Growth Of Rayleigh-Taylor Instability Research Articles

Rayleigh-Taylor instability growth control by an oscillating acceleration in heavy ion inertial fusion

Uniformity of heavy ion beam (HIB) illumination is one of key issues in HIB inertial confinement fusion (HIF) in order to compress a fuel sufficiently and release fusion energy effectively. In this paper a new mitigation method of the Rayleigh-Taylor (R-T) instability growth is presented to make a HIF target robust against a non-uniform implosion. In this study a new mitigation method of the R-T instability growth is proposed based on an oscillating perturbed acceleration, which can be realized by a rotation or oscillation of the HIB illumination axis onto a fuel pellet. The R-T instability analyses and fluid simulations demonstrate that the oscillating acceleration reduces the R-T instability growth significantly. In this paper a baseline steady acceleration g0 is perturbed by a perturbed oscillating acceleration δg, which is spatially non-uniform and oscillates in time (g0 >> δg). An example result shows an 84% reduction of the R-T instability growth. In the analytical work two stratified inviscid fluids are treated under the perturbed oscillating acceleration. The linear analysis shows that the R-T instability growth rate does not change from the standard expression of γ. However, the R-T instability growth is strongly affected and mitigated by the oscillating acceleration; The transverse velocity of w is derived at the interface of the two stratified fluids. The R-T instability is induced by δg. The result presents that the perturbed oscillating acceleration reduces the R-T instability growth significantly depending on the magnitude of the HIB oscillation frequency.

Simulation of the growth of the 3D Rayleigh-Taylor instability in supernova remnants using an expanding reference frame

Context: The Rayleigh-Taylor instabilities generated by the deceleration of a supernova remnant during the ejecta-dominated phase are known to produce finger-like structures in the matter distribution which modify the geometry of the remnant. The morphology of supernova remnants is also expected to be modified when efficient particle acceleration occurs at their shocks. Aims: The impact of the Rayleigh-Taylor instabilities from the ejecta-dominated to the Sedov-Taylor phase is investigated over one octant of the supernova remnant. We also study the effect of efficient particle acceleration at the forward shock on the growth of the Rayleigh-Taylor instabilities. Methods: We modified the Adaptive Mesh Refinement code RAMSES to study with hydrodynamic numerical simulations the evolution of supernova remnants in the framework of an expanding reference frame. The adiabatic index of a relativistic gas between the forward shock and the contact discontinuity mimics the presence of accelerated particles. Results: The great advantage of the super-comoving coordinate system adopted here is that it minimizes numerical diffusion at the contact discontinuity, since it is stationary with respect to the grid. We propose an accurate expression for the growth of the Rayleigh-Taylor structures that connects smoothly the early growth to the asymptotic self-similar behaviour. Conclusions: The development of the Rayleigh-Taylor structures is affected, although not drastically, if the blast wave is dominated by cosmic rays. The amount of ejecta that makes it into the shocked interstellar medium is smaller in the latter case. If acceleration occurs at both shocks the extent of the Rayleigh-Taylor structures is similar but the reverse shock is strongly perturbed.

THREE-DIMENSIONAL SIMULATIONS OF MIXING INSTABILITIES IN SUPERNOVA EXPLOSIONS

We present the first three-dimensional (3D) simulations of the large-scale mixing that takes place in the shock-heated stellar layers ejected in the explosion of a 15.5 solar-mass blue supergiant star. The outgoing supernova shock is followed from its launch by neutrino heating until it breaks out from the stellar surface more than two hours after the core collapse. Violent convective overturn in the post-shock layer causes the explosion to start with significant asphericity, which triggers the growth of Rayleigh-Taylor (RT) instabilities at the composition interfaces of the exploding star. Deep inward mixing of hydrogen (H) is found as well as fast-moving, metal-rich clumps penetrating with high velocities far into the H-envelope of the star as observed, e.g., in the case of SN 1987A. Also individual clumps containing a sizeable fraction of the ejected iron-group elements (up to several 0.001 solar masses) are obtained in some models. The metal core of the progenitor is partially turned over with Ni-dominated fingers overtaking oxygen-rich bullets and both Ni and O moving well ahead of the material from the carbon layer. Comparing with corresponding 2D (axially symmetric) calculations, we determine the growth of the RT fingers to be faster, the deceleration of the dense metal-carrying clumps in the He and H layers to be reduced, the asymptotic clump velocities in the H-shell to be higher (up to ~4500 km/s for the considered progenitor and an explosion energy of 10^{51} ergs, instead of <2000 km/s in 2D), and the outward radial mixing of heavy elements and inward mixing of hydrogen to be more efficient in 3D than in 2D. We present a simple argument that explains these results as a consequence of the different action of drag forces on moving objects in the two geometries. (abridged)

