Hydrodynamic Instability Growth Research Articles

Measurements of improved stability to achieve higher fuel compression in ICF

While nuclear fusion ignition has been achieved at the National Ignition Facility in inertial confinement fusion (ICF) experiments, obtaining higher gain and more efficient burn is still desired. In that regard, increasing the compression of the fuel is an important factor. In recent indirect-drive capsule implosions, the SQ-n campaign is testing the hypothesis that reducing the hydrodynamic growth of perturbations is key to achieving higher compression of high-density carbon based-ablators for ICF. SQ-n uses a design at lower adiabat with a ramped foot laser pulse shape to minimize early-time hydrodynamic instability growth, predicted to be reduced by a factor of 10, and an optimized ablator dopant distribution. Subsets of experiments were conducted within the SQ-n campaign to study the implosion symmetry, laser backscatter, stability, and compression. Only the latter two will be reviewed here. Shock timing experiments using the velocity interferometer system for any reflector diagnostic enabled the development of a gently accelerating shock velocity. The ice–ablator interface acceleration, important for managing the Richtmyer–Meshkov phase growth, was observed with refraction enhanced radiography and the ablation front growth was measured using radiography of pre-imposed modulations. Finally, layered tritium-hydrogen-deuterium (∼75% H, ∼25% T, ∼2–10% D) and deuterium–tritium implosions demonstrate that between 15% ± 3% and 30% ± 6% improved compression has been achieved.

Effect of surface roughness on phase transition timing in megaampere pulsed-power–driven exploding conductors

An understanding of material phase transitions in megaampere pulsed-power–driven exploding conductors is important for predicting the growth of hydrodynamic instabilities in magneto-inertial fusion concepts. This study analyzes phase transitions in electrical conductor explosions using 1D Lagrangian and 2D arbitrary Lagrangian–Eulerian resistive magnetohydrodynamic simulations to show that micrometer-scale surface roughness can lead to the electrothermal instability (ETI), a feedback effect that concentrates resistive heating and leads to early melting and ablation. Simulations of the Mykonos electrothermal instability II (METI-II) experiment show melting begins 19% sooner for machined rods with micrometer-scale surface roughness than for rods without these features. The surface magnetic field is 41 T around the initial region of melt, representing a lower magnitude than both the 86 T from 1D simulations and the 85 T threshold reported elsewhere. In 2D simulations with micrometer-scale surface roughness, temperature measurements indicate the critical point temperature of aluminum is reached 17% faster in comparison with 1D simulations. Values from 2D simulations with surface roughness align with predictions from ETI theory, and the observed temperature redistribution further supports the ETI as an underlying mechanism. Simulation results are validated against experimental photonic Doppler velocimetry data. This study shows 1D simulations are adequate to model conductors with sub-micrometer-scale surface roughness in this high-energy-density regime; however, 2D or 3D simulations are required to capture the full range of physics for accurately describing phase transitions in conductors with micrometer-scale or larger surface roughness.

Energy transfer and scale dynamics in 2D and 3D laser-driven jets

We demonstrate a methodology for diagnosing the multiscale dynamics and energy transfer in complex HED flows with realistic driving and boundary conditions. The approach separates incompressible, compressible, and baropycnal contributions to energy scale-transfer and quantifies the direction of these transfers in (generalized) wavenumber space. We use this to compare the kinetic energy (KE) transfer across scales in simulations of 2D axisymmetric vs fully 3D laser-driven plasma jets. Using the FLASH code, we model a turbulent jet ablated from an aluminum cone target in the configuration outlined by Liao et al. [Phys. Plasmas, 26 032306 (2019)]. We show that, in addition to its well known bias for underestimating hydrodynamic instability growth, 2D modeling suffers from significant spurious energization of the bulk flow by a turbulent upscale cascade. In 2D, this arises as vorticity and strain from instabilities near the jet's leading edge transfer KE upscale, sustaining a coherent circulation that helps propel the axisymmetric jet farther (≈25% by 3.5 ns) and helps keep it collimated. In 3D, the coherent circulation and upscale KE transfer are absent. The methodology presented here may also help with inter-model comparison and validation, including future modeling efforts to alleviate some of the 2D hydrodynamic artifacts highlighted in this study.

