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Interaction of high-power laser with planar target is studied by using radiation-hydrodynamics simulation. When the laser interacts with the tungsten planar target, the laser energy deposition is uneven due to thermal filamentation instability and other reasons, and density fluctuations will appear in the front of the plasma, resulting in obvious plasma filamentation in the later stage. The researches of four materials, i.e. aluminum, copper, tungsten and gold, show that in the high-Z material tungsten and gold, due to the strong radiative cooling effect, the filamentation phenomena of the density distribution, electron temperature distribution and pressure distribution obviously occur. The order of magnitude of filamentous plasma density is different from that of the surrounding plasma. The filamentation phenomenon is closely related to the non-uniform energy deposition of the laser and the radiative cooling effect, although the ray beam will cause inhomogeneity of the laser irradiation to a certain extent, this is not the main reason for the filamentation phenomenon observed in this paper. Owing to refraction, reflection and the thermal filamentation instability when the laser is transmitted in the ablation plasma, the laser energy is deposited unevenly, which generates instability seeds in the early stage of plasma formation. The radiative cooling effect then amplifies this instability seeds, creating a radiative cooling instability that eventually results in a filamentous distribution of physical quantities such as plasma density, temperature, and pressure. This filamentation phenomenon destroys the uniformity of the plasma to a certain extent, and lays the seeds for the growth of fluid instability, which will seriously affect fusion-related research. It is shown that radiative cooling is crucial to the filamentation phenomenon, which causes uneven distribution of the plasma pressure during the evolution of the plasma, thereby affecting its transverse motion and enhancing the density fluctuation. After the laser irradiation ends, the density fluctuation gradually develops into filamentations. We also find that the clear filamentation occurs only for high-Z materials like tungsten and gold, but not for the moderate-Z materials like aluminum and copper. This can be attributed to the fact that radiative cooling is stronger for the high-Z materials. Studying the filamentation effect in laser-irradiated planar targets can contribute to understanding the instability in laser plasma, and then suppressing this instability and improving the gain of fusion. The results here can thus be of reference significance to the research of laser fusion, laboratory astrophysics, and other applications of intense-laserdriving.
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Keywords:
- high power laser /
- plasma /
- radiative cooling /
- filamentation
[1] Basov N G, Krokhin O N 1964 J. Exp. Theor. Phys. 19 123
[2] 王淦昌 1987 中国激光 14 641
Google Scholar
Wang G C 1987 Chinese Laser 14 641
Google Scholar
[3] Nuckolls J, Wood L, Thiessen A, Zimmerman G 1972 Nature 239 139
Google Scholar
[4] Zhang G, Huang M, Bonasera A, Ma Y G, Shen B F, Wang H W, Wang W P, Xu J C, Fan G T, Fu H J, Xue H, Zheng H, Liu L X, Zhang S, Li W J, Cao X G, Deng X G, Li X Y, Liu Y C, Yu Y, Zhang Y, Fu C B, Zhang X P 2019 Phys. Lett. A 383 2285
Google Scholar
