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Early stage of explosive expansion in extreme ultraviolet source vessel

极紫外光源腔室中高温膨胀初期的流体动力学

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Abstract

In an extreme ultraviolet (EUV) vessel, intense heating occurs when a high-power laser irradiates tin droplets, generating extreme thermal pressure gradients that drive complex flow dynamics. This review focuses on two critical aspects governing flow properties and debris transport within the vessel: main shock behavior and thermal expansion dynamics. Key considerations include finite-source shock dynamics, environmental effects on shock propagation, gas contact motion, and interface instabilities. The evolution of the main shock and gas contact is primarily determined by the initial pressure ratio and sound speed ratio between the heat source and ambient gas. Furthermore, Rayleigh-Taylor and Richtmyer-Meshkov instabilities dominate the evolution of gas-gas interfaces. This work presents a comprehensive analysis of the complex flow mechanisms underlying early-stage, high-temperature flow expansion in EUV source vessels.

摘要

在极紫外(EUV)光源腔中, 当高功率激光轰击锡液滴时, 会产生高温热源, 极端的热压梯度驱动产生复杂的流体动力学行为. 本文重点介绍了腔室内影响流动特性和碎屑运输的两个关键物理过程: 主激波传播和热膨胀动力学. 关注的问题主要集中在: 有限大小热源的激波动力学、 环境气体对激波传播的影响、气体界面运动以及界面不稳定性. 主激波和气体界面的演变主要取决于热源和环境气体之间的初始压力比和声速比. 此外, Rayleigh-Taylor和Richtmyer-Meshkov不稳定性主导了气-气界面的演化. 本文全面综述并分析了EUV光源腔中高温热源膨胀初期的复杂流动过程.

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References

  1. V. Bakshi, EUV Lithography, Second Edition (SPIE, Bellingham, 2018).

    Book  Google Scholar 

  2. Z. J. Li, Y. Shen, and H. Ding, Flow pattern and wave propagation induced by local energy deposition at droplet surface, Sci. China-Phys. Mech. Astron. 68, 294706 (2025).

    Article  Google Scholar 

  3. S. R. Totorica, K. Lezhnin, D. J. Hemminga, J. Gonzalez, J. Sheil, A. Diallo, A. Hyder, and W. Fox, Acceleration mechanisms of energetic ion debris in laser-driven tin plasma EUV sources, Appl. Phys. Lett. 124, 174101 (2024).

    Article  Google Scholar 

  4. A. Sunahara, A. Hassanein, K. Tomita, S. Namba, and T. Higashiguchi, Optimization of extreme ultra-violet light emitted from the CO2 laser-irradiated tin plasmas using 2D radiation hydrodynamic simulations, Opt. Express 31, 31780 (2023).

    Article  Google Scholar 

  5. W. S. Meng, C. B. Zhao, J. Z. Wu, B. F. Wang, Q. Zhou, and K. L. Chong, Simulation of flow and debris migration in extreme ultraviolet source vessel, Phys. Fluids 36, 023322 (2024).

    Article  Google Scholar 

  6. Y. Gao, C. Chen, F. Wang, M. Li, and C. Sun, Characterization and removal of contaminants in lithography, Sci. China-Phys. Mech. Astron. 68, 294702 (2025).

    Article  Google Scholar 

  7. X. Chen, F. Liu, Y. Z. Wang, S. Y. Zhang, Q. Li, J. Z. Wu, B. F. Wang, K. L. Chong, C. Wang, J. H. Zhang, and Q. Zhou, Experimental study of the circular subsonic pipe jet expanding into near vacuum environment, Sci. China-Phys. Mech. Astron. 68, 294703 (2025).

    Article  Google Scholar 

  8. S. Jubin, A. T. Powis, W. Villafana, D. Sydorenko, S. Rauf, A. V. Khrabrov, S. Sarwar, and I. D. Kaganovich, Numerical thermalization in 2D PIC simulations: Practical estimates for low-temperature plasma simulations, Phys. Plasmas 31, 023902 (2024).

    Article  Google Scholar 

  9. M. Patel, J. Thomas, and H. C. Joshi, Experimental investigation of rarefied flows through supersonic nozzles, Vacuum 211, 111909 (2023).

    Article  Google Scholar 

  10. Q. Sun, X. Wang, and D. Zuo, Characteristics of tin droplet target system for EUV source research, Meas. Sci. Technol. 35, 035207 (2024).

