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Title: Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability

Abstract

The growth rate of the ablative Rayleigh-Taylor instability is approximated by {gamma}={radical}(kg/(1+kL))-{beta}km/{rho}{sub a}, where k is the perturbation wave number, g the gravity, L the density scale length, m the mass ablation rate, and {rho}{sub a} the peak target density. The coefficient {beta} was evaluated for the first time by measuring all quantities of this formula except for L, which was taken from the simulation. Although the experimental value of {beta}=1.2{+-}0.7 at short perturbation wavelengths is in reasonably good agreement with the theoretical prediction of {beta}=1.7, it is found to be larger than the prediction at long wavelengths.

Authors:
; ; ; ; ; ; ; ; ;  [1]
  1. Institute of Laser Engineering, Osaka University, 2-6 Yamada-oka, Suita, Osaka 565-0871 (Japan)
Publication Date:
OSTI Identifier:
20861646
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review Letters; Journal Volume: 98; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevLett.98.045002; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ABLATION; GRAVITATION; MASS; PERTURBATION THEORY; PLASMA DIAGNOSTICS; RAYLEIGH-TAYLOR INSTABILITY; SIMULATION; WAVELENGTHS

Citation Formats

Azechi, H., Sakaiya, T., Fujioka, S., Tamari, Y., Otani, K., Shigemori, K., Nakai, M., Shiraga, H., Miyanaga, N., and Mima, K. Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability. United States: N. p., 2007. Web. doi:10.1103/PHYSREVLETT.98.045002.
Azechi, H., Sakaiya, T., Fujioka, S., Tamari, Y., Otani, K., Shigemori, K., Nakai, M., Shiraga, H., Miyanaga, N., & Mima, K. Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability. United States. doi:10.1103/PHYSREVLETT.98.045002.
Azechi, H., Sakaiya, T., Fujioka, S., Tamari, Y., Otani, K., Shigemori, K., Nakai, M., Shiraga, H., Miyanaga, N., and Mima, K. Fri . "Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability". United States. doi:10.1103/PHYSREVLETT.98.045002.
@article{osti_20861646,
title = {Comprehensive Diagnosis of Growth Rates of the Ablative Rayleigh-Taylor Instability},
author = {Azechi, H. and Sakaiya, T. and Fujioka, S. and Tamari, Y. and Otani, K. and Shigemori, K. and Nakai, M. and Shiraga, H. and Miyanaga, N. and Mima, K.},
abstractNote = {The growth rate of the ablative Rayleigh-Taylor instability is approximated by {gamma}={radical}(kg/(1+kL))-{beta}km/{rho}{sub a}, where k is the perturbation wave number, g the gravity, L the density scale length, m the mass ablation rate, and {rho}{sub a} the peak target density. The coefficient {beta} was evaluated for the first time by measuring all quantities of this formula except for L, which was taken from the simulation. Although the experimental value of {beta}=1.2{+-}0.7 at short perturbation wavelengths is in reasonably good agreement with the theoretical prediction of {beta}=1.7, it is found to be larger than the prediction at long wavelengths.},
doi = {10.1103/PHYSREVLETT.98.045002},
journal = {Physical Review Letters},
number = 4,
volume = 98,
place = {United States},
year = {Fri Jan 26 00:00:00 EST 2007},
month = {Fri Jan 26 00:00:00 EST 2007}
}
  • A simple procedure is developed to determine the Froude number Fr, the effective power index for thermal conduction {nu}, the ablation-front thickness L{sub 0}, the ablation velocity V{sub a}, 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 {bold 29}, 2067 (1986)]. These quantities are then used to calculate the growth rate of the ablative Rayleigh{endash}Taylor instability using the theory developed by Goncharov {ital et al.} [Phys. Plasmas {bold 3}, 4665 (1996)]. The complicatedmore » expression of the growth rate (valid for arbitrary Froude numbers) derived by Goncharov {ital et al.} is simplified by using reasonably accurate fitting formulas. {copyright} {ital 1998 American Institute of Physics.}« less
  • A simple model for the instability of a steady ablation front is presented. The model is based on the sharp boundary approximation, but it is considered that, as far as the Rayleigh--Taylor instability regards, the front thickness is of the order of the minimum scale length of the density gradient. The model yields a general analytical expression for the linear growth rate, which does not depend explicitly on the particular process of energy deposition, which drives the ablation. For the specific case of electronic thermal conduction the model is in good agreement with previously reported numerical calculations. The growth ratemore » results to be well fitted by the so-called Takabe formula, and the coefficients in such a formula are analytically derived. {copyright} {ital 1995} {ital American} {ital Institute} {ital of} {ital Physics}.« less
  • We consider the Rayleigh-Taylor instability in exponential density profiles and derive two approximate expressions for the growth rate that are explicit and involve only the Atwood number {ital A} and the wave number {ital k}. Our results agree with the exact growth rate within 6--12 %. We also point out that a recently published expression deviates from the exact growth rate for practically all values of {ital A} and {ital k} (M. H. Emery, J. P. Dahlburg, and J. H. Gardner, Phys. Fluids 31, 1007 (1988)).
  • Growth rates of the Rayleigh-Taylor instability in foils accelerated with a laser beam smoothed by induced spatial incoherence were measured and compared with hydrodynamic code simulations. Modes with 150- and 100-..mu..m wavelengths grew at predicted rates. However, no growth was experimentally observed at a 50-..mu..m wavelength. Code simulations suggest that induced spatial incoherence can influence the 50-..mu..m Rayleigh-Taylor mode by delaying the start of its growth.
  • The nonlinear saturation amplitudes attained by Rayleigh--Taylor perturbations growing on ablatively stabilized laser fusion targets are crucial in determining the survival time of those targets. For a given set of baseline simulation parameters, the peak amplitude is found to be a progressive function of cross-sectional perturbation shape as well as of wave number, with three-dimensional (3-D) square modes and two-dimensional (2-D) axisymmetric bubbles saturating later, and at higher amplitudes than two-dimensional planar modes. In late nonlinear times hydrodynamic evolution diverges; the 3-D square mode bubble continues to widen, while the 2-D axisymmetric bubble fills in.