[5] Zhao J R, Zhang X P, Yuan D W, Li Y T, Li D Z, Rhee Y J, Zhang Z, Li F, Zhu B J, Li Yan F, Han B, Liu C, Ma Y, Li Yi F, Tao M Z, Li M H, Guo X, Huang X G, Fu S Z, Zhu J Q, Zhao G, Chen L M, Fu C B, Zhang J A 2016 Sci. Rep. 6 27363
Google Scholar
[6] Qi W, Zhang X H, Zhang B, He S K, Zhang F, Cui B, Yu M H, Dai Z H, Peng X Y, Gu Y Q 2019 Phys. Plasmas 26 043103
Google Scholar
[7] Kasperczuk A, Pisarczyk T, Borodziuk S, Ullschmied J, Krousky E, Masek K, Rohlena K, Skala J, Hora H 2006 Phys. Plasmas 13 062704
Google Scholar
[8] 郑无敌, 张国平 2008 计算物理 25 36
Google Scholar
Zheng W D, Zhang G P 2008 Computational Physics 25 36
Google Scholar
[9] Gao L, Nilson P M, Igumenshchev I V, Haines M G, Froula D H, Betti R, Meyerhofer D D 2015 Phys. Rev. Lett. 114 215003
Google Scholar
[10] Gao L, Nilson P M, Igumenshchev I V, Hu S X, Davies J R, Stoeckl C, Haines M G, Froula D H, Betti R, Meyerhofer D D 2012 Phys. Rev. Lett. 109 115001
Google Scholar
[11] Giulietti A, Coe S, Afshar-rad T, Desselberger M, Willi O, Danson C, Giulietti D 1991 Laser Interaction and Related Plasma Phenomena 155 261
[12] Watkins H C, Kingham R J 2018 Phys. Plasmas 25 092701
Google Scholar
[13] Afsharrad T, Coe S E, Willi O, Desselberger M 1992 Phys. Plasmas 4 051301
[14] 张家泰, 刘松芬, 胡北来 2003 52 1668
Google Scholar
Zhang J T, Liu S F, Hu B L 2003 Acta Phys. Sin. 52 1668
Google Scholar
[15] 李玉同, 张杰陈, 陈黎明, 赵理曾, 夏江帆, 滕浩, 李英俊, 朱成银, 江文勉 2001 50 204
Google Scholar
Li Y T, Zhang J, Chen L M, Zhao L Z, Xia J F, Teng H, Li Y J, Zhu C Y, Jiang W M 2001 Acta Phys. Sin. 50 204
Google Scholar
[16] Bret A, Firpo M C, Deutsch C 2005 Phys. Rev. Lett. 94 115002
Google Scholar
[17] Séguin F H, Li C K, Manuel M J E, Rinderknecht H G, Sinenian N, Frenie J A, Rygg J R, Hicks D G, Petrasso R D, Delettrez J, Betti R, Marshall F J, Smalyuk V A 2012 Phys. Plasmas 19 012701
Google Scholar
[18] Fox W, Fiksel G, Bhattacharjee A, Chang P Y, Germaschewski K, Hu S X, Nilson P M 2013 Phys. Rev. Lett. 111 225002
Google Scholar
[19] Manuel M J E, Khiar B, Rigon G, Albertazzi B, Klein S R, Kroll F, Brack F E, Michel T, Mabey P, Pikuz S, Williams J C, Koenig M, Casner A, Kuranz C C 2021 Matter Radiat. Extremes 6 026904
[20] Willi O, Rumsby P T, Hooker C, Raven A, Lin Z Q 1982 Opt. Commun. 41 110
Google Scholar
[21] Willi O, Rumsby P T, Sartang S 1981 IEEE J. Quantum Electron. 17 1909
Google Scholar
[22] Willi O, Afshar-rad T, Desselberger M, Dunne M, Edwards J, Gizzi L, Khattak F, Riley D, Taylor R, Viana S 1992 Laser Interaction and Related Plasma Phenomena 142 517
[23] Afshar-Rad T, Gizzi L A, Desselberger M, Khattak F, Willi O, Giulietti A 1992 Phys. Rev. Lett. 68 942
Google Scholar
[24] Desselberger M, Gizzi L, Barrow V, Edwards J, Khattak F, Viana S, Willi O, Danson C N 1992 Appl. Opt. 31 3759
Google Scholar
[25] Desselberger M, Afshar-rad T, Khattak F, Viana S, Willi O 1992 Phys. Rev. Lett. 68 1539
Google Scholar
[26] Lu Y, Tzeferacos P, Liang E, Follett R K, Gao L, Birkel A, Froula D H, Fu W, Ji H, Lamb D, Li C K, Sio H, Petrasso R, Wei M S 2019 Phys. Plasmas 26 022902
Google Scholar
[27] Flash Center for Computational Science, University of Chicago. http://flash.uchicago.edu [2019-03-29]
[28] More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 103059
[29] Eidmann K 1994 Laser Part. Beams 12 223
Google Scholar
[30] 田超, 单连强, 周维民, 高喆, 谷渝秋, 张保汉 2014 63 125205
Google Scholar
Tian C, Shan L Q, Zhou W M, Gao Z, Gu Y Q, Zhang B H 2014 Acta Phys. Sin. 63 125205
Google Scholar
[31] Lin Y, Kessler T J 1996 Opt. Lett. 21 1703
Google Scholar
[32] Skupsky S, Short R W, Kessler T, Craxton R S, Letzring S, Soures J M 1989 J. Appl. Phys. 66 3456
