Influence of piston nonuniformity and illumination on the formation of a hypersonic shock wave in a laser-driven shock wave

Objectives. The study investigates the influence of inhomogeneities of laser flux intensity and piston (mylar film) thickness in a laser shock tube by comparing the conditions for the formation and dynamics of shock wave propagation in a laser shock tube in the case of an open and closed plasma corona.

Methods. Along with mathematical modeling methods, analysis of the results of computational experiments was carried out using the two-dimensional Lagrangian program Atlant_C in cylindrical coordinates were used.

Results. The results of four series of calculations of the dynamics of hypersonic shock waves in a laser shock tube are presented: (1) formation and propagation of a shock wave in a profiled target; (2) formation and propagation of a shock wave with strong inhomogeneity of the incident laser flux; (3) comparison of the dynamics of shock waves for different values of the absorbed laser pulse energy and target (piston) thicknesses; (4) comparison of shock wave dynamics in the cases of open and closed plasma coronas.

Conclusions. Based on the results of the computational experiments, the following conclusions can be drawn: (1) as a strong shock wave propagates in the profiled piston, the pressure and density equalize in the transverse direction. If the duration of the laser pulse is noticeably longer than the transit time of the transverse shock waves in the target (piston), the shock wave front flattens out in the gas inside the LUT cell; (2) in cases when the incident laser pulse contains significant emission intensities or speckles (more than 10% of the pulse energy), jets are formed in the accelerated piston, which can overtake the shock wave front in the gas; (3) during laser heating of the target in the closed corona mode, the propagation velocity of the shock wave front increases by ~40%; (4) when the piston is destroyed due to strong nonuniformity of irradiation or development of hydrodynamic instability and fragmentation of the polymer CH film, a dense turbulent layer can form, which will also create a shock wave in the gas. This case requires separate consideration.

1. Basov N.G., Lebo I.G., Rozanov V.B. Fizika lazernogo termoyadernogo sinteza (Physics of Laser Thermonuclear Fusion). Moscow: Znanie; 1988, 172 p. (In Russ.).

2. Nevmerzhitskii N.V., Razin A.N., Kozlov V.I. Gidrodinamicheskie neustoichivosti v mishenyakh inertsial’nogo termoyadernogo sinteza (Hydrodynamic Instabilities in Inertial Thermonuclear Fusion Targets): Monograph. Sarov; 2024, 416 p. (In Russ.). ISBN 978-5-9515-0558-3

3. Zel’dovich Ya.B., Raizer Yu.P. Fizika udarnykh voln i vysokotemperaturnykh gidrodinamicheskikh yavlenii (Physics of Shock Waves and High-Temperature Hydrodynamic Effects). Moscow: Fizmatlit; 2008, 652 p. (In Russ.). ISBN 978-5-9291-0938-3

4. Landau L.D., Lifshits E. Gidrodinamika (Hydrodynamics). Moscow: Nauka; 1986, 736 p. (In Russ.).

5. Lebo I.G., Tishkin V.F. Issledovanie gidrodinamicheskoi neustoichivosti v zadachakh lazernogo termoyadernogo sinteza (Study of Hydrodynamic Instability in Laser Thermonuclear Fusion Problems). Moscow: Fizmatlit; 2006, 304 p. (In Russ.). ISBN 5-9221-0683-X

6. Bragin M.D., Gus’kov S.Y., Zmitrenko N.V., et al. Experimental and Numerical Investigation of the Dynamics of Development of Rayleigh–Taylor Instability at Atwood Numbers Close to Unity. Math. Models Comput. Simul. 2023;15(4):660–676. https://doi.org/10.1134/S2070048223040038 [Original Russian Text: Bragin M.D., Gus’kov S.Yu., Zmitrenko N.V., Kuchugov P.A., Lebo I.G., Levkina E.V., Nevmerzhitskii N.V., Sin’kova O.G., Statsenko V.P., Tishkin V.F., Farin I.R., Yanilkin Yu.V., Yakhin R.A. Experimental and Numerical Investigation of the Dynamics of Development of Rayleigh–Taylor Instability at Atwood Numbers Close to Unity. Matematicheskoe modelirovanie. 2023;35(1):59–82 (in Russ.). https://doi.org/10.20948/mm-2023-01-05, https://elibrary.ru/qfskuw ]

7. Craxton R.S., Anderson K.S, Boehly T.R., et al. Direct drive inertial confinement fusion: A review. Phys. Plasmas. 2015;22(1):110501. https://doi.org/10.1063/1.4934714

