bliss ES, Glaze J, Herris J, Holloway F, Hunt J, Johnson B, Kuizenga DJ, Ozarski R, Patton HG, Rupert P, Suski GJ, Swift C, Thompson C. The Shiva laser-fusion facility [J]. Quantum Electronics, IEEE Journal of,1981,17(9):1599-1619.
[8]Hunt JT, Speck DR. Present And Future Performance Of The Nova Laser System[J]. Optical Engineering,1989,28(4):284461-284461-.
[9]Boehly TR, Brown DL, Craxton RS, Keck RL, Knauer JP, Kelly JH, Kessler TJ, Kumpan SA, Loucks SJ, Letzring SA, Marshall FJ, McCrory RL, Morse SFB, Seka W, Soures JM, Verdon CP. Initial performance results of the OMEGA laser system[J]. Optics Communications, 1997,133(1-6):495-506.
[10]Xiao G, Fan D, Wang S, Lin Z, Gu Y, Zhu J, Zhen Y, Zhu J, Liu F, Chen S, Chen Q, Huang G, Deng X. SG-II solid state laser ICF system:proceedings of,1999[C].
[11]Mima K, Kato Y, Azechi H, Shigemori K, Takabe H, Miyanaga N, Kanabe T, Norimatsu T, Nishimura H, Shiraga H. Recent progress of implosion experiments with uniformity-improved GEKKO XII laser facility at the Institute of Laser Engineering, Osaka University[J]. Physics of Plasmas (1994-present),1996,3(5):2077-2083.
[12]Miller GH, Moses El, Wuest CR. The National Ignition Facility[J]. Optical Engineering, 2004,43(12):2841-2853.
[13]Hurricane O, Callahan D, Casey D, Celliers P, Cerjan C, Dewald E, Dittrich T, Doppner T, Hinkel D, Hopkins LB. Fuel gain exceeding unity in an inertially confined fusion implosion[J]. Nature,2014.
[14]Audi G, Wapstra A. The 1995 update to the atomic mass evaluation[J]. Nuclear Physics A, 1995,595(4):409-480.
[15]Adelberger E, Austin S, Bahcall J, Balantekin A, Bogaert G, Brown L, Buchmann L, Cecil F, Champagne A, De Braeckeleer L. Solar fusion cross sections[J]. arXiv preprint astro-ph/9805121,1998.
[16]Lawson JD. Some criteria for a power producing thermonuclear reactor[J]. Proceedings of the Physical Society Section B,1957,70(1):6.
[17]Atzeni S. Laser driven inertial fusion:the physical basis of current and recently proposed ignition experiments [J]. Plasma Physics and Controlled Fusion,2009,51(12):124029.
[18]Meyer-ter-Vehn J. Inertial confinement fusion driven by heavy ion beams[J]. Nuclear Physics News,1992,2(3):15-21.
[19]Lindl JD, Amendt P, Berger RL, Glendinning SG, Glenzer SH, Haan SW, Kauffman RL, Landen OL, Suter LJ. The physics basis for ignition using indirect-drive targets on the National Ignition Facility[J]. Physics of Plasmas (1994-present),2004,11(2):339-491.
[20]张维岩,叶文华,吴俊峰,缪文勇,范征锋,王立锋,谷建法,戴振生,曹柱荣,徐小文.激光间接驱动聚变内爆流体不稳定性研究[J].中国科学：物理学,力学,天文学,2014,(001)：1-23.
[21]Lindl J. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain[J]. Physics of Plasmas (1994-present),1995,2(11): 3933-4024.
[22]Kodama R, Norreys PA, Mima K, Dangor AE, Evans RG, Fujita H, Kitagawa Y, Krushelnick K, Miyakoshi T, Miyanaga N, Norimatsu T, Rose SJ, Shozaki T, Shigemori K, Sunahara A, Tampo M, Tanaka KA, Toyama Y, Yamanaka T, Zepf M. Fast heating of ultrahigh-density plasma as a step towards laser fusion ignition[J]. Nature,2001,412(6849):798-802.
[23]Kodama R, Shiraga H, Shigemori K, Toyama Y, Fujioka S, Azechi H, Fujita H, Habara H, Hall T, Izawa Y, Jitsuno T, Kitagawa Y, Krushelnick KM, Lancaster KL, Mima K, Nagai K, Nakai M, Nishimura H, Norimatsu T, Norreys PA, Sakabe S, Tanaka KA, Youssef A, Zepf M, Yamanaka T. Nuclear fusion:Fast heating scalable to laser fusion ignition[J]. Nature, 2002,418(6901):933-934.
[24]Atzeni S, Schiavi A, Marocchino A. Studies on the robustness of shock-ignited laser fusion targets[J]. Plasma Physics and Controlled Fusion,2011,53(3):035010.
[25]袁强,胡东霞,张鑫,赵军普,胡思得,黄文会,魏晓峰.激光聚变冲击点火物理特性研究[J].物理学报,2011,60(1)：15202-015202.
[26]Ribeyre X, Schurtz G, Lafon M, Galera S, Weber S. Shock ignition:an alternative scheme for HiPER[J]. Plasma Physics and Controlled Fusion,2009,51(1):015013.
[27]Boehly T, Craxton R, Hinterman T, Kelly J, Kessler T, Kumpan S, Letzring S, McCrory R, Morse S, Seka W. The upgrade to the OMEGA laser system[J]. Review of scientific instruments,1995,66(1):508-510.
[28]Fleurot N, Cavailler C, Bourgade JL. The Laser Megajoule (LMJ) Project dedicated to inertial confinement fusion:Development and construction status[J]. Fusion Engineering and Design,2005,74(1-4):147-154.
[29]Andre ML. The French megajoule laser project (LMJ)[J]. Fusion Engineering and Design, 1999,44(1):43-49.
[30]Hallo L, Olazabal-Loume M, Ribeyre X, Drean V, Schurtz G, Feugeas JL, Breil J, Ph N, Maire PH. Hydrodynamic and symmetry safety factors of HiPER's targets[J]. Plasma Physics and Controlled Fusion,2009,51 (1):014001.
[31]Zheng W, Zhang X, Wei X, Jing F, Sui Z, Zheng K, Yuan X, Jiang X, Su J, Zhou H. Status of the SG-III solid-state laser facility:proceedings of the Journal of Physics:Conference Series, 2008[C]. IOP Publishing.
[32]Lindl J, Landen O, Edwards J, Moses E, Team N. Review of the National Ignition Campaign 2009-2012[J]. Physics of Plasmas (1994-present),2014,21(2):020501.
