诱导空间非相干和消衍射透镜阵列联用方式束匀滑方案的腔壁辐照特性分析及优化 
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In the indirectly driven inertial confinement fusion facility, the high X-ray irradiation uniformity on the target pellet is the key to the success of the implosion. The uniformity of X-ray irradiation on the target pellet is primarily determined using the uniformity of laser irradiation on the hohlraum wall in the initial stage of laser irradiation on the hohlraum wall; the uniformity of irradiation on the hohlraum wall is determined using the symmetry of the distribution of laser spots on the hohlraum wall and the uniformity of the intensity of a single laser spot on the hohlraum, Therefore, it is necessary to analyze the irradiation uniformity of the laser quads on the hohlraum wall. Many researchers are currently studying the irradiation characteristics of the laser beam on the hohlraum wall, but the majority of them are discussing the beam smoothing scheme of the SSD, CPP, and PCP combination. Recently, the Shanghai Laser Plasma Research Institute proposed a broadband laser beam smoothing scheme based on induced spatial incoherence (ISI) and de-diffraction lens array (DLA). However, no research has been conducted on the irradiation characteristics of the laser beam on the hohlraum wall using this smoothing scheme. Therefore, this study analyzes and optimizes the irradiation characteristics of broadband laser quads on the hohlraum wall using DLA combined with ISI.
Aiming at laser quads configuration and cylindrical hohlraum structure in inertial confinement fusion (ICF) facility, the propagation model for the laser quads in the hohlraum based on broadband laser beam smoothed by ISI and de-DLA has been built up. The parameters of the broadband laser beam smoothing scheme have been optimized in this study via analyzing the influence of the focal length of the principal lens and DLA parameters on the irradiation characteristics on the hohlraum wall.
In the broadband laser beam smoothing scheme based on the combination of ISI and DLA, the mismatch between the focal length of the primary lens and the parameters of the hohlraum will deform the intensity envelope of laser spots on the hohlraum wall (Fig.4), resulting in laser spot overlap and irradiation nonuniformity (Fig.6). Increasing the focal length of the principal lens can effectively suppress the envelope distortion of laser spots on the hohlraum wall (Fig.7), thereby reducing the overlap of the laser spots and improving the irradiation uniformity on the hohlraum wall (Fig.12). Furthermore, by appropriately adjusting the number of DLA sub-lens and the long and short axes ratio of the sub-lens, the duty ratio of laser spots on the hohlraum wall increases, and irradiation uniformity of the laser quads on the hohlraum wall improves (Fig.14 and Table 2).
The propagation model for the laser quads in the hohlraum based on broadband laser beam smoothed using ISI and de-DLA has been built in this study, aiming at the optical path arrangement scheme and cylindrical target hohlraum structure of the NIF, and then the irradiation characteristics of the laser quads on the hohlraum wall have been analyzed and optimized. The results show that the mismatch between the focal length of the primary lens and parameters of the cylindrical target hohlraum will cause varying degrees of damage to the envelope of the laser spots on the hohlraum wall for beams with different incident angles, as a result of the laser spots overlapping on the hohlraum wall, the irradiation uniformity on the hohlraum wall greatly diminishes. The effect of the principal lens focal length, the number of DLA sub-lens, and the long and short axes ratio of the sub-lens on the intensity distribution of the laser quads on the hohlraum wall are discussed on this basis. The optimization of these parameters, such as the principal lens focal length, number of DLA sub-lens, the long and short axes ratio of the sub-lens, and incident angle of the laser quads, achieves the improvement of the irradiation uniformity on the hohlraum wall. The results show that increasing the focal length of the primary lens appropriately can effectively retain the envelope of the laser spots on the hohlraum wall for beams with different incident angles, minimizing the overlap of the laser spots on the hohlraum wall. Besides, the duty ratio of laser spots on the hohlraum wall increases, and the time required for beam smoothing reduces when the number of DLA sub-lens and the long and short axes ratio of the sub-lens are optimized. Furthermore, after optimizing the incident angle of the inner cone laser quads, the overlap of the inner and outer cones laser quads on the hohlraum wall is eliminated.
