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In laser direct-driven fusion, high power lasers are used to ablate the target shell, compress and heat the fuel with the spherical focusing rocket effect, to approach to the fusion ignition conditions. The shaped nanosecond laser pulses compress and accelerate the DT target symmetrically, and forms a high density plasma hot-spot at stagnation. The hydrodynamic instabilities, especially the Rayleigh-Taylor instability, which happens at the interface of plasmas, may destroy the compressed shells, and thus reduce the temperature and density of the hot-spot. In this paper is analyzed theoretically the hydrodynamic instability growth under the conditions in the 2020 winter experiment of the double-cone ignition scheme proposed by Zhang et al. (
2020 Philos. Trans. A Math. Phys. Eng. Sci. 378 20200015 ). Both analytical model and one-dimensional simulations indicate that the fuel shells are compressed with low adiabat under the current quasi-isentropic waveform. The Rayleigh-Taylor instability remains in safe region with a maximum perturbation amplitude reaching 0.25 of the shell thickness at the most peak grown moment. The growth of the hydrodynamic instabilities can be further reduced by increasing the thickness of the shell, through using high foot pre-pulses and improving the uniformity of the target surface and laser irradiation in the future design.[1] Nuckolls J, Wood L, Thiessen A, Zimmerman G 1972 Nature 239 139
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[2] McCrory R L, Regan S P, Loucks S J, et al. 2005 Nucl. Fusion 45 S283
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[3] Lindl J D, Amendt P, Berger R L, et al. 2004 Phys. Plasmas 11 339
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[4] Tabak M, Hammer J, Glinsky M E, et al. 1994 Phys. Plasmas 1 1626
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[5] Betti R, Hurricane O A 2016 Nat. Phys. 12 435
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[6] Gopalaswamy V, Betti R, Knauer J P, et al. 2019 Nature 565 581
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[7] Azechi H, Mima K, Shiraga S, et al. 2013 Nucl. Fusion 53 104021
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[9] Peterson J L, Clark D S, Masse L P, Suter L J 2014 Phys. Plasmas 21 092710
Google Scholar
[10] Takabe H, Mima K, Montierth L, Morse R L 1985 Phys. Fluids 28 3676
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[11] Betti R, Goncharov V N, McCrory R L, Verdon C P 1998 Phys. Plasmas 5 1446
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[12] 叶文华, 张维岩, 贺贤土 2000 物理学报 49 762
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Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762
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[13] Smalyuk V A, Weber C R, Landen O L, et al. 2020 Plasma Phys. Contr. F. 62 014007
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[14] Marinak M M, Kerbel G D, Gentile N A, Jones O, Munro D, Pollaine S, Dittrich T R, Haan S W 2001 Phys. Plasmas 8 2275
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[15] Smalyuk V A, Casey D T, Clark D S, et al. 2014 Phys. Rev. Lett. 112 185003
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[16] 缪文勇, 袁永腾, 丁永坤, 叶文华, 曹柱荣, 胡昕, 邓博, 吴俊峰, 张文海 2015 强激光与粒子束 27 032016
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Miao W Y, Yuan R T, Ding Y K, Ye W H, Cao Z R, Hu X, Deng B, Wu J F, Zhang W H 2015 High Power Laser and Particle Beams 27 032016
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[17] Wang L F, Wu J F, Ye W H, Dong J Q, Fang Z H, Jia G, Xie Z Y, Huang X G, Fu S Z, Zou S Y, Ding Y K, Zhang W Y, He X T 2020 Phys. Plasmas 27 072703
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Atzeni S, Meyer-Ter-Vehn J (translated by Shen B F) 2008 The Physics of Inertial Fusion (Beijing: Science Press) pp42, 175−176, 193−195, 212−213, 224−227 (in Chinese)
[19] Zhang J, Wang W M, Yang X H, Wu D, Ma Y Y, Jiao J L, Zhang Z, Wu F Y, Yuan X H, Li Y T, Zhu J Q 2020 Philos. Trans. A Math. Phys. Eng. Sci. 378 20200015
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[26] Robey H F, MacGowan B J, Landen O L, et al. 2013 Phys. Plasmas 20 052707
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[27] 穆宝忠, 吴雯靓, 伊圣振, 王新, 蒋励, 朱京涛, 王占山, 方智恒, 王伟, 傅思祖 2013 强激光与粒子束 25 903
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Mu BZ, Wu W L, Yi S Z, Wang X, Jiang L, Zhu J T, Wang Z S, Fang Z H, Wang W, Fu S Z 2013 Power Laser and Particle Beams 25 903
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[30] 吴俊峰, 叶文华, 张维岩, 贺贤土 2003 物理学报 52 1688
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Wu J F, Ye W H, Zhang W Y, He X T 2003 Acta Phys. Sin. 52 1688
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[31] Haan S W 1989 Phys. Rev. A Gen. Phys. 39 5812
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[32] Hu S X, Fiksel G, Goncharov V N, Skupsky S, Meyerhofer D D, Smalyuk V A 2012 Phys. Rev. Lett. 108 195003
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[33] 杨冬, 李志超, 李三伟, 等 2018 中国科学: 物理学 力学 天文学 48 065203
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Yang D, Li Z C, Li S W, et al. 2018 Sci. Sin-Phys. Mech. Astron. 48 065203
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[34] 余诗瀚, 李晓峰, 翁苏明, 赵耀, 马行行, 陈民, 盛政明 2021 强激光与粒子束 33 012006
Google Scholar
Yu S H, Li X F Feng S M, Zhao Y, Ma X X, Chen M, Sheng Z M 2021 Power Laser and Particle Beams 33 012006
Google Scholar
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图 1 理论模型中的双锥靶和近等熵激光波形 (a) 双锥靶示意图; (b) 近等熵激光波形
Figure 1. Double cone targets and quasi-isentropic waveform in the theoretical model: (a) Diagram of the double targets; (b) quasi-isentropic waveform.