    Article  Google Scholar 

  11. O. O. Versolato, Physics of laser-driven tin plasma sources of EUV radiation for nanolithography, Plasma Sources Sci. Technol. 28, 083001 (2019).

    Article  Google Scholar 

  12. Y. Hu, Z. Huang, Y. Cao, Q. Sun, H. Huang, C. Ding, and Z. Wang, Exploration of electron and ion thermodynamic models in laser-plasma expansion, Sci. China-Phys. Mech. Astron. 68, 294707 (2025).

    Article  Google Scholar 

  13. C. Cui, and J. Wang, Vlasov simulations of electric propulsion beam, Plasma Sources Sci. Technol. 33, 125005 (2024).

    Article  Google Scholar 

  14. Z. Huang, Y. Hu, J. Geng, C. Yang, and Q. Sun, Kinetic investigation of discharge performance for Xe, Kr, and Ar in a miniature ion thruster using a fast converging PIC-MCC-DSMC model, Plasma Sources Sci. Technol. 33, 095006 (2024).

    Article  Google Scholar 

  15. W. H. R. Chan, and I. D. Boyd, Grid-point requirements for direct kinetic simulation of weakly collisional plasma plume expansion, J. Comput. Phys. 475, 111861 (2023).

    Article  MathSciNet  Google Scholar 

  16. E. R. Kieft, J. J. A. M. van der Mullen, G. M. W. Kroesen, V. Banine, and K. N. Koshelev, Stark broadening experiments on a vacuum arc discharge in tin vapor, Phys. Rev. E 70, 066402 (2004).

    Article  Google Scholar 

  17. J. Iqbal, R. Ahmed, M. Rafique, M. Anwar-ul-Haq, and M. A. Baig, Spatial diagnostics of the laser-produced tin plasma in air, Laser Phys. 26, 076001 (2016).

    Article  Google Scholar 

  18. J. Scheers, A. Ryabtsev, A. Borschevsky, J. C. Berengut, K. Haris, R. Schupp, D. Kurilovich, F. Torretti, A. Bayerle, E. Eliav, W. Ubachs, O. O. Versolato, and R. Hoekstra, Energy-level structure of Sn3+ ions, Phys. Rev. A 98, 062503 (2018).

    Article  Google Scholar 

  19. E. Ahedo, Using electron fluid models to analyze plasma thruster discharges, J. Electr. Propuls. 2, 2 (2023).

    Article  Google Scholar 

  20. M. R. Mankbadi, and S. Balachandar, Compressible inviscid instability of rapidly expanding spherical material interfaces, Phys. Fluids 24, 034106 (2012).

    Article  Google Scholar 

  21. M. S. Plesset, On the Stability of Fluid Flows with Spherical Symmetry, J. Appl. Phys. 25, 96 (1954).

    Article  MathSciNet  Google Scholar 

  22. G. I. Bell, Taylor Instability on Cylinders and Spheres in the Small Amplitude Approximation, Technical Report (Los Alamos National Laboratory, 1951).

    Google Scholar 

  23. R. Epstein, On the Bell-Plesset effects: The effects of uniform compression and geometrical convergence on the classical Rayleigh-Taylor instability, Phys. Plasmas 11, 5114 (2004).

    Article  Google Scholar 

  24. M. R. Mankbadi, and S. Balachandar, Viscous effects on the non-classical Rayleigh-Taylor instability of spherical material interfaces, Shock Waves 23, 603 (2013).

    Article  Google Scholar 

  25. M. R. Mankbadi, and S. Balachandar, Multiphase effects on spherical Rayleigh-Taylor interfacial instability, Phys. Fluids 26, 023301 (2014).

    Article  Google Scholar 

  26. S. Annamalai, M. K. Parmar, Y. Ling, and S. Balachandar, Nonlinear Rayleigh-Taylor instability of a cylindrical interface in explosion flows, J. Fluids Eng. 136, 060910 (2014).

    Article  Google Scholar 

  27. W. Deng, Response of a millimeter-sized opaque drop to tightly focused nanosecond laser pulse, Sci. China Phys. Mech. Astron. 68, 294705 (2025).

    Article  Google Scholar 

  28. M. Brouillette, The Richtmyer-Meshkov instability, Annu. Rev. Fluid Mech. 34, 445 (2002).

    Article  MathSciNet  Google Scholar 

  29. Z. Zhou, J. Ding, and W. Cheng, Mixing and inter-scale energy transfer in Richtmyer-Meshkov turbulence, J. Fluid Mech. 984, A56 (2024).

