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Title: Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers

Abstract

Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble density increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.

Authors:
 [1];  [1];  [1];  [2];  [1]
  1. Univ. of Rochester, Rochester, NY (United States)
  2. Univ. of Science and Technology of China, Hefei (China)
Publication Date:
Research Org.:
Univ. of Rochester, Rochester, NY (United States). Lab. for Laser Energetics
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1417637
Report Number(s):
2017-162, 1368
Journal ID: ISSN 2470-0045; PLEEE8; 2017-162, 2324, 1368
Grant/Contract Number:
NA0001944; SC0014318; AC02-06CH11357; 20150568ER
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Physical Review E
Additional Journal Information:
Journal Volume: 97; Journal Issue: 1; Journal ID: ISSN 2470-0045
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS

Citation Formats

Zhang, H., Betti, R., Gopalaswamy, V., Yan, R., and Aluie, H. Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers. United States: N. p., 2018. Web. doi:10.1103/PhysRevE.97.011203.
Zhang, H., Betti, R., Gopalaswamy, V., Yan, R., & Aluie, H. Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers. United States. doi:10.1103/PhysRevE.97.011203.
Zhang, H., Betti, R., Gopalaswamy, V., Yan, R., and Aluie, H. 2018. "Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers". United States. doi:10.1103/PhysRevE.97.011203.
@article{osti_1417637,
title = {Nonlinear excitation of the ablative Rayleigh-Taylor instability for all wave numbers},
author = {Zhang, H. and Betti, R. and Gopalaswamy, V. and Yan, R. and Aluie, H.},
abstractNote = {Small-scale perturbations in the ablative Rayleigh-Taylor instability (ARTI) are often neglected because they are linearly stable when their wavelength is shorter than a linear cutoff. Using 2D and 3D numerical simulations, it is shown that linearly stable modes of any wavelength can be destabilized. This instability regime requires finite amplitude initial perturbations and linearly stable ARTI modes are more easily destabilized in 3D than in 2D. In conclusion, it is shown that for conditions found in laser fusion targets, short wavelength ARTI modes are more efficient at driving mixing of ablated material throughout the target since the nonlinear bubble density increases with the wave number and small scale bubbles carry a larger mass flux of mixed material.},
doi = {10.1103/PhysRevE.97.011203},
journal = {Physical Review E},
number = 1,
volume = 97,
place = {United States},
year = 2018,
month = 1
}

Journal Article:
Free Publicly Available Full Text
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  • The cutoff wave number of the incompressible ablative Rayleigh-Taylor instability is calculated using the physical optics approximation of the Wentzel-Kramers-Brillouin theory. It is found that a single value of the wave number [ital k] can correspond to multiple modes with different eigenfunctions and growth rates [gamma]. In the [gamma]-[ital k] plane the unstable spectrum is characterized by multiple branches with different cutoff wave numbers, and eigenfunctions with different number of zeros. The theory provides a formula for the cutoff wave number, valid in the regimes of interest for inertial confinement fusion capsules.
  • Weakly nonlinear stage of the ablative Rayleigh-Taylor instability has been studied by perturbation theory. Mode coupling of linear growing waves with wavenumbers {ital k}{sub {ital A}} and {ital k}{sub {ital B}} drives new excited waves with wavenumbers {ital k}{sub 0}(={ital k}{sub {ital A}}{plus_minus}{ital k}{sub {ital B}},2{ital k}{sub {ital A}},2{ital k}{sub {ital B}}). We have investigated time evolution of the excited waves and found that the ablation effect plays an important role even in nonlinear stage to reduce amplitude of the excited waves. Differences between an ablation surface and a classical contact surface have been discussed. Dependence of the excited wavemore » amplitude on the wavenumber {ital k}{sub 0}, the ablation velocity {ital v}{sub {ital a}}, and the effective gravity {ital g} is also investigated. {copyright} {ital 1996 American Institute of Physics.}« less
  • Here, a model for the nonlinear Rayleigh-Talyor instability (RTI) of a steady ablation front based on a sharp boundary approximation is presented. The model includes the effect of mass ablation and represents a basic tool for investigating many aspects of the nonlinear ablative RTI relevant to inertial confinement fusion. The single mode analysis shows the development of a nonlinear exponential instability for wave numbers close to the linear cutoff. Such a nonlinear instability grows at a rate faster than the linear growth rate and leads to saturation amplitudes significantly larger than the classical value 0.1 lambda. We also found thatmore » linearly stable perturbations with wave numbers larger than the linear cutoff become unstable when their initial amplitudes exceed a threshold vlaue. The shedding of long wavelength modes via mode coupling is much greater than predicted by the classical RTI theory. The effects of ablation on the evolution of a front of bubbles is also investigated and the front acceleration is computed.« less