8. Lebo I.G. Mathematical modeling of experiments on the interaction of a high-power ultraviolet laser pulse with condensed targets. Russian Technological Journal. 2023;11(3):86–103. https://doi.org/10.32362/2500-316X-2023-11-3-86-103

9. Samarskii A.A., Popov Yu.P. Raznostnye metody resheniya zadach gazovoi dinamiki (Difference Methods for Solving Problems of Gas Dynamics). Moscow: Nauka; 1992, 422 p. (In Russ.). ISBN 5-02-014577-7

10. Belotserkovskii O.M., Davydov Yu.M. Metod krupnykh chastits v gazovoi dinamike (Large Particle Method in Gas Dynamics). Moscow: Nauka; 1982, 391 p. (In Russ.). https://elibrary.ru/xqocjj

11. Godunov S.K., Zabrodin A.V., Ivanov M.Ya., Kraiko A.N., Prokopov G.P. Chislennoe reshenie mnogomernykh zadach gazovoi dinamiki (Numerical Solution of Multidimensional Gas Dynamics Problems). Moscow: Nauka; 1976, 400 p. (In Russ.).

12. Samarskii A.A. Teoriya raznostnykh skhem (Theory of Difference Schemes). Moscow: Nauka; 1990, 616 p. (In Russ.). ISBN 5-02-014576-9

13. Lebo I.G., Obruchev I.V. The modeling of two-dimensional vortex flows in a cylindrical channel using parallel calculations on a supercomputer. Russian Technological Journal. 2022;10(1):60–67. https://doi.org/10.32362/2500-316X-2022-10-1-60-67

14. Zvorykin V.D., Lebo I.G. Application of a high power KrF laser for the study of supersonic gas flows and the development of hydrodynamic instability in layered media. Quantum Electron. 2000;30(6):540–544. https://doi.org/10.1070/QE2000v030n06ABEH001761 [Original Russian Text: Zvorykin V.D., Lebo I.G. Application of a high power KrF laser for the study of supersonic gas flows and the development of hydrodynamic instability in layered media. Kvantovaya Elektronika. 2000;30(6):540–544 (in Russ.).]

15. Samarskii A.A., Mikhailov A.P. Matematicheskoe modelirovanie: Idei. Metody. Primery (Mathematical Modeling: Ideas. Methods. Examples). Moscow: Fizmatlit; 2005, 316 p. (In Russ.). ISBN 5-9221-0120-X

16. Zvorykin V.D., Lebo I.G. Laser and Target Experiments on KrF GARPUN laser installation at FIAN. Laser Part. Beams. 1999;17(1):69-88. https://doi.org/10.1017/S0263034699171064

17. Richtmyer R.D. Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Math. 1960;13(2): 297–319. https://doi.org/10.1002/cpa.3160130207

18. Meshkov E.E. Instability of the interface of two gases accelerated by a shock wave. Fluid Dyn. 1969;4(5):101–104. https://doi.org/10.1007/BF01015969 [Original Russian Text: Meshkov E.E. Instability of the interface of two gases accelerated by a shock wave. Izvestiya AN SSSR. Seriya Mekhanika zhidkosti i gaza. 1969;5:151–158 (in Russ.). Available from URL: https://mzg.ipmnet.ru/ru/get/1969/5/151-158. Accessed September 12, 2025]

19. Aleshin A.N., Zaitsev C.G., Lazareva E.V., Gamalii E.G., Lebo I.G., Rozanov V.B. A study of linear, non-linear and transition stages of Richtmyer–Meshkov instability. Dokl. Math. 1990;35(2):177–180. [Original Russian Text: Aleshin A.N., Zaitsev S.G., Lazareva E.V., Gamalii E.G., Lebo I.G., Rozanov V.B. A study of linear, non-linear and transition stages of Richtmyer–Meshkov instability. Doklady Akademii Nauk SSSR. 1990;310(5):1105–1108 (in Russ.).]

20. Zvorykin V.D. Dynamics of Hypersonic Shock Waves Generated by Laser Acceleration of Thin-Film Targets in a Laser Driven Shock Tube and Free Space. JETP Lett. 2025;122(6):354–360. https://doi.org/10.1134/S002136402560805X [Original Russian Text: Zvorykin V.D. Dynamics of Hypersonic Shock Waves Generated by Laser Acceleration of Thin Film Targets in a Laser-Driven Shock Tube and Free Space. Pis’ma v Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki. 2025;122(5-6):344–350 (in Russ.). https://www.elibrary.ru/xuqtzo ]