[33]Skupsky S, Marozas J, Craxton R, Betti R, Collins T, Delettrez J, Goncharov V, McKenty P, Radha P, Boehly T. Polar direct drive on the National Ignition Facility[J]. Physics of Plasmas (1994-present),2004,11(5):2763-2770.
[34]Miquel J-L, Lion C, Vivini P. The LMJ program:Overview and Status of LMJ & PETAL Projects:proceedings of the CLEO:Applications and Technology,2013[C]. Optical Society of America.
[35]王美聪,朱明智,陈刚,吴文凯,傅学农.大型ICF装置靶场传输光路排布研究[J]。激光与光电子学进展,2013,50(1)：158-163.
[36]郑万国,邓颖,周维.激光聚变研究中心激光技术研究进展[J].强激光与粒子束,2013,25(12)：3082-3090.
[37]Le Garrec B, Novaro M, Tyldesley M, Juarez R, Sanz J, Perlado M, Rus B, Collier J, Edwards C. HiPER laser reference design:proceedings of the SPIE Optics+ Optoelectronics, 2011 [C]. International Society for Optics and Photonics.
[38]范滇元,张小民.激光核聚变与高功率激光：历史与进展[J].物理,2010,(9)：589-596.
[39]Grubb SG. Cladding-pumped MOPA structure [M]. Google Patents.1995.
[40]Richardson D, Nilsson J, Clarkson W. High power fiber lasers:current status and future perspectives [Invited][J]. JOSA B,2010,27(11):B63-B92.
[41]Cheng M-Y, Chang Y-C, Galvanauskas A, Mamidipudi P, Changkakoti R, Gatchell P. High-energy and high-peak-power nanosecond pulsegeneration with beam quality control in 200-μm core highly multimode Yb-doped fiberamplifiers[J]. Optics Letters,2005,30(4):358-360.
[42]Mourou GA, Labaune C, Hulin D, Galvanauskas A. New amplifying laser concept for inertial fusion driver[J]. Journal of Physics:Conference Series,2008,112(3):032052.
[43]Labaune C, Hulin D, Galvanauskas A, Mourou GA. On the feasibility of a fiber-based inertial fusion laser driver[J]. Optics Communications,2008,281(15-16):4075-4080.
[44]McCrory R, Verdon C. Computer modeling and simulation in inertial confinement fusion[J]. Unknown,1989,1.
[45]Atzeni S, Meyer-ter-Vehn J. The Physics of Inertial Fusion:BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter:BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter[M]. Oxford University Press,2004.
[46]Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C. Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression[J]. Physical Review Letters,1984,53(11):1057.
[47]Rose HA, DuBois D. Statistical properties of laser hot spots produced by a random phase plate[J]. Physics of Fluids B:Plasma Physics (1989-1993),1993,5(2):590-596.
[48]Rose HA. Random phase plate hot spots and their effect on stimulated Brillouin backscatter and self-focusing[J]. Physics of Plasmas (1994-present),1995,2(6):2216-2223.
[49]Sergey GG, Vladimir ND, Roman AS. Formation of the uniform irradiation of a target in high-power laser facilities[J]. Quantum Electronics,2004,34(5):427.
[50]Deng X, Liang X, Chen Z, Yu W, Ma R. Uniform illumination of large targets using a lens array[J]. Applied optics,1986,25(3):377-381.
[51]Nishi N, Jitsuno T, Nakatsuka M, Nakai S. Improvement of laser-beam irradiation-intensity distribution using multi lens array and edge-shaped plates[J]. Optical Review,1998,5(5): 285-290.
[52]Nishi N, Jitsuno T, Tsubakimoto K, Matsuoka S, Miyanaga N, Nakatsuka M. Two-dimensional multi-lens array with circular aperture spherical lens for flat-top irradiation of inertial confinement fusion target[J]. Optical Review,2000,7(3):216-220.
[53]Dixit S, Thomas I, Rushford M, Merrill R, Perry M, Powell H, Nugent K. Kinoform phase plates for tailoring focal plane intensity profiles[J]. LLNL Rep UCRL-LR-105821-94-4,(Lawrence Livermore National Laboratory,1994),1994:152-159.
[54]Neauport J, Ribeyre X, Daurios J, Valla D, Lavergne M, Beau V, Videau L. Design and optical characterization of a large continuous phase plate for Laser Integration Line and laser Megajoule facilities[J]. Applied optics,2003,42(13):2377-2382.
[55]Lehmberg R, Schmitt A, Bodner S. Theory of induced spatial incoherence[J]. Journal of Applied Physics,1987,62(7):2680-2701.
[56]Skupsky S, Short RW, Kessler T, Craxton RS, Letzring S, Soures JM. Improved laser-beam uniformity using the angular dispersion of frequency-modulated light[J]. Journal of Applied Physics,1989,66(8):3456-3462.
[1]Bodner S. Critical elements of high gain laser fusion[J]. Journal of Fusion Energy,1981,1(3): 221-240.
[2]Thomas CE. Laser fusion target illumination system[J]. Appl Opt,1975,14(6):1267-1273.
[3]Howard JE. Uniform illumination of spherical laser fusion targets[J]. Appl Opt,1977,16(10): 2764-2773.
[4]Skupsky S, Lee K. Uniformity of energy deposition for laser driven fusion[J]. Journal of Applied Physics,1983,54(7):3662-3671.
[5]Schmitt AJ. Absolutely uniform illumination of laser fusion pellets[J]. Applied Physics Letters, 1984,44(4):399-401.
[6]Mark JWK. Near spherical illumination of ion-beam and laser targets [J]. Physics Letters A, 1986,114(8-9):458-464.
[7]Murakami M, Nishihara K, Azechi H. Irradiation nonuniformity due to imperfections of laser beams[J]. Journal of Applied Physics,1993,74(2):802-808.
[8]Murakami M. Irradiation system based on dodecahedron for inertial confinement fusion[J]. Applied Physics Letters,1995,66(13):1587-1589.
[9]Jun X, Baida L. Conditions for perfectly uniform irradiation of spherical laser fusion targets[J]. Journal of Optics,1998,29(4):282.
[10]Murakami M. Design of a conic irradiation system for laser fusion[J]. Fusion Engineering and Design,1999,44(1-4):111-115.
[11]Sergey GG, Vladimir ND, Roman AS. Formation of the uniform irradiation of a target in high-power laser facilities[J]. Quantum Electronics,2004,34(5):427.