1 引言
在间接驱动的惯性约束聚变装置中，靶丸均匀压缩对激光束在靶腔内壁的初始辐照均匀性提出了极高要求。一方面，激光光斑的局部非均匀性会加剧激光等离子体不稳定性(LPI)，在降低X射线转换效率的同时产生超热电子[1]；另一方面，腔壁上激光辐照的不均匀性会导致X射线的不均匀性，从而破坏靶丸压缩过程的对称性，进而导致点火失败。为了提高靶面(靶丸或靶腔壁)的辐照均匀性，人们已经发展了多种束匀滑技术，包括时域束匀滑技术、空域束匀滑技术及偏振匀滑技术(PS)[2]。基于宽带光源的束匀滑技术对LPI的抑制效果较好[3]，这类技术包括1983年Lehmberg等[4]提出的诱导空间非相干(ISI)匀滑技术，1991年日本Matsushima等[5-6]提出的宽带光角色散匀滑技术，1993年法国Veron等[7]提出的基于宽带光和多模光纤的匀滑技术，1993年日本Nakano等[8]提出的采用单模光纤降低时间相干性、采用多模光纤降低空间相干性的匀滑技术。2019年，上海激光等离子体研究所研制出了可以实现3.1 THz带宽的宽带二倍频激光装置“昆吾”[9-10]。2020年，美国罗切斯特大学激光能量实验室提出了建造具有10 THz带宽FLUX激光驱动器的计划[11-12]。由上海激光等离子体研究所提出的消衍射透镜阵列(DLA)联合ISI的匀滑方案[13]采用宽带光源进行辐照，通过设置透镜阵列中子透镜的厚度差，使透镜阵列(LA)各透射子光束的延时之差均超过了相干时间，实现了透射子光束在靶面上的非相干叠加；同时，该方案利用具有缓变透过率的消衍射透镜阵列抑制子透镜硬边衍射引起的靶面光强分布不均匀，极大地改善了靶面光强的均匀性。
在间接驱动惯性约束聚变装置中，靶丸的高均匀度X光辐照是内爆成功的关键。在激光辐照腔壁初期，靶丸的X光辐照均匀性主要由腔壁的激光辐照均匀性决定，而腔壁的辐照均匀性则由腔壁上单个光斑的光强均匀性和所有光斑的分布均匀性决定[14]。因此，分析腔壁的辐照均匀性是十分必要的。目前，已有许多学者对激光束的腔壁辐照特性进行了研究，但大多是针对光谱角色散(SSD)、连续相位板(CPP)、偏振控制板(PCP)联用的束匀滑方案进行讨论[15-16]，尚缺乏针对基于DLA联合ISI的宽带激光腔壁辐照特性的相关研究。本文通过建立基于ISI和DLA联用的宽带激光靶腔内光传输模型，分析了主焦距透镜和DLA参数对腔壁辐照特性的影响规律，进而对ISI和DLA进行了参数优化。
2 理论模型
图 1. 基于ISI与DLA联用的匀滑方案的靶腔内激光传输示意图
Fig. 1. Schematic illustration of laser beam smoothed by ISI and DLA in a cylindrical hohlraum
以美国国家点火(NIF)装置为例，其双端共注入192路激光束，采用2×2集束方式，共48个集束，平均分配在柱形腔两侧。
对于集束中的单激光束，其入射到DLA上的光场分布可以表示为
激光通过消衍射阵列透镜后的第(m, n)个子光束可以表示为
经推导，腔壁坐标系与入射光束所在坐标系之间的关系为
通过DLA后的第(m, n)个子光束经注入孔传输到柱形腔腔壁这一过程可用Collins公式描述，即：
单集束的焦面光斑尺寸可表示为[18]
3 数值模拟和分析
3.1 腔壁辐照特性分析
根据所建立的基于ISI与DLA联用的宽带激光束匀滑方案的靶腔内光传输模型，本课题组对不同角度入射集束在腔壁上的光强分布进行了数值模拟。计算所采用的参数如下[13]：主透镜直径D＝0.38 m，焦距f＝1.575 m；消衍射阵列透镜由7×7子透镜单元组成，总口径D1＝350 mm，子透镜长轴为d1＝50 mm, 短轴为d2＝35 mm，长短轴之比为10∶7，子透镜焦距fDLA＝78.75 m。由(9)式可知焦斑大小为1 mm×0.7 mm。DLA子透镜的等效软边光阑参数为：
以不同角度入射的集束首先会经柱形腔注入孔，然后在腔内传输一段距离到达腔壁，因此有必要分析集束在注入孔处的光强分布。
图 3. 不同入射角度集束在注入孔处的光强分布。(a)23.5°；(b)30°；(c)44.5°；(d)50°
Fig. 3. Intensity distributions of laser quad at laser entrance hole (LEH) with different incident angles. (a) 23.5°；(b) 30°；(c) 44.5°；(d) 50°
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图 4. 不同入射角度集束在腔壁上的光强分布。(a)～(d)ISI＋DLA方案；(e)～(h)CPP＋SSD方案