Shock-induced aerobreakup of a polymeric droplet

Droplet atomization through aerobreakup is omnipresent in various natural and industrial processes. Atomization of Newtonian droplets is a well-studied area; however, non-Newtonian droplets have received less attention despite their being frequently encountered. By subjecting polymeric droplets of different concentrations to the induced airflow behind a moving shock wave, we explore the role of elasticity in modulating the aerobreakup of viscoelastic droplets. Three distinct modes of aerobreakup are identified for a wide range of Weber number $({\sim }10^2\unicode{x2013}10^4)$ and elasticity number $({\sim }10^{-4}\unicode{x2013}10^2)$ variation: these modes are vibrational, shear-induced entrainment and catastrophic breakup modes. Each mode is described as a three-stage process. Stage I is droplet deformation, stage II is the appearance and growth of hydrodynamic instabilities and stage III is the evolution of liquid mass morphology. It is observed that elasticity plays an insignificant role in the first two stages but a dominant role in the final stage. The results are described with the support of adequate mathematical analysis.

On the importance of three-dimensional modeling for high-energy-density physics experiments

Laser-driven cylindrical implosion experiments enable direct measurements of hydrodynamic instability growth in convergent geometries, providing a wealth of validation data in the high-energy-density regime. These experiments are designed to be nearly axially invariant, allowing for modeling with complementary two-dimensional slices of the cylinder. Two distinct hydrodynamics codes are employed to model a subset of these experiments, and the results are shown to be in very good agreement with each other and the available experimental data. While this 2D modeling approach adequately captures most of the physics of the implosion and ensuing instability growth, there are crucial aspects from the three-dimensional nature of the experiments that are missed in 2D. The first fully 3D simulations of these experiments are presented, and small but significant differences are found to arise from both the axial and azimuthal non-uniformity in the laser drive. Recent experimental results confirming the drive asymmetry are discussed.

Thermal transport in warm dense matter revealed by refraction-enhanced x-ray radiography with a deep-neural-network analysis

Transport properties of high energy density matter affect the evolution of many systems, ranging from the geodynamo in the Earth’s core, to hydrodynamic instability growth in inertial confinement fusion capsules. Large uncertainties of these properties are present in the warm dense matter regime where both plasma models and condensed matter models become invalid. To overcome this limit, we devise an experimental platform based on x-ray differential heating and time-resolved refraction-enhanced radiography coupled to a deep neural network. We retrieve the first measurement of thermal conductivity of CH and Be in the warm dense matter regime and compare our measurement with the most commonly adopted models. The discrepancies observed are related to the estimation of a correction term from electron-electron collisions. The results necessitate improvement of transport models in the warm dense matter regime and could impact the understanding of the implosion performance for inertial confinement fusion.

Measuring the principal Hugoniot of inertial-confinement-fusion-relevant TMPTA plastic foams.

Wetted-foam layers are of significant interest for inertial-confinement-fusion capsules, due to the control they provide over the convergence ratio of the implosion and the opportunity this affords to minimize hydrodynamic instability growth. However, the equationof state for fusion-relevant foams are not well characterized, and many simulations rely on modeling such foams as a homogeneous medium with the foam average density. To address this issue, an experiment was performed using the VULCAN Nd:glass laser at the Central Laser Facility. The aim was to measure the principal Hugoniot of TMPTA plastic foams at 260mg/cm^{3}, corresponding to the density of liquid DT-wetted-foam layers, and their "hydrodynamic equivalent" capsules. A VISAR was used to obtain the shock velocity of both the foam and an α-quartz reference layer, while streaked optical pyrometry provided the temperature of the shocked material. The measurements confirm that, for the 20-120 GPa pressure range accessed, this material can indeed be well described using the equationof state of the homogeneous medium at the foam density.

Direct Measurement of Ice-Ablator Interface Motion for Instability Mitigation in Indirect Drive ICF Implosions.

In indirect drive inertial confinement fusion (ICF) implosions hydrodynamic instability growth at the imploding capsule ablator-DT fuel interface can reduce fuel compressibility and inject ablator into the hot spot hence reducing hot spot pressure and temperature. As a mitigation strategy, a gentle acceleration of this interface is predicted by simulations and theory to significantly reduce this instability growth in the early stage of the implosion. We have performed high-contrast, time-resolved x-ray refraction enhanced radiography (RER) to accurately measure the level of acceleration as a function of the initial laser drive time history for indirect-drive implosions on the National Ignition Facility. We demonstrate a transition from no acceleration to 20±1.8 μm ns^{-2} acceleration by tweaking the drive that should reduce the initial instabilities by an order of magnitude at high modes.

