In this research, the nonlinear evolution of jet-like spikes in the single-mode ablative Rayleigh-Taylor instability （ARTI） in the presence of preheating, is studied numerically. It is demonstrated that the preheating plays an essential role in the formation of jet-like spikes in the nonlinear ARTI. The evolution of jet-like spikes in the ARTI with preheating consists of three stages with distinctly different distinguishing features. In the early stage, the preheating contributes to significantly increase the density-gradient scale length and broaden the velocity profile of the ablation surface, where the former can reduce the linear growth of the ARTI and mitigate the growth of its harmonics. In the middle stage, the ablative Kelvin-Helmholtz instability is dramatically suppressed due to the ablation effects. In the late stage, the jet＇s length （i.e. bubble-spike amplitude） is further increased by the bubble acceleration in the highly nonlinear ARTI, resulting eventually in the formation of jet-like spikes.
The nonlinear saturation amplitude （NSA） of the fundamental mode in the classical Rayleigh-Taylor instability with a cylindrical geometry for an arbitrary Atwood number is analytically investigated by considering the nonlinear corrections up to the third order. The analytic results indicate that the effects of the initial radius of the interface （r0） and the Atwood number （A） play an important role in the NSA of the fundamental mode. The NSA of the fundamental mode first increases gently and then decreases quickly with increasing A. For a given A, the smaller the ro/λ（λ is the perturbation wavelength）, the larger the NSA of the fundamental mode. When ro/λ is large enough （r0 〉〉 λ）, the NSA of the fundamental mode is reduced to the prediction in the previous literatures within the framework of the third-order perturbation theory.
Rayleigh-Taylor instability of three fluid layers with two interfaces in cylindrical geometry is investigated analytically. The growth rates and the amplitudes of perturbation on the two interfaces are obtained. The feedback factor from outer to inner interface is larger than that from inner to outer interface under the same conditions. The growth rate on the initially unstable interface is larger than the corresponding result in planar geometry for low mode perturbation. The two interfaces are decoupled for a larger mode number perturbation. The dependencies of the amplitudes of perturbation on different initial conditions are analyzed. The negative feedback effect from initially stable interface to another unstable interface is observed. In the limit of infinity inner radius and finite shell thickness, the results in planar geometry are recovered.
Rayleigh–Taylor instability(RTI)in cylindrical geometry initiated by velocity and interface perturbations is investigated analytically through a third-order weakly nonlinear(WN)model.When the initial velocity perturbation is comparable to the interface perturbation,the coupling between them plays a significant role.The difference between the RTI growth initiated only by a velocity perturbation and that only by an interface perturbation in the WN stage is negligibly small.The effects of the mode number on the first three harmonics are discussed respectively.The low-mode number perturbation leads to large amplitudes of RTI growth.The Atwood number and initial perturbation dependencies of the nonlinear saturation amplitude of the fundamental mode are analyzed clearly.When the mode number of the perturbation is large enough,the WN results in planar geometry are recovered.
Rayleigh–Taylor instability（RTI） of three incompressible fluids with two interfaces in spherical geometry is derived analytically. The growth rate on the two interfaces and the perturbation feedthrough coefficients between two spherical interfaces are derived. For low-mode perturbation, the feedthrough effect from outer interface to inner interface is much more severe than the corresponding planar case, while the feedback from inner interface to the outer interface is smaller than that in planar geometry. The low-mode perturbations lead to the pronounced RTI growth on the inner interface of a spherical shell that are larger than the cylindrical and planar results. It is the low-mode perturbation that results in the difference between the RTI growth in spherical and cylindrical geometry. When the mode number of the perturbation is large enough, the results in cylindrical geometry are recovered.
The classical Rayleigh–Taylor instability（RTI） at the interface between two variable density fluids in the cylindrical geometry is explicitly investigated by the formal perturbation method up to the second order. Two styles of RTI, convergent（i.e., gravity pointing inward） and divergent（i.e., gravity pointing outwards） configurations, compared with RTI in Cartesian geometry, are taken into account. Our explicit results show that the interface function in the cylindrical geometry consists of two parts： oscillatory part similar to the result of the Cartesian geometry, and non-oscillatory one contributing nothing to the result of the Cartesian geometry. The velocity resulting only from the non-oscillatory term is followed with interest in this paper. It is found that both the convergent and the divergent configurations have the same zeroth-order velocity, whose magnitude increases with the Atwood number, while decreases with the initial radius of the interface or mode number. The occurrence of non-oscillation terms is an essential character of the RTI in the cylindrical geometry different from Cartesian one.
Inertial fusion energy （IFE） has been considered a promising, nearly inexhaustible source of sustainable carbon-free power for the world＇s energy future. It has long been recognized that the control of hydrodynamic instabilities is of critical importance for ignition and high-gain in the inertial-confinement fusion （ICF） hot-spot ignition scheme. In this mini-review, we summarize the progress of theoretical and simulation research of hydrodynamic instabilities in the ICF central hot-spot implosion in our group over the past decade. In order to obtain sufficient understanding of the growth of hydrodynamic instabilities in ICF, we first decompose the problem into different stages according to the implosion physics processes. The decomposed essential physics pro- cesses that are associated with ICF implosions, such as Rayleigh-Taylor instability （RTI）, Richtmyer-Meshkov instability （RMI）, Kelvin-Helmholtz instability （KHI）, convergent geometry effects, as well as perturbation feed-through are reviewed. Analyti- cal models in planar, cylindrical, and spherical geometries have been established to study different physical aspects, including density-gradient, interface-coupling, geometry, and convergent effects. The influence of ablation in the presence of preheating on the RTI has been extensively studied by numerical simulations. The KHI considering the ablation effect has been discussed in detail for the first time. A series of single-mode ablative RTI experiments has been performed on the Shenguang-II laser facility. The theoretical and simulation research provides us the physical insights of linear and weakly nonlinear growths, and nonlinear evolutions of the hydrodynamic instabilities in ICF implosions, which has directly supported the research of ICF ignition target design. The ICF hot-spot ignition implosion design that uses several controlling features, based on our current understanding of hydrodynamic instabilities, to address shell implosion stability, has been briefly described, severa
