Growth Of Rayleigh-Taylor Instability Research Articles

The effect of viscosity and resistivity on Rayleigh–Taylor instability induced mixing in magnetized high-energy-density plasmas

This work numerically investigates the role of viscosity and resistivity in Rayleigh–Taylor instabilities in magnetized high-energy-density (HED) plasmas for a high Atwood number and high plasma beta regimes surveying across plasma beta and magnetic Prandtl numbers. The numerical simulations are performed using the visco-resistive magnetohydrodynamic equations. Results presented here show that the inclusion of self-consistent viscosity and resistivity in the system drastically changes the growth of the Rayleigh–Taylor instability (RTI) as well as modifies its internal structure at smaller scales. It is seen here that the viscosity has a stabilizing effect on the RTI. Moreover, the viscosity inhibits the development of small-scale structures and also modifies the morphology of the tip of the RTI spikes. On the other hand, the resistivity reduces the magnetic field stabilization, supporting the development of small-scale structures. The morphology of the RTI spikes is seen to be unaffected by the presence of resistivity in the system. An additional novelty of this work is in the disparate viscosity and resistivity profiles that may exist in HED plasmas and their impact on RTI growth, morphology and the resulting turbulence spectra. Furthermore, this work shows that the dynamics of the magnetic field is independent of viscosity and likewise the resistivity does not affect the dissipation of enstrophy and kinetic energy. In addition, power law scalings of enstrophy, kinetic energy and magnetic field energy are provided in both the injection range and inertial sub-range, which could be useful for understanding RTI induced turbulent mixing in HED laboratory and astrophysical plasmas and could aid in the interpretation of observations of RTI-induced turbulence spectra.

Analytical studies of Rayleigh-Taylor instability growth of double-cone ignition scheme in 2020 winter experimental campaign

In laser direct-driven fusion, high power lasers are used to ablate the target shell, compress and heat the fuel with the spherical focusing rocket effect, to approach to the fusion ignition conditions. The shaped nanosecond laser pulses compress and accelerate the DT target symmetrically, and forms a high density plasma hot-spot at stagnation. The hydrodynamic instabilities, especially the Rayleigh-Taylor instability, which happens at the interface of plasmas, may destroy the compressed shells, and thus reduce the temperature and density of the hot-spot. In this paper is analyzed theoretically the hydrodynamic instability growth under the conditions in the 2020 winter experiment of the double-cone ignition scheme proposed by Zhang et al. (<ext-link ext-link-type="uri" xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="http://doi.org/10.3788/HPLPB20132504.0903">2020 <i>Philos. Trans. A Math. Phys. Eng. Sci.</i> <b>378</b> 20200015</ext-link>). Both analytical model and one-dimensional simulations indicate that the fuel shells are compressed with low adiabat under the current quasi-isentropic waveform. The Rayleigh-Taylor instability remains in safe region with a maximum perturbation amplitude reaching 0.25 of the shell thickness at the most peak grown moment. The growth of the hydrodynamic instabilities can be further reduced by increasing the thickness of the shell, through using high foot pre-pulses and improving the uniformity of the target surface and laser irradiation in the future design.

Effect of initial phase on the Rayleigh–Taylor instability of a finite-thickness fluid shell

Rayleigh–Taylor instability (RTI) of finite-thickness shell plays an important role in deep understanding the characteristics of shell deformation and material mixing. The RTI of a finite-thickness fluid layer is studied analytically considering an arbitrary perturbation phase difference on the two interfaces of the shell. The third-order weakly nonlinear (WN) solutions for RTI are derived. It is found the main feature (bubble-spike structure) of the interface is not affected by phase difference. However, the positions of bubble and spike are sensitive to the initial phase difference, especially for a thin shell (kd < 1), which will be detrimental to the integrity of the shell. Furthermore, the larger phase difference results in much more serious RTI growth, significant shell deformation can be obtained in the WN stage for perturbations with large phase difference. Therefore, it should be considered in applications where the interface coupling and perturbation phase effects are important, such as inertial confinement fusion.

Enhancement of Ablative Rayleigh-Taylor Instability Growth by Thermal Conduction Suppression in a Magnetic Field.