[12]Temporal M, Canaud B. Numerical analysis of the irradiation uniformity of a directly driven inertial confinement fusion capsule[J]. The European Physical Journal D,2009,55(1):139-145.
[13]Murakami M, Sarukura N, Azechi H, Temporal M, Schmitt AJ. Optimization of irradiation configuration in laser fusion utilizing self-organizing electrodynamic system[J]. Physics of Plasmas,2010,17(8):082702-082708.
[14]Temporal M, Canaud B, Laffite S, Le Garrec BJ, Murakami M. Illumination uniformity of a capsule directly driven by a laser facility with 32 or 48 directions of irradiation[J]. Physics of Plasmas,2010,17(6):064504-064504.
[15]Temporal M, Canaud B, Le Garrec BJ. Irradiation uniformity and zooming performances for a capsule directly driven by a 32x9 laser beams configuration[J]. Physics of Plasmas (1994-present),2010,17(2):-.
[16]Temporal M, Ramis R, Canaud B, Brandon V, Laffite S, Garrec BJL. Irradiation uniformity of directly driven inertial confinement fusion targets in the context of the shock-ignition scheme[J]. Plasma Physics and Controlled Fusion,2011,53(12):124008.
[17]Temporal M, Canaud B. Stochastic homogenization of the laser intensity to improve the irradiation uniformity of capsules directly driven by thousands laser beams [J]. The European Physical Journal D,2011,65(3):447-451.
[18]Schiavi A, Atzeni S, Marocchino A. Illumination stability for high-repetition-rate laser facilities in direct-drive inertial confinement fusion[J]. EPL,2011,94(3):35002.
[19]Temporal M, Canaud B, Garbett W, Philippe F, Ramis R. Polar direct drive illumination uniformity provided by the Orion facility [J]. The European Physical Journal D,2013,67(10): 1-7.
[20]Ramis R, Temporal M, Canaud B, Brandon V. Symmetry issues in Directly Irradiated Targets[J]. EPJ Web of Conferences,2013,59:02017.
[21]Temporal M, Canaud B, Brandon V. Illumination uniformity of capsules directly driven by a facility with thousands of laser beams[J]. EPJ Web of Conferences,2013,59:02015.
[22]Temporal M, Canaud B, Garbett WJ, Ramis R. Numerical analysis of the direct drive illumination uniformity for the Laser MegaJoule facility[J]. Physics of Plasmas (1994-present),2014,21(1):-.
[23]Mima K, Kato Y, Azechi H, Shigemori K, Takabe H, Miyanaga N, Kanabe T, Norimatsu T, Nishimura H, Shiraga H. Recent progress of implosion experiments with uniformity improved GEKKO XII laser facility at the Institute of Laser Engineering, Osaka University[J]. Physics of Plasmas (1994-present),1996,3(5):2077-2083.
[24]Boehly T, Craxton R, Hinterman T, Kelly J, Kessler T, Kumpan S, Letzring S, McCrory R, Morse S, Seka W. The upgrade to the OMEGA laser system[J]. Review of scientific instruments,1995,66(1):508-510.
[25]Desselberger M, Afshar-Rad T, Khattak F, Viana S, Willi O. Nonuniformity imprint on the ablation surface of laser-irradiated targets[J]. Physical Review Letters,1992,68(10):1539.
[26]Azechi H, Nakai M, Shigemori K, Miyanaga N, Shiraga H, Nishimura H, Honda M, Ishizaki R, Wouchuk JG, Takabe H, Nishihara K, Mima K, Nishiguchi A, Endo T. Direct-drive hydrodynamic instability experiments on the GEKKO XII laser[J]. Physics of Plasmas, 1997,4(11):4079-4089.
[27]Kidder RE. Laser-driven compression of hollow shells:power requirements and stability limitations[J]. Nuclear Fusion,1976,16(1):3.
[1]Murakami M. Irradiation system based on dodecahedron for inertial confinement fusion[J]. Applied Physics Letters,1995,66(13):1587-1589.
[2]谭吉春,魏晓峰.光束路径排布对称性与光功率分布均匀性[J].中国激光,2000,27(1)：28-32.
[3]Jun X, Baida L. Conditions for perfectly uniform irradiation of spherical laser fusion targets[J]. Journal of Optics,1998,29(4):282.
[4]Schmitt AJ. Absolutely uniform illumination of laser fusion pellets[J]. Applied Physics Letters, 1984,44(4):399-401.
[5]Mark JWK. Near spherical illumination of ion-beam and laser targets[J]. Physics Letters A, 1986,114(8-9):458-464.
[6]Murakami M, Sarukura N, Azechi H, Temporal M, Schmitt AJ. Optimization of irradiation configuration in laser fusion utilizing self-organizing electrodynamic system[J]. Physics of Plasmas,2010,17(8):082702-082708.
[7]Rakhmanov E, Saff E, Zhou Y. Minimal discrete energy on the sphere[J]. Math Res Lett, 1994,1(6):647-662.
[8]Altschuler EL, Williams TJ, Ratner ER, Tipton R, Stong R, Dowla F, Wooten F. Possible Global Minimum Lattice Configurations for Thomson's Problem of Charges on a Sphere[J]. Physical Review Letters,1997,78(14):2681-2685.
[9]Levin Y, Arenzon JJ. Why charges go to the surface:A generalized Thomson problem[J]. EPL (Europhysics Letters),2003,63(3):415.
[10]Altschuler EL, Perez-Garrido A. Global minimum for Thomson's problem of charges on a sphere[J]. Physical Review E,2005,71(4):047703.
[11]Xu T, Xu L, Wang A, Gu C, Wang S, Liu J, Wei A. Optimization of beam configuration in laser fusion based on the laser beam pattern[J]. Physics of Plasmas (1994-present), 2013,20(12):122702.
[12]Arfken GGB, Weber HJ. Mathematical Methods for Physicists[M]. Elsevier Academic Press, 2005.
[13]Erber T, Hockney G. Equilibrium configurations of N equal charges on a sphere[J]. Journal of Physics A:Mathematical and General,1991,24(23):L1369.
[14]Morris JR, Deaven DM, Ho KM. Genetic-algorithm energy minimization for point charges on a sphere[J]. Physical Review B,1996,53(4):R1740-R1743.
[15]Munera HA. Properties of discrete electrostatic systems[J].1986.
[16]Altschuler EL, Williams TJ, Ratner ER, Dowla F, Wooten F. Method of constrained global optimization[J]. Physical Review Letters,1994,72(17):2671-2674.
