Basic hydrodynamics of Richtmyer-Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions

Anisotropic evolutions of the magnetohydrodynamic Richtmyer-Meshkov instability induced by a converging shock

The investigation of the converging shock-induced Richtmyer-Meshkov instability, which arises from the interaction of converging shocks with the interface between materials of differing densities in cylindrical capsules, is of significant importance in the field of inertial confinement fusion (ICF). The use of converging shocks, which exhibit higher efficiency than planar shocks in the development of the RMI due to the Bell-Plesset effects, is particularly relevant to energy production in the ICF. Moreover, external magnetic fields are often utilized to mitigate the development of the RMI. This paper presents a systematic investigation of the anisotropic nature of the Richtmyer-Meshkov instability in magnetohydrodynamic induced by the interaction between converging shocks and perturbed semicylindrical density interfaces (DI) based on numerical simulations using Athena++. The results reveal that magnetic fields with β=1000, 100, and 10 (β is defined as the ratio of the plasma pressure to the magnetic pressure) lead to an anisotropic intensification of magnetic fields, anisotropic accelerations of various shock waves [including the converging incident shock (CIS), transmitted shock (TS), and reflected shock (RS)], and anisotropic growth of the DI with subsequent anisotropic vorticity distribution. Upon closer inspection, it becomes evident that these phenomena are strongly interconnected. In particular, the region where the wave front of the CIS impacts the middle point of semicylindrical DI, where the magnetic field is more perpendicular to the fluid motion, experiences a more significant amplification of the magnetic fields. This generates higher-pressure jumps, which in turn accelerates the shock wave near this region. Furthermore, the anisotropic amplification of the magnetic fields reduces the movement of the RMI near the middle point of semicylindrical DI and leads to the anisotropic formation of RMI-induced bubbles and spikes, as well as vortices. By examining vorticity distributions, the results underscore the crucial role of magnetic tension forces in inhibiting fluid rotation.

Interface dynamics and flow fields’ structure under thermal heat flux, thermal conductivity, destabilizing acceleration and inertial stabilization

Abstract

Interfaces and interfacial mixing are omnipresent in fluids, plasmas, materials in vastly different environments. A thorough understanding of their fundamentals is essential in many areas of science, mathematics, and technology. This work focuses on the classical problem of stability of a phase boundary that is a subject to fluxes of heat and mass across it for non-ideal thermally conducting fluids. We develop a rigorous theory resolving challenges not addressed before, including boundary conditions for thermal heat flux, structure of perturbation waves, and dependence of waves coupling on system parameters in a broad range of conditions. We discover the novel class of fluid instabilities in the three regimes—advection, diffusion, and low Mach—with properties that were never earlier discussed and that are defined by the interplay of the thermal heat flux, thermal conductivity and destabilizing acceleration with the inertial stabilization. We reveal the parameter controlling transitions between the regimes through varying the initial conditions. We find that the interface stability is set primarily by the macroscopic inertial mechanism balancing the destabilizing acceleration. The thermal heat flux and the microscopic thermodynamics create vortical fields in the bulk. By linking micro to macro scales, the interface is the place where balances are achieved.

Article highlights

Stability of ablation flows in inertial confinement fusion: Nonmodal effects

Fast transient growth of hydrodynamic perturbations due to nonmodal effects is shown to be possible in an ablation flow relevant to inertial confinement fusion (ICF). Likely to arise in capsule ablators with material inhomogeneities, such growths appear to be too fast to be detected by existing measurement techniques, cannot be predicted by any of the methods previously used for studying hydrodynamic instabilities in ICF, yet could cause early transitions to nonlinear regimes. These findings call for reconsidering the stability of ICF flows within the framework of nonmodal stability theory.

