Evolution of the rippled inner-interface-initiated ablative Rayleigh–Taylor instability in laser-ablating high-Z doped targets

The suppression of ablative Rayleigh–Taylor instability (ARTI) by a spatially modulated laser in inertial confinement fusion (ICF) is studied through numerical simulations. The results show that in the acceleration phase of ICF implosion, the growth of ARTI can be suppressed by using a short-wavelength spatially modulated laser. The ARTI growth rate decreases as the wavelength of the spatially modulated laser decreases, and ARTI is completely suppressed after a certain wavelength has been reached. A spatially uniform laser is introduced to keep the state of motion of the implosion fluid consistent, and it is found that the proportion of the spatially modulated laser required for complete suppression of ARTI decreases as the wavelength continues to decrease. We also optimize the spatial intensity distribution of the spatially modulated laser. In addition, as the duration of the spatially modulated laser decreases, the proportion required for completely suppressing ARTI increases, but the required energy decreases. When the perturbation wavenumber decreases, the wavelength of the spatially modulated laser required for complete suppression of ARTI becomes longer. In the case of multimode perturbation, ARTI can also be significantly suppressed by a spatially modulated laser, and the perturbation amplitude can be reduced to less than 10% of that without a spatially modulated laser. We believe that the conclusions drawn from our simulations can provide the basis for new approaches to control ARTI in ICF.

The self-generated magnetic field in three-dimensional (3-D) single-mode ablative Rayleigh–Taylor instability (ARTI) relevant to the acceleration phase of a direct-drive inertial confinement fusion (ICF) implosion is investigated. It is found that stronger magnetic fields up to a few thousand teslas can be generated by 3-D ARTI rather than by its two-dimensional (2-D) counterpart. The Nernst effects significantly alter the magnetic field convection and amplify the magnetic fields. The magnetic field of thousands of teslas yields the Hall parameter of the order of unity, leading to profound magnetized heat flux modification. While the magnetic field significantly accelerates the bubble growth in the short-wavelength 2-D modes through modifying the heat fluxes, the magnetic field mostly accelerates the spike growth but has little influence on the bubble growth in 3-D ARTI. The accelerated growth of spikes in 3-D ARTI is expected to enhance material mixing and degrade ICF implosion performance. This work is focused on a regime relevant to direct-drive ICF parameters at the National Ignition Facility, and it also covers a range of key parameters that are relevant to other ICF designs and hydrodynamic/astrophysical scenarios.

In laser-driven inertial confinement fusion (ICF) specifically with high laser intensities, energetic (hot) electrons (HEs) can be generated via laser-plasma instabilities. HEs can significantly impact the target performance by modifying the implosion hydrodynamics. In this paper, the effects of moderate-energy (about 20 to 40 keV) HEs on the evolution of two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) are studied through numerical simulations with a multigroup diffusion model in which the HE population is treated as a high-energy group launched from the boundary. With HEs present, it is found that ARTI linear growth rates are reduced even though the acceleration of the implosion shell is enhanced by HEs. The reduction in the linear growth rate is owing to the increase in the ablation velocity and the density scale length, and this stabilization effect is greater in the shorter-wavelength modes and/or higher-energy HE cases. The ARTI linear growth does not get mitigated monotonically as the HE number density increases for a given fixed HE kinetic energy. The HE number density minimizing the ARTI growth rate is found, likely due to the competition of the stabilizing and destabilizing hydrodynamic-parameter variations caused by HEs.

