The dependence of the Richtmyer–Meshkov instability (RMI) on post-shock Atwood number ($A_1$) is experimentally investigated for a heavy–light single-mode interface. We create initial interfaces with density ratios of heavy to light gases ranging from 1.73 to 34.07, and achieve the highest $|A_1|$ value reported to date for gaseous-interface experiments (0.95). For the first time, spike acceleration is observed in experiments with a heavy–light configuration. The models for the start-up, linear and weakly nonlinear evolution stages are evaluated over a wide range of $A_1$ conditions. Specifically, the models proposed by Li et al. (Phys. Fluids, vol. 36, 2024, 056104) and Wouchuk & Nishihara (Phys. Plasmas, vol. 4, 1997, 1028–1038) effectively describe the start-up and linear stages, respectively, across all cases. None of the considered nonlinear models is valid under all $A_1$ conditions. Based on the dependence of spike and bubble evolutions on $A_1$ provided by the present work and previous study (Chen et al., J. Fluid Mech., vol. 975, 2023, A29), the SEA model (Sadot et al., Phys. Rev. Lett., vol. 80, 1998, pp. 1654–1657), whose expression has clear physical meanings, is modified by revising the coefficient that governs its prediction for early-time evolution. The modified model applies to prediction of the weakly nonlinear evolution of RMI with $A_1$ ranging from −0.95 to −0.35 and from 0.30 to 0.86. Based on this model, an approximation of the critical $A_1$ for the occurrence of spike acceleration is obtained.

The manipulation of the Richtmyer–Meshkov instability growth at a heavy–light interface via successive shocks is theoretically analysed and experimentally realized in a specific shock-tube facility. An analytical model is developed to forecast the interface evolution before and after the second shock impact, and the possibilities for the amplitude evolution pattern are systematically discussed. Based on the model, the parameter conditions for each scenario are designed, and all possibilities are experimentally realized by altering the time interval between two shock impacts. These findings may enhance the understanding of how successive shocks influence hydrodynamic instabilities in practical applications.

External seeded free-electron lasers (FELs) have exhibited substantial progress in diverse applications over the last decade. However, the frequency up-conversion efficiency in single-stage seeded FELs, particularly in high-gain harmonic generation (HGHG), remains constrained to a modest level. This limitation restricts its capability to conduct experiments within the ‘water window’. This paper presents a novel method for generating coherent X-ray FEL pulses in the water window region based on the HGHG scheme with multi-stage harmonic cascade. Without any additional modifications to the HGHG configuration, simulation results demonstrate the generation of intense 3 nm coherent FEL radiation using an external ultraviolet seed laser. This indicates an increase of the harmonic conversion number to approximately 90. A preliminary experiment is performed to evaluate the feasibility of this method. The proposed approach could potentially serve as an efficient method to broaden the wavelength coverage accessible to both existing and planned seeded X-ray FEL facilities.

The effects of reshock conditions, including the interface evolution state before reshock and the second shock intensity, on interface instability induced by two successive shocks propagating in the same direction are investigated via shock-tube experiments. It is observed that the reshock promotes the interface instability, and the post-reshock perturbation evolution relates to both the pre-reshock interface evolution state and second shock intensity. For the linear evolution of the twice-shocked interface, existing models perform poorly when either the pre-reshock interface shape effect or the secondary compression effect is pronounced, as current reduction factors fail to accurately describe these effects. Besides, the reshock-induced linear amplitude growth rate shows a non-monotonic dependence on the scaled pre-reshock amplitude, primarily due to the shape effect of the pre-reshock interface. For the post-reshock nonlinear evolution, the model proposed by Zhang & Guo (J. Fluid Mech., vol. 786, 2016, pp. 47–61) offers reasonable predictions when the second shock is weak. However, when the second shock is moderately strong, the model overestimates the bubble growth and underestimates the spike evolution under the influence of the significant secondary compression effect. Furthermore, empirical linear and nonlinear models capable of describing the dependence of the post-reshock evolution on reshock conditions are proposed based on the present experimental results and existing models.