Ablative Rayleigh-Taylor instability growth was investigated to elucidate the fundamental physics of thermal conduction suppression in a magnetic field. Experiments found that unstable modulation growth is faster in an external magnetic field. This result was reproduced by a magnetohydrodynamic simulation based on a Braginskii model of electron thermal transport. An external magnetic field reduces the electron thermal conduction across the magnetic field lines because the Larmor radius of the thermal electrons in the field is much shorter than the temperature scale length. Thermal conduction suppression leads to spatially nonuniform pressure and reduced thermal ablative stabilization, which in turn increases the growth of ablative Rayleigh-Taylor instability.

Constraining computational modeling of indirect drive double shell capsule implosions using experiments

Double shell capsule implosions are an alternative approach to achieving alpha heating on the National Ignition Facility. Current machining techniques construct the outer shell as two hemispheres that are glued together, and the deuterium and tritium (DT) liquid inside the inner shell will be injected by a fill tube. These features introduce asymmetries and jetting that may disrupt the confinement of the DT fuel if not carefully controlled. Simulations indicate that in order to achieve high yields in the laboratory, these features as well as susceptibility to the Rayleigh–Taylor instability (RTI) must be mitigated. Due to uncertainties in computational models and the expense of using the best physics models at adequate resolution in three dimensions, our computational modeling must be constrained by experiments. We report on the results of recent hydrogrowth radiography and dual-axis keyhole experiments with double shell targets that have been used to evaluate our modeling of the outer shell joint as well as the impacts of high-energy x-ray preheat that strongly impacts RTI growth. Our simulations show good agreement with the experimental data and inform several important modeling choices.

Analytical studies of Rayleigh-Taylor instability growth in 2020 DCI winter experimental campaign

直接驱动激光聚变通过整形后的纳秒脉冲激光辐照氘氚（DT）球壳靶,经球对称压缩加速后,在中心转滞获得高温等离子体热斑，实现聚变点火.在球壳靶受到压缩和加速过程中等离子体界面的流体力学不稳定性,特别是瑞利-泰勒不稳定性的增长有可能会对压缩壳层造成破坏,导致点火的失败.本文通过理论解析和数值模拟,对2020年冬季实验条件下双锥对撞点火方案中的流体力学不稳定性增长进行了分析.结果显示理论模型与一维数值模拟中对整体压缩和加速过程的描述基本一致,在当前的近等熵波形下金锥中的壳层靶实现了低熵压缩,同时瑞利-泰勒不稳定性增长导致的最危险时刻扰动振幅和壳层厚度比可以达到约0.25,壳层依然处于安全状态,但当初始壳层表面扰动均方根振幅大于22 nm时,则可能出现壳层的破裂.因此，下一轮实验前的靶设计与驱动激光脉冲波形设计中可以通过增加靶壳层厚度、提高预脉冲强度、减小靶表面的粗糙度和提高激光辐照的匀滑度等方式来抑制不稳定性增长.

Hybrid target design for imprint mitigation in direct-drive inertial confinement fusion.

A target design for mitigating the Rayleigh-Taylor instability is proposed for use in high energy density and direct-drive inertial confinement fusion experiments. In this scheme, a thin gold membrane is offset from the main target by several-hundred microns. A strong picket on the drive beams is incident upon this membrane to produce x rays which generate the initial shock through the target. The main drive follows shortly thereafter, passing through the ablated shell and directly driving the main target. The efficacy of this scheme is demonstrated through experiments performed at the OMEGA EP facility, showing a reduction of the Rayleigh-Taylor instability growth which scales exponentially with frequency, suppressing development by at least a factor of 5 for all wavelengths below 100 μm. This results in a delay in the time of target perforation by ∼40%.

Using the SMG scheme to study the Rayleigh-Taylor instability growth in solids

Rayleigh-Taylor instability RTI occurs while a less dense fluid is accelerating a denser one Rayleigh (1883); Taylor (1950)[1,2]. Under gravity the material strength damps and prevents RTI formation in solids. However, at higher accelerations RTI will prevail. The Staggered Mesh Godunov (SMG) scheme for Lagrangian Luttwak and Falcovitz (2006)[3] and ALE Luttwak and Falcovitz (2005)[4] hydrodynamics is applied to study the effect of yield strength on the RTI growth. A test problem is set up which extends for solids a well-known test for RTI growth in fluids Loubere et al. (2010)[5]. The SMG scheme employs frame-invariant slope limiters. The convex hull based VIP limiter Luttwak and Falcovitz (2011); Luttwak and Falcovitz (2010)[6,7] is used for vectors and oriented Bounding Box based limiter Luttwak (2015)[8] for the stress tensor. This way, we prevent numerical effects of symmetry breaking to interfere, while following the RTI growth.