Google Scholar
[33] Lefebvre E, Berger R L, Langdon A B, MacGowan B J, Rothenberg J E, Williams E A 1998 Phys. Plasmas 5 2701
Google Scholar
[34] Lal A K, Marsh K A, Clayton C E, Joshi C, McKinstrie C J, Li J S, Johnston T W 1997 Phys. Rev. Lett. 78 670
Google Scholar
[35] Dhareshwar L J, Naik P A, Sarkar S, Khan M, Chakraborty B 1992 Phys. Fluids B 4 1635
Google Scholar
[36] Nicolaï P, Tikhonchuk V T, Kasperczuk A, Pisarczyk T, Borodziuk S, Rohlena K, Ullschmied J 2006 Phys. Plasmas 13 062701
Google Scholar
[37] 青波 2017 中国工程物理研究院科技年报 29
Qing B 2017 Annual Report of Science and Technology of China Academy of Engineering Physics 29 (in Chinese)
[38] Nicolaï P, Tikhonchuk V T, Kasperczuk A, Pisarczyk T, Borodzziuk S, Rohlena K, Ullschmied J 2007 Astrophys. Space Sci. 307 87
Google Scholar
[39] 阿蔡塞 S 著 (沈百飞 译) 2008 惯性聚变物理 (北京: 科学出版社) 第300页
Atzeni S (translated by Shen B F) 2004 The Physics of Inertial Fusion (Beijing: Science Press) p300 (in Chinese)
[40] Evans R G 1981 J. Phys. D: Appl. Phys. 14 173
Google Scholar
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图 1 激光打靶模型. 其中黄色区域为钨靶, 蓝色区域为氦气, 蓝色中间区域为射线束描述的激光功率分布, 激光由下往上入射到钨靶
Figure 1. Schematics of the laser-target interaction. The yellow region is the tungsten target, the blue region is the background helium, and the middle region is the distribution of laser power. The laser is incident on the tungsten target from bottom to top.
图 2 L2激光辐照钨靶的能量沉积及密度分布 t = 4 ns (a), t = 5 ns (b) 时密度背景上的能量沉积, 红色表示射线束的能量沉积; (c) t = 7 ns, (d) t = 8 ns时二维密度分布; (e) t = 7 ns , (f) t = 8 ns时Z = 500 μm处密度线分布
Figure 2. Energy deposition and density distributions of L2 laser irradiating the tungsten target: Energy deposition on the density background at t = 4 ns (a) and 5 ns (b), the red color for the energy deposition of the ray beam; 2D density distribution at t = 7 ns (c) and 8 ns (d); the profile of density at Z = 500 μm along R direction at t = 7 ns (e) and 8 ns (f).
图 3 L2激光辐照钨靶的电子温度分布 t = 7 ns (a)和t = 8 ns (b) 时二维电子温度分布; t = 7 ns (c) 和t = 8 ns (d) 时 Z = 500 μm处电子温度线分布
Figure 3. Electron temperature distribution for L2 laser irradiating the tungsten target: 2D electron temperature distribution at t = 7 ns (a) and 8 ns (b); (c), (d) profile of electron temperature at Z = 500 μm along the R direction at t = 7 ns (c) and 8 ns (d).
图 4 L2激光辐照钨靶的压强分布 5 ns (a), 7 ns (c)和8 ns (e)时二维压强分布; 5 ns (b), 7 ns (d)和8 ns (f) 时Z = 500 μm处的压强线分布
Figure 4. Pressure distribution of L2 laser irradiating the tungsten target: 2D pressure distribution at t = 5 ns (a), t = 7 ns (c) and t = 8 ns (e); the profile of pressure at Z = 500 μm along R direction at t = 5 ns (b), t = 7 ns (d) and t = 8 ns (f)
图 5 无辐射下L2激光辐照钨靶的模拟 (a) 4 ns时的密度分布和能量沉积, 红色表示射线束的能量沉积; (b) 7 ns时二维密度分布; (c) 7 ns时Z = 500 μm处密度线分布
Figure 5. Simulation of L2 laser irradiating the tungsten target without radiation: (a) Energy deposition at 4 ns, the red for the energy deposition of the ray beam; (b) 2D density distribution at 7 ns; (c) the density profile along the R direction at Z = 500 μm and t = 7 ns.
图 6 L2激光辐照钨靶的辐射温度分布 4 ns (a)和5 ns (b)时二维辐射温度分布; 4 ns (c)和5 ns (d)时 Z = 700 μm处辐射温度线分布
Figure 6. Radiation temperature distribution of L2 laser irradiating the tungsten target: 2D radiation temperature distribution at t = 4 ns (a) and t = 5 ns (b); the profile of radiation temperature at Z = 700 μm along R direction at t = 4 ns (c) and 5 ns (d).
图 7 t = 3 ns有无辐射时L2激光辐照钨靶的等离子体速度分布
Figure 7. Plasma velocity distribution at t = 3 ns of L2 laser irradiating the tungsten target with and without radiation.
