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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. [ABSTRACT FROM AUTHOR]

The fully three-dimensional Rayleigh–Taylor instability in spherical geometry is investigated in the weakly nonlinear regime. A theoretical model is developed for incompressible fluid and ideal Euler equations. Third-order solutions are derived for interface perturbations of spherical harmonic modes, Y n , m . Interface evolution, fundamental mode growth, the generated spectrum, and bubble growth are determined. It is found that the fastest growing modes satisfy the relation m ≃ (n + 1) / 2. The generated spectra demonstrate the feedback of mode coupling, which greatly depends on the azimuthal mode numbers. The growth factors are nearly the same for bubbles at different latitudes and bubbles with initially round cross-sectional perturbation shapes grow faster. [ABSTRACT FROM AUTHOR]

A two-dimensional thin shell model has been developed for the Rayleigh-Taylor instability in spherical geometry. The present model generalizes the work of Ott [Phys. Rev. Lett. 29, 1429 (1972)] to the case of spherical geometry. The governing equations for the shell motion and the deformation are obtained analytically and solved numerically. The linear growth rates from our model agree well with those from Mikaelian's work but are slightly larger than those from the classical prediction for low-mode perturbations. The perturbation amplitudes and bubble velocities from our model are in general agreement with those from the weakly nonlinear model of Zhang [Phys. Plasmas 24, 062703 (2017)] and Layzer's model [Astrophys. J. 122, 1 (1955)], respectively. Moreover, the present model can investigate the shell evolution initialized by multimode axisymmetric perturbations in spherical geometry. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Nonlinear amplitude saturation (NAS) of the fundamental mode of Rayleigh-Taylor instability (RTI) in a finite-thickness incompressible fluid layer is investigated analytically by considering high-order corrections (HOCs) up to the ninth order. The results of classical RTI [Liu et al., Phys. Plasmas 19, 042705 (2012)] can be recovered for the normalized fluid thickness kd→∝. It is found that the NAS of the fundamental mode on the lower and upper interfaces is clearly larger than its third-order counterpart [Wang et al., Phys. Plasmas 21, 122710 (2014)] when the HOCs are considered, especially for the lower (linearly unstable) interface. Furthermore, the NAS on both interfaces exhibits the trend of convergence with increasing order of corrections. [ABSTRACT FROM AUTHOR]

In this research, a weakly nonlinear (WN) model for the incompressible Rayleigh-Taylor instability in cylindrical geometry [Wang et al., Phys. Plasmas 20, 042708 (2013)] is generalized to spherical geometry. The evolution of the interface with an initial small-amplitude single-mode perturbation in the form of Legendre mode (Pn) is analysed with the third-order WN solutions. The transition of the small-amplitude perturbed spherical interface to the bubble-and-spike structure can be observed by our model. For single-mode perturbation Pn, besides the generation of P2n and P3n, which are similar to the second and third harmonics in planar and cylindrical geometries, many other modes in the range of P0-P3n are generated by mode-coupling effects up to the third order. With the same initial amplitude, the bubbles at the pole grow faster than those at the equator in the WN regime. Furthermore, it is found that the behavior of the bubbles at the pole is similar to that of threedimensional axisymmetric bubbles, while the behavior of the bubbles at the equator is similar to that of two-dimensional bubbles. [ABSTRACT FROM AUTHOR]

While progress towards hot-spot ignition has been made achieving an alpha-heating dominated state in high-foot implosion experiments [Hurricane et al., Nat. Phys. 12, 800 (2016)] on the National Ignition Facility, improvements are needed to increase the fuel compression for the enhancement of the neutron yield. A strategy is proposed to improve the fuel compression through the recompression of a shock/compression wave generated by the end of the main drive portion of a high-foot pulse shape. Two methods for the peak pulse recompression, namely, the decompression- and-recompression (DR) and simple recompression schemes, are investigated and compared. Radiation hydrodynamic simulations confirm that the peak pulse recompression can clearly improve fuel compression without significantly compromising the implosion stability. In particular, when the convergent DR shock is tuned to encounter the divergent shock from the capsule center at a suitable position, not only the neutron yield but also the stability of stagnating hot-spot can be noticeably improved, compared to the conventional high-foot implosions [Hurricane et al., Phys. [ABSTRACT FROM AUTHOR]