Design of Cylindrical Implosion Experiments to Demonstrate Scale-Invariant Rayleigh-Taylor Instability Growth

Radiation-hydrodynamics simulations are used to design laser-driven cylindrical implosion experiments to directly measure hydrodynamic instability growth in convergent geometry. Designs for two different size targets, varying in radial dimension by a factor of three, are presented. A set of beam pointings and powers are identified for each scale design that result in a nearly axially uniform implosion of an embedded marker layer. The implosion trajectories are shown to be scale-invariant between designs, with nearly identical scaled acceleration profiles. Linear theory and radiation-hydrodynamics simulations predict that Rayleigh-Taylor instability growth of an azimuthal perturbation, machined on the inner surface of the embedded marker, is also scale-invariant between designs.

Demonstration of Scale-Invariant Rayleigh-Taylor Instability Growth in Laser-Driven Cylindrical Implosion Experiments.

Rayleigh-Taylor instability growth is shown to be hydrodynamically scale invariant in convergent cylindrical implosions for targets that varied in radial dimension and implosion timescale by a factor of 3. The targets were driven directly by laser irradiation providing a short impulse, and instability growth at an embedded aluminum interface occurs as it converges radially inward by a factor of 2.25 and decelerates on a central foam core. Late-time growth factors of 14 are observed for a single-mode m=20 azimuthal perturbation at both scales, despite the differences in laser drive conditions between the experimental facilities, consistent with predictions from radiation-hydrodynamics simulations. This platform enables detailed investigations into the limits of hydrodynamic scaling in high-energy-density systems.

Hydro-scaling of direct-drive cylindrical implosions at the OMEGA and the National Ignition Facility

Deceleration-phase Rayleigh–Taylor instability (RTI) growth during inertial confinement fusion capsule implosions significantly affects the performance as it mixes cold ablator material into the fuel. Precise measurements of such instability growth are essential for both validating the existing simulation codes and improving our predictive capability. RTI measurements on the inner surface of a spherical shell are limited and are often inferred indirectly at limited convergence. In contrast, cylindrical implosions allow for direct diagnostic access to the converging interface by imaging down the cylinder axis while retaining the effects of convergence. We have performed direct-drive cylindrical implosion experiments at both the OMEGA and the NIF laser facilities using scaled targets. RTI growth is demonstrated to be scale-invariant between the cylindrical targets at OMEGA and similar targets at the NIF, which are scaled up by a factor of three in the radial dimension. Single-mode (m = 20) instability growth factors of ∼14 are measured at a convergence ratio (CR) ∼ 2.5 with nearly identical mode growth at both scales. The measurements are in agreement with xRAGE radiation-hydrodynamics simulations. In addition, we have developed the Bayesian-inference-engine method to account for the variations in the target alignment, magnification, and the parallax effect in the measurement, allowing a more precise comparison between the experimental data and the simulations.

Using cylindrical implosions to investigate hydrodynamic instabilities in convergent geometry

Hydrodynamic instabilities such as the Rayleigh–Taylor (RT) and Richtmyer–Meshkov instabilities disrupt inertial confinement fusion (ICF) implosions through the growth of 3D perturbations. Growth of these 3D imperfections at the interfaces of an ICF capsule during implosion lead to mixing between materials that is detrimental to performance. These instabilities have been studied extensively in planar geometry, but such experiments lack the effects of convergence in spherical implosions. While several studies have been performed in spherical geometry, these often lack a direct means to measure perturbation growth. Experiments in cylindrical geometry include convergence effects while maintaining direct diagnostic access. Although cylinders have less compression than spheres, they do provide an excellent platform to validate modeling for convergent geometries. The problem with previous cylindrical implosion experiments was that the convergence ratios were limited to ∼4. With the National Ignition Facility (NIF), larger cylindrical targets can be driven to convergences of 10–15 while maintaining a large enough final diameter to measure perturbation growth. This paper reviews the design process used to both benchmark radiation hydrodynamics codes and enable 1D post-processed simulations to explore design space to separate compression effects from acceleration/deceleration RT instability. Results from 1D simulations suggest that cylindrical implosions on the NIF can produce high-convergence experiments to validate RT instability growth for ICF implosions.

