Linear Perturbation Amplification in Self-Similar Ablation Flows of Inertial Confinement Fusion

Abéguilé, Florian; Boudesocque-Dubois, Carine; Clarisse, Jean-Marie; Gauthier, Serge; Saillard, Yves

doi:10.1103/physrevlett.97.035002

Cited by 14 publications

(32 citation statements)

References 23 publications

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“…Goncharov had pointed out that long-wavelength modes with kD c < 1 grow because of the combined effect of the RM-like and Landau-Darrieus instabilities (Landau & Lifshitz 1987), although the modes with kD c > 1 are stable and experience oscillatory behaviour by the dynamic overpressure, where D c is the length of the thermal conduction region. Abéguilé et al had obtained a self-similar model with continuous unsteady compressible ablation flows (Abéguilé et al 2006;Clarisse et al 2008). That model reveals the existence of three different regimes of kD c for the evolution of the ablation surface deformation.…”

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

confidence: 99%

“…Finite length effects of the thermal conduction region on the ablative RMI have been recently considered in detail (Abéguilé et al 2006;Goncharov et al 2006;Gotchev et al 2006;Clarisse et al 2008). Goncharov had pointed out that long-wavelength modes with kD c < 1 grow because of the combined effect of the RM-like and Landau-Darrieus instabilities (Landau & Lifshitz 1987), although the modes with kD c > 1 are stable and experience oscillatory behaviour by the dynamic overpressure, where D c is the length of the thermal conduction region.…”

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

confidence: 99%

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Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

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%

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Nishihara

Wouchuk

Matsuoka

et al. 2010

Phil. Trans. R. Soc. A.

130

128

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“…[16][17][18] This idea has already been successfully applied to the linear stability of self-similar ablation flows in the case of an ideal gas. 19,20…”

Section: Discussionmentioning

confidence: 99%

Self-similar solutions for a nonlinear radiation diffusion equation

et al. 2006

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This paper considers the hydrodynamic equations with nonlinear conduction when the internal energy and the opacity have power-law dependences in the density and in the temperature. This system models the situation in which a dense solid is brought into contact with a thermal bath. It supports self-similar solutions that depend on the surface temperature. The self-similar solution can exhibit a shock wave followed by an ablation front if the surface temperature does not increase too fast in time, but it can exhibit a heat front followed by an isothermal shock otherwise. These flows are carefully studied in order to clarify the role of the initial solid density in the energy absorption and the ablation process. Comparisons with numerical simulations show excellent agreement.

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“…[6][7][8][9][10] These particular solutions remain difficult to compute numerically. For specific boundary conditions, there are simplified solutions expressible in terms of ordinary differential equations.…”

Section: Introductionmentioning

confidence: 99%

Principles of the radiative ablation modeling

2010

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Indirectly driven inertial confinement fusion ͑ICF͒ rests on the setting up of a radiation temperature within a laser cavity and on the optimization of the capsule implosion ablated by this radiation. In both circumstances, the ablation of an optically thick medium is at work. The nonlinear radiation conduction equations that describe this phenomenon admit different kinds of solutions called generically Marshak waves. In this paper, a completely analytic model is proposed to describe the ablation in the subsonic regime relevant to ICF experiments. This model approximates the flow by a deflagrationlike structure where Hugoniot relations are used in the stationary part from the ablation front up to the isothermal sonic Chapman-Jouguet point and where the unstationary expansion from the sonic point up to the external boundary is assumed quasi-isothermal. It uses power law matter properties. It can also accommodate arbitrary boundary conditions provided the ablation wave stays very subsonic and the surface temperature does not vary too quickly. These requirements are often met in realistic situations. Interestingly, the ablated mass rate, the ablation pressure, and the absorbed radiative energy depend on the time history of the surface temperature, not only on the instantaneous temperature values. The results compare very well with self-similar solutions and with numerical simulations obtained by hydrodynamic code. This analytic model gives insight into the physical processes involved in the ablation and is helpful for optimization and sensitivity studies in many situations of interest: radiation temperature within a laser cavity, acceleration of finite size medium, and ICF capsule implosion, for instance.

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Linear Perturbation Amplification in Self-Similar Ablation Flows of Inertial Confinement Fusion

Cited by 14 publications

References 23 publications

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

Self-similar solutions for a nonlinear radiation diffusion equation

Principles of the radiative ablation modeling

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