    Article  MathSciNet  Google Scholar 

  30. V. Rodriguez, R. Saurel, G. Jourdan, and L. Houas, Impulsive dispersion of a granular layer by a weak blast wave, Shock Waves 27, 187 (2017).

    Article  Google Scholar 

  31. M. L. Wong, J. R. Baltzer, D. Livescu, and S. K. Lele, Analysis of second moments and their budgets for Richtmyer-Meshkov instability and variable-density turbulence induced by reshock, Phys. Rev. Fluids 7, 044602 (2022).

    Article  Google Scholar 

  32. W. G. Zeng, J. H. Pan, Y. T. Sun, and Y. X. Ren, Turbulent mixing and energy transfer of reshocked heavy gas curtain, Phys. Fluids 30, 064106 (2018).

    Article  Google Scholar 

  33. Z. Yan, Y. Fu, L. Wang, C. Yu, and X. Li, Effect of chemical reaction on mixing transition and turbulent statistics of cylindrical Richtmyer-Meshkov instability, J. Fluid Mech. 941, A55 (2022).

    Article  MathSciNet  Google Scholar 

  34. K. Balakrishnan, and S. Menon, On the role of ambient reactive particles in the mixing and afterburn behind explosive blast waves, Combust. Sci. Tech. 182, 186 (2010).

    Article  Google Scholar 

  35. K. Balakrishnan, and S. Menon, A multiphase buoyancy-drag model for the study of Rayleigh-Taylor and Richtmyer-Meshkov instabilities in dusty gases, Laser Part. Beams 29, 201 (2011).

    Article  Google Scholar 

  36. P. E. Crittenden, and S. Balachandar, The stability of the contact interface of cylindrical and spherical shock tubes, Phys. Fluids 30, 064101 (2018).

    Article  Google Scholar 

  37. B. Musci, S. Petter, G. Pathikonda, D. Ranjan, and N. Denissen, in An experimental study of the blast driven rayleigh-taylor and Richtmyer-Meshkov instabilities: Preliminary results: Proceedings of the 16th International Workshop on the Physics of Compressible Turbulent Mixing, Marseille, 2018.

    Google Scholar 

  38. Y. Zhou, R. J. R. Williams, P. Ramaprabhu, M. Groom, B. Thornber, A. Hillier, W. Mostert, B. Rollin, S. Balachandar, P. D. Powell, A. Mahalov, and N. Attal, Rayleigh-Taylor and Richtmyer-Meshkov instabilities: A journey through scales, Phys. D-NOnlinear Phenom. 423, 132838 (2021).

    Article  MathSciNet  Google Scholar 

  39. G. I. Taylor, The formation of a blast wave by a very intense explosion I. Theoretical discussion, Proc. R. Soc. Lond. 201, 159 (1950).

    Google Scholar 

  40. G. I. Taylor, The air wave surrounding an expanding sphere, Proc. R. Soc. Lond. 186, 273 (1946).

    MathSciNet  Google Scholar 

  41. G. B. Whitham, The propagation of spherical blast, Proc. R. Soc. Lond. 203, 571 (1950).

    MathSciNet  Google Scholar 

  42. L. I. Sedov, Similarity and Dimensional Methods in Mechanics (Academic Press, New York, 1959).

    Google Scholar 

  43. H. L. Brode, Numerical solutions of spherical blast waves, J. Appl. Phys. 26, 766 (1955).

    Article  MathSciNet  Google Scholar 

  44. D. W. Boyer, An experimental study of the explosion generated by a pressurized sphere, J. Fluid Mech. 9, 401 (1960).

    Article  Google Scholar 

  45. P. L. Sachdev, Shock Waves and Explosions (Chapman & Hall/CRC, New York, 2004).

    Google Scholar 

  46. H. L. Brode, Theoretical Solutions of Spherical Shock Tube Blasts, Technical Report (Rand Corporation, 1957).

    Google Scholar 

  47. J. A. McFadden, Initial behavior of a spherical blast, J. Appl. Phys. 23, 1269 (1952).

    Article  MathSciNet  Google Scholar 

  48. H. L. Brode, Blast wave from a spherical charge, Phys. Fluids 2, 217 (1959).

    Article  Google Scholar 

  49. M. P. Friendman, A simplified analysis of spherical and cylindrical blast waves, J. Fluid Mech. 11, 1 (1961).

    Article  MathSciNet  Google Scholar 

  50. W. D. Hayes, The propagation upward of the shock wave from a strong explosion in the atmosphere, J. Fluid Mech. 32, 317 (1968).