[1]Delsarte P, Goethals JM, Seidel JJ. Spherical codes and designs[J]. Geometriae Dedicata, 1977,6(3):363-388.
[2]Bannai E. Spherical t-designs which are orbits of finite groups[J].1984:341-354.
[3]Bajnok B. Construction of spherical t-designs[J]. Geometriae Dedicata,1992,43(2):167-179.
[4]Hardin R, Sloane N. A new approach to the construction of optimal designs[J]. Journal of statistical planning and inference,1993,37(3):339-369.
[5]Hardin RH, Sloane NJA. McLaren's improved snub cube and other new spherical designs in three dimensions[J]. Discrete & Computational Geometry,1996,15(4):429-441.
[6]Seidel J. Definitions for spherical designs[J]. Journal of statistical planning and inference, 2001,95(1):307-313.
[7]Bannai E, Bannai E. A survey on spherical designs and algebraic combinatorics on spheres[J]. European Journal of Combinatorics,2009,30(6):1392-1425.
[8]Grabner PJ, Tichy RF. Spherical designs, discrepancy and numerical integration[J]. mathematics of computation,1993,60(201):327-336.
[9]Murakami M. Irradiation system based on dodecahedron for inertial confinement fusion[J]. Applied Physics Letters,1995,66(13):1587-1589.
[10]Kidder RE. Laser-driven compression of hollow shells:power requirements and stability limitations[J]. Nuclear Fusion,1976,16(1):3.
[11]Murakami M, Sarukura N, Azechi H, Temporal M, Schmitt AJ. Optimization of irradiation configuration in laser fusion utilizing self-organizing electrodynamic system [J]. Physics of Plasmas,2010,17(8):082702-082708.
[12]Xu T, Xu L, Wang A, Gu C, Wang S, Liu J, Wei A. Optimization of beam configuration in laser fusion based on the laser beam pattern[J]. Physics of Plasmas (1994-present), 2013,20(12):122702.
[1]Speck D, Bliss ES, Glaze J, Herris J, Holloway F, Hunt J, Johnson B, Kuizenga DJ, Ozarski R, Patton HG, Rupert P, Suski GJ, Swift C, Thompson C. The Shiva laser-fusion facility[J]. Quantum Electronics, IEEE Journal of,1981,17(9):1599-1619.
[2]Hunt JT, Speck DR. Present And Future Performance Of The Nova Laser System[J]. Optical Engineering,1989,28(4):284461-284461-.
[3]Boehly TR, Brown DL, Craxton RS, Keck RL, Knauer JP, Kelly JH, Kessler TJ, Kumpan SA, Loucks SJ, Letzring SA, Marshall FJ, McCrory RL, Morse SFB, Seka W, Soures JM, Verdon CP. Initial performance results of the OMEGA laser system[J]. Optics Communications, 1997,133(1-6):495-506.
[4]Mima K, Kato Y, Azechi H, Shigemori K, Takabe H, Miyanaga N, Kanabe T, Norimatsu T, Nishimura H, Shiraga H. Recent progress of implosion experiments with uniformity improved GEKKO Ⅻ laser facility at the Institute of Laser Engineering, Osaka University[J]. Physics of Plasmas (1994-present),1996,3(5):2077-2083.
[5]Xiao G, Fan D, Wang S, Lin Z, Gu Y, Zhu J, Zhen Y, Zhu J, Liu F, Chen S, Chen Q, Huang G, Deng X. SG-Ⅱ solid state laser ICF system:proceedings of,1999[C].
[6]Miller GH, Moses EI, Wuest CR. The National Ignition Facility [J]. Optical Engineering, 2004,43(12):2841-2853.
[7]Fleurot N, Cavailler C, Bourgade JL. The Laser M6gajoule (LMJ) Project dedicated to inertial confinement fusion:Development and construction status[J]. Fusion Engineering and Design, 2005,74(1-4):147-154.
[8]Zheng W, Zhang X, Wei X, Jing F, Sui Z, Zheng K, Yuan X, Jiang X, Su J, Zhou H. Status of the SG-Ⅲ solid-state laser facility:proceedings of the Journal of Physics:Conference Series, 2008[C]. IOP Publishing.
[9]Fan TY. Laser beam combining for high-power, high-radiance sources[J]. Selected Topics in Quantum Electronics, IEEE Journal of,2005,11(3):567-577.
[10]Cheng M-Y, Chang Y-C, Galvanauskas A, Mamidipudi P, Changkakoti R, Gatchell P. High-energy and high-peak-power nanosecond pulsegeneration with beam quality control in 200-μm core highly multimode Yb-doped fiberamplifiers[J]. Optics Letters,2005,30(4):358-360.
[11]Richardson D, Nilsson J, Clarkson W. High power fiber lasers:current status and future perspectives [Invited][J]. JOSA B,2010,27(11):B63-B92.
[12]Labaune C, Hulin D, Galvanauskas A, Mourou GA. On the feasibility of a fiber-based inertial fusion laser driver[J]. Optics Communications,2008,281(15-16):4075-4080.
[13]Lu B. Laser Optics-Beam Characterization, Propagation and Transformation, Resonator Technology and Physics (Beijin [M]. Higher Education Press) p390 (in Chinese).2003.
[14]吕百达.激光光学[M].四川大学出版社,1986.
[15]Al-Rashed A-AR, Saleh BEA. Decentered Gaussian beams[J]. Applied optics,1995,34(30): 6819-6825.
[16]Huang Z, Wei X, Li M, Wang J, Lin H, Xu D, Deng Y, Zhang R. Coherent and incoherent combination of Gaussian beams employing lens array distributed on the spherical chamber[J]. Applied optics,2012,51(10):1546-1551.
[17]Song L. Small circle subdivision method for development of global sampling grid[D],1997.
[2]Basov NG, Krokhin ON. CONDITIONS FOR HEATING UP OF A PLASMA BY THE RADIATION FROM AN OPTICAL GENERATOR[J]. Journal Name:Zh Eksperim i Teor Fiz; Journal Volume:Vol:46; Other Information:Orig Receipt Date:31-DEC-64,1964: Medium:X; Size:Pages:171-175.
[3]王淦昌.利用大能量大功率的光激射器产生中子的建议[J].原子能科学技术,1988,(01)：7-12.
[4]Kidder RE. Laser fusion:the first ten years (1962-1972):proceedings of,1998[C].