Viscous Rayleigh-Taylor Instability Experiments at High Pressure and Strain Rate

Experimental results showing significant reductions from classical in the Rayleigh-Taylor instability growth rate due to high pressure effective lattice viscosity are presented. Using a laser created ramped drive, vanadium samples are compressed and accelerated quasi-isentropically at approximately 1 Mbar peak pressures, while maintaining the sample in the solid state. Comparisons with simulations and theory indicate that the high pressure, high strain rate conditions trigger a phonon drag mechanism, resulting in the observed high effective lattice viscosity and strong stabilization of the Rayleigh-Taylor instability.

Destabilizing effect of compressibility on Rayleigh–Taylor instability for fluids with fixed density profile

Analytical solutions for the growth rate of the Rayleigh–Taylor instability (RTI) for two superimposed fluids of exponentially varying densities are obtained by variational approach, which has been introduced to solve the eigenvalue problems related to RTI for inviscid compressible fluid. In order to distinguish the effect of density profile from compressibility effects, two independent parameters have been introduced to describe the static fluid states, one (Pa) is for the variation of pressure near the interface and the other (Pb) for setting the density profile. Three factors related to the RTI growth for compressible fluids have been discussed in detail. For incompressible fluids, the only factor to affect the RTI growth is the density profile. While for compressible fluids, besides the density profile, the specific heat ratio and the interface pressure also contribute to the growth rate of RTI. Analytic dispersion relations and growth rates have been compared to numerical results. It is found that compressibility alone acts a destabilizing role for fluids with fixed density profile.

Indirect drive ablative Rayleigh–Taylor experiments with rugby hohlraums on OMEGA

Results of ablative Rayleigh–Taylor instability growth experiments performed in indirect drive on the OMEGA laser facility [T. R. Boehly, D. L. Brown, S. Craxton et al., Opt. Commun. 133, 495 (1997)] are reported. These experiments aim at benchmarking hydrocodes simulations and ablator instabilities growth in conditions relevant to ignition in the framework of the Laser MégaJoule [C. Cavailler, Plasma Phys. Controlled Fusion 47, 389 (2005)]. The modulated samples under study were made of germanium-doped plastic (CHGe), which is the nominal ablator for future ignition experiments. The incident x-ray drive was provided using rugby-shaped hohlraums [M. Vandenboomgaerde, J. Bastian, A. Casner et al., Phys. Rev. Lett. 99, 065004 (2007)] and was characterized by means of absolute time-resolved soft x-ray power measurements through a dedicated diagnostic hole, shock breakout data and one-dimensional and two-dimensional (2D) side-on radiographies. All these independent x-ray drive diagnostics lead to an actual on-foil flux that is about 50% smaller than laser-entrance-hole measurements. The experimentally inferred flux is used to simulate experimental optical depths obtained from face-on radiographies for an extensive set of initial conditions: front-side single-mode (wavelength λ=35, 50, and 70 μm) and two-mode perturbations (wavelength λ=35 and 70 μm, in phase or in opposite phase). Three-dimensional pattern growth is also compared with the 2D case. Finally the case of the feedthrough mechanism is addressed with rear-side modulated foils.

Implosion dynamics and K-shell x-ray generation in large diameter stainless steel wire array Z pinches with various nesting configurations

Nested stainless steel wire array variations were investigated on the 20MA Z machine [R. B. Spielman et al., Phys. Plasmas 5, 2105 (1998)]. In order to reach experimentally observed electron temperatures near 3.8keV and excite the K shell, these ∼6.7keV photon energy x-ray sources must be of large initial diameter (45–80mm) which poses a concern for magnetic Rayleigh–Taylor instability growth. We discuss the implosion dynamics in these large diameter wire arrays, including an analysis of the ablation phase indicating that the prefill material is snowplowed at large radius. Nested array configurations with various mass and radius ratios are compared for instability mitigation and K-shell scaling. Degradation of the K-shell x-ray power and yield was observed for shots that did not have simultaneous implosion of the outer and inner wire arrays. Shots that were designed per this constraint exhibited K-shell yield scaling consistent with the model of J. W. Thornhill et al. [IEEE Trans. Plasma Sci. 34, 2377 (2006)] which had been benchmarked to single array results. This lends confidence to K-shell yield predictions using this model for future shots on the refurbished Z machine. Initial results employing a triple nested wire array to stabilize the large diameter implosion are also reported.