Long-duration direct drive hydrodynamics experiments on the National Ignition Facility: Platform development and numerical modeling with CHIC

We report on a novel planar direct-drive platform for hydrodynamics experiments on the National Ignition Facility (NIF). Its commissioning has been performed as part of the NIF Discovery Science Program. This platform enables the use of a 30 ns drive at an average intensity of 200 TW/cm2, creating a planar shock and ablation front over a 2 mm radius. To benchmark the performance of this design, the planarity of both the shock and ablation fronts has been measured between 26 ns and 28 ns after the start of the laser drive in a 3 mm-thick CH foil. The platform was then used to measure late-time Rayleigh-Taylor instability (RTI) growth at the ablation front for a 2D-rippled 300 μm-thick CH foil. Simultaneously, a numerical platform has been developed with the CHIC radiation hydrodynamics code at the CELIA laboratory. The CHIC numerical platform allows, for the first time, a complete simulation of the experiments over 30 ns to be performed. Large-scale simulations recover the trajectory and the 2D RTI growth measurements. They are further compared with half-mode simulations performed with identical parameters. We show that both numerical techniques fit with analytical modeling of RTI growth and discuss plans for future campaigns.

Measurements of Rayleigh–Taylor instability growth of laser-shocked iron–silicon alloy

ABSTRACTThe Rayleigh–Taylor (RT) instability of liquid iron alloys is important for understanding the core formation mechanism in the Earth. Here we first report the measurement of RT instability growth for a liquid iron–silicon (Fe–Si) alloy, which is one of the major candidate for the material of the Earth’s core, using a high power laser. We optimized the measurement setup and analytical technique to observe the growth of perturbation on an Fe–Si sample surface. The growth of perturbation amplitude on the Fe–Si alloy under high pressure and temperature was successfully observed using in situ X-ray radiography. The growth rate of the RT instability for the Fe–Si alloy on about 1000 GPa was estimated to be 0.3 ns−1.

Conditions for the development of Rayleigh-Taylor instability on the spherical flame front

The instability of the flame front is one of the actual problems of modern fluid and gas mechanics. Depending on the processes determining the growth of inhomogeneities, the hydrodynamic (Darrieus-Landau), diffusive-thermal, and Rayleigh-Taylor instabilities are distinguished for a free spherical flame. The present work is devoted to the conditions for the development of the latter. Rayleigh-Taylor instability arises at the interface of two fluids of different density in the presence of acceleration directed from the lighter to the heavier one. When the flame propagates, combustion products with less density move with acceleration in a denser gas. When the acceleration vector and the density gradient at the flame front are co-directed, instability develops. To investigate the development of instabilities, a series of experiments was carried out. Transparent latex shells were filled with a pre-prepared hydrogen-air mixture. In different series of experiments, the percentage of hydrogen changed. The flame was ignited by a spark discharge with energy of 1 mJ, a spark gap located in the center of the shell. Registration of the flame front propagation was performed using the schlieren method implemented in the shadow device IAB-451 and the high-speed VideoSprint camera. The video was shot at a frame rate of 500 to 1000 fps with an exposure of 500 μs. To automate the processing of images in the Matlab environment, a program is written that converts a set of images of the expanding flame front into a dependence of the mean radius on time. It is found that at the initial stage of propagation there are both acceleration and deceleration of the flame front. Experimentally obtained propagation parameters of the flame front are supplemented by calculations carried out on an analytical model from the literature.

Characterizing the modulation transfer function for X-ray radiography in high energy density experiments.

The Modulation Transfer Function (MTF) is an established means for characterizing imaging performance of X-ray radiography systems. We report on experiments using high energy, laser-driven X-ray radiography systems that assess performance using MTF values measured with the knife-edge projection method. The broadband, hard X-ray systems under study use line-projection imaging produced by narrowing the laser-generated X-ray source with a slit. We find that good contrast resolution can be achieved (the MTF = 0.5 at 75 μm wavelength) and that this performance is reproduced on different laser facilities. We also find that the MTF is sensitive both to the thickness of the line-projection slit and to the backing material thickness under the knife-edge. Both these sensitivities are due to a common mechanism, namely induced changes in the spectrally-averaged spatial widths of the X-ray source. The same line-projection system is also used on experimental campaigns measuring Rayleigh-Taylor instability growth by dynamically imaging sinusoidal, high Z micro-targets with wavelengths of 100 μm or less. By applying the measured MTF values to correct the ripple target contrast measurements, we can predict ripple growth to approximately 10% accuracy.

A platform for x-ray Thomson scattering measurements of radiation hydrodynamics experiments on the NIF.