[5]Nuckolls J, Wood L, Thiessen A, Zimmerman G. Laser Compression of Matter to Super-High Densities:Thermonuclear (CTR) Applications[J]. Nature,1972,239(5368):139-142.
[6]Basov NG, Boiko VA, Zakharov SM, Krokhin ON, Sklizkov GV. Generation of Neutrons in a Laser CD2 Plasma Heated by Pulses of Nanosecond Duration[M].1971.
[7]Speck D, Bliss ES, Glaze J, Herris J, Holloway F, Hunt J, Johnson B, Kuizenga DJ, Ozarski R, Patton HG, Rupert P, Suski GJ, Swift C, Thompson C. The Shiva laser-fusion facility [J]. Quantum Electronics, IEEE Journal of,1981,17(9):1599-1619.
[8]Hunt JT, Speck DR. Present And Future Performance Of The Nova Laser System[J]. Optical Engineering,1989,28(4):284461-284461-.
[9]Boehly TR, Brown DL, Craxton RS, Keck RL, Knauer JP, Kelly JH, Kessler TJ, Kumpan SA, Loucks SJ, Letzring SA, Marshall FJ, McCrory RL, Morse SFB, Seka W, Soures JM, Verdon CP. Initial performance results of the OMEGA laser system[J]. Optics Communications, 1997,133(1-6):495-506.
[10]Xiao G, Fan D, Wang S, Lin Z, Gu Y, Zhu J, Zhen Y, Zhu J, Liu F, Chen S, Chen Q, Huang G, Deng X. SG-II solid state laser ICF system:proceedings of,1999[C].
[11]Mima K, Kato Y, Azechi H, Shigemori K, Takabe H, Miyanaga N, Kanabe T, Norimatsu T, Nishimura H, Shiraga H. Recent progress of implosion experiments with uniformity-improved GEKKO XII laser facility at the Institute of Laser Engineering, Osaka University[J]. Physics of Plasmas (1994-present),1996,3(5):2077-2083.
[12]Miller GH, Moses El, Wuest CR. The National Ignition Facility[J]. Optical Engineering, 2004,43(12):2841-2853.
[13]Hurricane O, Callahan D, Casey D, Celliers P, Cerjan C, Dewald E, Dittrich T, Doppner T, Hinkel D, Hopkins LB. Fuel gain exceeding unity in an inertially confined fusion implosion[J]. Nature,2014.
[14]Audi G, Wapstra A. The 1995 update to the atomic mass evaluation[J]. Nuclear Physics A, 1995,595(4):409-480.
[15]Adelberger E, Austin S, Bahcall J, Balantekin A, Bogaert G, Brown L, Buchmann L, Cecil F, Champagne A, De Braeckeleer L. Solar fusion cross sections[J]. arXiv preprint astro-ph/9805121,1998.
[16]Lawson JD. Some criteria for a power producing thermonuclear reactor[J]. Proceedings of the Physical Society Section B,1957,70(1):6.
[17]Atzeni S. Laser driven inertial fusion:the physical basis of current and recently proposed ignition experiments [J]. Plasma Physics and Controlled Fusion,2009,51(12):124029.
[18]Meyer-ter-Vehn J. Inertial confinement fusion driven by heavy ion beams[J]. Nuclear Physics News,1992,2(3):15-21.
[19]Lindl JD, Amendt P, Berger RL, Glendinning SG, Glenzer SH, Haan SW, Kauffman RL, Landen OL, Suter LJ. The physics basis for ignition using indirect-drive targets on the National Ignition Facility[J]. Physics of Plasmas (1994-present),2004,11(2):339-491.
[20]张维岩,叶文华,吴俊峰,缪文勇,范征锋,王立锋,谷建法,戴振生,曹柱荣,徐小文.激光间接驱动聚变内爆流体不稳定性研究[J].中国科学：物理学,力学,天文学,2014,(001)：1-23.
[21]Lindl J. Development of the indirect-drive approach to inertial confinement fusion and the target physics basis for ignition and gain[J]. Physics of Plasmas (1994-present),1995,2(11): 3933-4024.
[22]Kodama R, Norreys PA, Mima K, Dangor AE, Evans RG, Fujita H, Kitagawa Y, Krushelnick K, Miyakoshi T, Miyanaga N, Norimatsu T, Rose SJ, Shozaki T, Shigemori K, Sunahara A, Tampo M, Tanaka KA, Toyama Y, Yamanaka T, Zepf M. Fast heating of ultrahigh-density plasma as a step towards laser fusion ignition[J]. Nature,2001,412(6849):798-802.
[23]Kodama R, Shiraga H, Shigemori K, Toyama Y, Fujioka S, Azechi H, Fujita H, Habara H, Hall T, Izawa Y, Jitsuno T, Kitagawa Y, Krushelnick KM, Lancaster KL, Mima K, Nagai K, Nakai M, Nishimura H, Norimatsu T, Norreys PA, Sakabe S, Tanaka KA, Youssef A, Zepf M, Yamanaka T. Nuclear fusion:Fast heating scalable to laser fusion ignition[J]. Nature, 2002,418(6901):933-934.
[24]Atzeni S, Schiavi A, Marocchino A. Studies on the robustness of shock-ignited laser fusion targets[J]. Plasma Physics and Controlled Fusion,2011,53(3):035010.
[25]袁强,胡东霞,张鑫,赵军普,胡思得,黄文会,魏晓峰.激光聚变冲击点火物理特性研究[J].物理学报,2011,60(1)：15202-015202.
[26]Ribeyre X, Schurtz G, Lafon M, Galera S, Weber S. Shock ignition:an alternative scheme for HiPER[J]. Plasma Physics and Controlled Fusion,2009,51(1):015013.
[27]Boehly T, Craxton R, Hinterman T, Kelly J, Kessler T, Kumpan S, Letzring S, McCrory R, Morse S, Seka W. The upgrade to the OMEGA laser system[J]. Review of scientific instruments,1995,66(1):508-510.
[28]Fleurot N, Cavailler C, Bourgade JL. The Laser Megajoule (LMJ) Project dedicated to inertial confinement fusion:Development and construction status[J]. Fusion Engineering and Design,2005,74(1-4):147-154.
[29]Andre ML. The French megajoule laser project (LMJ)[J]. Fusion Engineering and Design, 1999,44(1):43-49.
[30]Hallo L, Olazabal-Loume M, Ribeyre X, Drean V, Schurtz G, Feugeas JL, Breil J, Ph N, Maire PH. Hydrodynamic and symmetry safety factors of HiPER's targets[J]. Plasma Physics and Controlled Fusion,2009,51 (1):014001.
