• Matter and Radiation at Extremes
  • Vol. 8, Issue 1, 016901 (2023)
J. Y. Fu1, H. S. Zhang2、a), H. B. Cai2, P. L. Yao3, and S. P. Zhu2、3、4
Author Affiliations
  • 1Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China
  • 2Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, People’s Republic of China
  • 3Graduate School, China Academy of Engineering Physics, P.O. Box 2101, Beijing 100088, People’s Republic of China
  • 4Science and Technology on Plasma Physics Laboratory, Laser Fusion Research Center, CAEP, Mianyang 621900, People’s Republic of China
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    DOI: 10.1063/5.0106832 Cite this Article
    J. Y. Fu, H. S. Zhang, H. B. Cai, P. L. Yao, S. P. Zhu. Effect of ablation on the nonlinear spike growth for the single-mode ablative Rayleigh–Taylor instability[J]. Matter and Radiation at Extremes, 2023, 8(1): 016901 Copy Citation Text show less
    References

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

    [2] L.Rayleigh. Scientific Papers, 200(1900).

    [3] J. D.Lindl. Inertial Confinement Fusion, 11(1998).

    [4] V. N.Gamezo, N.Gamezo V., M.Khokhlov A., S.Oran E., Y.Chtchelkanova A., R. and, A. M.Khokhlov, N.Gamezo V., M.Khokhlov A., S.Oran E., Y.Chtchelkanova A., R. and, E. S.Oran, N.Gamezo V., M.Khokhlov A., S.Oran E., Y.Chtchelkanova A., R. and, A. Y.Chtchelkanova, N.Gamezo V., M.Khokhlov A., S.Oran E., Y.Chtchelkanova A., R. and, R. O.Rosenberg. Thermonuclear supernovae: Simulations of the deflagration stage and their implications. Science, 299, 77(2003).

    [5] R. S.Craxton, S.Craxton R., S.Anderson K., R.Boehly T., N.Goncharov V., R.Hardinget al. D., K. S.Anderson, S.Craxton R., S.Anderson K., R.Boehly T., N.Goncharov V., R.Hardinget al. D., T. R.Boehly, S.Craxton R., S.Anderson K., R.Boehly T., N.Goncharov V., R.Hardinget al. D., V. N.Goncharov, S.Craxton R., S.Anderson K., R.Boehly T., N.Goncharov V., R.Hardinget al. D., D. R.Hardinget?al.. Direct-drive inertial confinement fusion: A review. Phys. Plasmas, 22, 110501(2015).

    [6] A. R.Bell. Turbulent amplification of magnetic field and diffusive shock acceleration of cosmic rays. Mon. Not. R. Astron. Soc., 353, 550(2004).

    [7] S. E.Bodner. Rayleigh-Taylor instability and laser-pellet fusion. Phys. Rev. Lett., 33, 761(1974).

    [8] H.Takabe, H.Takabe, K.Mima, L.Montierth, R. and, K.Mima, H.Takabe, K.Mima, L.Montierth, R. and, L.Montierth, H.Takabe, K.Mima, L.Montierth, R. and, R. L.Morse. Self‐consistent growth rate of the Rayleigh–Taylor instability in an ablatively accelerating plasma. Phys. Fluids, 28, 3676(1985).

    [9] J.Sanz. Self-consistent analytical model of the Rayleigh-Taylor instability in inertial confinement fusion. Phys. Rev. Lett., 73, 2700(1994).

    [10] R.Betti, R.Betti, N.Goncharov V., L.McCrory R., C. and, V. N.Goncharov, R.Betti, N.Goncharov V., L.McCrory R., C. and, R. L.McCrory, R.Betti, N.Goncharov V., L.McCrory R., C. and, C. P.Verdon. Self‐consistent cutoff wave number of the ablative Rayleigh–Taylor instability. Phys. Plasmas, 2, 3844(1995).

    [11] V. N.Goncharov, N.Goncharov V., R.Betti, L.McCrory R., C. and, R.Betti, N.Goncharov V., R.Betti, L.McCrory R., C. and, R. L.McCrory, N.Goncharov V., R.Betti, L.McCrory R., C. and, C. P.Verdon. Self‐consistent stability analysis of ablation fronts with small Froude numbers. Phys. Plasmas, 3, 4665(1996).