We present an experimental design for a radiation hydrodynamics experiment at the National Ignition Facility that measures the electron temperature of a shocked region using the x-ray Thomson scattering technique. Previous National Ignition Facility experiments indicate a reduction in Rayleigh-Taylor instability growth due to high energy fluxes, compared to the shocked energy flux, from radiation and electron heat conduction. In order to better quantify the effects of these energy fluxes, we modified the previous experiment to allow for non-collective x-ray Thomson scattering to measure the electron temperature. Photometric calculations combined with synthetic scattering spectra demonstrate an estimated noise.

Mixing driven by transient buoyancy flows. I. Kinematics

Mixing of two miscible liquids juxtaposed inside a cavity initially separated by a divider, whose buoyancy-driven motion is initiated via impulsive perturbation of divider motion that can generate the Richtmyer-Meshkov instability, is investigated experimentally. The measured Lagrangian history of interface motion that contains the continuum mechanics of mixing shows self-similar nearly Gaussian length stretch distribution for a wide range of control parameters encompassing an approximate Hele-Shaw cell to a three-dimensional cavity. Because of the initial configuration of the interface which is parallel to the gravitational field, we show that at critical initial potential energy mixing occurs through the stretching of the interface, which shows frontogenesis, and folding, owing to an overturning motion that results in unstable density stratification and produces an ideal condition for the growth of the single wavelength Rayleigh-Taylor instability. The initial perturbation of the interface and flow field generates the Kelvin-Helmholtz instability and causes kinks at the interface, which grow into deep fingers during overturning motion and unfold into local whorl structures that merge and self-organize into the Rayleigh-Taylor morphology (RTM) structure. For a range of parametric space that yields two-dimensional flows, the unfolding of the instability through a supercritical bifurcation yields an asymmetric pairwise structure exhibiting smooth RTM that transitions to RTM fronts with fractal structures that contain small length scales for increasing Peclet numbers. The late stage of the RTM structure unfolds into an internal breakwave that breaks down through wall and internal collision and sets up the condition for self-induced sloshing that decays exponentially as the two fluids become stably stratified with a diffusive region indicating local molecular diffusion.

Coupling between velocity and interface perturbations in cylindrical Rayleigh–Taylor instability**Project supported by the National Natural Science Foundation of China (Grant Nos. 11275031, 11475034, 11575033, and 11274026) and the National Basic Research Program of China (Grant No. 2013CB834100).

Rayleigh–Taylor instability (RTI) in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear (WN) model. When the initial velocity perturbation is comparable to the interface perturbation, the coupling between them plays a significant role. The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small. The effects of the mode number on the first three harmonics are discussed respectively. The low-mode number perturbation leads to large amplitudes of RTI growth. The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly. When the mode number of the perturbation is large enough, the WN results in planar geometry are recovered.

Solar activity variations of equatorial spread F occurrence and sustenance during different seasons over Indian longitudes: Empirical model and causative mechanisms

A comprehensive analysis using nearly two decades of ionosonde data is carried out on the seasonal and solar cycle variations of Equatorial Spread F (ESF) irregularities over magnetic equatorial location Trivandrum (8.5°N, 77°E). The corresponding Rayleigh Taylor (RT) instability growth rates (γ) are also estimated. A seasonal pattern of ESF occurrence and the corresponding γ is established for low solar (LSA), medium solar (MSA) and high solar (HSA) activity periods. For LSA, it is seen that the γ maximizes during post sunset time with comparable magnitudes for autumnal equinox (AE), vernal equinox (VE) and winter solstice (WS), while for summer solstice (SS) it maximizes in the post-midnight period. Concurrent responses are seen in the ESF occurrence pattern. For MSA, γ maximizes during post-sunset for VE followed by WS and AE while SS maximises during post-midnight period. The ESF occurrence for MSA is highest for VE (80%), followed by AE (70%), WS (60%) and SS (50%). In case of HSA, maximum γ occurs for VE followed by AE, WS and SS. The concurrent ESF occurrence maximizes for VE and AE (90%), WS and SS at 70%.The solar cycle variation of γ is examined. γ shows a linear variation with F10.7 cm flux. Further, ESF percentage occurrence and duration show an exponential and linear variation respectively with γ. An empirical model on the solar activity dependence of ESF occurrence and sustenance time over Indian longitudes is arrived at using the database spanning two solar cycles for the first time.