The influence of thin-shell effects on the nonlinear evolution of two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) is studied in the parameter range of inertial confinement fusion implosions. A new phase of unsaturated nonlinear bubble evolution caused by thin-shell effects is found. This is different from the traditional opinion that the bubble velocity becomes saturated after the ARTI evolution enters a highly nonlinear regime. A modified bubble velocity formula is proposed, based on the Betti–Sanz model [Betti and Sanz, Phys. Rev. Lett. 97, 205002 (2006)], considering the thin-shell effects. It is shown that the bubble velocity becomes saturated in the thick-target case after the ARTI evolution enters a highly nonlinear regime. In this case, the Betti–Sanz bubble dynamics model can predict the evolution of bubble velocity. However, when the thin-shell effects become significant in the case of kD0 < 100, where D0 is the initial thickness of the target and k is the perturbation wavenumber, the difference of the average acceleration between the bubble vertex and the spike tip can be much more significant than that of the thick-target case. In this situation, the nonlinear evolution of the ARTI bubbles will accelerate without saturation until the target breakup, which cannot be depicted by the Betti–Sanz model while the improved theory formula is applicative. The Betti–Sanz model and the improved theory formula are independent of the initial perturbation amplitude.
A thin shell model is developed to describe the nonlinear fluid instability growth in a gravitational field or/and driven by a pressure difference in cylindrical convergent geometry in the style of Ott [Phys. Lett. 29, 1429 (1972)]. The differential equations of motion are obtained by analyzing the forces (i.e., the gravitational field and pressure difference) on the cylindrical thin shell. The nonlinear evolution and deformation of the thin shell in the presence of the gravitational field or/and pressure difference are investigated by numerical calculations. When the perturbed thin shell is driven by the gravitational field, the linear growth rates obtained from our model are compared with the analytical formula and they agree well with each other. Furthermore, the evolution of thin shell overall agrees with the weakly nonlinear (WN) theory [Wang et al., Phys. Plasmas 20, 042708 (2013)]. When the thin shell with an unperturbed interface is driven by a nonuniform pressure difference with a single-mode spatial modulation, the perturbation growth can be observed at the surface. In addition, mode-coupling processes between the single-mode perturbed interface and the large-scale drive asymmetry on the thin shell are addressed.
In the present letter, we propose the design of a wedged-peak pulse at the late stage of indirect drive. Our simulations of one- and two-dimensional radiation hydrodynamics show that the wedged-peak-pulse design can raise the drive pressure and capsule implosion velocity without significantly raising the fuel adiabat. It can thus balance the energy requirement and hydrodynamic instability control at both ablator/fuel interface and hot-spot/fuel interface. This investigation has implication in the fusion ignition at current mega-joule laser facilities.
The mechanism of jet-like spike formation from the ablative Rayleigh-Taylor instability (ARTI) in the presence of preheating is reported. It is found that the preheating plays an essential role in the formation of the jet-like spikes. In the early stage, the preheating significantly increases the plasma density gradient, which can reduce the linear growth of ARTI and suppress its harmonics. In the middle stage, the preheating can markedly increase the vorticity convection and effectively reduce the vorticity intensity resulting in a broadened velocity shear layer near the spikes. Then the growth of ablative Kelvin-Helmholtz instability is dramatically suppressed and the ARTI remains dominant. In the late stage, nonlinear bubble acceleration further elongates the bubble-spike amplitude and eventually leads to the formation of jet-like spikes.
A weakly nonlinear theoretical model is established for the two-dimensional incompressible Rayleigh–Taylor–Kelvin–Helmholtz instability (RT–KHI). The evolution of the perturbation interface is analytically studied by the third-order solution of the planar RT–KHI induced by a single-mode surface perturbation. The difference between the weakly nonlinear growth for Rayleigh–Taylor instability (RTI), Kelvin–Helmholtz instability (KHI), and RT–KHI in plane geometry is discussed. The trend of bubble and spike amplitudes with the Atwood number and the Richardson number is discussed in detail. The bubble and spike amplitudes of RT–KHI change from the KHI case to the RTI case as the Richardson number increases. The deflecting distance of bubble and spike vertices becomes smaller compared to the KHI case as the Richardson number increases. The dependence of the nonlinear saturation amplitude of RT–KHI on the Atwood number, the Richardson number, and the initial perturbation is obtained. The Richardson number is as vital to the nonlinear saturation amplitude as the Atwood number. It is found that the variation of the nonlinear saturation amplitude with the Atwood number at different Richardson numbers is divided into three parts, namely, “RTI-like part,” “transition part,” and “KHI-like part.” In the transition part, the trend of the nonlinear saturation amplitude increasing with the Atwood number is completely opposite to the RTI and KHI cases. Finally, the theory is compared to the numerical simulation under identical initial conditions and displays good correspondence in the linear and weakly nonlinear stages.