图 2 简化理论模型示意图
Figure 2. Sketch of the simplified theoretical model.
图 3 冲击波压缩阶段不同时刻空间密度分布 (a) 1.0 ns时刻空间密度分布; (b) 2.06 ns时刻空间密度分布; (c) 2.5 ns时刻空间密度分布; (d) 2.9 ns时刻空间密度分布
Figure 3. Density profile at different time in shock wave compress stage: (a) Density profile at 1.0 ns; (b) density profile at 2.06 ns; (c) density profile at 2.5 ns; (d) density profile at 2.9 ns.
图 4 壳层飞行轨迹和加速过程壳层厚度 (a) 壳层内外表面飞行轨迹; (b) 加速过程壳层厚度变化
Figure 4. Trajectories of the shell and shell thickness during the acceleration-phase: (a) Trajectories of inside and outside surface of the shell; (b) variation of the shell thickness during the acceleration-phase.
图 5 冬季实验对撞等离子体自发光信号强度变化
Figure 5. Temporal evolution of self-emission signal of colliding plasma.
图 6 壳层外表面最小密度梯度标长Lmin
Figure 6. The minimum density-gradient scale length on the outside surface of the shell.
图 7 壳层外表面最终扰动振幅
Figure 7. Final perturbation amplitudes of the outside surface of the shell.
图 8 不同时刻壳层厚度和外表面扰动振幅的演化
Figure 8. Evolution of the thickness of the shell and perturbation amplitudes of the outside surface in different times.
表 1 实验、理论和一维模拟中对撞等离子体自发光信号时间对比
Table 1. Temporal comparison of self-emission signal of colliding plasma in experiment, theoretical model and 1D simulation.
Time/ns 对撞信号开始时刻 对撞信号结束时刻 总持续时间 实验 1.0 1.8 0.8 理论模型 0.9 1.75 0.85 一维模拟 1.1 1.83 0.73 
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[1] Nuckolls J, Wood L, Thiessen A, Zimmerman G 1972 Nature 239 139
Google Scholar
[2] McCrory R L, Regan S P, Loucks S J, et al. 2005 Nucl. Fusion 45 S283
Google Scholar
[3] Lindl J D, Amendt P, Berger R L, et al. 2004 Phys. Plasmas 11 339
Google Scholar
[4] Tabak M, Hammer J, Glinsky M E, et al. 1994 Phys. Plasmas 1 1626
Google Scholar
[5] Betti R, Hurricane O A 2016 Nat. Phys. 12 435
Google Scholar
[6] Gopalaswamy V, Betti R, Knauer J P, et al. 2019 Nature 565 581
Google Scholar
[7] Azechi H, Mima K, Shiraga S, et al. 2013 Nucl. Fusion 53 104021
Google Scholar
[8] Goncharov V N 1999 Phys. Rev. Lett. 82 2091
Google Scholar
[9] Peterson J L, Clark D S, Masse L P, Suter L J 2014 Phys. Plasmas 21 092710
Google Scholar
[10] Takabe H, Mima K, Montierth L, Morse R L 1985 Phys. Fluids 28 3676
Google Scholar
[11] Betti R, Goncharov V N, McCrory R L, Verdon C P 1998 Phys. Plasmas 5 1446
Google Scholar
[12] 叶文华, 张维岩, 贺贤土 2000 物理学报 49 762
Google Scholar
Ye W H, Zhang W Y, He X T 2000 Acta Phys. Sin. 49 762
Google Scholar
[13] Smalyuk V A, Weber C R, Landen O L, et al. 2020 Plasma Phys. Contr. F. 62 014007
Google Scholar
[14] Marinak M M, Kerbel G D, Gentile N A, Jones O, Munro D, Pollaine S, Dittrich T R, Haan S W 2001 Phys. Plasmas 8 2275
Google Scholar
