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Linear perturbation response of self-similar ablative flows relevant to inertial confinement fusion

Published online by Cambridge University Press:  31 July 2008

J.-M. CLARISSE ,
C. BOUDESOCQUE-DUBOIS  and
S. GAUTHIER
J.-M. CLARISSE
Affiliation:
CEA, DIF, F-91297 Arpajon, France
C. BOUDESOCQUE-DUBOIS
Affiliation:
CEA, DIF, F-91297 Arpajon, France
S. GAUTHIER
Affiliation:
CEA, DIF, F-91297 Arpajon, France
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Abstract

A family of exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction is proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Dynamical multi-domain Chebyshev spectral methods are employed for computing both the similarity solution and its time-dependent linear perturbations. This approach has been exploited to analyse the linear stability properties of two self-similar ablative configurations subjected to direct laser illumination asymmetries. Linear perturbation temporal and reduced responses are analysed, evidencing a maximum instability for illumination asymmetries of zero transverse wavenumber as well as three distinct regimes of ablation-front distortion evolution, and emphasizing the importance of the mean flow unsteadiness, compressibility and stratification.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 609 , 25 August 2008 , pp. 1 - 48
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Abéguilé, F., Boudesocque-Dubois, C., Clarisse, J.-M., Gauthier, S. & Saillard, Y. 2006 Linear perturbation amplification in self-similar ablation flows of inertial confinement fusion. Phys. Rev. Lett. 97, 035002.CrossRefGoogle ScholarPubMed
Aglitskiy, Y., Velikovich, A. L., Karasik, M., Serlin, V., Pawley, C. J., Schmitt, A. J., Obenschain, S. P., Mostovych, A. N., Gardner, J. H. & Metzler, N. 2002 Direct observation of mass oscillations due to ablative Richtmyer–Meshkov instability and feedout in planar plastic targets. Phys. Plasmas 9, 2264–2276.Google Scholar
Anisimov, S. I. 1970 Self-similar thermal wave in a two-temperature plasma heated by a laser pulse. sov. phys. JETP Lett. 12, 287–289.Google Scholar
Barenblatt, G. 1979 Similarity, Self-Similarity and Intermediate Asymptotics. Consultants Bureau, New-York.CrossRefGoogle Scholar
Barrero, A. & Sanmartín, J. R. 1977 Self-similar motion of laser fusion plasma. Absorption in an unbounded plasma. Phys. Fluids 20, 1155–1163.CrossRefGoogle Scholar
Betti, R., Goncharov, V. N., McCrory, R. L. & Verdon, C. P. 1995 Self-consistent cutoff wave number of the ablative Rayleigh–Taylor instability. Phys. Plasmas 2, 3844–3851.Google Scholar
Betti, R., Goncharov, V. N., McCrory, R. L., Sorotokin, P. & Verdon, C. P. 1996 Self-consistent stability analysis of ablation fronts in inertial confinement fusion. Phys. Plasmas 3, 2122–2128.Google Scholar
Bodner, S. E. 1974 Rayleigh–Taylor instability and laser-pellet fusion. Phys. Rev. Lett. 33, 761–764.Google Scholar
Bodner, S. E., Colombant, D. G., Gardner, J. H., Lehmberg, R. H., Obenschain, S. P., Philipps, L., Schmitt, A. J., Sethian, J. D., McCrory, R. L., Seka, W., Verdon, C. P., Knauer, J. P., Afeyan, B. B. & Powell, H. T. 1998 Direct-drive laser fusion: status and prospects. Phys. Plasmas 5, 1901–1918.CrossRefGoogle Scholar
