Growth rates of the ablative Rayleigh–Taylor instability in inertial confinement fusion

A simple procedure is developed to determine the Froude number Fr, the effective power index for thermal conduction ν, the ablation-front thickness L0, the ablation velocity Va, and the acceleration g of laser-accelerated ablation fronts. These parameters are determined by fitting the density and pressure profiles obtained from one-dimensional numerical simulations with the analytic isobaric profiles of Kull and Anisimov [Phys. Fluids 29, 2067 (1986)]. These quantities are then used to calculate the growth rate of the ablative Rayleigh–Taylor instability using the theory developed by Goncharov et al. [Phys. Plasmas 3, 4665 (1996)]. The complicated expression of the growth rate (valid for arbitrary Froude numbers) derived by Goncharov et al. is simplified by using reasonably accurate fitting formulas.

[1]  Stephen M. Lane,et al.  HYADES—A plasma hydrodynamics code for dense plasma studies , 1994 .

[2]  J. D. Kilkenny,et al.  A review of the ablative stabilization of the Rayleigh--Taylor instability in regimes relevant to inertial confinement fusion , 1994 .

[3]  Robert L. McCrory,et al.  Self‐consistent stability analysis of ablation fronts in inertial confinement fusion , 1996 .

[4]  J. Lindl.  Development of the indirect‐drive approach to inertial confinement fusion and the target physics basis for ignition and gain , 1995 .

[5]  Steven A. Orszag,et al.  Nonlinear effects of multifrequency hydrodynamic instabilities on ablatively accelerated thin shells , 1982 .

[6]  S. Atzeni.  Ablative stabilization of short wavelength Rayleigh-Taylor instability , 1996 .

[7]  J. Nuckolls,et al.  Laser Compression of Matter to Super-High Densities: Thermonuclear (CTR) Applications , 1972, Nature.

[8]  R. Betti,et al.  Self‐consistent cutoff wave number of the ablative Rayleigh–Taylor instability , 1995 .

[9]  H. Kull.  Incompressible description of Rayleigh–Taylor instabilities in laser‐ablated plasmas , 1989 .

[10]  Stephen Wolfram,et al.  The Mathematica book (3rd ed.) , 1996 .

[11]  Adam T. Drobot,et al.  Computer Applications in Plasma Science and Engineering , 2011, Springer New York.

[12]  S. P. Gill,et al.  Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena , 2002 .

[13]  A. R. Piriz,et al.  Rayleigh-Taylor instability of steady ablation fronts: The discontinuity model revisited , 1997 .

[14]  L. Spitzer,et al.  TRANSPORT PHENOMENA IN A COMPLETELY IONIZED GAS , 1953 .

[15]  Mikaelian.  LASNEX simulations of the classical and laser-driven Rayleigh-Taylor instability. , 1990, Physical review. A, Atomic, molecular, and optical physics.

[16]  Sanz.  Self-consistent analytical model of the Rayleigh-Taylor instability in inertial confinement fusion. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[17]  S. Anisimov,et al.  Ablative stabilization in the incompressible Rayleigh--Taylor instability , 1986 .

[18]  Kunioki Mima,et al.  Self‐consistent growth rate of the Rayleigh–Taylor instability in an ablatively accelerating plasma , 1985 .

[19]  Stephen Wolfram,et al.  The Mathematica Book , 1996 .

[20]  G. Taylor.  The instability of liquid surfaces when accelerated in a direction perpendicular to their planes. I , 1950, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[21]  R. Betti,et al.  Self‐consistent stability analysis of ablation fronts with large Froude numbers , 1996 .

[22]  M. Liberman,et al.  Stabilization of the Rayleigh–Taylor instability by convection in smooth density gradient: Wentzel–Kramers–Brillouin analysis , 1992 .

[23]  Stephen E. Bodner,et al.  Rayleigh-Taylor Instability and Laser-Pellet Fusion , 1974 .