In recent decades, radiative transfer through the binary stochastic mixtures (i.e., a fraction of particulate high-Z materials are randomly dispersed into the low-Z background material, where the label Z means the atomic number) has received great attention in many scientific and engineering disciplines, accurate and efficient simulations in multidimensions are much in demand. In this work, we primarily focus on the efficient algorithms for accurately simulating radiative transfer in binary stochastic mixtures in two dimensions. Our computational model is to solve the radiation-material coupled equations for an ensemble of binary stochastic mixtures. In this context, a subgrid-based nearest-neighbor searching (SNNS) algorithm is introduced to explicitly model the binary stochastic mixture, resulting in an O(N) scaling with the number of particles, which is more flexible than the fast random sequential addition (RSA) algorithm. In order to accurately determine the grid-based parameters, a particle-resolved algorithm is developed by dividing the relationship between the particle’s location and the grid into four categories, reproducing analytical results exactly and efficiently. A parallel algorithm using the spatial domain decomposition with directed acylic graph (DAG) techniques is proposed to efficiently solve the radiation-material coupled equations. These algorithms are combined to enable accurate and efficient simulations in two dimensions, which is validated by reported benchmark results. We find that convergent results require a sufficiently high resolution of the particle and a high-order quadrature. Although results based on one physical realization are somewhat representative, the ensemble-averaged results are more meaningful to avoid the statistical anomalies in some cases. Moreover, case studies on the influence of particle size distribution, the validation of the effective opacity models, and the particle size effect are presented and analyzed. Our work provides efficient algorithms for routinely simulating radiative transfer in binary stochastic mixtures in multidimensions, which can yield the benchmark results for analytical homogenized models of relevance.

A nonextensive statistical approach is developed to investigate the equations of state of partially ionized plasmas containing nonthermal free electrons. The average-atom model is adopted to simulate the plasma ionization balance, in which the κ-Fermi distribution is applied for the free electrons. We introduce a nonequilibrium kinetic temperature that consistently characterizes the electron mean kinetic energy. The κ-Fermi distribution substantially reduces the electron pressure and the average ionization degree of the plasma, which has a much more significant impact on high-Z plasmas than low-Z plasmas. This should influence the plasma hydrodynamics remarkably when nonthermal electrons are present, such as in the Hohlraum dynamics of laser-driven inertial confinement fusion.

We revisit radiative transfer in purely absorbing binary stochastic mixtures. To this end, benchmark results of the ensemble-averaged specific radiation intensity for one-dimensional (1D) arbitrary mixtures are presented based on the renewal theory, which can quantitatively reproduce high-accuracy numerical simulation data. We are for the first time to derive the analytical solutions for periodic statistics, which precisely follow the benchmarks in cases considered. Furthermore, we propose a delta-function expansion method to approximate the statistical distributions for non-Markovian mixtures, which successfully explains the remarkable transition of oscillating structures from periodic to block statistics. The accuracy of present approximate method is compared to the Markov-based correction approach and benchmark solutions in several typical cases. Our results provide new understanding on absorption-dominated radiative transfer in binary stochastic mixtures.

We investigate two-center plasma screening effects on thermonuclear reactions of D-T, p-^11B, and ^12C-^12C, spanning from classical to degenerate regimes. The two-center screening potential is obtained within a finite-temperature Thomas-Fermi-Dirac framework, capturing two-ion correlations as the leading-order many-body effect. Combining the resulting screened Coulomb potential with a complex Woods-Saxon nuclear potential, we solve the stationary Schrödinger equation to obtain the fusion tunneling probabilities and the corresponding reaction rates. Compared to Debye-Hückel results, the present screening potential is stronger in weakly coupled and weakly degenerate regimes but weaker in strongly coupled and strongly degenerate regimes. Consequently, the fusion enhancement factors are amplified in the former but suppressed in the latter. An underlying interplay between two mechanisms is identified: the nonlinear polarization of ions tends to reduce the screening effect, whereas the nonlinear polarization of electrons tends to enhance it. This subtle competition is governed by the plasma coupling strength and degeneracy. These findings highlight that a two-center treatment is important for predicting fusion rates in dense plasmas.

