Instability of a contact surface driven by a nonuniform shock wave

Abstract

Stability of a uniform contact surface is investigated in the case when a nonuniform shock wave passes through the surface. The nonuniform shock is generated by a rippled piston that moves with constant velocity. The amplitude of the shock oscillates and decreases as it propagates. A uniform contact surface is found to be unstable after the nonuniform shock passes across it. The growth rate depends sensitively on the phase of the oscillating shock wave at the time when the shock hits the contact surface. The physical mechanism of the instability is qualitatively discussed. The linear and nonlinear evolutions of the instability are studied. In particular, the dependence of the linear case on the Atwood number for a weak shock is investigated. Properties of this stability are found to exhibit differences from those of the standard Richtmyer-Meshkov instability in both the linear and nonlinear cases. ͓S1063-651X͑96͒50406-X͔ PACS number͑s͒: 52.35.ϪgIn inertial confinement fusion, fuel is required to be compressed approximately up to 1000 times solid density. An asymmetric implosion associated with hydrodynamic instabilities disturbs uniform high density compression and reduces fusion reaction yield. Nonuniform laser irradiation leads to nonuniform ablation and thus to the generation of nonuniform shock waves. This could seed density perturbations that will grow later due to the Rayleigh-Taylor ͑RT͒ instability in the acceleration phase. This happens even if the target surface is initially uniform.It is well known that a nonuniform contact surface becomes unstable when a ͑uniform͒ shock wave passes through the contact surface because of the so-called Richtmyer-Meshkov ͑RM͒ instability ͓1,2͔. In this paper we investigate the stability of a uniform contact surface when the nonuniform shock passes through it. It will be shown that the uniform contact surface becomes unstable and the growth rate depends on the phase of the oscillating shock wave at the time when the shock hits the material interface. Both linear and nonlinear evolutions of the instability are found to have differences from the RM instability.We consider a shock wave driven by a rippled piston as shown in Fig. 1͑a͒. In the figure, the piston is located at zϭ0 in a reference frame moving with the piston, and the shock propagates in the z direction with the speed of v s relatively to the piston. We consider the surface modulation of the piston to be given as a 0 exp͑ikx͒, where a 0 and k are the amplitude and the wave number, respectively. The surface modulation of the piston induces perturbations of velocity u, density , and pressure p in the shock compressed region.In the linear theory ͓1͔, the pressure perturbation in the shock compressed region satisfies the wave equation:where c 1 is the sound speed in the shock compressed region. The subscripts 0, 1, and 2 denote, respectively, the values ahead of the shock, behind the shock, and beyond the contact surface as shown in Fig. 1͑a͒. The superscripts 0 and 1 denote the unperturbed and first-order quantities...

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

“…Once a rippled shock is launched, a pressure perturbation is induced by lateral fluid motion behind the shock, and the pressure perturbation causes the ripple of the shock front to be reversed and subsequently oscillate, similar to the shockinterface interaction discussed before. However, compared with the rippled shock driven by a rippled rigid piston (dotted line in figure 7; Briscoe & Kovitz 1968;Ishizaki et al 1996), the amplitude of the shock surface ripple driven by laser ablation decays much faster than that driven by a rigid piston. The pressure perturbation increases the deformation of the ablation front monotonously.…”

Laser-induced evolution of hypocycloidal formation of vortex filaments from nonlinear Rayleigh–Taylor instability in a thin layer of molten metal

“…The dependence of the growth rates on the shock phase was found to be similar even for different Atwood numbers. 9 We have shown that the contour of the vortex filament selforganization depends on the phase of the RT instability modes.…”

First Measurements of Fuel-Ablator Interface Instability Growth in Inertial Confinement Fusion Implosions on the National Ignition Facility

“…Instability growth at the fuel-ablator interface can originate either from a local perturbation at this interface or from a perturbation that imprints from the ablation front [20][21][22][23][24][25][26]. These experiments address both scenarios.…”