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Non-linear characteristics of Rayleigh–Taylor instable perturbations

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Abstract

The direct numerical simulation method is adopted to study the non-linear characteristics of Rayleigh–Taylor instable perturbations at the ablation front of a 200 μm planar CH ablation target. In the simulation, the classical electrical thermal conductivity is included, and NND difference scheme is used. The linear growth rates obtained from the simulation agree with the Takabe formula. The amplitude distribution of the density perturbation at the ablation front is obtained for the linear growth case. The non-linear characteristics of Rayleigh–Taylor instable perturbations are analyzed and the numerical results show that the amplitude distributions of the compulsive harmonics are very different from that of the fundamental perturbation. The characteristics of the amplitude distributions of the harmonics and their fast growth explain why spikes occur at the ablation front. The numerical results also show that non-linear effects have relations with the phase differences of double mode initial perturbations, and different phase differences lead to varied spikes.

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References

  1. Shiau, J.N., Goldman, E.B., Werg, C.I.: Linear stability analysis of laser-driven spherical implosions. Phys. Rev. Lett. 32, 352–355 (1974)

    Article  Google Scholar 

  2. Goncharov, V.N., Betti, R., Sorotokin, P. et al.: Self-consistent stability analysis of ablation fronts with large Froude numbers. Phys. Plasmas 3, 1402–1414 (1996)

    Article  MathSciNet  Google Scholar 

  3. Wang, L.L., Li, J.C.: Numerical study on the Rayleigh–Taylor instability with various initial length scale. High Power Laser Particle Beams 15, 1195–1199 (2003)

    Google Scholar 

  4. Lindl, J.D., Amendt, P., Berger, R.L. et al.: The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11, 339–491 (2004)

    Article  Google Scholar 

  5. Qin, C.S., Wang, P., Zhang, F.G.: Rayleigh–Taylor and Kelvin–Helmholtz instability of compressible fluid. Acta Mech. Sin. 36, 655–663 (2004) (in Chinese)

    Google Scholar 

  6. Qi, J., Ye, W.H.: Three dimensional parallel computation of laser ablative Rayleigh–Taylor instability. Chin. J. Comput. Phys. 19, 388–392 (2002) (in Chinese)

    Google Scholar 

  7. Sun, Q., Zhou, B., Shen, J. et al.: Modulation targets in Rayleigh–Taylor instability experiments for the ICF study. High Power Laser Particle Beams 16, 1535–1539 (2004)

    Google Scholar 

  8. Kull, H.J.: Incompressible description of Rayleigh–Taylor instabilities in laser-ablated plasmas. Phys. Fluids B 1, 170–182 (1989)

    Article  Google Scholar 

  9. Dahlburg, J.P., Gardner, J.H.: The effect of shape in the three-dimensional ablative Rayleigh–Taylor instability. I: Single-mode perturbations. Phys. Fluids B 5, 571–584 (1993)

    Article  Google Scholar 

  10. Taylor, G.: The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. Proc. R. Lond. Ser. A 201, 192–196 (1950)

    Article  MATH  Google Scholar 

  11. McCrory, R.L., Montierth, L., Morse, R.L., Verdon, C.P.: Laser interaction and related plasma phenomena, vol. 5, pp. 713–742. Plenum, New York (1981)

    Google Scholar 

  12. Takabe, H., Mima, K., Montierth, L. et al.: Self-consistent growth rate of the Rayleigh–Taylor instability in an ablatively accelerating plasma. Phys. Fluids 28, 3676–3682 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  13. Betti, R., Goncharov, V.N., McCrory, R.L. et al.: Growth rates of the ablative Rayleigh–Taylor instability in inertial confinement fusion. Phys. Plasmas 5, 1446–1454 (1998)

    Article  Google Scholar 

  14. Ye, W.H., Zhang, W.Y., He, X.T.: Stabilization of ablative Rayleigh–Taylor instability due to change of the Atwood number. Phys. Rev. E 65, 057401 (2002)

    Article  Google Scholar 

  15. Fan, Z.F., Luo, J.S., Ye, W.H.: Compressible Rayleigh–Taylor instability with preheat in inertial confinement fusion. Chin. Phys. Lett. 24, 2308–2311 (2007)

    Article  Google Scholar 

  16. Jacobs, J.W., Catton, I.: Three-dimensional Rayleigh–Taylor instability. Part 1. Weakly nonlinear theory. J. Fluid Mech. 187, 329–352 (1988)

    Article  MATH  Google Scholar 

  17. Sanz, J., Rami’rez, J., Ramis, R. et al.: Nonlinear theory of the ablative Rayleigh–Taylor instability. Phys. Rev. Lett. 89, 195002 (2002)

    Article  Google Scholar 

  18. Garnier, J., Masse, L.: Statistical approach of weakly nonlinear ablative Rayleigh–Taylor instability. Phys. Plasmas 12, 062707 (2005)

    Article  Google Scholar 

  19. Zhang, H.X.: Non-oscillatory and non-free-parameter dissipation difference scheme. Acta Aerodyn. Sin. 6, 143–165 (1988) (in Chinese)

    Google Scholar 

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Authors and Affiliations

  1. Department of Fluid Mechanics, School of Mechanics, Tianjin University, Tianjin, 300072, China

    Zhengfeng Fan & Jisheng Luo

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  1. Zhengfeng Fan
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  2. Jisheng Luo
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Correspondence to Zhengfeng Fan.

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The English text was polished by Keren Wang.

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Fan, Z., Luo, J. Non-linear characteristics of Rayleigh–Taylor instable perturbations. Acta Mech. Sin. 24, 143–149 (2008). https://doi.org/10.1007/s10409-007-0135-9

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  • DOI: https://doi.org/10.1007/s10409-007-0135-9

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