Pathways towards break even for low convergence ratio direct-drive inertial confinement fusion

Following indirect-drive experiments which demonstrated promising performance for low convergence ratios (below 17), previous direct-drive simulations identified a fusion-relevant regime which is expected to be robust to hydrodynamic instability growth. This paper expands these results with simulated implosions at lower energies of 100 and 270 kJ, and ‘hydrodynamic equivalent’ capsules which demonstrate comparable convergence ratio, implosion velocity and in-flight aspect ratio without the need for cryogenic cooling, which would allow the assumptions of one-dimensional-like performance to be tested on current facilities. A range of techniques to improve performance within this regime are then investigated, including the use of two-colour and deep ultraviolet laser pulses. Finally, further simulations demonstrate that the deposition of electron energy into the hotspot of a low convergence ratio implosion through auxiliary heating also leads to significant increases in yield. Results include break even for 1.1 MJ of total energy input (including an estimated 370 kJ of short-pulse laser energy to produce electron beams for the auxiliary heating), but are found to be highly dependent upon the efficiency with which electron beams can be created and transported to the hotspot to drive the heating mechanism.

Impact of different electron thermal conductivity models on the performance of cryogenic implosions

The electron thermal conduction strongly affects the hot-spot formation and the hydrodynamic instability growth in inertial confinement fusion implosions. A harmonic-mean flux-limited conductivity model has been widely used in implosion simulations. In this paper, using the high foot implosion N140520 as an example, we have performed a series of one-dimensional (1D) no-alpha simulations to quantify the impact of different conductivity models including the Spitzer–Harm model, the Lee–More model, and the recently proposed coupled Gericke-Murillo-Schlanges model [Ma et al., Phys. Rev. Lett. 122, 015001 (2019)] with the flux limiter fe ranging from 0.03 to 0.15 on the performance of cryogenic implosions. It is shown that varying fe has a bigger impact on the performance than changing conductivity models. Therefore, we have only performed two-dimensional (2D) no-alpha simulations using the Lee–More model with different flux limiters feLM to quantify the effect of the electron thermal conduction on the performance, with single-mode velocity perturbations with different mode numbers L seeded on the inner shell surface near the peak implosion velocity. We find that in both the 1D implosions and the 2D implosions with the same L, increasing fe leads to more hot-spot mass and lower hot-spot-averaged ion temperature, resulting in approximately constant hot-spot internal energy. In addition, the no-alpha yield Ynα is dominated by the neutron-averaged ion temperature Tn in these two cases. Increasing feLM from 0.0368 to 0.184 reduces Tn by ∼15% in 1D and by ∼20% for the 2D implosions with the same L, both leading to a ∼20% reduction in Ynα.

Double cylinder target design for study of hydrodynamic instabilities in multi-shell ICF

Cylindrical implosions are used to study hydrodynamic instability growth for inertial confinement fusion (ICF) applications, as the cylindrical geometry allows for easier diagnostic access while retaining convergence effects. In this work, we use the established cylindrical implosion platform [Palaniyappan et al., Phys. Plasmas 27, 042708 (2020)] to inform the double shell ICF campaign [Montgomery et al., Phys. Plasmas 25, 092706 (2018)]. We present a design for a double cylindrical target as an analogue to the double shell ICF capsule in order to study hydrodynamic instability growth on the high-Z inner shell. Our design work is done with two-dimensional (2D) Eulerian radiation-hydrodynamics simulations, considering the axial uniformity of the implosion and feasibility of measuring the instability growth of pre-seeded single mode sinusoidal perturbations. We discuss in depth the design for a target to be directly driven at the OMEGA laser facility [Boehly et al., Opt. Commun. 133, 495 (1997)]. We evaluate the design for axial implosion symmetry and visibility of instability growth using synthetic radiographs constructed from the simulations, as the instability growth on the inner cylinder is experimentally measured using x-ray radiography of the implosion. We find that the seeded perturbation growth on the inner cylinder should be visible in an experiment, even with axial implosion asymmetry and preheat. We compare our 2D simulations with linear theory predictions for perturbation growth and show that a cylinder with lower azimuthal mode number (mode-20) perturbations compares more favorably with linear theory, while a cylinder with higher azimuthal mode number (mode-40) perturbations at the same starting amplitude saturates and is over-predicted by linear theory.