Fig. 4. Intensity distributions of laser quad on hohlraum wall with different incident angles. (a)(d) ISI＋DLA scheme；(e)(h) CPP＋SSD scheme
表 1. 腔壁光斑的能量利用率
Table 1. Energy efficiency of hohlraum wall spot
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图 5. DLA各子光束在离焦面上的一维光强分布(Δ＝3mm)
Fig. 5. One-dimensional intensity distribution of each transmitted sub-beam of DLA on the target plane when Δ＝3 mm
在分析了单集束在腔壁上的光强分布后，本课题组进一步计算了所有集束在靶腔壁上的光场分布，以便对腔壁辐照特性进行分析。
本课题组进一步研究了ISI＋DLA宽带激光束匀滑方案的关键参数(主透镜焦距和DLA参数)对腔壁辐照特性的影响，并对ISI＋DLA宽带激光束匀滑方案的关键参数进行设计和优化，以改善腔壁辐照均匀性。
3.2 ISI＋DLA宽带激光束匀滑方案关键参数的设计及优化
23.5°入射的集束腔壁光斑变形最严重，且与44.5°集束腔壁光斑之间的交叉重叠较明显，因此以内环23.5°入射单集束为例，讨论主透镜焦距以及DLA子透镜数目、子透镜长短轴之比对腔壁光斑光强分布的影响。
3.2.2 主透镜焦距
根据(9)式，在改变主透镜焦距时，需要同比例改变子透镜的焦距，以保证注入孔处的光斑尺寸基本不变。
图 7. 不同主透镜焦距下集束的腔壁光强分布。(a)f＝1.575 m；(b)f＝4 m；(c)f＝7.7 m
Fig. 7. Intensity distributions of laser quad on the hohlraum wall with different focal lengths of principal lens. (a) f＝1.575 m; (b) f＝4 m; (c) f＝7.7 m
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采用FOPAI[24]和PSD[25]对腔壁光斑的辐照特性进行定量分析，其中，FOPAI为超过阈值强度的峰值热斑与焦斑总功率的比值，PSD表示焦斑的功率谱密度。
图 8. 不同主透镜焦距下腔壁光斑的FOPAI曲线和PSD曲线。(a)FOPAI曲线；(b)PSD曲线
Fig. 8. FOPAI and PSD curves of laser spots on hohlraum wall with different focal lengths of principal lens. (a) FOPAI curves; (b) PSD curves
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3.2.3 DLA子透镜数目和子透镜长短轴之比
由3.2.1可知，当主透镜焦距增大到4 m时，腔壁光斑包络得到明显改善。接下来在主透镜焦距为4 m的基础上，进一步讨论子透镜数目和子透镜长短轴之比等DLA参数对集束腔壁光强分布的影响。需要说明的是，由(9)式可知，当改变子透镜数目即改变子透镜口径时，子透镜焦距也需同比例改变，以保证注入孔处光斑尺寸基本不变。
图 9. 不同子透镜数目下集束的腔壁光强分布。(a)6×6；(b)5×5；(c)4×4；(d)3×3
Fig. 9. Intensity distributions of laser quads on hohlraum wall with different sub-lens numbers. (a) 6×6; (b) 5×5; (c) 4×4; (d) 3×3
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图 10. 不同子透镜数目下腔壁光斑的FOPAI曲线和PSD曲线。(a)FOPAI曲线；(b)PSD曲线
Fig. 10. FOPAI and PSD curves of laser spots on hohlraum wall with different sub-lens numbers. (a) FOPAI curves; (b) PSD curves
从
由(9)式可知，调整子透镜长短轴之比，可以改变光斑在y方向(即柱形腔圆周方向)的尺寸。
图 11. 不同子透镜长短轴比例下集束的腔壁光强分布。
Fig. 11. Intensity distribution of laser quad on hohlraum wall with different sub-lens long and short axes ratios