Rayleigh–Taylor instability in cylindrical geometry with compressible fluids

A linear stability analysis of the Rayleigh–Taylor instability (RTI) between two ideal inviscid immiscible compressible fluids in cylindrical geometry is performed. Three-dimensional (3D) cylindrical as well as two-dimensional (2D) axisymmetric and circular unperturbed interfaces are considered and compared to the Cartesian cases with planar interface. Focuses are on the effects of compressibility, geometry, and differences between the convergent (gravity acting inward) and divergent (gravity acting outward) cases on the early instability growth. Compressibility can be characterized by two independent parameters—a static Mach number based on the isothermal sound speed and the ratio of specific heats. For a steady initial unperturbed state, these have opposite influence, stabilization and destabilization, on the instability growth, similar to the Cartesian case [D. Livescu, Phys. Fluids 16, 118 (2004)]. The instability is found to grow faster in the 3D cylindrical than in the Cartesian case in the convergent configuration but slower in the divergent configuration. In general, the direction of gravity has a profound influence in the cylindrical cases but marginal for planar interface. For the 3D cylindrical case, instability grows faster in the convergent than in the divergent arrangement. Similar results are obtained for the 2D axisymmetric case. However, as the flow transitions from the 3D cylindrical to the 2D circular case, the results above can be qualitatively different depending on the Atwood number, interface radius, and compressibility parameters. Thus, 2D circular calculations of RTI growth do not seem to be a good model for the fully 3D cylindrical case.

Rayleigh–Taylor instability growth on low-density foam targets

In recent laser fusion programs, foam cryogenic targets have been developed as promising targets which have a great potential to realize efficient nuclear fusion. The foam is porous plastic material having a microstructure inside. We observed the growth of the Rayleigh–Taylor (RT) instability on the foam target with initial surface perturbation for the first time. The measured RT growth rate on the foam target was clearly suppressed in comparison to that of normal-density polystyrene (CH) targets. The values of the RT growth rate for the low-density foam target and the normal-density CH target were 0.84±0.15 (1∕ns) and 1.33±0.1 (1∕ns), respectively.

National Ignition Facility target design and fabrication

AbstractThe current capsule target design for the first ignition experiments at the NIF Facility beginning in 2009 will be a copper-doped beryllium capsule, roughly 2 mm in diameter with 160-µm walls. The capsule will have a 75-µm layer of solid deuterium-tritium on the inside surface, and the capsule will be powered by X-rays generated from a gold/uranium cocktail hohlraum. The design specifications are extremely rigorous, particularly with respect to interfaces, which must be very smooth to inhibit Rayleigh-Taylor instability growth. This paper outlines the current design, and focuses on the challenges and advances in capsule fabrication and characterization; hohlraum fabrication, and deuterium-tritium layering and characterization.

Compressibility Effects on the Rayleigh–Taylor Instability Growth Rates

Effects of two compressibility parameters, i.e. the ratio of specific heats and the equilibrium pressure at the interface, on the Rayleigh–Taylor instability (RTI) growth rates are studied under the same initial conditions, which include the mass, pressure profile, and density profile of the two superposed fluids. The results obtained reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. The influences of the ratio of specific heats on the RTI growth rates are not only stabilized but also destabilized. The effects of the equilibrium pressure at the interface on the growth rates are destabilized.

Reduction of the Rayleigh-Taylor instability growth with cocktail color irradiation

A novel method for reducing the Rayleigh-Taylor instability (RTI) growth in inertial confinement fusion (ICF) targets is reported. It is well known that high-density compression of ICF targets is potentially prevented by the RTI. Previous studies [K. Shigemori et al., Phys. Rev. Lett. 78, 250 (1997), S. G. Glendinning et al., Phys. Rev. Lett. 78, 3318 (1997), and H. Azechi et al., Phys. Plasmas 4, 4079 (1997)] have indicated that nonlocal electron heat transport enhances the effect on the ablative stabilization of the RTI growth with long wavelength laser irradiation. Planar target experiments, using a small fraction of a long wavelength laser (λ=0.53 or 1.05μm) in addition to the main drive laser (λ=0.35μm), were conducted to verify the RTI reduction by inducing the effect of the nonlocal electron heat transport. The measured RTI growth rate for this “cocktail-color” laser irradiation was clearly reduced from that for the “single-color” short-wavelength laser irradiation. The experimental growth factors are in good agreement with the ablative RTI formula coupled with a one-dimensional Fokker-Planck simulation code.

