Ablative Rayleigh-Taylor Instability Research Articles

Dynamic stabilization of ablative Rayleigh-Taylor instability in the presence of a temporally modulated laser pulse.

This paper presents a numeric study of the dynamic stabilization of the ablative Rayleigh-Taylor instability (ARTI) in the presence of a temporally modulated laser pulse. The results show that the specially modulated laser produces a dynamically stabilized configuration near the ablation front. The physical features of the relevant laser-driven parameters in the unperturbed ablative flows have been analyzed to reveal the inherent stability mechanism underlying the dynamically stabilized configuration. A single-mode ARTI for the modulated laser pulse is first compared with that of the unmodulated laser pulse. The results show that the modulated laser stabilizes the surface perturbations and reduces the linear growth rate and enhancement of the cutoff wavelength. For multimode perturbations, the dynamic stabilization effect of the modulated laser pulse contributes to suppress the small-scale structure and reduce the width of the mixing layer. Moreover, the results show that the stabilization effect of the modulated laser pulse decreases as the maximum wavelength increases.

Effect of hot-electron preheating on the multimode bubble-front growth of the ablative Rayleigh–Taylor instability

Hot electrons (HEs) generated via parametric instabilities at high laser intensities are a critical concern of laser-driven inertial confinement fusion (ICF), which can significantly impact the ICF performance by preheating the target. In this paper, the effects of HE preheating with moderate HE energy on the evolution of two-dimensional multimode ablative Rayleigh–Taylor instability (ARTI) up to the self-similar growth stage are studied through numerical simulations with a multigroup diffusion model. It is found that HE preheating stabilizes the linear growth of multimode ARTI and delays the onset of the self-similar growth regime. This time delay is more significant for the short-wavelength mode ARTI and higher energy HE cases. It is also shown that the variation of self-similar growth coefficients under HE preheating is not very significant. The delay to the onset of the nonlinear stage of multimode ARTI by HE preheating with moderate energy may be beneficial to ICF implosions.

The importance of Righi–Leduc heat flux to the ablative Rayleigh–Taylor instability during a laser irradiating targets

Abstract The Righi–Leduc heat flux generated by the self-generated magnetic field in the ablative Rayleigh–Taylor instability driven by a laser irradiating thin targets is studied through two-dimensional extended-magnetohydrodynamic simulations. The perturbation structure gets into a low magnetization state though the peak strength of the self-generated magnetic field could reach hundreds of teslas. The Righi–Leduc effect plays an essential impact both in the linear and nonlinear stages, and it deflects the total heat flux towards the spike base. Compared to the case without the self-generated magnetic field included, less heat flux is concentrated at the spike tip, finally mitigating the ablative stabilization and leading to an increase in the velocity of the spike tip. It is shown that the linear growth rate is increased by about 10% and the amplitude during the nonlinear stage is increased by even more than 10% due to the feedback of the magnetic field, respectively. Our results reveal the importance of Righi–Leduc heat flux to the growth of the instability and promote deep understanding of the instability evolution together with the self-generated magnetic field, especially during the acceleration stage in inertial confinement fusion.

Growth of ablative Rayleigh-Taylor instability induced by time-varying heat-flux perturbation

The evolution of ablative Rayleigh–Taylor instability (ARTI) induced by single-mode stationary and time-varying perturbations in heat flux is studied numerically in two dimensions. Compared with the stationary case, time-varying heat-flux perturbation mitigates ARTI growth because of the enhanced thermal smoothing induced by the wave-like traveling heat flux. A resonance is found to form when the phase velocity of the heat-flux perturbation matches the average sound speed in the ablation region. In the resonant regime, the coherent density and temperature fluctuations enhance the electron thermal conduction in the ablation region and lead to larger ablation pressure and effective acceleration, which consequently yield higher linear growth rate and saturated bubble velocity. The enhanced effective acceleration offers increased implosion velocity but can also compromise the integrity of inertial confinement fusion shells by causing faster ARTI growth.

Effects of ablation velocity on ablative Rayleigh–Taylor instability

The influence of the ablation velocity Va on the evolution of single-mode ablative Rayleigh–Taylor instability from the linear to the deeply nonlinear phases is investigated via two-dimensional numerical simulations. Linear growth rates from simulations agree well with the asymptotic theory except for larger discrepancies in the intermediate Froude number regime. The weakly nonlinear growth behavior of the bubble amplitude is found dependent on a critical perturbation wavenumber in a broad Froude number regime. For a linearly stable mode, its nonlinear excitation threshold is higher for larger Va and thus harder to be exceeded. For short-wavelength modes taking significant ablation effects, the bubble penetration velocity is found to reaccelerate after the first saturation and eventually saturate at a larger value with larger Va, due to stronger vortex-acceleration effects and more significant increase in g.