    Article  Google Scholar 

  51. M. Lutzky, and D. L. Lehto, Scaling of spherical blasts, J. Appl. Phys. 41, 844 (1970).

    Article  Google Scholar 

  52. T. G. Liu, B. C. Khoo, and K. S. Yeo, The numerical simulations of explosion and implosion in air: Use of a modified Harten’s TVD scheme, Int. J. Numer. Meth. Fluids 31, 661 (1999).

    Article  MathSciNet  Google Scholar 

  53. S. M. Liang, J. S. Wang, and H. Chen, Numerical study of spherical blast-wave propagation and reflection, Shock Waves 12, 59 (2002).

    Article  Google Scholar 

  54. Z. Zarei, and D. L. Frost, Simplified modeling of blast waves from metalized heterogeneous explosives, Shock Waves 21, 425 (2011).

    Article  Google Scholar 

  55. Y. Ling, A. Haselbacher, and S. Balachandar, Importance of unsteady contributions to force and heating for particles in compressible flows, Int. J. Multiphase Flow 37, 1026 (2011).

    Article  Google Scholar 

  56. Y. Ling, A. Haselbacher, and S. Balachandar, Importance of unsteady contributions to force and heating for particles in compressible flows. Part 2: Application to particle dispersal by blast waves, Int. J. Multiphase Flow 37, 1013 (2011).

    Article  Google Scholar 

  57. G. B. Whitham, On the propagation of shock waves through regions of non-uniform area or flow, J. Fluid Mech. 4, 337 (1958).

    Article  MathSciNet  Google Scholar 

  58. G. B. Whitham, Linear and Nonlinear Waves (John Wiley & Sons, Inc., Hoboken, 1974).

    Google Scholar 

  59. G. I. Taylor, The formation of a blast wave by a very intense explosion II. The atomic explosion of 1945, Proc. R. Soc. Lond. 201, 175 (1950).

    Google Scholar 

  60. Y. Ling, and S. Balachandar, Asymptotic scaling laws and semi-similarity solutions for a finite-source spherical blast wave, J. Fluid Mech. 850, 674 (2018).

    Article  MathSciNet  Google Scholar 

  61. A. Sakurai, On the propagation and structure of the blast wave, I, J. Phys. Soc. Jpn. 8, 662 (1953).

    Article  MathSciNet  Google Scholar 

  62. X. Kong, H. Zhou, J. Xu, C. Zheng, A. Lu, and W. Wu, Scaling of confined explosion and structural response, Thin-Walled Struct. 186, 110656 (2023).

    Article  Google Scholar 

  63. F. C. Salvado, A. J. Tavares, F. Teixeira-Dias, and J. B. Cardoso, Confined explosions: The effect of compartment geometry, J. Loss Prevent. Proc. Ind. 48, 126 (2017).

    Article  Google Scholar 

  64. Q. Ma, K. Chong, B. Wang, and Q. Zhou, Strong shock propagation for the finite-source circular blast in a confined domain, Appl. Math. Mech.-Engl. Ed. 45, 1071 (2024).

    Article  MathSciNet  Google Scholar 

  65. G. G. Bach, A. L. Kuhl, and A. K. Oppenheim, On blast waves in exponential atmospheres, J. Fluid Mech. 71, 105 (1975).

    Article  Google Scholar 

  66. D. D. Laumbach, and R. F. Probstein, A point explosion in a cold exponential atmosphere, J. Fluid Mech. 35, 53 (1969).

    Article  Google Scholar 

  67. N. H. Abuyazid, X. Chen, D. Mariotti, P. Maguire, C. J. Hogan Jr, and R. M. Sankaran, Understanding the depletion of electrons in dusty plasmas at atmospheric pressure, Plasma Sources Sci. Technol. 29, 075011 (2020).

    Article  Google Scholar 

  68. N. Balcon, A. Aanesland, and R. Boswell, Pulsed RF discharges, glow and filamentary mode at atmospheric pressure in argon, Plasma Sources Sci. Technol. 16, 217 (2007).

    Article  Google Scholar 

  69. N. H. Abuyazid, N. B. Üner, S. M. Peyres, and R. Mohan Sankaran, Charge decay in the spatial afterglow of plasmas and its impact on diffusion regimes, Nat. Commun. 14, 6776 (2023).