图 8 在不同物质中由对数密度表示成丝现象的强弱
Figure 8. Logarithmic density versus atomic number, showing the strength of filamentation for different materials.
表 1 激光参数
Table 1. Laser parameters.
$ 激光简称 $ ${\text{L}}1$ ${\text{L2}}$ ${\text{L3}}$ $ 能量E/\text{kJ} $ $1.5$ $1.5$ $1.5$ $ 时间t/\text{ns} $ $[0, 0.1, 5, 5.1]$ $[0, 0.1, 5, 5.1]$ $[0, 0.1, 5, 5.1]$ $ 功率P/\text{GW} $ $[0, 300, 300, 0]$ $[0, 300, 300, 0]$ $[0, 300, 300, 0]$ $ 焦斑半径r/\text{μm} $ $200$ $300$ $400$ $光强I/(\text{W}\cdot{\text{cm} }^{-2})$ $2.387 \times {10^{14}}$ $1.061 \times {10^{14}}$ $5.968 \times {10^{13}}$ $ 波长\lambda /\text{μm} $ $1.053$ $1.053$ $1.053$ 
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[1] Basov N G, Krokhin O N 1964 J. Exp. Theor. Phys. 19 123
[2] 王淦昌 1987 中国激光 14 641
Google Scholar
Wang G C 1987 Chinese Laser 14 641
Google Scholar
[3] Nuckolls J, Wood L, Thiessen A, Zimmerman G 1972 Nature 239 139
Google Scholar
[4] Zhang G, Huang M, Bonasera A, Ma Y G, Shen B F, Wang H W, Wang W P, Xu J C, Fan G T, Fu H J, Xue H, Zheng H, Liu L X, Zhang S, Li W J, Cao X G, Deng X G, Li X Y, Liu Y C, Yu Y, Zhang Y, Fu C B, Zhang X P 2019 Phys. Lett. A 383 2285
Google Scholar
[5] Zhao J R, Zhang X P, Yuan D W, Li Y T, Li D Z, Rhee Y J, Zhang Z, Li F, Zhu B J, Li Yan F, Han B, Liu C, Ma Y, Li Yi F, Tao M Z, Li M H, Guo X, Huang X G, Fu S Z, Zhu J Q, Zhao G, Chen L M, Fu C B, Zhang J A 2016 Sci. Rep. 6 27363
Google Scholar
[6] Qi W, Zhang X H, Zhang B, He S K, Zhang F, Cui B, Yu M H, Dai Z H, Peng X Y, Gu Y Q 2019 Phys. Plasmas 26 043103
Google Scholar
[7] Kasperczuk A, Pisarczyk T, Borodziuk S, Ullschmied J, Krousky E, Masek K, Rohlena K, Skala J, Hora H 2006 Phys. Plasmas 13 062704
Google Scholar
[8] 郑无敌, 张国平 2008 计算物理 25 36
Google Scholar
Zheng W D, Zhang G P 2008 Computational Physics 25 36
Google Scholar
[9] Gao L, Nilson P M, Igumenshchev I V, Haines M G, Froula D H, Betti R, Meyerhofer D D 2015 Phys. Rev. Lett. 114 215003
Google Scholar
[10] Gao L, Nilson P M, Igumenshchev I V, Hu S X, Davies J R, Stoeckl C, Haines M G, Froula D H, Betti R, Meyerhofer D D 2012 Phys. Rev. Lett. 109 115001
Google Scholar
[11] Giulietti A, Coe S, Afshar-rad T, Desselberger M, Willi O, Danson C, Giulietti D 1991 Laser Interaction and Related Plasma Phenomena 155 261
[12] Watkins H C, Kingham R J 2018 Phys. Plasmas 25 092701
Google Scholar
[13] Afsharrad T, Coe S E, Willi O, Desselberger M 1992 Phys. Plasmas 4 051301
[14] 张家泰, 刘松芬, 胡北来 2003 52 1668
Google Scholar
Zhang J T, Liu S F, Hu B L 2003 Acta Phys. Sin. 52 1668
Google Scholar
[15] 李玉同, 张杰陈, 陈黎明, 赵理曾, 夏江帆, 滕浩, 李英俊, 朱成银, 江文勉 2001 50 204
Google Scholar
Li Y T, Zhang J, Chen L M, Zhao L Z, Xia J F, Teng H, Li Y J, Zhu C Y, Jiang W M 2001 Acta Phys. Sin. 50 204
Google Scholar
[16] Bret A, Firpo M C, Deutsch C 2005 Phys. Rev. Lett. 94 115002
Google Scholar
[17] Séguin F H, Li C K, Manuel M J E, Rinderknecht H G, Sinenian N, Frenie J A, Rygg J R, Hicks D G, Petrasso R D, Delettrez J, Betti R, Marshall F J, Smalyuk V A 2012 Phys. Plasmas 19 012701