Abstract The hydrodynamic instability growth seeded by localized perturbations exerts a significant influence on the performance of inertial confinement fusion implosions. Direct-drive, planar target ablative hydrodynamic instability growth simulations were performed to study the evolution of localized perturbations at peak drive intensities of ignition designs. The study focused on hydrodynamic instability seeded by Gaussian bumps and rectangular pits on the target outer surface at a laser intensity of about $9 \times 10^{14} \, \rm W/cm^2$. The findings indicated that the nonlinear growth of localized perturbations is significantly influenced by nonlocal electron heat transport. It was observed that the small-scale Gaussian bump experiences a phase reversal before the target acceleration phase and evolves into an isolated bubble, with spikes growing obliquely on both sides tending to heal the void created by the bubble. Notably, nonlocal electron heat transport effects slow down void healing and nonlinear bubble growth, which can prevent defects from penetrating the target shell prematurely. For rectangular pits with larger lateral dimensions, no overall phase reversal occurs before target acceleration, and the nonlinear bubble growth is similarly suppressed.
These findings underscore the importance of considering nonlocal electron heat transport effects in multi-dimensional implosion simulations.
A weakly nonlinear model is proposed for the multi-mode incompressible Rayleigh-Taylor instability in two-dimensional spherical geometry. The second-order solutions are derived, which can be applied to arbitrary small initial perturbations. The cosine-type and the Gaussian-type perturbations are discussed in detail. The growth of perturbations at the pole and that at the equator are compared, and the geometry effect is analyzed. It is found that the initial identical perturbation at the pole and the equator in the cross-sectional view will grow asymmetrically. In the linear regime, the perturbation amplitudes at the pole grow faster than those at the equator due to the different topologies. The geometry effect accelerates the ingoing motion and slows down the outgoing motion in the weakly nonlinear regime. This effect is stronger at the pole than that at the equator.
In this research, competitions between Rayleigh–Taylor instability (RTI) and Kelvin–Helmholtz instability (KHI) in two-dimensional incompressible fluids within a linear growth regime are investigated analytically. Normalized linear growth rate formulas for both the RTI, suitable for arbitrary density ratio with continuous density profile, and the KHI, suitable for arbitrary density ratio with continuous density and velocity profiles, are obtained. The linear growth rates of pure RTI (γRT), pure KHI (γKH), and combined RTI and KHI (γtotal) are investigated, respectively. In the pure RTI, it is found that the effect of the finite thickness of the density transition layer (Lρ) reduces the linear growth of the RTI (stabilizes the RTI). In the pure KHI, it is found that conversely, the effect of the finite thickness of the density transition layer increases the linear growth of the KHI (destabilizes the KHI). It is found that the effect of the finite thickness of the density transition layer decreases the “effective” or “local” Atwood number (A) for both the RTI and the KHI. However, based on the properties of γRT∝A and γKH∝1−A2, the effect of the finite thickness of the density transition layer therefore has a completely opposite role on the RTI and the KHI noted above. In addition, it is found that the effect of the finite thickness of the velocity shear layer (Lu) stabilizes the KHI, and for the most cases, the combined effects of the finite thickness of the density transition layer and the velocity shear layer (Lρ=Lu) also stabilize the KHI. Regarding the combined RTI and KHI, it is found that there is a competition between the RTI and the KHI because of the completely opposite effect of the finite thickness of the density transition layer on these two kinds of instability. It is found that the competitions between the RTI and the KHI depend, respectively, on the Froude number, the density ratio of the light fluid to the heavy one, and the finite thicknesses of the density transition layer and the velocity shear layer. Furthermore, for the fixed Froude number, the linear growth rate ratio of the RTI to the KHI decreases with both the density ratio and the finite thickness of the density transition layer, but increases with the finite thickness of the velocity shear layer and the combined finite thicknesses of the density transition layer and the velocity shear layer (Lρ=Lu). In summary, our analytical results show that the effect of the finite thickness of the density transition layer stabilizes the RTI and the overall combined effects of the finite thickness of the density transition layer and the velocity shear layer (Lρ=Lu) also stabilize the KHI. Thus, it should be included in applications where the transition layer effect plays an important role, such as the formation of large-scale structures (jets) in high energy density physics and astrophysics and turbulent mixing.
Two-plasmon-decay instability (TPD) poses a critical target preheating risk in direct-drive inertial confinement fusion. In this paper, TPD collectively driven by dual laser beams consisting of a normal-incidence laser beam (Beam-N) and a large-angle-incidence laser beam (Beam-L) is investigated via particle-in-cell simulations. It is found that significant TPD growth can develop in this regime at previously unexpected low laser intensities if the intensity of Beam-L exceeds the large-angle-incidence threshold. Both beams contribute to the growth of TPD in a “seed-amplification” manner in which the absolute instability driven by Beam-L provides the seeds that are convectively amplified by Beam-N, making TPD energetically important and causing significant pump depletion and hot-electron generation.
We investigate herein how long-wavelength perturbations affect the nonlinear evolution of the multimode ablative Rayleigh–Taylor instability (ARTI). A single-mode ARTI with an initial small amplitude is first investigated to validate the reliability of the proposed simulation code. The results show that both linear growth rates and asymptotic bubble velocities obtained from simulations are in reasonable agreement with theoretical results. Initial perturbations with different long-wavelength perturbations are compared to investigate the contribution of the long-wavelength perturbations to the nonlinear evolution of the ARTI mixing. Beyond the nonlinear saturation limit [S. W. Haan, Phys. Rev. A 39, 5812 (1989)], the long-wavelength perturbation promotes the ARTI mixing and facilitates the development of the large-scale structure on the ablation surface. In the self-similar analysis, the simulation results indicate that the self-similar growth parameters decrease with increasing initial longest-wavelength modes.
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