[31]Zheng W, Zhang X, Wei X, Jing F, Sui Z, Zheng K, Yuan X, Jiang X, Su J, Zhou H. Status of the SG-III solid-state laser facility:proceedings of the Journal of Physics:Conference Series, 2008[C]. IOP Publishing.
[32]Lindl J, Landen O, Edwards J, Moses E, Team N. Review of the National Ignition Campaign 2009-2012[J]. Physics of Plasmas (1994-present),2014,21(2):020501.
[33]Skupsky S, Marozas J, Craxton R, Betti R, Collins T, Delettrez J, Goncharov V, McKenty P, Radha P, Boehly T. Polar direct drive on the National Ignition Facility[J]. Physics of Plasmas (1994-present),2004,11(5):2763-2770.
[34]Miquel J-L, Lion C, Vivini P. The LMJ program:Overview and Status of LMJ & PETAL Projects:proceedings of the CLEO:Applications and Technology,2013[C]. Optical Society of America.
[35]王美聪,朱明智,陈刚,吴文凯,傅学农.大型ICF装置靶场传输光路排布研究[J]。激光与光电子学进展,2013,50(1)：158-163.
[36]郑万国,邓颖,周维.激光聚变研究中心激光技术研究进展[J].强激光与粒子束,2013,25(12)：3082-3090.
[37]Le Garrec B, Novaro M, Tyldesley M, Juarez R, Sanz J, Perlado M, Rus B, Collier J, Edwards C. HiPER laser reference design:proceedings of the SPIE Optics+ Optoelectronics, 2011 [C]. International Society for Optics and Photonics.
[38]范滇元,张小民.激光核聚变与高功率激光：历史与进展[J].物理,2010,(9)：589-596.
[39]Grubb SG. Cladding-pumped MOPA structure [M]. Google Patents.1995.
[40]Richardson D, Nilsson J, Clarkson W. High power fiber lasers:current status and future perspectives [Invited][J]. JOSA B,2010,27(11):B63-B92.
[41]Cheng M-Y, Chang Y-C, Galvanauskas A, Mamidipudi P, Changkakoti R, Gatchell P. High-energy and high-peak-power nanosecond pulsegeneration with beam quality control in 200-μm core highly multimode Yb-doped fiberamplifiers[J]. Optics Letters,2005,30(4):358-360.
[42]Mourou GA, Labaune C, Hulin D, Galvanauskas A. New amplifying laser concept for inertial fusion driver[J]. Journal of Physics:Conference Series,2008,112(3):032052.
[43]Labaune C, Hulin D, Galvanauskas A, Mourou GA. On the feasibility of a fiber-based inertial fusion laser driver[J]. Optics Communications,2008,281(15-16):4075-4080.
[44]McCrory R, Verdon C. Computer modeling and simulation in inertial confinement fusion[J]. Unknown,1989,1.
[45]Atzeni S, Meyer-ter-Vehn J. The Physics of Inertial Fusion:BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter:BeamPlasma Interaction, Hydrodynamics, Hot Dense Matter[M]. Oxford University Press,2004.
[46]Kato Y, Mima K, Miyanaga N, Arinaga S, Kitagawa Y, Nakatsuka M, Yamanaka C. Random phasing of high-power lasers for uniform target acceleration and plasma-instability suppression[J]. Physical Review Letters,1984,53(11):1057.
[47]Rose HA, DuBois D. Statistical properties of laser hot spots produced by a random phase plate[J]. Physics of Fluids B:Plasma Physics (1989-1993),1993,5(2):590-596.
[48]Rose HA. Random phase plate hot spots and their effect on stimulated Brillouin backscatter and self-focusing[J]. Physics of Plasmas (1994-present),1995,2(6):2216-2223.
[49]Sergey GG, Vladimir ND, Roman AS. Formation of the uniform irradiation of a target in high-power laser facilities[J]. Quantum Electronics,2004,34(5):427.
[50]Deng X, Liang X, Chen Z, Yu W, Ma R. Uniform illumination of large targets using a lens array[J]. Applied optics,1986,25(3):377-381.
[51]Nishi N, Jitsuno T, Nakatsuka M, Nakai S. Improvement of laser-beam irradiation-intensity distribution using multi lens array and edge-shaped plates[J]. Optical Review,1998,5(5): 285-290.
[52]Nishi N, Jitsuno T, Tsubakimoto K, Matsuoka S, Miyanaga N, Nakatsuka M. Two-dimensional multi-lens array with circular aperture spherical lens for flat-top irradiation of inertial confinement fusion target[J]. Optical Review,2000,7(3):216-220.
[53]Dixit S, Thomas I, Rushford M, Merrill R, Perry M, Powell H, Nugent K. Kinoform phase plates for tailoring focal plane intensity profiles[J]. LLNL Rep UCRL-LR-105821-94-4,(Lawrence Livermore National Laboratory,1994),1994:152-159.
[54]Neauport J, Ribeyre X, Daurios J, Valla D, Lavergne M, Beau V, Videau L. Design and optical characterization of a large continuous phase plate for Laser Integration Line and laser Megajoule facilities[J]. Applied optics,2003,42(13):2377-2382.
[55]Lehmberg R, Schmitt A, Bodner S. Theory of induced spatial incoherence[J]. Journal of Applied Physics,1987,62(7):2680-2701.
[56]Skupsky S, Short RW, Kessler T, Craxton RS, Letzring S, Soures JM. Improved laser-beam uniformity using the angular dispersion of frequency-modulated light[J]. Journal of Applied Physics,1989,66(8):3456-3462.
[1]Bodner S. Critical elements of high gain laser fusion[J]. Journal of Fusion Energy,1981,1(3): 221-240.
[2]Thomas CE. Laser fusion target illumination system[J]. Appl Opt,1975,14(6):1267-1273.
[3]Howard JE. Uniform illumination of spherical laser fusion targets[J]. Appl Opt,1977,16(10): 2764-2773.
[4]Skupsky S, Lee K. Uniformity of energy deposition for laser driven fusion[J]. Journal of Applied Physics,1983,54(7):3662-3671.
[5]Schmitt AJ. Absolutely uniform illumination of laser fusion pellets[J]. Applied Physics Letters, 1984,44(4):399-401.
[6]Mark JWK. Near spherical illumination of ion-beam and laser targets [J]. Physics Letters A, 1986,114(8-9):458-464.