    [12] R.Betti, R.Betti, N.Goncharov V., L.McCrory R., C. and, V. N.Goncharov, R.Betti, N.Goncharov V., L.McCrory R., C. and, R. L.McCrory, R.Betti, N.Goncharov V., L.McCrory R., C. and, C. P.Verdon. Growth rates of the ablative Rayleigh–Taylor instability in inertial confinement fusion. Phys. Plasmas, 5, 1446(1998).

    [13] J.Sanz, J.Sanz, R.Betti, R.Ramis, J.Ramírez and, R.Betti, J.Sanz, R.Betti, R.Ramis, J.Ramírez and, R.Ramis, J.Sanz, R.Betti, R.Ramis, J.Ramírez and, J.Ramírez. Nonlinear theory of the ablative Rayleigh–Taylor instability. Plasma Phys. Controlled Fusion, 46, B367(2004).

    [14] H.Zhang, H.Zhang, R.Betti, V.Gopalaswamy, R.Yan, H.Aluie and, R.Betti, H.Zhang, R.Betti, V.Gopalaswamy, R.Yan, H.Aluie and, V.Gopalaswamy, H.Zhang, R.Betti, V.Gopalaswamy, R.Yan, H.Aluie and, R.Yan, H.Zhang, R.Betti, V.Gopalaswamy, R.Yan, H.Aluie and, H.Aluie. Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers. Phys. Rev. E, 97, 011203(R)(2018).

    [15] D.Layzer. On the instability of superposed fluids in a gravitational field. Astrophys. J., 122, 1(1955).

    [16] V. N.Goncharov. Analytical model of nonlinear, single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers. Phys. Rev. Lett., 88, 134502(2002).

    [17] D.Oron, D.Oron, L.Arazi, D.Kartoon, A.Rikanati, U.Alon, D.Shvarts and, L.Arazi, D.Oron, L.Arazi, D.Kartoon, A.Rikanati, U.Alon, D.Shvarts and, D.Kartoon, D.Oron, L.Arazi, D.Kartoon, A.Rikanati, U.Alon, D.Shvarts and, A.Rikanati, D.Oron, L.Arazi, D.Kartoon, A.Rikanati, U.Alon, D.Shvarts and, U.Alon, D.Oron, L.Arazi, D.Kartoon, A.Rikanati, U.Alon, D.Shvarts and, D.Shvarts. Dimensionality dependence of the Rayleigh–Taylor and Richtmyer–Meshkov instability late-time scaling laws. Phys. Plasmas, 8, 2883(2001).

    [18] S. I.Sohn. Vortex model and simulations for Rayleigh-Taylor and Richtmyer-Meshkov instabilities. Phys. Rev. E, 69, 036703(2004).

    [19] X.He, X.He, R.Zhang, S.Chen, G. and, R.Zhang, X.He, R.Zhang, S.Chen, G. and, S.Chen, X.He, R.Zhang, S.Chen, G. and, G. D.Doolen. On the three-dimensional Rayleigh–Taylor instability. Phys. Fluids, 11, 1143(1999).

    [20] P.Ramaprabhu, and P.Ramaprabhu, G.Dimonte. Single-mode dynamics of the Rayleigh-Taylor instability at any density ratio. Phys. Rev. E, 71, 036314(2005).

    [21] P.Ramaprabhu, P.Ramaprabhu, G.Dimonte, P.Woodward, C.Fryer, G.Rockefelleret?al., G.Dimonte, P.Ramaprabhu, G.Dimonte, P.Woodward, C.Fryer, G.Rockefelleret?al., P.Woodward, P.Ramaprabhu, G.Dimonte, P.Woodward, C.Fryer, G.Rockefelleret?al., C.Fryer, P.Ramaprabhu, G.Dimonte, P.Woodward, C.Fryer, G.Rockefelleret?al., G.Rockefelleret?al.. The late-time dynamics of the single-mode Rayleigh-Taylor instability. Phys. Fluids, 24, 074107(2012).

    [22] J. P.Wilkinson, P.Wilkinson J., J. W.Jacobs. Experimental study of the single-mode three-dimensional Rayleigh-Taylor instability. Phys. Fluids, 19, 124102(2007).

    [23] R.Betti, and R.Betti, J.Sanz. Bubble acceleration in the ablative Rayleigh-Taylor instability. Phys. Rev. Lett., 97, 205002(2006).