It is demonstrated that the growth of acceleration-phase instabilities in inertial confinement fusion implosions can be controlled, especially in the high-foot implosions [O. A. Hurricane et al., Phys. Plasmas 21, 056314 (2014)] on the National Ignition Facility. However, the excessive growth of the deceleration-phase instabilities can still destroy the hot spot ignition. A scheme is proposed to retard the deceleration-phase Rayleigh-Taylor instability growth by shock collision near the waist of the inner shell surface. Two-dimensional radiation hydrodynamic simulations confirm the improved deceleration-phase hot spot stability properties without sacrificing the fuel compression. [ABSTRACT FROM AUTHOR]

In this research, a weakly nonlinear (WN) model has been developed considering the growth of a small perturbation on a cylindrical interface between two incompressible fluids which is subject to arbitrary radial motion. We derive evolution equations for the perturbation amplitude up to third order, which can depict the linear growth of the fundamental mode, the generation of the second and third harmonics, and the third-order (second-order) feedback to the fundamental mode (zeroorder). WN solutions are obtained for a special uniformly convergent case. WN analyses are performed to address the dependence of interface profiles, amplitudes of inward-going and outwardgoing parts, and saturation amplitudes of linear growth of the fundamental mode on the Atwood number, the mode number (m), and the initial perturbation. The difference of WN evolution in cylindrical geometry from that in planar geometry is discussed in some detail. It is shown that interface profiles are determined mainly by the inward and outward motions rather than bubbles and spikes. The amplitudes of inward-going and outward-going parts are strongly dependent on the Atwood number and the initial perturbation. For low-mode perturbations, the linear growth of fundamental mode cannot be saturated by the third-order feedback. For fixed Atwood numbers and initial perturbations, the linear growth of fundamental mode can be saturated with increasing m. The saturation amplitude of linear growth of the fundamental mode is typically 0.2λ-0.6λ for m<100, with λ being the perturbation wavelength. Thus, it should be included in applications where Bell-Plesset [G. I. Bell, Los Alamos Scientific Laboratory Report No. LA-1321, 1951; M. S. Plesset, J. Appl. Phys. 25, 96 (1954)] converging geometry effects play a pivotal role, such as inertial confinement fusion implosions. [ABSTRACT FROM AUTHOR]

A weakly nonlinear (WN) model has been developed for the Rayleigh-Taylor instability of a finite-thickness incompressible fluid layer (slab). We derive the coupling evolution equations for perturbations on the (upper) "linearly stable" and (lower) "linearly unstable" interfaces of the slab. Expressions of temporal evolutions of the amplitudes of the perturbation first three harmonics on the upper and lower interfaces are obtained. The classical feedthrough (interface coupling) solution obtained by Taylor [Proc. R. Soc. London A 201, 192 (1950)] is readily recovered by the first-order results. Our third-order model can depict the WN perturbation growth and the saturation of linear (exponential) growth of the perturbation fundamental mode on both interfaces. The dependence of the WN perturbation growth and the slab distortion on the normalized layer thickness (kd) is analytically investigated via the third-order solutions. Comparison is made with Jacobs-Catton's formula [J. W. Jacobs and I. Catton, J. Fluid Mech. 187, 329 (1988)] of the position of the "linearly unstable" interface. Using a reduced formula, the saturation amplitude of linear growth of the perturbation fundamental mode is studied. It is found that the finite-thickness effects play a dominant role in the WN evolution of the slab, especially when kd<1. Thus, it should be included in applications where the interface coupling effects are important, such as inertial confinement fusion implosions and supernova explosions. [ABSTRACT FROM AUTHOR]

In this research, a series of single-mode, indirect-drive, ablative Rayleigh-Taylor (RT) instability experiments performed on the Shenguang-II laser facility [X. T. He and W. Y. Zhang, Eur. Phys. J. D 44, 227 (2007)] using planar target is reported. The simulation results from the one-dimensional hydrocode for the planar foil trajectory experiment indicate that the energy flux at the hohlraum wall is obviously less than that at the laser entrance hole. Furthermore, the non-Planckian spectra of x-ray source can strikingly affect the dynamics of the foil flight and the perturbation growth. Clear images recorded by an x-ray framing camera for the RT growth initiated by small- and largeamplitude perturbations are obtained. The observed onset of harmonic generation and transition from linear to nonlinear growth regime is well predicted by two-dimensional hydrocode simulations. [ABSTRACT FROM AUTHOR]