Within the equilibrium-diffusion approximation for radiation, we perform a linear stability analysis of the compressible Rayleigh-Taylor instability in a stratified, isothermal background. Radiation alters the growth rate by modulating the fluid's effective compressibility. Radiative diffusion enhances compressibility, driving the growth rate from the adiabatic toward the isothermal limit as the Péclet number Pe decreases. In contrast, radiation pressure reduces compressibility, steering the growth rate toward the incompressible limit as the Mihalas number R decreases. These competing effects are governed by the key dimensionless groups Pe (convective versus diffusive transport) and R (material versus radiation pressure). The impact of radiation is most pronounced at low Atwood numbers (At), high stratification parameters (Sr), or large interface thicknesses (δ).

A reshock experiment for investigating the growth of material mixing driven by the Richtmyer-Meshkov instability has been conducted at the SG 100 kJ Laser Facility. We present a novel measurement technique for capturing the density field and the temporal evolution of the mixing width in rough aluminum subjected to reshocks under extreme conditions. The temporal evolution of the aluminum layer width obtained from backlit X-ray radiography demonstrates a sharp increase in width caused by reshocks, and simulations using the BHR-2 turbulent mixing model show excellent agreement with the measured aluminum layer width. Moreover, by utilizing a quasi-monochromatic X-ray imaging system at 5.2 keV, based on Bragg reflection from a spherically curved quartz crystal, we demonstrate direct quantification of the aluminum density field in mixed regions for the first time in a indirectly driven reshock experiment. The deviation between the calculated and actual density values is significantly less than 10% when the density of the aluminum region is below 0.7 g/cm(3). The density field provides further information about variable-density turbulent mixing, which improves the constraints on simulations and enhances predictive capabilities for inertial confinement fusion target design and astrophysical shock scenarios.

Within the framework of the precluster model of alpha decay, we extend the celebrated Floquet-Volkov theory in multiphoton ionization processes to calculate the alpha-decay rates of the even-even nuclear elements, specifically 94 Pu, under linearly polarized intense keV x-ray laser fields. Our calculations indicate that in the x-ray regime, an intense laser field can significantly enhance the decay rates of these nuclei by several orders of magnitude with the help of multiphoton processes. The nucleus 94238Pu with lower decay energies seems to be more sensitive to x-ray laser fields and shows a relatively larger enhancement, due to the fact that its relatively higher Coulomb barrier can be influenced more significantly through the multiphoton-assisted quantum tunneling. Some implications are discussed.

We study the impact of dimension on the radiative transfer (i.e., thermal x-ray transport) through the nonscattering random medium within the coupling of radiation to material. To this purpose, our approach is based on the direct numerical simulations (DNSs) combined with developed analytical models. Systematic calculations for 29 different sets of physical parameters show two- and three-dimensional transport results are similar, while a remarkable problem-dependent difference is observed in most cases between one and two dimensions, which are explicitly analyzed by using the dimension compression method. Furthermore, we find a good scaling law with respect to the effective optical thickness, thereby we propose an analytical model to predict the impact of dimension and a good agreement with DNS results is identified. In addition, we develop a simple formula to account for the maximum dimensional effect when the materials' opacity contrast is infinitely large. Our work provides a clear physical picture and predictable analytical models for the influence of dimension on the radiative transfer in the thermally participating random media.

Homogenization of random media is a practical approach to efficiently simulate stochastic radiative transfer, which requires establishing a reliable effective opacity model. In this work, a new effective opacity model is developed by considering the two-point spatial correlations of the opacity fluctuation, which is further simplified by introducing the analytically empirical function of the optical depth. Our new model has been extensively verified by comparing with direct numerical simulations (DNSs) of stochastic radiative transfer in participating random media in two dimensions. A systematic comparison with existing effective opacity models in the literature is made. For more than 50 different sets of physical parameters of random media, including constant and temperature-dependent opacities, it shows that our new model is the most accurate, which can reproduce the DNS transport results within a relative error of 5% in most cases. In contrast, the performance of existing models is problem-dependent, and it yields considerable errors spanning over three orders of magnitude. The reasons why the newly developed model works well and why existing models fail are also discussed. For more realistic problems, radiative transfer in the aluminum-foam mixture is investigated, where our new model shows the best performance among analytical effective opacity models. In addition, the newly developed model's limitations are briefly analyzed.