Boudesocque-Dubois, C. 2000 Perturbations linéaires d'une solution autosemblable de l'hydrodynamique avec conduction non linéaire. PhD thesis, Université de Paris 6.Google Scholar
Boudesocque-Dubois, C. & Clarisse, J.-M. 2003 Investigation of linear perturbation growth in a planar ablation flow. In ECLIM 2002: 27th European Conference on Laser Interaction with Matter (ed. Krokhin, O. N., Gus'kov, S. Y. & Merkul'ev, Y. A.), Proc. SPIE, vol. 5228, pp. 172–183.Google Scholar
Boudesocque-Dubois, C., Clarisse, J.-M. & Gauthier, S. 2001 Hydrodynamic stability of ablation fronts: linear perturbation of a self-similar solution. In ECLIM 2000: 26th European Conference on Laser Interaction with Matter (ed. Kálal, M., Rohlena, K. & Šiňor, M.), Proc. SPIE, vol. 4424, pp. 220–223.Google Scholar
Boudesocque-Dubois, C., Clarisse, J.-M. & Gauthier, S. 2003 A spectral Chebyshev method for linear stability analysis of one-dimensional exact solutions of gas dynamics. J. Comput. Phys. 184, 592–618.CrossRefGoogle Scholar
Boudesocque-Dubois, C., Gauthier, S. & Clarisse, J.-M. 2008 Self-similar solutions of unsteady ablation flows in inertial confinement fusion. J. Fluid Mech. 603, 151–178.CrossRefGoogle Scholar
Brueckner, K. A. & Jorna, S. 1974 Laser-driven fusion. Rev. Mod. Phys. 46, 325–367.CrossRefGoogle Scholar
Brun, L., Dautray, R., Delobeau, F., Patou, C., Perrot, F., Reisse, J.-M., Sitt, B. & Watteau, J.-P. 1977 Physical models and mathematical simulation of laser-driven implosion and their relations with experiments. In Laser Interaction and Related Plasma Phenomena, vol. 4B (ed. Schwarz, H. J. & Hora, H.), pp. 1059–1080. Plenum.CrossRefGoogle Scholar
Buresi, E., Coutant, J., Dautray, R., Decroisette, M., Duborgel, B., Guillaneux, P., Launspach, J., Nelson, P., Patou, C., Reisse, J.-M. & Watteau, J.-P. 1986 Laser program development at CEL-V: overview of recent experimental results. Laser Part. Beams 4, 531.Google Scholar
Bychkov, V. V., Golberg, S. M. & Liberman, M. A. 1991 Growth rate of the Rayleigh–Taylor instability in an ablatively accelerated inhomogeneous plasma. Sov. Phys. JETP 73, 642–653.Google Scholar
Bychkov, V. V., Golberg, S. M. & Liberman, M. A. 1994 Self-consistent model of the Rayleigh–Taylor instability in ablatively accelerated laser plasma. Phys. Plasmas 1, 2976–2986.Google Scholar
Clarisse, J.-M., Boudesocque-Dubois, C., Gauthier, S. & Abéguilé, F. 2006 Linear perturbation amplification in ICF self-similar ablation flows. J. Phys. IV France 133, 111–115.CrossRefGoogle Scholar
Duderstadt, J. & Moses, G. 1982 Inertial Confinement Fusion. Wiley-Interscience.Google Scholar
Emery, M. H., Gardner, J. H., Lehmberg, R. H. & Obenschain, S. P. 1991 Hydrodynamic target response to an induced spatial incoherence-smoothed laser beam. Phys. Fluids B 3, 2640–2651.Google Scholar
Fortin, X. & Canaud, B. 2000 Direct drive laser fusion calculations at CEA. In IFSA 99 — Inertial fusion sciences and applications (ed. Labaune, C., Hogan, W. J. & Tanaka, K. A.), pp. 102–105. Elsevier.Google Scholar
Gauthier, S., Le Creurer, B., Abéguilé, F., Boudesocque-Dubois, C. & Clarisse, J.-M. 2005 A self-adaptive domain decomposition method with Chebyshev method. Intl J. Pure Appl. Maths 24, 553–577.Google Scholar
Germain, P. & Muller, P. 1994 Introduction à la mécanique des milieux continus, 2nd edn. Masson, Paris.Google Scholar