The coupling of Richtmyer–Meshkov instability (RMI) and Kelvin–Helmholtz instability (KHI), referred to as RM-KHI, on a shock-accelerated inclined single-mode air–SF$_6$ interface is studied through shock-tube experiments, focusing on the evolution of the perturbation distributed along the inclined interface. To clearly capture the linear (overall linear to nonlinear) evolution of RM-KHI, a series of experiments with a weak (relatively strong) incident shock is conducted. For each series of experiments, various $\theta _{i}$ (angle between incident shock and equilibrium position of the initial interface) are considered. The nonlinear flow features manifest earlier and develop faster when $\theta _{i}$ is larger and/or shock is stronger. In addition, the interface with $\theta _{i}>0^{\circ }$ evolves obliquely along its equilibrium position under the effect of KHI. RMI dominates the early-time amplitude evolution regardless of $\theta _{i}$ and shock intensity, which arises from the discrepancy in the evolution laws between RMI and KHI. KHI promotes the post-early-stage amplitude growth and its contribution is related positively to $\theta _{i}$. An evident exponential-like amplitude evolution behaviour emerges in RM-KHI with a relatively strong shock and large $\theta _{i}$. The linear model proposed by Mikaelian (Phys. Fluids, vol. 6, 1994, pp. 1943–1945) is valid for RM-KHI within the linear period. In contrast, the adaptive vortex model (Sohn et al., Phys. Rev. E, vol. 82, 2010, p. 046711) can effectively predict both the interface morphology and overall amplitude evolutions from the linear to nonlinear regimes.

Shock-tube experiments and theoretical studies have been performed to highlight mode-coupling in an air–SF$_6$–air fluid layer. Initially, the two interfaces of the layer are designed as single mode with different basic modes. It is found that as the two perturbed interfaces become closer, interface coupling induces a different mode from the basic mode on each interface. Then mode coupling further generates new modes. Based on the linear model (Jacobs et al., J. Fluid Mech., vol. 295, 1995, pp. 23–42), a modified model is established by considering the different accelerations of two interfaces and the waves’ effects in the layer, and provides good predictions to the linear growth rates of the basic modes and the modes generated by interface coupling. It is observed that interface coupling behaves differently to the nonlinear growth of the basic modes, which can be characterized generally by the existing or modified nonlinear model. Moreover, a new modal model is established to quantify the mode-coupling effect in the layer. The mode-coupling effect on the amplitude growth is negligible for the basic modes, but is significant for the interface-coupling modes when the initial wavenumber of one interface is twice the wavenumber of the other interface. Finally, amplitude freeze-out of the second single-mode interface is achieved theoretically and experimentally through interface coupling. These findings may be helpful for designing the target in inertial confinement fusion to suppress the hydrodynamic instabilities.

Let G be a finite group. A subgroup A of G is said to be S-permutable in G if A permutes with every Sylow subgroup P of G, that is, $AP=PA$. Let $A_{sG}$ be the subgroup of A generated by all S-permutable subgroups of G contained in A and $A^{sG}$ be the intersection of all S-permutable subgroups of G containing A. We prove that if G is a soluble group, then S-permutability is a transitive relation in G if and only if the nilpotent residual $G^{\mathfrak {N}}$ of G avoids the pair $(A^{s G}, A_{sG})$, that is, $G^{\mathfrak {N}}\cap A^{sG}= G^{\mathfrak {N}}\cap A_{sG}$ for every subnormal subgroup A of G.

The laboratory generation and diagnosis of uniform near-critical-density (NCD) plasmas play critical roles in various studies and applications, such as fusion science, high energy density physics, astrophysics as well as relativistic electron beam generation. Here we successfully generated the quasistatic NCD plasma sample by heating a low-density tri-cellulose acetate (TCA) foam with the high-power-laser-driven hohlraum radiation. The temperature of the hohlraum is determined to be 20 eV by analyzing the spectra obtained with the transmission grating spectrometer. The single-order diffraction grating was employed to eliminate the high-order disturbance. The temperature of the heated foam is determined to be T = 16.8 ± 1.1 eV by analyzing the high-resolution spectra obtained with a flat-field grating spectrometer. The electron density of the heated foam is about $N_e=4.0\pm 0.3\times {10}^{20}{\text{cm}}^{-3}$ under the reasonable assumption of constant mass density.

In preparation for an experiment with a laser-generated intense proton beam at the Laser Fusion Research Center at Mianyang to investigate the 11B(p,α)2α reaction, we performed a measurement at very low proton energy between 140 keV and 172 keV using the high-voltage platform at the Institute of Modern Physics, Lanzhou. The aim of the experiment was to test the ability to use CR-39 track detectors for cross-section measurements and to remeasure the cross-section of this reaction close to the first resonance using the thick target approach. We obtained the cross-section σ = 45.6 ± 12.5 mb near 156 keV. Our result confirms the feasibility of CR-39 type track detector for nuclear reaction measurement also in low-energy regions.