Stability study of planar targets using standard and adiabat shaping pulses

The hydrodynamic stability of a planar target is considered for the conditions of the direct drive inertial confinement fusion. It has been recently proposed to reduce the ablative Rayleigh-Taylor instability growth by using the adiabat shaping in the ablation zone. In this work, we consider the relaxation adiabat shaping scheme [K. Anderson and R. Betti, Phys. Plasmas 11, 5 (2004); R. Betti, K. Anderson, J. P. Knauer, T. J. B. Collins, R. L. McCrory, P. W. McKenty, and S. Skupsky, Phys. Plasmas 12, 042703 (2005)]. In this scheme, a prepulse (“picket”) is followed by a relaxation period, when the laser is turned off. A parametric study of picket parameters is performed with a code dedicated to the linear stability analysis on the basis of spherical realistic simulations including full physics. The influence of the picket parameters is investigated numerically. Simulations show that the set picket/relaxation time mainly determines the target stability and that the adiabat shaping scheme modifies the perturbed state before the main acceleration. In particular, the perturbed density level is reduced in the cases studied. Finally, several planar configurations have been used to look into the details of perturbation growth. It has been found that stabilization increases with prepulse intensity at the beginning of the acceleration phase.

K -shell and extreme ultraviolet spectroscopic signatures of structured Ar puff Z-pinch loads with high K-shell x-ray yield

Structured 12-cm-diam Ar gas-puff loads have recently produced Z-pinch implosions with reduced Rayleigh-Taylor instability growth and increased K-shell x-ray yield [H. Sze, J. Banister, B. H. Failor, J. S. Levine, N. Qi, A. L. Velikovich, J. Davis, D. Lojewski, and P. Sincerny, Phys. Rev. Lett. 95, 105001 (2005)]. To better understand the dynamics of these loads, we have measured the extreme ultraviolet (XUV) emission resolved radially, spectrally, and axially. Radial measurements indicated a compressed diameter of ≈3mm, consistent with the observed load inductance change and an imploded-mass consisting of a ≈1.5-mm-diam, hot, K-shell-emitting core and a cooler surrounding blanket. Spectral measurements indicate that, if the load is insufficiently heated, then radiation from the core will rapidly photoheat the outer blanket, producing a strong increase in XUV emission. Also, adding a massive center jet (⩾20% of load mass) increases the rise and fall times of the XUV emission to ⩾40ns, consistent with a more adiabatic compression and heating of the load. Axial measurements show that, despite differences in the XUV and K-shell emission time histories, the K-shell x-ray yield is insensitive to axial variations in load mass.

&amp;lt;i&amp;gt;F&amp;lt;/i&amp;gt;-region Pedersen conductivity deduced using the TIMED/GUVI limb retrievals

Abstract. As a proxy of the Rayleigh-Taylor instability growth rate for equatorial plasma bubbles, we investigate the flux-tube integrated F-region Pedersen conductivity (ΣPF) using the electron density profiles (EDPs) provided by the Global Ultraviolet Imager (GUVI) on board the Thermosphere Ionosphere and Mesosphere Energetics and Dynamics (TIMED) satellite. The investigation is conducted using the EDPs obtained in the Atlantic sector at 19:00-22:00 LT during 4–17 August and 6-16 December 2002. The seasonal difference of the strength and location of the equatorial ionization anomalies (EIAs) induces a significant difference in the deduced ΣPF. Much stronger EIAs are created at higher altitudes and latitudes in December rather than in August. At 19:00–20:00 LT, the peak value of the ΣPF has 23 mhos at 1100 km apex height during 14–16 December and 18mhos at 600 km during 15–17 August. The ΣPF decreases as local time progresses. Therefore, ΣPF provides a preferred condition for the growth of bubbles to higher altitudes at 19:00-20:00 LT than at later hours, in December rather than in August in the Atlantic sector.

Bell-Plesset effects for an accelerating interface with contiguous density gradients

A Plesset-type treatment [M. S. Plesset, J. Appl. Phys. 25, 96 (1954)] is used to assess the effects of contiguous density gradients at an accelerating spherical classical interface on Rayleigh-Taylor and Bell-Plesset perturbation growth. Analytic expressions are obtained that describe enhanced Rayleigh-Taylor instability growth from contiguous density gradients aligned with the acceleration and which increase the effective Atwood number of the perturbed interface. A new pathway for geometric amplification of surface perturbations on an accelerating interface with contiguous density gradients is identified. A resonance condition between the density-gradient scale length and the radius of the interface is also predicted based on a linearized analysis of Bernoulli’s equation, potentially leading to enhanced perturbation growth. Comparison of the analytic treatment with detailed two-dimensional single-mode growth-factor simulations shows good agreement for low-mode numbers where the effects of spherical geometry are most manifested.

