Propagation of a Rippled Shock Wave Driven by Nonuniform Laser Ablation

Ishizaki, R.; Nishihara, Katsunobu

doi:10.1103/physrevlett.78.1920

Cited by 105 publications

(89 citation statements)

References 16 publications

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“…The wave equation for the pressure perturbation in the shockcompressed region can be solved analytically with proper boundary conditions as described earlier (Richtmyer 1960;Zaidel 1960;Briscoe & Kovitz 1968;Ishizaki et al 1996;Ishizaki & Nishihara 1997. The boundary conditions at the ablation surface are obtained by linearizing the CJ jump conditions, which give the relationships between the perturbations at the ablation front and those at the sonic point (Wouchuk & Piriz 1995;Ishizaki & Nishihara 1997. The first-order quantities at the sonic point are assumed to satisfy the condition that the local Mach number is equal to unity.…”

Section: (E) Rm-like Instabilities and Ablative Rmimentioning

confidence: 99%

“…The interaction between the rippled shock front and the ablation surface through sound waves may induce RM-like instability. It is important to study such growth of RM-like instabilities because they determine the seed of the RT instability that develops during the acceleration phase in ICF (Emery et al 1991;Desselberger et al 1995;Endo et al 1995;Azechi et al 1997;Ishizaki & Nishihara 1997Taylor et al 1997;Nishihara et al 1998;Goncharov 1999;Matsui et al 1999;Goncharov et al 2000;Velikovich et al 2000). A simple analytical model was developed to study propagation of a rippled shock associated with the initial surface roughness of a target in Ishizaki & Nishihara (1997.…”

Section: (E) Rm-like Instabilities and Ablative Rmimentioning

confidence: 99%

“…Region 0 is in a uniform state ahead of the shock; region 1 is the shock-compressed region; region A is an ablation layer between the ablation front and the sonic point; region 2 beyond the sonic point is an isothermal rarefaction region. The Rankine-Hugoniot and Chapman-Jouguet deflagration jump conditions were applied at the shock and ablation fronts, respectively, in Ishizaki & Nishihara (1997. They also assumed that the fluid velocity of the sonic point relative to the ablation surface is equal to the sound speed of the sonic point and that the density of the sonic point is the critical density (Manheimer & Colombant 1984).…”

Section: (E) Rm-like Instabilities and Ablative Rmimentioning

confidence: 99%

“…It is also an important phenomenon in inertial confinement fusion (ICF), as it invariably develops during the early stages of target irradiation, when a sequence of shocks travels through the target. As the shock fronts are not uniform, their corrugations will induce a highly perturbed flow behind them, which will be the seed for the Rayleigh-Taylor instability (RTI) that occurs later during the acceleration phase of the target (Ishizaki & Nishihara 1997;Piriz et al 1997;Nishihara et al 1998;Goncharov 1999;Velikovich et al 2000). The RMI has also been thoroughly studied in experiments designed in shock tubes (Jones & Jacobs 1997;Zabusky 1999;Brouillette 2002) and has also become a fascinating research topic in the field of high-energy density experiments in matter.…”

Section: Introductionmentioning

confidence: 99%

“…Comparisons with recent experiments and simulations are shown. We also discuss some RM-like instabilities, including ablative RMI (Ishizaki & Nishihara 1997;Goncharov 1999), which show stabilization of the instability owing to mass flow through the surface and dynamical overpressure in a corona.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

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130

128

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A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

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Section: (E) Rm-like Instabilities and Ablative Rmimentioning

confidence: 99%

Section: (E) Rm-like Instabilities and Ablative Rmimentioning

confidence: 99%

Section: (E) Rm-like Instabilities and Ablative Rmimentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

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130

128

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show abstract

Multiple elastic shock waves in cubic single crystals

Liu

et al. 2023

Shock Waves

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Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

2016

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A theoretical model is proposed to describe fully nonlinear dynamics of interfaces in twodimensional MHD flows based on an idea of non-uniform current-vortex sheet. Application of vortex sheet model to MHD flows has a crucial difficulty because of non-conservative nature of magnetic tension. However it is shown that when a magnetic field is initially parallel to an interface, the concept of vortex sheet can be extended to MHD flows (current-vortex sheet). Two-dimensional MHD flows are then described only by a one-dimensional Lagrange parameter on the sheet. It is also shown that bulk magnetic field and velocity can be calculated from their values on the sheet. The model is tested by MHD Richtmyer-Meshkov instability with sinusoidal vortex sheet strength. Two-dimensional ideal MHD simulations show that the nonlinear dynamics of a shocked interface with density stratification agrees fairly well with that for its corresponding potential flow. Numerical solutions of the model reproduce properly the results of the ideal MHD simulations, such as the roll-up of spike, exponential growth of magnetic field, and its saturation and oscillation. Nonlinear evolution of the interface is found to be determined by the Alfvén and Atwood numbers. Some of their dependence on the sheet dynamics and magnetic field amplification are discussed. It is shown by the model that the magnetic field amplification occurs locally associated with the nonlinear dynamics of the current-vortex sheet. We expect that our model can be applicable to a wide variety of MHD shear flows.

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Propagation of a Rippled Shock Wave Driven by Nonuniform Laser Ablation

Cited by 105 publications

References 16 publications

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Multiple elastic shock waves in cubic single crystals

Nonlinear Dynamics of Non-uniform Current-Vortex Sheets in Magnetohydrodynamic Flows

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