High-Z dopants such as chlorine, bromine and silicon in carbon–hydrogen polymer (CH) targets play a crucial role during the ablation of inertial confinement fusion (ICF). These dopants can serve as diagnostic tools in experiments and mitigate hot electron preheating, but they also influence the laser ablation. In this paper, the process of high-power laser ablating doped CH targets has been studied through radiation hydrodynamic simulations. Our findings reveal that the laser absorption rate in the doped targets increase as a result of the increasing electron-ion collision frequency. This leads to the increase of the electron, ion and radiation temperatures. Furthermore, high-Z dopants contribute to a decrease in the ablation pressure, which tends to a constant. Moreover, the saturation phenomenon of the mass ablation rate has been found. For the targets with low doping ratios (e.g. 6.25%–12.5%), the mass ablation rate increases until reaching the saturation at a doping ratio of 18.75%, after which it decreases. This indicates that an appropriate doping ratio can increase the laser absorption and ablation. The results are helpful to comprehensively understand the effects of high-Z dopant on all stages of ICF.

In inertial confinement fusion, pellet implosion efficiency can be severely limited by hydrodynamic instabilities. In particular, the ablation front instability -- ablative Rayleigh-Taylor instability -- plays a major role. Linear stability analyses of ablation fronts have been mostly performed under several assumptions: isobaricity, steadiness, continuous/discontinuous flows. In more general cases, such analyses inevitably resort to solving initial boundary value problems for linear perturbations. The physical model used here is that of ideal gas dynamics with nonlinear heat conduction. A general numerical approach for solving both one-dimensional flows and linear perturbations is briefly presented. Linear perturbation evolutions from initial external surface defects are investigated for a self-similar ablation flow of a semi-infinite slab, initiated from rest.

The effects of high-Z dopant on the laser-driven ablative Richtmyer–Meshkov instability (RMI) are investigated by theoretical analysis and radiation hydrodynamics simulations. It is found that the oscillation amplitude of ablative RMI depends on the ablation velocity, the blow-off plasma velocity and the post-shock sound speed. Owing to enhancing the radiation at the plasma corona and increasing the radiation temperature at the ablation front, the high-Z dopant in plastic target can significantly increase the ablation velocity and the blow-off plasma velocity, leading to an increase in oscillation frequency and a reduction in oscillation amplitude of the ablative RMI. The high-Z dopant in plastic target is beneficial to reduce the seed of ablative Rayleigh–Taylor instability. These results are helpful for the design of direct drive inertial confinement fusion capsules.

The ablative Rayleigh-Taylor (RT) instability is a central issue in the performance of laser-accelerated inertial-confinement-fusion targets. Historically, the accurate numerical simulation of this instability has been a challenging task for many radiation hydrodynamics codes, particularly when it comes to capturing the ablatively stabilized region of the linear dispersion spectrum and modeling ab initio perturbations. Here, we present recent results from two-dimensional numerical simulations of the ablative RT instability in planar laser-ablated foils that were performed using the Eulerian code FastRad3D. Our study considers polystyrene, (cryogenic) deuterium-tritium, and beryllium target materials, quarter- and third-micron laser light, and low and high laser intensities. An initial single-mode surface perturbation is modeled in our simulations as a small modulation to the target mass density and the ablative RT growth-rate is calculated from the time history of areal-mass variations once the target reaches a steady-state acceleration. By performing a sequence of such simulations with different perturbation wavelengths, we generate a discrete dispersion spectrum for each of our examples and find that in all cases the linear RT growth-rate γ is well described by an expression of the form γ=α [kg/(1+ϵ kLm)]1/2−βkVa, where k is the perturbation wavenumber, g is the acceleration of the target, Lm is the minimum density scale-length, Va is the ablation velocity, and ϵ is either one or zero. The dimensionless coefficients α and β in the above formula depend on the particular target and laser parameters and are determined from two-dimensional simulation results through the use of a nonlinear curve-fitting procedure. While our findings are generally consistent with those of Betti et al. (Phys. Plasmas 5, 1446 (1998)), the ablative RT growth-rates predicted in this investigation are somewhat smaller than the values previously reported for the same target and laser parameters. It is speculated that differences in the equation-of-state and opacity models are largely responsible for the discrepancy. Resolution of this issue awaits the development of better experimental diagnostics capable of measuring small-wavelength (5–20 μm) perturbation growth due to the ablative RT instability in the linear regime.