[7]Murakami M, Nishihara K, Azechi H. Irradiation nonuniformity due to imperfections of laser beams[J]. Journal of Applied Physics,1993,74(2):802-808.
[8]Murakami M. Irradiation system based on dodecahedron for inertial confinement fusion[J]. Applied Physics Letters,1995,66(13):1587-1589.
[9]Jun X, Baida L. Conditions for perfectly uniform irradiation of spherical laser fusion targets[J]. Journal of Optics,1998,29(4):282.
[10]Murakami M. Design of a conic irradiation system for laser fusion[J]. Fusion Engineering and Design,1999,44(1-4):111-115.
[11]Sergey GG, Vladimir ND, Roman AS. Formation of the uniform irradiation of a target in high-power laser facilities[J]. Quantum Electronics,2004,34(5):427.
[12]Temporal M, Canaud B. Numerical analysis of the irradiation uniformity of a directly driven inertial confinement fusion capsule[J]. The European Physical Journal D,2009,55(1):139-145.
[13]Murakami M, Sarukura N, Azechi H, Temporal M, Schmitt AJ. Optimization of irradiation configuration in laser fusion utilizing self-organizing electrodynamic system[J]. Physics of Plasmas,2010,17(8):082702-082708.
[14]Temporal M, Canaud B, Laffite S, Le Garrec BJ, Murakami M. Illumination uniformity of a capsule directly driven by a laser facility with 32 or 48 directions of irradiation[J]. Physics of Plasmas,2010,17(6):064504-064504.
[15]Temporal M, Canaud B, Le Garrec BJ. Irradiation uniformity and zooming performances for a capsule directly driven by a 32x9 laser beams configuration[J]. Physics of Plasmas (1994-present),2010,17(2):-.
[16]Temporal M, Ramis R, Canaud B, Brandon V, Laffite S, Garrec BJL. Irradiation uniformity of directly driven inertial confinement fusion targets in the context of the shock-ignition scheme[J]. Plasma Physics and Controlled Fusion,2011,53(12):124008.
[17]Temporal M, Canaud B. Stochastic homogenization of the laser intensity to improve the irradiation uniformity of capsules directly driven by thousands laser beams [J]. The European Physical Journal D,2011,65(3):447-451.
[18]Schiavi A, Atzeni S, Marocchino A. Illumination stability for high-repetition-rate laser facilities in direct-drive inertial confinement fusion[J]. EPL,2011,94(3):35002.
[19]Temporal M, Canaud B, Garbett W, Philippe F, Ramis R. Polar direct drive illumination uniformity provided by the Orion facility [J]. The European Physical Journal D,2013,67(10): 1-7.
[20]Ramis R, Temporal M, Canaud B, Brandon V. Symmetry issues in Directly Irradiated Targets[J]. EPJ Web of Conferences,2013,59:02017.
[21]Temporal M, Canaud B, Brandon V. Illumination uniformity of capsules directly driven by a facility with thousands of laser beams[J]. EPJ Web of Conferences,2013,59:02015.
[22]Temporal M, Canaud B, Garbett WJ, Ramis R. Numerical analysis of the direct drive illumination uniformity for the Laser MegaJoule facility[J]. Physics of Plasmas (1994-present),2014,21(1):-.
[23]Mima K, Kato Y, Azechi H, Shigemori K, Takabe H, Miyanaga N, Kanabe T, Norimatsu T, Nishimura H, Shiraga H. Recent progress of implosion experiments with uniformity improved GEKKO XII laser facility at the Institute of Laser Engineering, Osaka University[J]. Physics of Plasmas (1994-present),1996,3(5):2077-2083.
[24]Boehly T, Craxton R, Hinterman T, Kelly J, Kessler T, Kumpan S, Letzring S, McCrory R, Morse S, Seka W. The upgrade to the OMEGA laser system[J]. Review of scientific instruments,1995,66(1):508-510.
[25]Desselberger M, Afshar-Rad T, Khattak F, Viana S, Willi O. Nonuniformity imprint on the ablation surface of laser-irradiated targets[J]. Physical Review Letters,1992,68(10):1539.
[26]Azechi H, Nakai M, Shigemori K, Miyanaga N, Shiraga H, Nishimura H, Honda M, Ishizaki R, Wouchuk JG, Takabe H, Nishihara K, Mima K, Nishiguchi A, Endo T. Direct-drive hydrodynamic instability experiments on the GEKKO XII laser[J]. Physics of Plasmas, 1997,4(11):4079-4089.
[27]Kidder RE. Laser-driven compression of hollow shells:power requirements and stability limitations[J]. Nuclear Fusion,1976,16(1):3.
[1]Murakami M. Irradiation system based on dodecahedron for inertial confinement fusion[J]. Applied Physics Letters,1995,66(13):1587-1589.
[2]谭吉春,魏晓峰.光束路径排布对称性与光功率分布均匀性[J].中国激光,2000,27(1)：28-32.
[3]Jun X, Baida L. Conditions for perfectly uniform irradiation of spherical laser fusion targets[J]. Journal of Optics,1998,29(4):282.
[4]Schmitt AJ. Absolutely uniform illumination of laser fusion pellets[J]. Applied Physics Letters, 1984,44(4):399-401.
[5]Mark JWK. Near spherical illumination of ion-beam and laser targets[J]. Physics Letters A, 1986,114(8-9):458-464.
[6]Murakami M, Sarukura N, Azechi H, Temporal M, Schmitt AJ. Optimization of irradiation configuration in laser fusion utilizing self-organizing electrodynamic system[J]. Physics of Plasmas,2010,17(8):082702-082708.
[7]Rakhmanov E, Saff E, Zhou Y. Minimal discrete energy on the sphere[J]. Math Res Lett, 1994,1(6):647-662.
[8]Altschuler EL, Williams TJ, Ratner ER, Tipton R, Stong R, Dowla F, Wooten F. Possible Global Minimum Lattice Configurations for Thomson's Problem of Charges on a Sphere[J]. Physical Review Letters,1997,78(14):2681-2685.
[9]Levin Y, Arenzon JJ. Why charges go to the surface:A generalized Thomson problem[J]. EPL (Europhysics Letters),2003,63(3):415.
[10]Altschuler EL, Perez-Garrido A. Global minimum for Thomson's problem of charges on a sphere[J]. Physical Review E,2005,71(4):047703.
[11]Xu T, Xu L, Wang A, Gu C, Wang S, Liu J, Wei A. Optimization of beam configuration in laser fusion based on the laser beam pattern[J]. Physics of Plasmas (1994-present), 2013,20(12):122702.