The stability of buoyant bubbles in the atmospheres of galaxy clusters

The buoyant rise of hot plasma bubbles inflated by AGN outflows in galaxy clusters can heat the cluster gas and thereby compensate radiative energy losses of this material. Numerical simulations of this effect often show the complete disruption of the bubbles followed by the mixing of the bubble material with the surrounding cluster gas due to fluid instabilities on the bubble surface. This prediction is inconsistent with the observations of apparently coherent bubble structures in clusters. We derive a general description in the linear regime of the growth of instabilities on the surface between two fluids under the influence of a gravitational field, viscosity, surface tension provided by a magnetic field and relative motion of the two fluids with respect to each other. We demonstrate that Kelvin-Helmholtz instabilities are always suppressed, if the fluids are viscous. They are also suppressed in the inviscid case for fluids of very different mass densities. We show that the effects of shear viscosity as well as a magnetic fields in the cluster gas can prevent the growth of Rayleigh-Taylor instabilities on relevant scale lengths. R-T instabilities on pc-scales are suppressed even if the kinematic viscosity of the cluster gas is reduced by two orders of magnitude compared to the value given by Spitzer for a fully ionised, unmagnetised gas. Similarly, magnetic fields exceeding a few microG result in an effective surface tension preventing the disruption of bubbles. For more massive clusters, instabilities on the bubble surface grow faster. This may explain the absence of thermal gas in the north-west bubble observed in the Perseus cluster compared to the apparently more disrupted bubbles in the Virgo cluster.

Compressible Rayleigh–Taylor instabilities in supernova remnants

Partial modeling of the hydrodynamic evolution of the supernovae is one of the prominent applications of laboratory astrophysics. In particular the role of Rayleigh–Taylor instability (RTI) in supernova evolution needs to be explained. In this paper we analyze the compressibility effects on the RTI in the linear regime. We compare the compressible isothermal and stratified incompressible RTI growth rates and analyze the vorticity generation at the interface. We show that for several configurations the effect of compressibility can be significant in supernovae remnants.

Compressibility effects on the Rayleigh–Taylor instability growth between immiscible fluids

The linearized Navier–Stokes equations for a system of superposed immiscible compressible ideal fluids are analyzed. The results of the analysis reconcile the stabilizing and destabilizing effects of compressibility reported in the literature. It is shown that the growth rate n obtained for an inviscid, compressible flow in an infinite domain is bounded by the growth rates obtained for the corresponding incompressible flows with uniform and exponentially varying density. As the equilibrium pressure at the interface p∞ increases (less compressible flow), n increases towards the uniform density result, while as the ratio of specific heats γ increases (less compressible fluid), n decreases towards the exponentially varying density incompressible flow result. This remains valid in the presence of surface tension or for viscous fluids and the validity of the results is also discussed for finite size domains. The critical wavenumber imposed by the presence of surface tension is unaffected by compressibility. However, the results show that the surface tension modifies the sensitivity of the growth rate to a differential change in γ for the lower and upper fluids. For the viscous case, the linearized equations are solved numerically for different values of p∞ and γ. It is found that the largest differences compared with the incompressible cases are obtained at small Atwood numbers. The most unstable mode for the compressible case is also bounded by the most unstable modes corresponding to the two limiting incompressible cases.

Non-spherical core collapse supernovae

Two-dimensional simulations of a Type II and a Type Ib-like supernova explosion are presented that encompass shock revival by neutrino heating, neutrino-driven convection, explosive nucleosynthesis, the growth of Rayleigh-Taylor instabilities, and the propagation of newly formed metal clumps through the exploding star. In both cases we find very high Ni56 velocities of 17000 km/s shortly after shock-revival, and a complete fragmentation of the progenitor's metal core within the first few minutes after core bounce, due to the growth of Rayleigh-Taylor instabilities at the Si/O and (C+O)/He composition interfaces. This leads to the formation of high-velocity, metal-rich clumps which eventually decouple from the flow and move ballistically through the ejecta. Maximum final metal velocities of 3500-5500 km/s and 1200 km/s are obtained for the Type Ib model and the Type II model, respectively. The low maximum metal velocities in the Type II model, which are significantly smaller than those observed in SN 1987A, are due to the massive hydrogen envelope of the progenitor. The envelope forces the supernova shock to decelerate strongly, leaving behind a reverse shock below the He/H interface, which interacts with the clumps and slows them down significantly. This reverse shock is absent in the Type Ib-like model. The latter is in fairly good agreement with observations of Type Ib supernovae. In addition, in this case the pattern of clump formation in the ejecta is correlated with the convective pattern prevailing during the shock-revival phase. This might be used to deduce observational constraints for the dynamics during this early phase of the evolution, and the role of neutrino heating in initiating the explosion.