Goncharov, V. N., Skupsky, S., Boehly, T. R., Knauer, J. P., McKenty, P., Smalyuk, V. A., Town, R. P., Gotchev, O. V., Betti, R. & Meyerhofer, D. D. 2000 A model of laser imprinting. Phys. Plasmas 7, 2062–2068.Google Scholar
Goncharov, V. N., Gotchev, O. V., Vianello, E., Boehly, T. R., Knauer, J. P., McKenty, P. W., Radha, P. B., Regan, S. P., Sangster, T. C., Skupsky, S., Smalyuk, V. A., Betti, R., McCrory, R. L., Meyerhofer, D. D. & Cherfils-Clérouin, C. 2006 Early stage of implosion in inertial confinement fusion: shock timing and perturbation evolution. Phys. Plasmas 13, 012702.Google Scholar
Gustafsson, B. & Sundström, A. 1978 Incompletely parabolic problems in fluid dynamics. SIAM J. Appl. Maths 35, 343–357.CrossRefGoogle Scholar
Holstein, P.-A., André, M., Casanova, M., Chaland, F., Charpin, C., Cherfils, C., Divol, L., Dumont, H., Galmiche, D., Giorla, J., Hallo, L., Laffite, S., Lours, L., Monteil, M.-C., Mourenas, D., Poggi, F., Saillard, Y., Schurtz, G., Valadon, M., Vanderhaegen, D. & Wagon, F. 2000 Target design for the LMJ. CR Acad. Sci. Paris 1, ser. IV, 693–704.Google Scholar
Ishizaki, R. & Nishihara, K. 1997 Propagation of a rippled shock wave driven by nonuniform laser ablation. Phys. Rev. Lett. 78, 1920–1923.CrossRefGoogle Scholar
Kull, H. J. 1989 Incompressible description of Rayleigh–Taylor instabilities in laser-ablated plasmas. Phys. Fluids B 1, 170–182.CrossRefGoogle Scholar
Kull, H. J. & Anisimov, S. I. 1986 Ablative stabilization in the incompressible Rayleigh–Taylor instability. Phys. Fluids 29, 2067–2075.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics. Pergamon.Google Scholar
Ledoux, P. & Walraven, T. 1958 Variable stars. In Handbuch der Physik, pp. 353–604. Springer.Google Scholar
Lombard, V., Boudesocque-Dubois, C., Clarisse, J.-M. & Gauthier, S. 2007 Kovàsznay modes in stability of self-similar ablation flows. In 34th EPS Conference on Plasma Physics, Europhysics Conference Abstracts, vol. 31F. EPS.Google Scholar
Marshak, R. 1958 Effect of radiation on shock wave behavior. Phys. Fluids 1, 24–29.Google Scholar
Meshkov, E. E. 1969 Instability of the interface of two gases accelerated by a shock wave. Sov. Fluid Dyn. 4, 101–104.Google Scholar
Metzler, N., Velikovich, A. L. & Gardner, J. H. 1999 Reduction of early-time perturbation growth in ablatively driven laser target using tailored density profiles. Phys. Plasmas 6, 3283–3295.Google Scholar
Metzler, N., Velikovich, A. L., Schmitt, A. J., Karasik, M., Serlin, V., Mostovych, A. N., Obenschain, S. P., Gardner, J. H. & Aglitskiy, Y. 2003 Laser imprint reduction with a shaping pulse, oscillatory Richtmyer–Meshkov to Rayleigh–Taylor transition and other coherent effects in plastic-foam targets. Phys. Plasmas 10, 1897–1905.CrossRefGoogle Scholar
Nishihara, K., Ishizaki, R., Wouchuk, J. G., Fukuda, Y. & Shimuta, Y. 1998 Hydrodynamic perturbation growth in start-up phase in laser implosion. Phys. Plasmas 5, 1945–1952.Google Scholar
Nuckolls, J., Wood, L., Thiessen, A. & Zimmerman, G. 1972 Laser compression of matter to super-high densities: thermonuclear (CTR) applications. Nature 239, 139–142.Google Scholar
Pakula, R. & Sigel, R. 1985 Self-similar expansion of dense matter due to heat transfer by nonlinear conduction. Phys. Fluids 28, 232–244.Google Scholar
Piriz, A. R. 2001 a Hydrodynamic instability of ablation fronts in inertial confinement fusion. Phys. Plasmas 8, 997–1002.Google Scholar