[12]Arfken GGB, Weber HJ. Mathematical Methods for Physicists[M]. Elsevier Academic Press, 2005.
[13]Erber T, Hockney G. Equilibrium configurations of N equal charges on a sphere[J]. Journal of Physics A:Mathematical and General,1991,24(23):L1369.
[14]Morris JR, Deaven DM, Ho KM. Genetic-algorithm energy minimization for point charges on a sphere[J]. Physical Review B,1996,53(4):R1740-R1743.
[15]Munera HA. Properties of discrete electrostatic systems[J].1986.
[16]Altschuler EL, Williams TJ, Ratner ER, Dowla F, Wooten F. Method of constrained global optimization[J]. Physical Review Letters,1994,72(17):2671-2674.
[1]Delsarte P, Goethals JM, Seidel JJ. Spherical codes and designs[J]. Geometriae Dedicata, 1977,6(3):363-388.
[2]Bannai E. Spherical t-designs which are orbits of finite groups[J].1984:341-354.
[3]Bajnok B. Construction of spherical t-designs[J]. Geometriae Dedicata,1992,43(2):167-179.
[4]Hardin R, Sloane N. A new approach to the construction of optimal designs[J]. Journal of statistical planning and inference,1993,37(3):339-369.
[5]Hardin RH, Sloane NJA. McLaren's improved snub cube and other new spherical designs in three dimensions[J]. Discrete & Computational Geometry,1996,15(4):429-441.
[6]Seidel J. Definitions for spherical designs[J]. Journal of statistical planning and inference, 2001,95(1):307-313.
[7]Bannai E, Bannai E. A survey on spherical designs and algebraic combinatorics on spheres[J]. European Journal of Combinatorics,2009,30(6):1392-1425.
[8]Grabner PJ, Tichy RF. Spherical designs, discrepancy and numerical integration[J]. mathematics of computation,1993,60(201):327-336.
[9]Murakami M. Irradiation system based on dodecahedron for inertial confinement fusion[J]. Applied Physics Letters,1995,66(13):1587-1589.
[10]Kidder RE. Laser-driven compression of hollow shells:power requirements and stability limitations[J]. Nuclear Fusion,1976,16(1):3.
[11]Murakami M, Sarukura N, Azechi H, Temporal M, Schmitt AJ. Optimization of irradiation configuration in laser fusion utilizing self-organizing electrodynamic system [J]. Physics of Plasmas,2010,17(8):082702-082708.
[12]Xu T, Xu L, Wang A, Gu C, Wang S, Liu J, Wei A. Optimization of beam configuration in laser fusion based on the laser beam pattern[J]. Physics of Plasmas (1994-present), 2013,20(12):122702.
[1]Speck D, Bliss ES, Glaze J, Herris J, Holloway F, Hunt J, Johnson B, Kuizenga DJ, Ozarski R, Patton HG, Rupert P, Suski GJ, Swift C, Thompson C. The Shiva laser-fusion facility[J]. Quantum Electronics, IEEE Journal of,1981,17(9):1599-1619.
[2]Hunt JT, Speck DR. Present And Future Performance Of The Nova Laser System[J]. Optical Engineering,1989,28(4):284461-284461-.
[3]Boehly TR, Brown DL, Craxton RS, Keck RL, Knauer JP, Kelly JH, Kessler TJ, Kumpan SA, Loucks SJ, Letzring SA, Marshall FJ, McCrory RL, Morse SFB, Seka W, Soures JM, Verdon CP. Initial performance results of the OMEGA laser system[J]. Optics Communications, 1997,133(1-6):495-506.
[4]Mima K, Kato Y, Azechi H, Shigemori K, Takabe H, Miyanaga N, Kanabe T, Norimatsu T, Nishimura H, Shiraga H. Recent progress of implosion experiments with uniformity improved GEKKO Ⅻ laser facility at the Institute of Laser Engineering, Osaka University[J]. Physics of Plasmas (1994-present),1996,3(5):2077-2083.
[5]Xiao G, Fan D, Wang S, Lin Z, Gu Y, Zhu J, Zhen Y, Zhu J, Liu F, Chen S, Chen Q, Huang G, Deng X. SG-Ⅱ solid state laser ICF system:proceedings of,1999[C].
[6]Miller GH, Moses EI, Wuest CR. The National Ignition Facility [J]. Optical Engineering, 2004,43(12):2841-2853.
[7]Fleurot N, Cavailler C, Bourgade JL. The Laser M6gajoule (LMJ) Project dedicated to inertial confinement fusion:Development and construction status[J]. Fusion Engineering and Design, 2005,74(1-4):147-154.
[8]Zheng W, Zhang X, Wei X, Jing F, Sui Z, Zheng K, Yuan X, Jiang X, Su J, Zhou H. Status of the SG-Ⅲ solid-state laser facility:proceedings of the Journal of Physics:Conference Series, 2008[C]. IOP Publishing.
[9]Fan TY. Laser beam combining for high-power, high-radiance sources[J]. Selected Topics in Quantum Electronics, IEEE Journal of,2005,11(3):567-577.
[10]Cheng M-Y, Chang Y-C, Galvanauskas A, Mamidipudi P, Changkakoti R, Gatchell P. High-energy and high-peak-power nanosecond pulsegeneration with beam quality control in 200-μm core highly multimode Yb-doped fiberamplifiers[J]. Optics Letters,2005,30(4):358-360.
[11]Richardson D, Nilsson J, Clarkson W. High power fiber lasers:current status and future perspectives [Invited][J]. JOSA B,2010,27(11):B63-B92.
[12]Labaune C, Hulin D, Galvanauskas A, Mourou GA. On the feasibility of a fiber-based inertial fusion laser driver[J]. Optics Communications,2008,281(15-16):4075-4080.
[13]Lu B. Laser Optics-Beam Characterization, Propagation and Transformation, Resonator Technology and Physics (Beijin [M]. Higher Education Press) p390 (in Chinese).2003.
[14]吕百达.激光光学[M].四川大学出版社,1986.
[15]Al-Rashed A-AR, Saleh BEA. Decentered Gaussian beams[J]. Applied optics,1995,34(30): 6819-6825.
[16]Huang Z, Wei X, Li M, Wang J, Lin H, Xu D, Deng Y, Zhang R. Coherent and incoherent combination of Gaussian beams employing lens array distributed on the spherical chamber[J]. Applied optics,2012,51(10):1546-1551.
[17]Song L. Small circle subdivision method for development of global sampling grid[D],1997.