Google Scholar
[18] Fox W, Fiksel G, Bhattacharjee A, Chang P Y, Germaschewski K, Hu S X, Nilson P M 2013 Phys. Rev. Lett. 111 225002
Google Scholar
[19] Manuel M J E, Khiar B, Rigon G, Albertazzi B, Klein S R, Kroll F, Brack F E, Michel T, Mabey P, Pikuz S, Williams J C, Koenig M, Casner A, Kuranz C C 2021 Matter Radiat. Extremes 6 026904
[20] Willi O, Rumsby P T, Hooker C, Raven A, Lin Z Q 1982 Opt. Commun. 41 110
Google Scholar
[21] Willi O, Rumsby P T, Sartang S 1981 IEEE J. Quantum Electron. 17 1909
Google Scholar
[22] Willi O, Afshar-rad T, Desselberger M, Dunne M, Edwards J, Gizzi L, Khattak F, Riley D, Taylor R, Viana S 1992 Laser Interaction and Related Plasma Phenomena 142 517
[23] Afshar-Rad T, Gizzi L A, Desselberger M, Khattak F, Willi O, Giulietti A 1992 Phys. Rev. Lett. 68 942
Google Scholar
[24] Desselberger M, Gizzi L, Barrow V, Edwards J, Khattak F, Viana S, Willi O, Danson C N 1992 Appl. Opt. 31 3759
Google Scholar
[25] Desselberger M, Afshar-rad T, Khattak F, Viana S, Willi O 1992 Phys. Rev. Lett. 68 1539
Google Scholar
[26] Lu Y, Tzeferacos P, Liang E, Follett R K, Gao L, Birkel A, Froula D H, Fu W, Ji H, Lamb D, Li C K, Sio H, Petrasso R, Wei M S 2019 Phys. Plasmas 26 022902
Google Scholar
[27] Flash Center for Computational Science, University of Chicago. http://flash.uchicago.edu [2019-03-29]
[28] More R M, Warren K H, Young D A, Zimmerman G B 1988 Phys. Fluids 31 103059
[29] Eidmann K 1994 Laser Part. Beams 12 223
Google Scholar
[30] 田超, 单连强, 周维民, 高喆, 谷渝秋, 张保汉 2014 63 125205
Google Scholar
Tian C, Shan L Q, Zhou W M, Gao Z, Gu Y Q, Zhang B H 2014 Acta Phys. Sin. 63 125205
Google Scholar
[31] Lin Y, Kessler T J 1996 Opt. Lett. 21 1703
Google Scholar
[32] Skupsky S, Short R W, Kessler T, Craxton R S, Letzring S, Soures J M 1989 J. Appl. Phys. 66 3456
Google Scholar
[33] Lefebvre E, Berger R L, Langdon A B, MacGowan B J, Rothenberg J E, Williams E A 1998 Phys. Plasmas 5 2701
Google Scholar
[34] Lal A K, Marsh K A, Clayton C E, Joshi C, McKinstrie C J, Li J S, Johnston T W 1997 Phys. Rev. Lett. 78 670
Google Scholar
[35] Dhareshwar L J, Naik P A, Sarkar S, Khan M, Chakraborty B 1992 Phys. Fluids B 4 1635
Google Scholar
[36] Nicolaï P, Tikhonchuk V T, Kasperczuk A, Pisarczyk T, Borodziuk S, Rohlena K, Ullschmied J 2006 Phys. Plasmas 13 062701
Google Scholar
[37] 青波 2017 中国工程物理研究院科技年报 29
Qing B 2017 Annual Report of Science and Technology of China Academy of Engineering Physics 29 (in Chinese)
[38] Nicolaï P, Tikhonchuk V T, Kasperczuk A, Pisarczyk T, Borodzziuk S, Rohlena K, Ullschmied J 2007 Astrophys. Space Sci. 307 87
Google Scholar
[39] 阿蔡塞 S 著 (沈百飞 译) 2008 惯性聚变物理 (北京: 科学出版社) 第300页
Atzeni S (translated by Shen B F) 2004 The Physics of Inertial Fusion (Beijing: Science Press) p300 (in Chinese)
[40] Evans R G 1981 J. Phys. D: Appl. Phys. 14 173
Google Scholar
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