    Article  Google Scholar 

  70. O. Petruk, Approximations of the self-similar solution for a blastwave in a medium with power-law density variation, Astron. Astrophys. 357, 686 (2000).

    Google Scholar 

  71. S. S. Harilal, C. V. Bindhu, M. S. Tillack, F. Najmabadi, and A. C. Gaeris, Internal structure and expansion dynamics of laser ablation plumes into ambient gases, J. Appl. Phys. 93, 2380 (2003).

    Article  Google Scholar 

  72. S. Mahmood, R. S. Rawat, S. V. Springham, T. L. Tan, and P. Lee, Material ablation and plasma plume expansion study from Fe and graphite targets in Ar gas atmosphere, Appl. Phys. A 101, 695 (2010).

    Article  Google Scholar 

  73. P. Sankar, H. D. Shashikala, and R. Philip, Ion dynamics of a laser produced aluminium plasma at different ambient pressures, Appl. Phys. A 124, 26 (2018).

    Article  Google Scholar 

  74. Z. Zhao, and W. Li, Numerical simulation of laser-produced plasma expansion on a droplet surface, Sci. Rep. 13, 4085 (2023).

    Article  Google Scholar 

  75. A. K. Sharma, and R. K. Thareja, Plume dynamics of laser-produced aluminum plasma in ambient nitrogen, Appl. Surf. Sci. 243, 68 (2005).

    Article  Google Scholar 

  76. Rayleigh, Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density, Proc. London Math. Soc. s1–14, 170 (1882).

    Article  MathSciNet  Google Scholar 

  77. G. I. Taylor, The instability of liquid surfaces when accelerated in a direction perpendicular to their planes, I. Proc. R. Soc. Lond. A 201, 192 (1950).

    Article  MathSciNet  Google Scholar 

  78. M. A. Price, V. T. Nguyen, O. Hassan, and K. Morgan, A method for compressible multimaterial flows with condensed phase explosive detonation and airblast on unstructured grids, Comput. Fluids 111, 76 (2015).

    Article  MathSciNet  Google Scholar 

  79. S. Courtiaud, N. Lecysyn, G. Damamme, T. Poinsot, and L. Selle, Analysis of mixing in high-explosive fireballs using small-scale pressurised spheres, Shock Waves 29, 339 (2019).

    Article  Google Scholar 

  80. W. H. R. Chan, K. Hara, and I. D. Boyd, Effects of multi-dimensionality and energy exchange on electrostatic current-driven plasma instabilities and turbulence, J. Plasma Phys. 90, 905900206 (2024).

    Article  Google Scholar 

  81. B. J. Balakumar, G. C. Orlicz, J. R. Ristorcelli, S. Balasubramanian, K. P. Prestridge, and C. D. Tomkins, Turbulent mixing in a Richtmyer-Meshkov fluid layer after reshock: Velocity and density statistics, J. Fluid Mech. 696, 67 (2012).

    Article  Google Scholar 

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Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11988102, 12432011, 12422208, 12421002, 12372220, 12372219, and 52450304).

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Authors and Affiliations

  1. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai Institute of Applied Mathematics and Mechanics, School of Mechanics and Engineering Science, Shanghai University, Shanghai, 200072, China

    Qihang Ma  (马琦航), Kai Leong Chong  (庄启亮), Bofu Wang  (王伯福) & Quan Zhou  (周全)

  2. Key Laboratory of Advanced Display and System Application, Ministry of Education, School of Microelectronics, Shanghai University, Shanghai, 200072, China

    Jianhua Zhang  (张建华)

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  1. Qihang Ma  (马琦航)
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Contributions

Author contributions Qihang Ma, Kai Leong Chong, Bofu Wang, Jianhua Zhang, and Quan Zhou designed the research. Qihang Ma wrote the first draft of the manuscript. Qihang Ma and Bofu Wang set up the experiment set-up and processed the experiment data. Kai Leong Chong, Bofu Wang, Jianhua Zhang, and Quan Zhou helped organize the manuscript. Qihang Ma, Kai Leong Chong, Bofu Wang, Jianhua Zhang, and Quan Zhou revised and edited the final version.

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Correspondence to Bofu Wang  (王伯福) or Jianhua Zhang  (张建华).

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Ma, Q., Chong, K.L., Wang, B. et al. Early stage of explosive expansion in extreme ultraviolet source vessel. Acta Mech. Sin. 42, 125295 (2026). https://doi.org/10.1007/s10409-025-25295-x

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