Richtmyer–Meshkov instability (RMI) at a light–heavy single-mode interface over a wide range of post-shock Atwood numbers $A_1$ is studied systematically through elaborate experiments. The interface generation and $A_1$ variation are achieved by the soap-film technology and gas-layer scheme, respectively. Qualitatively, the nonlinear interface evolution features, including spike, bubble and roll-up structures, are more significant in RMI with higher $A_1$. Quantitatively, both the impulsive model and an analytical linear model perform well in predicting the linear growth rate under a wide range of $A_1$ conditions. For the weakly nonlinear stage, the significant spike acceleration occurring when $A_1$ is high, which is observed experimentally for the first time, results in the evolution law of RMI with high $A_1$ being different from the counterpart with low or intermediate $A_1$. None of the considered nonlinear models is found to be applicable for RMI under all $A_1$ conditions, and the predictive capabilities of these models are analysed and summarized. Based on the present experimental results, an empirical nonlinear model is proposed for RMI over a wide range of $A_1$. Further, modal analysis shows that in RMI with high (low or intermediate) $A_1$, high-order harmonics evolve rapidly (slowly) and cannot (can) be ignored. Accordingly, for RMI with high (low or intermediate) $A_1$, the modal model proposed by Zhang & Sohn (Phys. Fluids, vol. 9, 1997, pp. 1106–1124) is less (more) accurate than the one proposed by Vandenboomgaerde et al. (Phys. Fluids, vol. 14, 2002, pp. 1111–1122), since the former ignores perturbation solutions higher than fourth order (the latter retains only terms with the highest power in time).

Attenuation and even freeze-out (amplitude growth stagnation) of the perturbation amplitude growth of a shocked SF$_6$–air interface are first realized in shock-tube experiments through reflected rarefaction waves, which produce reverse baroclinic vorticity offsetting the vorticity deposited by the shock. A theoretical model is constructed to predict the perturbation growth after the impact of rarefaction waves, and seven possibilities of amplitude growth are analysed. Experimentally, a planar air–helium interface is used to produce reflected rarefaction waves. Through changing the perturbation wavelength and the time interval of two impacts, five experiments with specific initial conditions are carried out, and three different possibilities of perturbation growth attenuation are realized.

We report the first shock-tube experiments on two-dimensional dual-mode air–SF$_6$ interfaces with different initial spectra subjected to a convergent shock wave. The convergent shock tube is specially designed with a tail opening to highlight the Bell–Plesset (BP) and mode-coupling effects on amplitude development of fundamental mode (FM). The results show that the BP effect promotes the occurrence of mode coupling, and the feedback of high-order modes to the FM also arises earlier in convergent geometry than that in its planar counterpart. Relatively, the amplitude growth of the FM with a higher mode number is inhibited by the feedback, and saturates earlier. The FM with a lower mode number is affected more heavily by the BP effect, and finally dominates the flow. A new model is proposed to well predict the amplitude growths of the FM and high-order modes in convergent geometry. In particular, for FM that reaches its saturation amplitude, the post-saturation relation is introduced in the model to achieve a better prediction.

‘Freeze-out’ of amplitude growth, i.e. the amplitude growth stagnation of a shocked helium–air interface, is realized through a reflected shock, which produces baroclinic vorticity of the opposite sign to that deposited by the first shock. Theoretically, a model is constructed to calculate the relations among the initial parameters for achieving freeze-out. In particular, if the amplitude growth is within the linear regime at the arrival of the reflected shock, the time interval between the impacts of two shock waves is linearly related to the initial perturbation wavelength, and is independent of the initial perturbation amplitude. Experimentally, an air–SF$_6$ (or air–argon) plane interface is adopted to produce a weak reflected shock. Seven experimental runs with specific initial conditions are examined. For all cases, freeze-out is achieved after the reflected shock impact under the designed conditions.