    [24] R.Yan, R.Yan, R.Betti, J.Sanz, H.Aluie, B.Liu, A.Frank and, R.Betti, R.Yan, R.Betti, J.Sanz, H.Aluie, B.Liu, A.Frank and, J.Sanz, R.Yan, R.Betti, J.Sanz, H.Aluie, B.Liu, A.Frank and, H.Aluie, R.Yan, R.Betti, J.Sanz, H.Aluie, B.Liu, A.Frank and, B.Liu, R.Yan, R.Betti, J.Sanz, H.Aluie, B.Liu, A.Frank and, A.Frank. Three-dimensional single-mode nonlinear ablative Rayleigh-Taylor instability. Phys. Plasmas, 23, 022701(2016).

    [25] T.Wei, and T.Wei, D.Livescu. Late-time quadratic growth in single-mode Rayleigh-Taylor instability. Phys. Rev. E, 86, 046405(2012).

    [26] A.Hamzehloo, A.Hamzehloo, P.Bartholomew, S.Laizet and, P.Bartholomew, A.Hamzehloo, P.Bartholomew, S.Laizet and, S.Laizet. Direct numerical simulations of incompressible Rayleigh–Taylor instabilities at low and medium Atwood numbers. Phys. Fluids, 33, 054114(2021).

    [27] L.Duchemin, L.Duchemin, C.Josserand, P.Clavin and, C.Josserand, L.Duchemin, C.Josserand, P.Clavin and, P.Clavin. Asymptotic behavior of the Rayleigh-Taylor instability. Phys. Rev. Lett., 94, 224501(2005).

    [28] J. O.Kane, O.Kane J., F.Robey H., A.Remington B., P.Drake R., J.Knaueret?al., H. F.Robey, O.Kane J., F.Robey H., A.Remington B., P.Drake R., J.Knaueret?al., B. A.Remington, O.Kane J., F.Robey H., A.Remington B., P.Drake R., J.Knaueret?al., R. P.Drake, O.Kane J., F.Robey H., A.Remington B., P.Drake R., J.Knaueret?al., J.Knaueret?al.. Interface imprinting by a rippled shock using an intense laser. Phys. Rev. E, 63, 055401(R)(2001).

    [29] A.Casner, A.Casner, A.Smalyuk V., L.Masse, I.Igumenshchev, S.Liberatoreet?al., V. A.Smalyuk, A.Casner, A.Smalyuk V., L.Masse, I.Igumenshchev, S.Liberatoreet?al., L.Masse, A.Casner, A.Smalyuk V., L.Masse, I.Igumenshchev, S.Liberatoreet?al., I.Igumenshchev, A.Casner, A.Smalyuk V., L.Masse, I.Igumenshchev, S.Liberatoreet?al., S.Liberatoreet?al.. Designs for highly nonlinear ablative Rayleigh-Taylor experiments on the National Ignition Facility. Phys. Plasmas, 19, 082708(2012).

    [30] L. F.Wang, F.Wang L., H.Ye W., T.He X., Y.Zhang W., M.Shenget al. Z., W. H.Ye, F.Wang L., H.Ye W., T.He X., Y.Zhang W., M.Shenget al. Z., X. T.He, F.Wang L., H.Ye W., T.He X., Y.Zhang W., M.Shenget al. Z., W. Y.Zhang, F.Wang L., H.Ye W., T.He X., Y.Zhang W., M.Shenget al. Z., Z. M.Shenget?al.. Formation of jet-like spikes from the ablative Rayleigh-Taylor instability. Phys. Plasmas, 19, 100701(2012).

    [31] J.Sanz, J.Sanz, J.Ramírez, R.Ramis, R.Betti, R. and, J.Ramírez, J.Sanz, J.Ramírez, R.Ramis, R.Betti, R. and, R.Ramis, J.Sanz, J.Ramírez, R.Ramis, R.Betti, R. and, R.Betti, J.Sanz, J.Ramírez, R.Ramis, R.Betti, R. and, R. P. J.Town. Nonlinear theory of the ablative Rayleigh-Taylor instability. Phys. Rev. Lett., 89, 195002(2002).

    [32] W. H.Ye, H.Ye W., F.Wang L., X. and, L. F.Wang, H.Ye W., F.Wang L., X. and, X. T.He. Spike deceleration and bubble acceleration in the ablative Rayleigh–Taylor instability. Phys. Plasmas, 17, 122704(2010).

    [33] K. O.Mikaelian. Explicit expressions for the evolution of single-mode Rayleigh-Taylor and Richtmyer-Meshkov instabilities at arbitrary Atwood numbers. Phys. Rev. E, 67, 026319(2003).

    [34] K. O.Mikaelian. Solution to Rayleigh-Taylor instabilities: Bubbles, spikes, and their scalings. Phys. Rev. E, 89, 053009(2014).