从
综上所述，ISI＋DLA宽带激光束匀滑方案关键参数的设计和优化结果如下：当主透镜焦距为4 m时，集束腔壁光斑包络保持得较好并具有较好的均匀性；对于腔壁光斑变形最严重的23.5°入射的集束，DLA子镜数目为5×5时(即子透镜长轴d1＝70 mm，短轴d2＝49 mm时)，可在保持腔壁光斑均匀性的前提下，有效减少宽带激光束匀滑所需的时间。值得指出的是，DLA子透镜长短轴之比可以根据不同入射角度集束在腔壁上的辐照情况进行合理选择，以便控制腔壁光斑的长短轴尺寸，进一步改善腔壁辐照的均匀性。
3.3 腔壁辐照特性优化
基于3.2节所述ISI＋DLA宽带激光束匀滑方案关键参数的优化方法及结果，本课题组进一步对所有集束在腔壁上的辐照特性进行了数值模拟。
图 12. 主透镜焦距和DLA子透镜数目优化后的腔壁环带光场分布
Fig. 12. Laser field distribution of laser quads on hohlraum wall after adjustment of the number of DLA sub-lens and the focal length of principal lens
与
图 13. 内环集束入射角度优化后的腔壁环带光场分布
Fig. 13. Laser field distribution of inner laser quad on hohlraum wall after adjusting incident angle of inner laser quads
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图 14. 外环集束子透镜长短轴比例优化后的腔壁环带光场分布
Fig. 14. Laser field distribution of outer laser quad on hohlraum wall after optimizing sub-lens long and short axes ratio of outer laser quads
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表 2. 腔壁光斑的占空比和光通量对比度
Table 2. Duty ratio and contrast of laser spots on hohlraum wall
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4 结论
针对NIF装置的光路排布方案和柱形靶腔结构，建立了基于ISI与DLA联用的宽带激光束匀滑方案的靶腔内光传输模型，进而对腔壁辐照特性进行分析和优化。结果表明，主透镜焦距与柱形靶腔参数的不匹配会对不同入射角度集束在腔壁处的光斑包络造成不同程度的破坏，从而导致腔壁光斑交叉重叠，严重破坏腔壁辐照的均匀性。在此基础上，讨论了主透镜焦距以及DLA子透镜数目、子透镜长短轴之比等参数对集束腔壁光强分布的影响，并通过对主透镜焦距以及DLA子透镜数目、子透镜长短轴之比、集束的入射角度等参数进行优化，实现了腔壁辐照均匀性的改善。研究结果表明，适当增大主透镜焦距，可以有效保持不同入射角度集束在腔壁处光斑的包络，从而减轻腔壁光斑的交叉重叠。合理选取DLA的子透镜数目和子透镜长短轴比例，可在保持腔壁光斑均匀性的前提下，有效减少束匀滑所需的时间和提高腔壁光斑的占空比。此外，适当调节内环集束的入射角度，可避免内环与外环集束在腔壁上的交叉重叠。
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Article Outline
张鑫, 熊皓, 钟哲强, 张彬. 诱导空间非相干和消衍射透镜阵列联用方式束匀滑方案的腔壁辐照特性分析及优化[J]. 中国激光, 2022, 49(4): 0405002. Xin Zhang, Hao Xiong, Zheqiang Zhong, Bin Zhang. Analysis and Optimization of Irradiation Characteristics of Laser Quads on Hohlraum Wall Based on Broadband Laser Beams Smoothed Using Induced Spatial Incoherence and De-Diffraction Lens Array[J]. Chinese Journal of Lasers, 2022, 49(4): 0405002.
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