Self-generated magnetic fields in single-mode ablative Rayleigh–Taylor instability (ARTI) relevant to the acceleration phase of inertial confinement fusion (ICF) implosions are studied via two dimensional simulations. In ARTI, ∼100 T magnetic fields can be generated via the Biermann battery source without considering the Nernst effect. The Nernst effect significantly compresses the magnetic field against the electron temperature gradient and amplifies the peak value by more than three times. A scaling law for the magnetic flux is obtained, and it well predicts the evolution of the magnetic field from linear to deeply nonlinear phases of ARTI. The self-generated magnetic field reduces the ablation near the spike and reduces the width of bubbles by magnetizing the electron heat flows, which results in higher magnitude vorticity inside the bubble and enhances the nonlinear ARTI bubble penetration velocity for short-wavelength modes. The bubble velocity boosting due to self-generated magnetic field indicates the larger impact of the short-wavelength ARTI modes on ICF implosion performance than previously expected.

Hot electrons (HEs) generated via parametric instabilities at high laser intensities are a critical concern of laser-driven inertial confinement fusion (ICF), which can significantly impact the ICF performance by preheating the target. In this paper, the effects of HE preheating with moderate HE energy on the evolution of two-dimensional multimode ablative Rayleigh–Taylor instability (ARTI) up to the self-similar growth stage are studied through numerical simulations with a multigroup diffusion model. It is found that HE preheating stabilizes the linear growth of multimode ARTI and delays the onset of the self-similar growth regime. This time delay is more significant for the short-wavelength mode ARTI and higher energy HE cases. It is also shown that the variation of self-similar growth coefficients under HE preheating is not very significant. The delay to the onset of the nonlinear stage of multimode ARTI by HE preheating with moderate energy may be beneficial to ICF implosions.

Effects of bromine (Br) dopant on the growth of radiation-driven ablative Rayleigh–Taylor instability (RTI) in plastic foils are studied by radiation hydrodynamics simulations and theoretical analysis. It is found that the Br-dopant in plastic foil reduces the seed of ablative RTI. The main reasons of the reduction are attributed to the smaller oscillation amplitude of ablative Richtmyer–Meshkov instability (RMI) induced by the smaller post-shock sound speed, and the smaller oscillation frequency of ablative RMI induced by the smaller ablation velocity and blow-off plasma velocity. The Br-dopant also decreases the linear growth rate of ablative RTI due to the smaller acceleration. Treating the perturbation growth as a function of foil’s displacement, the perturbation growth would increase in Br-doped foil at the phase of ablative RTI, which is attributed to the decrease of the ablation velocity and the density gradient scale length. The results are helpful for further understanding the influence of high-Z dopant on the radiation-driven ablative RTI.

X-ray drive asymmetry is one of the main seeds of low-mode implosion asymmetry that blocks further improvement of the nuclear performance of “high-foot” experiments on the National Ignition Facility [Miller et al., Nucl. Fusion 44, S228 (2004)]. More particularly, the P2 asymmetry of Au's M-band flux can also severely influence the implosion performance of ignition capsules [Li et al., Phys. Plasmas 23, 072705 (2016)]. Here we study the smoothing effect of mid- and/or high-Z dopants in ablator on Au's M-band flux asymmetries, by modeling and comparing the implosion processes of a Ge-doped ignition capsule and a Si-doped one driven by X-ray sources with P2 M-band flux asymmetry. As the results, (1) mid- or high-Z dopants absorb hard X-rays (M-band flux) and re-emit isotropically, which helps to smooth the asymmetric M-band flux arriving at the ablation front, therefore reducing the P2 asymmetries of the imploding shell and hot spot; (2) the smoothing effect of Ge-dopant is more remarkable than Si-dopant because its opacity in Au's M-band is higher than the latter's; and (3) placing the doped layer at a larger radius in ablator is more efficient. Applying this effect may not be a main measure to reduce the low-mode implosion asymmetry, but might be of significance in some critical situations such as inertial confinement fusion (ICF) experiments very near the performance cliffs of asymmetric X-ray drives.

