Linear perturbation response of self-similar ablative flows relevant to inertial confinement fusion

Abstract

A family of exact similarity solutions for inviscid compressible ablative flows in slab symmetry with nonlinear heat conduction is proposed for studying unsteadiness and compressibility effects on the hydrodynamic stability of ablation fronts relevant to inertial confinement fusion. Dynamical multi-domain Chebyshev spectral methods are employed for computing both the similarity solution and its time-dependent linear perturbations. This approach has been exploited to analyse the linear stability properties of two self-similar ablative configurations subjected to direct laser illumination asymmetries. Linear perturbation temporal and reduced responses are analysed, evidencing a maximum instability for illumination asymmetries of zero transverse wavenumber as well as three distinct regimes of ablation-front distortion evolution, and emphasizing the importance of the mean flow unsteadiness, compressibility and stratification.

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

“…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.…”

“…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.…”

Investigation of supersonic heat-conductivity hyperbolic waves in radiative ablation flows

“…An intermediate approach between simplified modelings and simulations uses self-similar solutions to the Euler equations with nonlinear heat conduction [19][20][21]. Such solutions, known since Marshak [22], present the advantage over isobaric, isothermal or stationary solutions of rendering, without further approximations, compressibility, nonuniformity and unsteadiness of ablation waves.…”

Hydrodynamic instability of elastic-plastic solid plates at the early stage of acceleration

“…Such a situation has not been frequently considered in the literature. In fact, it has been investigated by Clarisse et al [43] for the case of an ablation front by using a self-similar solution for describing the ideal gas mean flow profiles in order to take into account the unsteadiness and compressibility effects on the instability evolution.…”