Experiments on the single-mode Richtmyer–Meshkov instability with reshock at high energy densities

The hydrodynamic instability growth of a reshocked single-mode interface between high energy density fluids is studied. A laser-driven shock wave is used to drive an initially solid, sinusoidal interface between a dense plastic (1.43 g/cc) and a light foam (≈ 0.110 g/cc). After the interface has grown to a nonlinear state where the amplitude is of order of the wavelength, it is reshocked. The reshock compresses the nonlinear perturbation, which then grows at about twice the rate. While the pre-reshock growth rate is sensitive to the initial amplitude and wavelength of the perturbation, the post-reshock growth rate is comparatively insensitive to the initial condition. Qualitatively, we observe that the perturbations are less coherent after reshock, consistent with the idea that having a reshock accelerates the transition to turbulence. We find that some memory of the initial condition remains, even after reshock at late time: it appears if the initial perturbations have large enough wavelengths, and the flow structure of size comparable to the initial wavelength persists through reshock. Our results agree with design simulations and are consistent with the phenomenology of reshock studies in conventional gaseous shock tubes.

Design of a high energy density experiment to measure the suppression of hydrodynamic instability in an applied magnetic field

A transverse magnetic field can suppress the hydrodynamic instability growth of an unstable plasma interface. This effect, of interest to inertial confinement fusion and astrophysics, has mostly been studied via simulation. Here, we present the design of an experiment at the National Ignition Facility (NIF) to demonstrate this effect in a laboratory. Simulations indicate that the timescale for the diffusion of the magnetic field across the mixing region should be at least comparable to the timescale of the instability growth in order to have a measurable suppression effect. This motivates the use of lower density target materials than usual high energy density (HED) hydrodynamics experiments to permit faster hydrodynamics and higher plasma conductivities (through higher temperature), for a given laser drive and magnetic field. We discuss a target design for creating a Rayleigh–Taylor unstable HED plasma interface that uses 320 mg/cc iodine-doped carbon foam as the heavy material, 20 mg/cc carbon foam as the light material, and a 6 μm amplitude, a 120 μm wavelength ripple machined at the interface, which shows a measurable suppression effect with a nominal NIF drive and a 30 T magnetic field (the present facility limit). Models indicate lower density foams that may display even larger suppression effects, as the Hohlraum drive also radiatively preheats the foam to permit even higher temperatures and, hence, higher conductivities.

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.

Hohlraum x-ray preheat asymmetry measurement at the ICF capsule via Mo ball fluorescence imaging.

In inertial confinement fusion, penetrating asymmetric hohlraum preheat radiation (>1.8 keV, which includes high temperature coronal M-band emission from laser spots) can lead to asymmetric ablation front and ablator-fuel interface hydrodynamic instability growth in the imploding capsule. First experiments to infer the preheat asymmetries at the capsule were performed on the National Ignition Facility for high density carbon (HDC) capsules in low density fill (0.3 mg/cc 4He) Au hohlraums by time resolved imaging of 2.3 keV fluorescence emission of a smaller Mo sphere placed inside the capsule. Measured Mo emission is pole hot (P2 > 0) since M-band is generated mainly by the outer laser beams as their irradiance at the hohlraum wall is 5× higher than for the inner beams. P2 has a large swing vs time, giving insight into the laser heated hohlraum dynamics. P4 asymmetry is small at the sphere due to efficient geometric smoothing of hohlraum P4 asymmetries at large hohlraum-to-capsule radii ratios. The asymmetry at the HDC capsule is inferred from the Mo emission asymmetry accounting for the Mo/HDC radius difference and HDC capsule opacity.

High-volume and -adiabat capsule (“HVAC”) ignition: Lowered fuel compression requirements using advanced Hohlraums

Lower-than-expected deuterium–tritium fuel areal densities have been experimentally inferred across a variety of high-convergence, nominally low-adiabat implosion campaigns at the National Ignition Facility (NIF) using cylinder-shaped Hohlraums [Hurricane et al., Phys. Plasmas 26, 052704 (2019)]. A leading candidate explanation is the presence of atomic mix between the fuel and ablator from hydrodynamic instability growth [Clark et al., Phys. Plasmas 26, 050601 (2019)], leading to reduced fuel compressibility and an effectively higher (in-flight) fuel adiabat α. Tolerating a high-α implosion can be obtained with significantly higher capsule absorbed energy Ecap according to the one-dimensional (1-D) ignition-threshold-factor analytic scaling [S. Atzeni and J. Meyer-ter-Vehn, Nucl. Fusion 41, 465 (2001)], ITF∼Ecap·α−1.8. Recent experiments with large Al shells in rugby-shaped Hohlraums have established high laser-capsule coupling efficiencies of ≽ 30% [Ping et al., Nat. Phys. 15, 138 (2019)], enabling a path to Ecap≽ 0.5 MJ at the NIF and increased performance margin M ≡ ITF − 1. The ability to operate at high adiabat with large capsules using nonstandard Hohlraums leads to the predicted onset of a volume-ignition mode, defined as when both the entire fuel is the “hot spot” and inertial confinement is principally provided by the ablator compared with the compressed fuel. Such an ignition mode, normally reserved for high-Z targets, e.g., double shells [Amendt et al., Phys. Plasmas 14, 056312 (2007)], is predicted to lead to lower fuel convergence and less exposure to mix due to the intended high adiabat—but at the expense of ∼3–4 × reduced (1-D) yield compared with conventional central hot-spot ignition designs.