In this paper, we study the rapid transition in Richtmyer–Meshkov instability (RMI) with reshock through three-dimensional double-layer swirling vortex rings. The rapid transition in RMI with reshock has an essential influence on the evolution of supernovas and the ignition of inertial confinement fusion, which has been confirmed in numerical simulations and experiments in shock-tube and high-energy-density facilities over the past few years. Vortex evolution has been confirmed to dominate the late-time nonlinear development of the perturbed interface. However, few studies have investigated the three-dimensional characteristics and nonlinear interactions among vortex structures during the transition to turbulent flows. The coexistence of co-rotating and counter-rotating vortices is hypothesized to induce successive large-scale strain fields, which are the main driving sources for rapid development. The three-dimensional effect is reflected in the presence of local swirling motion in the azimuthal direction, and it decreases the translation velocity of a vortex ring. Large-, middle- and small-scale strain fields are employed to describe the development process of RMI with reshock, e.g. vorticity deposited by the reshock, formation of the coexistence of the co-rotating and counter-rotating vortices, iterative cascade under the amplification of the strain fields and viscous dissipation to internal energy. This provides theoretical suggestions for designing practical applications, such as the estimation of the hydrodynamic instability and mixing during the late-time acceleration phase of the inertial confinement fusion.

We investigate the fusion cross sections of light nuclei in the presence of linearly polarized intense laser fields. By combining the Coulomb-Volkov solutions with the complex spherical square-well nuclear potential, we derive an explicit formulation of the multiphoton cross section in a self-consistent manner. Our analysis is specifically focused on deuteron-triton (DT) and proton-boron (p 11B) fusion reactions, both of which have garnered widespread attention. The theoretical results reveal that, under conditions of longer laser wavelengths and lower incident particle kinetic energies, a few thousands of photons can participate in the fusion reactions, resulting in a substantial enhancement of fusion cross sections by almost ten orders of magnitude. We elucidate the multiphoton mechanism underlying these findings and discuss their implications.

Modeling the nonequilibrium process between ions and electrons is of great importance in laboratory fusion ignition, laser-plasma interaction, and astrophysics. For hot and dense plasmas, theoretical descriptions of Coulomb collisions remain complicated due to quantum effect at short distances and screening effect at long distances. In this paper, we propose an analytical screened quantum statistical potential that takes into account both the short-range quantum diffraction effect and the long-range screening effect. By implementing the newly developed potential into the binary scattering framework, the electron-proton temperature relaxation in hot-dense hydrogen plasmas is investigated. In both the classical and quantum limits, analytical expressions for the Coulomb logarithm have been obtained, which are generally embedded in an asymptotic matching formula. Quantitative comparisons with molecular dynamics simulations and recent OMEGA experiments demonstrate that the present modeling is well suited to describe the temperature relaxation process between electrons and ions in hot-dense plasmas.

We study radiative transfer in participating binary stochastic mixtures in two dimensions (2D) by developing an accurate and efficient simulation tool. For two different sets of physical parameters, 2D benchmark results are presented, and it is found that the influence of the stochastic mixture on radiative transfer is clearly parameter-dependent. Our results confirm that previous multidimensional results obtained in different studies are basically consistent, which is interpreted in terms of the relationship between the photon mean free path lp and the system size L. Nonlinear effects, including those due to scattering and radiation–material coupling, are also discussed. To further understand the particle size effect, we employ a dimensionless parameter lp/L, from which a critical particle size can be derived. On the basis of further 2D simulations, we find that an inhomogeneous mix is obtained for lp/L > 0.1. Furthermore, 2D material temperature distributions reveal that self-shielding and particle–particle shielding of radiation occur, and are enhanced when lp/L is increased. Our work is expected to provide benchmark results to verify proposed homogenized models and/or other codes for stochastic radiative transfer in realistic physical scenarios.