Multimode Hydrodynamic Instability Growth of Preimposed Isolated Defects in Ablatively Driven Foils

The Nike KrF laser facility was used to study the evolution of isolated defects with characteristic sizes of <1 to 10s of μm in laser-accelerated plastic foils. The experimental platform permitted, for the first time, the systematic study of localized perturbation growth, which is inherently multimode, through ablative Richtmyer-Meshkov and Rayleigh-Taylor stages and into the strongly nonlinear regime. Initial target defects were relatively large amplitude, but spatially localized, and emulated tent, fill-tube, and other nonuniformities that are present in inertial confinement fusion capsules. Face-on x-ray radiography indicated initial growth of the perturbation in both depth and width, followed by its apparent closure due to oblique spike growth. Hollow jetlike profiles of laterally expanding, rising, Rayleigh-Taylor bubbles were observed on the rear surface of the target from each isolated defect. Radiation hydrodynamic simulations provided insight into the mechanism of the closure and other features of the bubble and spike evolution specific to isolated defects.

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

We carry out a numerical investigation of three-dimensional linear perturbations in a self-similar ablation wave in slab symmetry, representative of the shock transit phase of a pellet implosion in inertial confinement fusion (ICF). The physics of ablation is modeled by the equation of gas dynamics with a nonlinear heat conduction as an approximation for radiation transport. Linear perturbation responses of the flow, its external surface, and shock-wave front, when excited by external pressure or heat-flux perturbation pulses, are computed by fully taking into account the flow compressibility, nonuniformity, and unsteadiness. These responses show the effective propagation, at supersonic speeds, of perturbations from the flow external surface through the whole conduction region of the ablation wave, beyond its Chapman-Jouguet point, and up to the ablation front, after the birth of the ablation wave. This supersonic forward propagation of perturbations is evidenced by means of a set of appropriate pseudocharacteristic variables and is analyzed to be associated to the "heat-conductivity" waves previously identified by Clarisse et al. [J. Fluid Mech. 848, 219 (2018)JFLSA70022-112010.1017/jfm.2018.343]. Such heat-conductivity linear waves are found to prevail over heat diffusion as a feedthrough mechanism [Aglitskiy et al., Philos. Trans. R. Soc. A 368, 1739 (2010)PTRMAD1364-503X10.1098/rsta.2009.0131] for perturbations of longitudinal characteristic lengths of the order of-or larger than-the conduction region size, and long transverse wavelengths with respect to this region size, and over time scales shorter to much shorter than the shock transit phase duration. This mechanism, which results from the dependency of the heat conductivity on temperature and density in conjunction with a flow temperature stratification, is expected to occur for other types of nonlinear heat conductions-e.g., electron heat conduction-as well as to be efficient at transmitting large scale perturbations from the surrounding of an ICF pellet to its inner compressed core at later times of its implosion. Besides, the proposed set of pseudocharacteristic variables are recommended for analyzing perturbation dynamics in an ablation flow as it furnishes additional propagation information over the fundamental linear modes of fluid dynamics [Kovásznay, J. Aeronautic. Sci. 20, 657 (1953)1936-995610.2514/8.2793], especially in the flow conduction region.

Morphodynamics of a dense particulate medium under radial explosion

In this paper, we investigate the initiation and growth of instability patterns arising from the shock loaded internal surfaces of granular rings confined in a Hele-Shaw cell using both experimental and numerical approaches. A variety of patterns are formed in granular media consisting of grains with varying morphologies. When the particle shape becomes increasingly irregular, and/or the gap in the Hele-Shaw cell becomes narrower, it is increasingly hard for confined particles to fluidize. Consequently the emergent pattern transitions from a smooth circle with trivial undulation which grows in a self-similar manner to an unstable finger-like structure with significant tip-splitting. The distinct growth mode of the well-defined instability pattern is closely associated with its inception phase alongside the transmission of the compaction front. The runaway growth of the incipient perturbations gives rise to the unstable growth of the late-time finger-like instabilities. Conversely the minimal growth of the perturbations in the inception phase guarantees the ensuing self-similar growth of the instability patterns featuring insignificant corrugation. The grain-scale simulations reveal the fundamental role played by the heterogeneous non-linear force network inherent to granular media in the stable-to-unstable transition of the instability pattern. The present work reveals the correlation between the grain-scale physics underpinning the formation of surface instability upon shock loading granular media and the nature of the resulting macro-scale instability patterns. The macroscopic flowability of particles through the confined space is found to be the foremost indicator of the nature of the shock induced granular instability pattern.