Piriz, A. R. 2001 b Compressibility effects on the Rayleigh–Taylor instability of an ablation front. Phys. Plasmas 8, 5268–5276.CrossRefGoogle Scholar
Piriz, A. R. & Portugues, R. F. 2003 Landau–Darrieus instability in an ablation front. Phys. Plasmas 10, 2449–2456.Google Scholar
Piriz, A. R., Sanz, J. & Ibañez, L. F. 1997 Rayleigh–Taylor instability of steady ablation fronts: the discontinuity model revisited. Phys. Plasmas 4, 1117–1126.CrossRefGoogle Scholar
Pulicani, J. P. 1988 A spectral multi-domain method for the solution of 1-D-Helmholtz and Stokes-type equations. Computers Fluids 16, 207–215.Google Scholar
Rayleigh, Lord 1883 Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density. Proc. Lond. Math. Soc. 14, 170–177 (In Scientific Papers, vol. 2, pp. 200–207. Cambridge University Press 1900.)Google Scholar
Reinicke, P. & Meyer-ter-Vehn, J. 1991 The point explosion with heat conduction. Phys. Fluids A 3, 1807–1818.CrossRefGoogle Scholar
Richtmyer, R. D. 1960 Taylor instability in shock acceleration of compressible fluids. Commun. Pure Appl. Maths 13, 297–319.CrossRefGoogle Scholar
Sanmartín, J. R. & Barrero, A. 1978 a Self-similar motion of laser half-space plasma. I. Deflagration regime. Phys. Fluids 21, 1957–1966.Google Scholar
Sanmartín, J. R. & Barrero, A. 1978 b Self-similar motion of laser half-space plasma. II. Thermal wave and intermediate regimes. Phys. Fluids 21, 1967–1971.CrossRefGoogle Scholar
Sanz, J. 1996 Self-consistent analytical model of the Rayleigh–Taylor instability in inertial confinement fusion. Phys. Rev. E 53, 4026–4045.Google ScholarPubMed
Sanz, J., Piriz, A. R. & Tomasel, F. G. 1992 Self-similar model for tamped ablation driven by thermal radiation. Phys. Fluids B 4, 683–692.CrossRefGoogle Scholar
Sanz, J., Masse, L. & Clavin, P. 2006 The linear Darrieus–Landau and Rayleigh–Taylor instabilities in inertial confinement fusion revisited. Phys. Plasmas 13, 102702.CrossRefGoogle Scholar
Schmitt, A. J., Velikovich, A. L., Gardner, J. H., Pawley, C., Obenschain, S. P., Aglitskiy, Y. & Chan, Y. 2001 Growth of pellet imperfections and laser imprint in direct drive inertial confinement fusion targets. Phys. Plasmas 8, 2287–2295.Google Scholar
Stoker, J. J. 1958 Water Waves. Wiley-Interscience.Google Scholar
Strikwerda, J. C. 1977 Initial boundary value problems for incompletely parabolic systems. Commun. Pure Appl. Maths 30, 797–822.Google Scholar
Takabe, H., Mima, K., Montierth, L. & Morse, R. L. 1985 Self-consistent growth rate of the Rayleigh–Taylor instability in an ablatively accelerating plasma. Phys. Fluids 28, 3676–3682.Google Scholar
Taylor, G. I. 1950 The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I. Proc. R. Soc. Lond. A 201, 192–196.Google Scholar
Taylor, R. J., Dahlburg, J. P., Iwase, A., Gardner, J. H., Fyfe, D. E. & Willi, O. 1996 Measurement and simulation of laser imprinting and consequent Rayleigh–Taylor growth. Phys. Rev. Lett. 76, 1643–1646.Google Scholar
Velikovich, A. L., Dahlburg, J. P., Gardner, J. H. & Taylor, R. J. 1998 Saturation of perturbation growth in ablatively driven planar laser targets. Phys. Plasmas 5, 1491–1505.Google Scholar
Williamson, J. H. 1980 Low-storage Runge–Kutta schemes. J. Comput. Phys. 35, 48–56.Google Scholar
Zel'dovich, Y. & Raizer, Y. 1967 Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena. Academic.Google Scholar