A response to commenter Ke Lan's comment on our paper published in Nature Communications (2023)14:5782 by J. Yan et al

Electron-proton energy relaxation rates are assessed using molecular dynamics (MD) simulations in weakly-coupled hydrogen plasmas. To this end, we use various approaches to extract the energy relaxation rate from MD-simulated temperatures, and we find that existing extracting approaches may yield results with a sizable discrepancy larger than the variance between analytical models, which is further verified by well-known case studies. Present results show that two of the extracting approaches can produce identical results, which is attributed to a proper treatment of relaxation evolution. To discriminate the use of various methods, an empirical criterion with respect to initial plasma temperatures is proposed, which can self-consistently explain the cases considered. In addition, for a transient electron-proton plasma, we show that it is possible to extrapolate the Coulomb logarithm from that derived by initial plasma parameters in a single MD calculation, which is reasonably consistent with previous MD data. Our results are helpful to obtain accurate MD-based energy relaxation rates.

In laser-driven inertial confinement fusion, driving pressure boosting and smoothing are major challenges. A proposed hybrid-drive (HD) scheme can offer such ideal HD pressure performing stable implosion and nonstagnation ignition. Here we report that in the hemispherical and planar ablator targets installed in the semicylindrical hohlraum scaled down from the spherical hohlraum of the designed ignition target, under indirect-drive (ID) laser energies of ~43–50 kJ, the peak radiation temperature of 200 ± 6 eV is achieved. And using only direct-drive (DD) laser energies of 3.6–4.0 kJ at an intensity of 1.8 × 10 15 W/cm 2 , in the hemispherical and planar targets the boosted HD pressures reach 3.8–4.0 and 3.5–3.6 times the radiation ablation pressure respectively. In all the above experiments, significant HD pressure smoothing and the important phenomenon of how a symmetric strong HD shock suppresses the asymmetric ID shock pre-compressed fuel are demonstrated. The backscattering and hot-electron energy fractions both of which are about one-third of that in the DD scheme are also measured.

By adopting heat conduction of the Spitzer form in implicit large eddy simulations, the effect of high-intensity heat conduction on turbulence induced by the ablative Rayleigh-Taylor instability is studied in this paper. The height of the spike and bubble exhibit self-similar evolution with t(2) dependence by the late stage of simulations, while heat conduction suppresses the coefficient of spike a(s) and slightly enhances that of the bubble a(b). Heat conduction displays a strong damping effect for small-scale fluctuations of the temperature and density field, resulting in a much steeper slope for energy spectra in intermediate scales. The diffusion effect is responsible for the suppression of temperature fluctuations, and velocity dilatation is shown to be a possible route for heat conduction to affect density fluctuations. The impact of heat conduction on the velocity field is relatively weak, with vertical velocity spectra exhibiting classical Kolmogorov inertial range in intermediate scales. By comparing enstrophy profiles, it is found that vorticity tends to peak at the bubble side in cases with high-intensity heat conduction.

针对三维球形靶丸内爆高效模拟需求和传统笛卡尔正交网格上辐射加源困难的问题,发展一种多块结构非正交网格生成方法,并基于此种计算网格提出高效的三维扩散格式并行算法,将其应用于辐射流体方程组的求解和三维内爆不对称性的数值模拟,数值结果显示了算法的有效性.并行性能测试显示该算法可扩展到5400个核上,并行效率达到69％.

Metal plates containing penetrating gap may eject high velocity material outward from the gap opening under strong impact loading. Experiments have observed that some facts significantly affect the gap ejection behavior, such as metal properties, gap size, and loading method. Since the shape of the gap is the strip with a much greater depth than width, the mature instability theory is hard to apply, and it is difficult to accurately predict the mass and the velocity of the ejecta under this situation. In this paper, we develop a model for this case based on the shaped charge jet theory. The modeling is divided into two parts: the approximately steady jet formed by the long distance closure of gap in the depth direction, and the overturning of the interface after the gap closure reaches the surface. The theoretical model can precisely predict the total mass and maximum velocity of the ejecta. Thereafter, the verification of the theoretical model is carried out with the experiments and the simulation of the detonation-driven lead and copper metal plates containing penetration gaps. The total mass and maximum velocity of the ejecta obtained from the theoretical model agree well with the experimental and simulation results. The experimental phenomenon of the needle-like and mushroom-like ejecta formation is interpreted by the jet incoherence theory, and we proposed a method to determine the ejection coefficient of the theoretical model from this. Finally, a theoretical estimate model for metal gap ejection under sliding detonation loading is presented. The model in this paper can also be applied to the metal gap ejection phenomena formed by non-penetrating elongated gaps closure that satisfying the conditions of steady jet formation.