Rayleigh-Taylor instabilities in high-energy density settings on the National Ignition Facility

The Rayleigh-Taylor (RT) instability occurs at an interface between two fluids of differing density during an acceleration. These instabilities can occur in very diverse settings, from inertial confinement fusion (ICF) implosions over spatial scales of [Formula: see text] cm (10-1,000 μm) to supernova explosions at spatial scales of [Formula: see text] cm and larger. We describe experiments and techniques for reducing ("stabilizing") RT growth in high-energy density (HED) settings on the National Ignition Facility (NIF) at Lawrence Livermore National Laboratory. Three unique regimes of stabilization are described: (i) at an ablation front, (ii) behind a radiative shock, and (iii) due to material strength. For comparison, we also show results from nonstabilized "classical" RT instability evolution in HED regimes on the NIF. Examples from experiments on the NIF in each regime are given. These phenomena also occur in several astrophysical scenarios and planetary science [Drake R (2005) Plasma Phys Controlled Fusion 47:B419-B440; Dahl TW, Stevenson DJ (2010) Earth Planet Sci Lett 295:177-186].

Interface dynamics: Mechanisms of stabilization and destabilization and structure of flow fields

Interfacial mixing and transport are nonequilibrium processes coupling kinetic to macroscopic scales. They occur in fluids, plasmas, and materials over celestial events to atoms. Grasping their fundamentals can advance a broad range of disciplines in science, mathematics, and engineering. This paper focuses on the long-standing classic problem of stability of a phase boundary-a fluid interface that has a mass flow across it. We briefly review the recent advances in theoretical and experimental studies, develop the general theoretical framework directly linking the microscopic interfacial transport to the macroscopic flow fields, discover mechanisms of interface stabilization and destabilization that have not been discussed before for both inertial and accelerated dynamics, and chart perspectives for future research.

Two-dimensional implosion simulations with a kinetic particle code

We perform two-dimensional implosion simulations using a Monte Carlo kinetic particle code. The application of a kinetic transport code is motivated, in part, by the occurrence of nonequilibrium effects in inertial confinement fusion capsule implosions, which cannot be fully captured by hydrodynamic simulations. Kinetic methods, on the other hand, are able to describe both continuum and rarefied flows. We perform simple two-dimensional disk implosion simulations using one-particle species and compare the results to simulations with the hydrodynamics code rage. The impact of the particle mean free path on the implosion is also explored. In a second study, we focus on the formation of fluid instabilities from induced perturbations. We find good agreement with hydrodynamic studies regarding the location of the shock and the implosion dynamics. Differences are found in the evolution of fluid instabilities, originating from the higher resolution of rage and statistical noise in the kinetic studies.

Evolution of surface structure in laser-preheated perturbed materials

We report an experimental and computational study investigating the effects of laser preheat on the hydrodynamic behavior of a material layer. In particular, we find that perturbation of the surface of the layer results in a complex interaction, in which the bulk of the layer develops density, pressure, and temperature structure and in which the surface experiences instability-like behavior, including mode coupling. A uniform one-temperature preheat model is used to reproduce the experimentally observed behavior, and we find that this model can be used to capture the evolution of the layer, while also providing evidence of complexities in the preheat behavior. This result has important consequences for inertially confined fusion plasmas, which can be difficult to diagnose in detail, as well as for laser hydrodynamics experiments, which generally depend on assumptions about initial conditions in order to interpret their results.

Reynolds number effects on the single-mode Richtmyer-Meshkov instability

The Reynolds number effects on the nonlinear growth rates of the Richtmyer-Meshkov instability are investigated using two-dimensional numerical simulations. A decrease in Reynolds number gives an increased time to reach nonlinear saturation, with Reynolds number effects only significant in the range Re<256. Within this range there is a sharp change in instability properties. The bubble and spike amplitudes move towards equal size at lower Reynolds numbers and the bubble velocities decay faster than predicted by Sohn's model [S.-I. Sohn, Phys. Rev. E 80, 055302 (2009)PLEEE81539-375510.1103/PhysRevE.80.055302]. Predicted amplitudes show reasonable agreement with the existing theory of Carles and Popinet [P. Carles and S. Popinet, Phys. Fluids Lett. 13, 1833 (2001)10.1063/1.1377863; Eur. J. Mech. B 21, 511 (2002)EJBFEV0997-754610.1016/S0997-7546(02)01199-8] and Mikaelian [K. O. Mikaelian, Phys. Rev. E 47, 375 (1993)1063-651X10.1103/PhysRevE.47.375; K. O. Mikaelian, Phys. Rev. E 87, 031003 (2013)PLEEE81539-375510.1103/PhysRevE.87.031003], with the former being the closest match to the current computations.