First study of Hohlraum x-ray preheat asymmetry inside an ICF capsule

In indirect drive inertial confinement fusion (ICF), laser induced Hohlraum preheat radiation (so-called M-band, >1.8 keV) asymmetry will lead to asymmetric ablation front and ablator–fuel interface hydrodynamic instability growth in an imploding capsule. First experiments to infer the M-band asymmetries at the capsule were performed on the National Ignition Facility for high density carbon (HDC) ICF capsules in low density fill (0.3 mg/cc 4He) Au Hohlraums by time resolved imaging of 2.3 keV fluorescence emission of a smaller Mo sphere placed inside the capsule. Measured Mo emission is pole hot (P2 > 0) since M-band is generated mainly by the outer laser beams as their irradiance at the Hohlraum wall is 5× higher than for the inner beams. P2 has a greater negative than positive swing vs time [Δ(P2/P0)/Δt ∼ 0.2/ns], giving insight into laser heated Hohlraum dynamics. P4 asymmetry is small at the sphere due to efficient geometric smoothing of Hohlraum asymmetries at large Hohlraum-to-capsule ratios. The M-band P2 history is qualitatively reproduced by radiation hydrodynamic HYDRA simulations. The smaller P2 than that calculated earlier suggests either less outer beam spot motion and/or preheat emission. At late times, the observed P2 swing is larger and P4 is more negative than simulated, which could be due to inner beams being stopped more in the outer beams wall plasma bubble than simulated. Asymmetry at the HDC capsule inner surface (“ice–ablator interface”) is also inferred from the Mo emission asymmetry by an analytic viewfactor model, accounting for the Mo/HDC radius difference and HDC capsule opacity.

The structure of weakly magnetized γ-ray burst jets

ABSTRACT The interaction of gamma-ray burst (GRB) jets with the dense media into which they are launched promote the growth of local hydrodynamic instabilities along the jet boundary. In a companion paper, we study the evolution of hydrodynamic (unmagnetized) jets, finding that mixing of jet–cocoon material gives rise to an interface layer, termed jet–cocoon interface (JCI), which contains a significant fraction of the system energy. We find that the angular structure of the jet + JCI, when they reach the homologous phase, can be approximated by a flat core (the jet) + a power-law function (the JCI) with indices that depend on the degree of mixing. In this paper, we examine the effect of subdominant toroidal magnetic fields on the jet evolution and morphology. We find that weak fields can stabilize the jet against local instabilities. The suppression of the mixing diminishes the JCI and thus reshapes the jet’s post-breakout structure. Nevertheless, the overall shape of the outflow can still be approximated by a flat core + a power-law function, although the JCI power-law decay is steeper. The effect of weak fields is more prominent in long GRB jets, where the mixing in hydrodynamic jets is stronger. In short GRB jets, there is small mixing in both weakly magnetized and unmagnetized jets. This result influences the expected jet emission which is governed by the jet’s morphology. Therefore, prompt and afterglow observations in long GRBs may be used as probes for the magnetic nature at the base of the jets.

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.

Measurement of hydrodynamic instability growth during the deceleration of an inertial confinement fusion implosion

This paper presents an exploration of potential mitigation methods for the gas fuel fill tube in Inertial Confinement Fusion (ICF) implosions at the National Ignition Facility (NIF), and the impact of hydrodynamic growth seeded from other target imperfections using a specialized low convergence implosion experiment. Enhanced x-ray self- emission of this experiment design allows the impact of hydrodynamic growth through the deceleration phase of the implosion to be examined.Experiments are presented comparing the perturbation visible during the implosion deceleration that are seeded by the fill tube, through varying the initial geometry in otherwise similar implosions. We further extend the experiment to explore the impact of isolated high atomic number 'dots' of 5 and 20 µm diameter. These isolated dots are compared in two different ‘High Density Carbon’ ablator designs in a gold hohlraum. The experiment series finds a correlation to number of high frequency self-emission features observed in deceleration and degradation in total Deuterium-Deuterium neutron yield.