Richtmyer–Meshkov instability induced by two successive shock waves is experimentally studied in a specific shock tube. To create two successive shock waves synchronously, a driver section is added between the driver and driven sections of the standard shock tube, and an electronically controlled membrane rupture equipment is adopted. The shock-tube flow after the membranes rupture is well described by combining the shock relations, isentropic wave relations with compatibility relations across the contact surface (region). The new shock tube is capable of generating two successive shock waves with controllable strengths and time interval, and provides a relatively ‘clean’ wave system. Then the developments of single-mode light–heavy interfaces with different initial conditions induced by two successive shock waves are investigated. The initial amplitudes are all small enough such that the first-shocked interface is within the linear growth regime at the arrival of the second shock. The results show that if the pre-second-shock perturbation amplitude is small, the linear, nonlinear and modal evolutions of the double-shocked interface can be reasonably predicted by the existing models proposed for predicting the perturbation growth induced by a single shock. For the double-shocked interface, the second shock provides an additional perturbation velocity field to the original one introduced by the first shock impact. The validity of the linear superposition model indicates that the linear superposition of these two perturbation velocity fields is satisfied. Therefore, a double-shocked interface evolves similarly to a single-shocked interface provided that their postshock amplitudes and linear growth rates are the same.

The two-dimensional (2-D) unsteady shock reflection over a single wedge is studied theoretically and numerically, and the emphasis is placed on the trajectory of the triple point (TP). Skews’ relation and the three-shock theory are, respectively, used for determining the trajectory angles of the corner-generated disturbance and the TP, and, subsequently, a model capable of predicting the TP trajectory is established for 2-D unsteady shock reflections over a single wedge. Then, a systematically numerical study is carried out on the 2-D unsteady shock reflection over a single wedge, including five types of shock reflection with the wedge angle increased and five types of shock reflection with the wedge angle decreased. It is found that the Mach stem is always slightly concavely (convexly) curved for reflections with the wedge angle increased (decreased), which should be caused by corner-generated compression (rarefaction) waves propagating along the Mach stem. The new model reasonably predicts the TP trajectory in all the 2-D unsteady shock reflections, and its performance is related not only to the variation trend of the wedge angle (increase or decrease), but also to the type of shock and the initial wedge angle. Specifically, for the shock reflection with the wedge angle increased (decreased), the model generally provides a slightly better (worse) prediction if the TP trajectory angle calculated by the three-shock theory is compulsively modified. The shock-shock/expansion polar analysis presented can partially explain the model performance for predicting the TP trajectory.

We describe finite soluble nonnilpotent groups in which every minimal nonnilpotent subgroup is abnormal. We also show that if G is a nonsoluble finite group in which every minimal nonnilpotent subgroup is abnormal, then G is quasisimple and $Z(G)$ is cyclic of order $|Z(G)|\in \{1, 2, 3, 4\}$ .

Due to less light scattering and a better signal-to-noise ratio in deep imaging, two-photon fluorescence microscopy (TPFM) has been widely used in biomedical photonics since its advent. However, optical aberrations degrade the performance of TPFM in terms of the signal intensity and the imaging depth and therefore restrict its application. Here, we introduce adaptive optics based on the genetic algorithm to detect the distorted wavefront of the excitation laser beam and then perform aberration correction to optimize the performance of TPFM. By using a spatial light modulator as the wavefront controller, the correction phase is obtained through a signal feedback loop and a process of natural selection. The experimental results show that the signal intensity and imaging depth of TPFM are improved after aberration correction. Finally, the method was applied to two-photon fluorescence lifetime imaging, which helps to improve the signal-to-noise ratio and the accuracy of lifetime analysis. Furthermore, the method can also be implemented in other experiments, such as three-photon microscopy, light-sheet microscopy, and super-resolution microscopy.

In this paper, we report the study of degradation for a kind of ideal mandrel material called poly-α-methylstyrene based on theoretical and experimental methods. First-principles calculations reveal two types of process: depolymerization and hydrogen-transfer-induced chain scission. The energy barrier for the former (0.68–0.82 eV) is smaller than that for most of the latter (1.39–4.23 eV). More importantly, reaction rates suggest that the former is fast whereas the latter is mostly slow, which can result in a difference of 5–31 orders of magnitude at 550 K. Furthermore, a thermogravimetric experiment shows that the activation energy of 2.53 eV for degradation is between those of fast and slow processes, corresponding to the theoretical average value of multiple reaction paths. Thus, a mandrel degradation model combining fast and slow processes is established at the atomic level. Our work provides a direction for research into the key technology of target fabrication in inertial confinement fusion.