    [35] L.Spitzer, and L.Spitzer, R.H?rm. Transport phenomena in a completely ionized gas. Phys. Rev., 89, 977(1953).

    [36] J.Xin, J.Xin, R.Yan, Z.-H.Wan, D.-J.Sun, J.Zhenget?al., R.Yan, J.Xin, R.Yan, Z.-H.Wan, D.-J.Sun, J.Zhenget?al., Z.-H.Wan, J.Xin, R.Yan, Z.-H.Wan, D.-J.Sun, J.Zhenget?al., D.-J.Sun, J.Xin, R.Yan, Z.-H.Wan, D.-J.Sun, J.Zhenget?al., J.Zhenget?al.. Two mode coupling of the ablative Rayleigh-Taylor instabilities. Phys. Plasmas, 26, 032703(2019).

    [37] H.Zhang, H.Zhang, R.Betti, R.Yan, D.Zhao, D.Shvarts, H.Aluie and, R.Betti, H.Zhang, R.Betti, R.Yan, D.Zhao, D.Shvarts, H.Aluie and, R.Yan, H.Zhang, R.Betti, R.Yan, D.Zhao, D.Shvarts, H.Aluie and, D.Zhao, H.Zhang, R.Betti, R.Yan, D.Zhao, D.Shvarts, H.Aluie and, D.Shvarts, H.Zhang, R.Betti, R.Yan, D.Zhao, D.Shvarts, H.Aluie and, H.Aluie. Self-similar multimode bubble-front evolution of the ablative Rayleigh-Taylor instability in two and three dimensions. Phys. Rev. Lett., 121, 185002(2018).

    [38] H.Zhang, H.Zhang, R.Betti, R.Yan, H.Aluie and, R.Betti, H.Zhang, R.Betti, R.Yan, H.Aluie and, R.Yan, H.Zhang, R.Betti, R.Yan, H.Aluie and, H.Aluie. Nonlinear bubble competition of the multimode ablative Rayleigh–Taylor instability and applications to inertial confinement fusion. Phys. Plasmas, 27, 122701(2020).

    [39] P. W.McKenty, W.McKenty P., N.Goncharov V., P. R., S.Skupsky, R.Betti, R. and, V. N.Goncharov, W.McKenty P., N.Goncharov V., P. R., S.Skupsky, R.Betti, R. and, R. P. J.Town, W.McKenty P., N.Goncharov V., P. R., S.Skupsky, R.Betti, R. and, S.Skupsky, W.McKenty P., N.Goncharov V., P. R., S.Skupsky, R.Betti, R. and, R.Betti, W.McKenty P., N.Goncharov V., P. R., S.Skupsky, R.Betti, R. and, R. L.McCrory. Analysis of a direct-drive ignition capsule designed for the National Ignition Facility. Phys. Plasmas, 8, 2315(2001).

    [40] X.Bian, X.Bian, H.Aluie, D.Zhao, H.Zhang, D.Livescu and, H.Aluie, X.Bian, H.Aluie, D.Zhao, H.Zhang, D.Livescu and, D.Zhao, X.Bian, H.Aluie, D.Zhao, H.Zhang, D.Livescu and, H.Zhang, X.Bian, H.Aluie, D.Zhao, H.Zhang, D.Livescu and, D.Livescu. Revisiting the late-time growth of single-mode Rayleigh–Taylor instability and the role of vorticity. Physica D, 403, 132250(2020).

    [41] L. F.Wang, F.Wang L., C.Xue, H.Ye W., Y. and, C.Xue, F.Wang L., C.Xue, H.Ye W., Y. and, W. H.Ye, F.Wang L., C.Xue, H.Ye W., Y. and, Y. J.Li. Destabilizing effect of density gradient on the Kelvin–Helmholtz instability. Phys. Plasmas, 16, 112104(2009).

    [42] L. F.Wang, F.Wang L., H.Ye W., Y. and, W. H.Ye, F.Wang L., H.Ye W., Y. and, Y. J.Li. Numerical investigation on the ablative Kelvin-Helmholtz instability. Europhys. Lett., 87, 54005(2009).

    J. Y. Fu, H. S. Zhang, H. B. Cai, P. L. Yao, S. P. Zhu. Effect of ablation on the nonlinear spike growth for the single-mode ablative Rayleigh–Taylor instability[J]. Matter and Radiation at Extremes, 2023, 8(1): 016901
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