[15] Smalyuk V A, Casey D T, Clark D S, et al. 2014 Phys. Rev. Lett. 112 185003
Google Scholar
[16] 缪文勇, 袁永腾, 丁永坤, 叶文华, 曹柱荣, 胡昕, 邓博, 吴俊峰, 张文海 2015 强激光与粒子束 27 032016
Google Scholar
Miao W Y, Yuan R T, Ding Y K, Ye W H, Cao Z R, Hu X, Deng B, Wu J F, Zhang W H 2015 High Power Laser and Particle Beams 27 032016
Google Scholar
[17] Wang L F, Wu J F, Ye W H, Dong J Q, Fang Z H, Jia G, Xie Z Y, Huang X G, Fu S Z, Zou S Y, Ding Y K, Zhang W Y, He X T 2020 Phys. Plasmas 27 072703
Google Scholar
[18] 阿蔡塞等著 (沈百飞译) 2008 惯性聚变物理 (北京: 科学出版社) 第42, 175−176, 193−195, 212−213, 224−227页
Atzeni S, Meyer-Ter-Vehn J (translated by Shen B F) 2008 The Physics of Inertial Fusion (Beijing: Science Press) pp42, 175−176, 193−195, 212−213, 224−227 (in Chinese)
[19] Zhang J, Wang W M, Yang X H, Wu D, Ma Y Y, Jiao J L, Zhang Z, Wu F Y, Yuan X H, Li Y T, Zhu J Q 2020 Philos. Trans. A Math. Phys. Eng. Sci. 378 20200015
Google Scholar
[20] Azechi H, Sakaiya T, Watari T, et al. 2009 Phys. Rev. Lett. 102 235002
Google Scholar
[21] Ramis R, Meyer-ter-Vehn J 2016 Comput. Phys. Commun. 203 226
Google Scholar
[22] Betti R, Chang P Y, Spears B K, Anderson K S, Edwards J, Fatenejad M, Lindl J D, McCrory R L, Nora R, Shvarts D 2010 Phys. Plasmas 17 058102
Google Scholar
[23] Mora P 1982 Phys. Fluids 25 1051
Google Scholar
[24] Caruso A, Gratton R 1968 Plasma Phys. 10 867
Google Scholar
[25] Miller J E, Boehly T R, Melchior A, et al. 2007 Rev. Sci. Instrum. 78 034903
Google Scholar
[26] Robey H F, MacGowan B J, Landen O L, et al. 2013 Phys. Plasmas 20 052707
Google Scholar
[27] 穆宝忠, 吴雯靓, 伊圣振, 王新, 蒋励, 朱京涛, 王占山, 方智恒, 王伟, 傅思祖 2013 强激光与粒子束 25 903
Google Scholar
Mu BZ, Wu W L, Yi S Z, Wang X, Jiang L, Zhu J T, Wang Z S, Fang Z H, Wang W, Fu S Z 2013 Power Laser and Particle Beams 25 903
Google Scholar
[28] Marshall F J, Oertel J A 1997 Rev. Sci. Instrum. 68 735
Google Scholar
[29] Craxton R S, Anderson K S, Boehly T R, et al. 2015 Phys. Plasmas 22 110501
Google Scholar
[30] 吴俊峰, 叶文华, 张维岩, 贺贤土 2003 物理学报 52 1688
Google Scholar
Wu J F, Ye W H, Zhang W Y, He X T 2003 Acta Phys. Sin. 52 1688
Google Scholar
[31] Haan S W 1989 Phys. Rev. A Gen. Phys. 39 5812
Google Scholar
[32] Hu S X, Fiksel G, Goncharov V N, Skupsky S, Meyerhofer D D, Smalyuk V A 2012 Phys. Rev. Lett. 108 195003
Google Scholar
[33] 杨冬, 李志超, 李三伟, 等 2018 中国科学: 物理学 力学 天文学 48 065203
Google Scholar
Yang D, Li Z C, Li S W, et al. 2018 Sci. Sin-Phys. Mech. Astron. 48 065203
Google Scholar
[34] 余诗瀚, 李晓峰, 翁苏明, 赵耀, 马行行, 陈民, 盛政明 2021 强激光与粒子束 33 012006
Google Scholar
Yu S H, Li X F Feng S M, Zhao Y, Ma X X, Chen M, Sheng Z M 2021 Power Laser and Particle Beams 33 012006
Google Scholar
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