Weakly nonlinear (WN) Rayleigh-Taylor instability (RTI) initiated by single-mode cosinusoidal interface and velocity perturbations is investigated analytically up to the third order. Expressions of the temporal evolutions of the amplitudes of the first three harmonics are derived. It is shown that there are coupling between interface and velocity perturbations, which plays a prominent role in the WN growth. When the 'equivalent amplitude' of the initial velocity perturbation, which is normalized by its linear growth rate, is compared to the amplitude of the initial interface perturbation, the coupling between them dominates the WN growth of the RTI. Furthermore, the RTI would be mitigated by initiating a velocity perturbation with a relative phase shift against the interface perturbation. More specifically, when the phase shift between the interface perturbation and the velocity perturbation is π and their equivalent amplitudes are equal, the RTI could be completely quenched. If the equivalent amplitude of the initial velocity perturbation is equal to the initial interface perturbation, the difference between the WN growth of the RTI initiated by only an interface perturbation and by only a velocity perturbation is found to be asymptotically negligible. The dependence of the WN growth on the Atwood numbers and the initial perturbation amplitudes is discussed. In particular, we investigate the dependence of the saturation amplitude (time) of the fundamental mode on the Atwood numbers and the initial perturbation amplitudes. It is found that the Atwood numbers and the initial perturbation amplitudes play a crucial role in the WN growth of the RTI. Thus, it should be included in applications where the seeds of the RTI have velocity perturbations, such as inertial confinement fusion implosions and supernova explosions. [ABSTRACT FROM AUTHOR]

In this research, density gradient effects (i.e., finite thickness of ablation front effects) in ablative Rayleigh-Taylor instability (ARTI), in the presence of preheating within the weakly nonlinear regime, are investigated numerically. We analyze the weak, medium, and strong ablation surfaces which have different isodensity contours, respectively, to study the influences of finite thickness of ablation front on the weakly nonlinear behaviors of ARTI. Linear growth rates, generation coefficients of the second and the third harmonics, and coefficients of the third-order feedback to the fundamental mode are obtained. It is found that the linear growth rate which has a remarkable maximum, is reduced, especially when the perturbation wavelength λ is short and a cut-off perturbation wavelength λc appears when the perturbation wavelength λ is sufficiently short, where no higher harmonics exists when λ<λc. The phenomenon of third-order positive feedback to the fundamental mode near the λc [J. Sanz et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier et al., Phys. Rev. Lett. 90, 185003 (2003); J. Garnier and L. Masse, Phys. Plasmas 12, 062707 (2005)] is confirmed in numerical simulations, and the physical mechanism of the third-order positive feedback is qualitatively discussed. Moreover, it is found that generations and growths of the second and the third harmonics are stabilized (suppressed and reduced) by the ablation effect. Meanwhile, the third-order negative feedback to the fundamental mode is also reduced by the ablation effect, and hence, the linear saturation amplitude (typically ~0.2λ in our simulations) is increased significantly and therefore exceeds the classical prediction 0.1λ, especially for the strong ablation surface with a small perturbation wavelength. Overall, the ablation effect stabilizes the ARTI in the weakly nonlinear regime. Numerical results obtained are in general agreement with the recent weakly nonlinear theories and simulations as proposed [J. Sanz et al., Phys. Rev. Lett. 89, 195002 (2002); J. Garnier et al., Phys. Rev. Lett. 90, 185003 (2003); J. Garnier and L. Masse, Phys. Plasmas 12, 062707 (2005)]. [ABSTRACT FROM AUTHOR]

In this paper, the effects of magnetic field gradient (i.e., the magnetic field transition layer effects) on the Rayleigh-Taylor instability (RTI) with continuous magnetic field and density profiles are investigated analytically. The transition layers of magnetic field and density with two different typical profiles are studied and the analytic expressions of the linear growth rate of the RTI are obtained. It is found that the magnetic field effects strongly reduce the linear growth rate of the RTI, especially when the perturbation wavelength is short. The linear growth rate of the RTI increases with the thickness of the magnetic field transition layer, especially for the case of small thickness of the magnetic field transition layer. When the magnetic field transition layer width is long enough, the linear growth rate of the RTI can be saturated. Thus when one increases the width of the magnetic field transition layer, the linear growth rate of the RTI increases only in a certain range, which depends on the magnetic field strength. The numerical results are compared with the analytic linear growth rates and they agree well with each other. [ABSTRACT FROM AUTHOR]