Burn efficiency Φ is a key for commercial feasibility of fusion power stations for inertial fusion energy, while Φ is usually lower than 30% in the central ignition scheme of inertial confinement fusion (ICF). A recent conceptual design for a 10 MJ laser driver [Z. Sui and K. Lan, Matter Radiat. Extremes 9, 043002 (2024)] provides new room for target design to achieve a higher Φ. Here, we take the advantage of fuel density in reaction rate and propose a novel amplifier scheme for increasing Φ via two cascading explosions by ICF. The amplifier scheme can be realized either by indirect-drive or by direct-drive. Here, we give a 1D design for an indirect-driven amplifier capsule containing 2.02 mg DT fuel under a 300 eV radiation generated by a 10 MJ and 1785 TW laser inside an octahedral spherical hohlraum. At stagnation, it forms an extremely dense shell surrounding central hot fuel, with a density ratio of shell to central >20. About 53 ps after stagnation, benefiting from the extremely high density of the shell and the deposition of α particles generated in the central hot fuel, the primary explosion happens in the shell. Then, the primary explosion in the shell drives the central fuel to converge spherically toward the center. At about 18 ps after the primary explosion, the central fuel converges at center with 1100 g/cm3, 770 keV, and 320 Tbar, leading to the secondary explosion inside this extremely hot and dense fireball. As a result, the amplifier capsule has Φ = 48% and G = 33 at convergence ratio Cr = 24. This novel scheme can achieve a relatively high burn efficiency at a relatively low Cr, which can greatly relax the stringent requirements of high gain fusion on hot spot ignition conditions and engineering issues.

Ablative Rayleigh–Taylor instability in the limit of an infinitely large density ratio

Academic tests in physical regimes not encountered in Inertial Confinement Fusion will help to build a better understanding of hydrodynamic instabilities and constitute the scientifically grounded validation complementary to fully integrated experiments. Under the National Ignition Facility (NIF) Discovery Science program, recent indirect drive experiments have been carried out to study the ablative Rayleigh-Taylor Instability (RTI) in transition from weakly nonlinear to highly nonlinear regime [A. Casner et al., Phys. Plasmas 19, 082708 (2012)]. In these experiments, a modulated package is accelerated by a 175 eV radiative temperature plateau created by a room temperature gas-filled platform irradiated by 60 NIF laser beams. The unique capabilities of the NIF are harnessed to accelerate this planar sample over much larger distances (≃1.4 mm) and longer time periods (≃12 ns) than previously achieved. This extended acceleration could eventually allow entering into a turbulent-like regime not precluded by the theory for the RTI at the ablation front. Simultaneous measurements of the foil trajectory and the subsequent RTI growth are performed and compared with radiative hydrodynamics simulations. We present RTI growth measurements for two-dimensional single-mode and broadband multimode modulations. The dependence of RTI growth on initial conditions and ablative stabilization is emphasized, and we demonstrate for the first time in indirect-drive a bubble-competition, bubble-merger regime for the RTI at ablation front.

Ablative Rayleigh–Taylor instability (ARTI) and nonlocal heat transport are the critical problems in laser-driven inertial confinement fusion, while their coupling with each other is not completely understood yet. Here the ARTI in the presence of nonlocal heat transport is studied self-consistently for the first time theoretically and by using radiation hydrodynamic simulations. It is found that the nonlocal heat flux generated by the hot electron transport tends to attenuate the growth of instability, especially for short wavelength perturbations. A linear theory of the ARTI coupled with the nonlocal heat flux is developed, and a prominent stabilization of the ablation front via the nonlocal heat flux is found, in good agreement with numerical simulations. This effect becomes more significant as the laser intensity increases. Our results should have important references for the target designing for inertial confinement fusion.