Scale-to-scale energy transfer in mixing flow induced by the Richtmyer-Meshkov instability

The Richtmyer-Meshkov instability (RMI) mixing flow induced by a planar shock wave of Mach 1.6 is investigated using direct numerical simulation method. Interfacial perturbations of different scales between air and sulfur hexafluoride are introduced to study the effect of the initial conditions. Focus is placed on the analysis of the scale-to-scale transfer of kinetic energy in both Fourier and physical spaces. The kinetic energy injected from the perturbation scales is transferred to both larger and smaller scales in an average sense within the inner mixing zone (IMZ) at early times and is mainly passed down into smaller scales at the late stage. The physical-space energy flux due to the subgrid-scale (SGS) stress is studied using a filtering approach in order to shed light on the physical origin of the scale-to-scale kinetic energy transfer. It is found that the pointwise SGS energy flux is highly correlated with the local spike and bubble structures in the IMZ. Moreover, it turns out that the mean SGS energy flux is mainly ascribed to the component in the direction of shock wave propagation. An analysis using the method of conditional averaging manifests that the generation of local SGS energy flux is associated with the property of the surrounding flow induced by quadrupolar or dipolar vortex structures.

Passage of a shock wave through inhomogeneous media and its impact on gas-bubble deformation

The paper investigates shock-induced vortical flows within inhomogeneous media of nonuniform thermodynamic properties. Numerical simulations are performed using a Eulerian type mathematical model for compressible multicomponent flow problems. The model, which accounts for pressure nonequilibrium and applies different equations of state for individual flow components, shows excellent capabilities for the resolution of interfaces separating compressible fluids as well as for capturing the baroclinic source of vorticity generation. The developed finite volume Godunov type computational approach is equipped with an approximate Riemann solver for calculating fluxes and handles numerically diffused zones at flow component interfaces. The computations are performed for various initial conditions and are compared with available experimental data. The initial conditions promoting a shock-bubble interaction process include weak to high planar shock waves with a Mach number ranging from 1.2 to 3 and isolated cylindrical bubble inhomogeneities of helium, argon, nitrogen, krypton, and sulphur hexafluoride. The numerical results reveal the characteristic features of the evolving flow topology. The impulsively generated flow perturbations are dominated by the reflection and refraction of the shock, the compression, and acceleration as well as the vorticity generation within the medium. The study is further extended to investigate the influence of the ratio of the heat capacities on the interface deformation.

Observation of strong oscillations of areal mass in an unsupported shock wave

An experimental study of hydrodynamic perturbation evolution in a strong unsupported shock wave, which is immediately followed by an expansion wave, is reported. A planar solid plastic target rippled on the front side is irradiated with a 350-450 ps long laser pulse. The perturbation evolution in the target is observed using face-on monochromatic x-ray radiography during and for up to 4 ns after the laser pulse. The theoretically predicted large oscillations of the areal mass in the target are observed for the first time. Multiple phase reversals of the areal mass modulation are detected.

Turbulent mixing and beyond

Turbulence is a supermixer. Turbulent mixing has immense consequences for physical phenomena spanning astrophysical to atomistic scales under both high- and low-energy-density conditions. It influences thermonuclear fusion in inertial and magnetic confinement systems; governs dynamics of supernovae, accretion disks and explosions; dominates stellar convection, planetary interiors and mantle-lithosphere tectonics; affects premixed and non-premixed combustion; controls standard turbulent flows (wall-bounded and free-subsonic, supersonic as well as hypersonic); as well as atmospheric and oceanic phenomena (which themselves have important effects on climate). In most of these circumstances, the mixing phenomena are driven by non-equilibrium dynamics. While each article in this collection dwells on a specific problem, the purpose here is to seek a few unified themes amongst diverse phenomena.