Effect of initial phase on the ablative Rayleigh–Taylor instability

The effect of initial perturbation phase on the ablative Rayleigh–Taylor instability is investigated by numerical simulations. We aim at the growth of harmonic amplitudes and the formation of spikes and bubbles in single- and two-mode coupling cases, respectively. In the two-mode coupling case, two kinds of simulations are performed: two modes with relatively small linear growth rate difference and two modes with relatively large linear growth rate difference. The initial relative phase between the original two modes has a significant effect on the growth of harmonic amplitudes, and in different initial relative phases, the structures of spikes and bubbles begin to show great differences in the nonlinear stage. Fortunately, the harmonic amplitudes are weakened at a specific initial relative phase. This has a certain enlightening significance for the stabilization of ablative Rayleigh–Taylor instability.

Effect of compressibility on ablative Rayleigh–Taylor instability

Effect of compressibility on ablative Rayleigh–Taylor instability

Effect of long-wavelength perturbations in nonlinear evolution of the ablative Rayleigh–Taylor mixing

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.

Ablative Rayleigh–Taylor instability driven by time-varying acceleration

Ablative Rayleigh–Taylor instability driven by time-varying acceleration

Numerical study of the high-intensity heat conduction effect on turbulence induced by the ablative Rayleigh–Taylor instability

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 t2 dependence by the late stage of simulations, while heat conduction suppresses the coefficient of spike αs and slightly enhances that of the bubble αb. 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.

Coupled model analysis of the ablative Rayleigh–Taylor instability

The weakly nonlinear stage of the ablative Rayleigh–Taylor instability (ARTI) is investigated by expanded hydrodynamic equations in which the third-order corrections of the two-mode perturbations are considered. In the present coupling model, two linear perturbations are simultaneously added near the ablation front at the initial moment, and we have derived the first three coupling harmonics. Furthermore, the coupling model analysis is studied via direct numerical simulation as well. When the original two fundamental modes are always dominant over other modes, the time evolution of the density amplitudes for these modes agrees well with the results of direct numerical simulation. It is found that the harmonics are stabilized by the mode coupling effects, and the long wavelength mode of the fundamental modes tends to dominate the growth of the ARTI. Two-mode coupling is one of the restriction factors for the realization of controlled inertial confinement fusion. Therefore, the coupling harmonics excited by two-mode perturbations have good application potential and are worth further study.

Role of hot electrons in mitigating ablative Rayleigh–Taylor instability

In laser-driven inertial confinement fusion (ICF) specifically with high laser intensities, energetic (hot) electrons (HEs) can be generated via laser-plasma instabilities. HEs can significantly impact the target performance by modifying the implosion hydrodynamics. In this paper, the effects of moderate-energy (about 20 to 40 keV) HEs on the evolution of two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) are studied through numerical simulations with a multigroup diffusion model in which the HE population is treated as a high-energy group launched from the boundary. With HEs present, it is found that ARTI linear growth rates are reduced even though the acceleration of the implosion shell is enhanced by HEs. The reduction in the linear growth rate is owing to the increase in the ablation velocity and the density scale length, and this stabilization effect is greater in the shorter-wavelength modes and/or higher-energy HE cases. The ARTI linear growth does not get mitigated monotonically as the HE number density increases for a given fixed HE kinetic energy. The HE number density minimizing the ARTI growth rate is found, likely due to the competition of the stabilizing and destabilizing hydrodynamic-parameter variations caused by HEs.

Self-similar bubble-front evolutions of ablative Rayleigh–Taylor instability seeded by localized perturbations

Two-dimensional numerical simulations are carried out to investigate the nonlinear bubble growth of ablative Rayleigh–Taylor instability (ARTI) seeded by localized perturbations (LPs), where the LPs are described by a Gaussian mode. It is found that the nonlinear bubble-front penetration of LP-seeded ARTI follows the self-similar scaling law αbAT∫gdt2, different from the classical case, where the self-similar behavior is not observed. It is also found that the quadratic growth coefficient αb in the LP-seeded ARTI mainly depends on the initial perturbation amplitude and initial perturbation width. When the perturbation amplitude is small, αb has a value of ∼0.03, which is not sensitive to the perturbation width. As the perturbation amplitude increases, the value of αb increases, and the phenomenon is more significant when the perturbation width is narrower. It is shown that the increase in αb is due to the spike-induced upward jet and the ablation-generated vorticity inside the bubble.

Nonlinear ablative Rayleigh-Taylor instability: Increased growth due to self-generated magnetic fields.

The growth rate of the nonlinear ablative Rayleigh-Taylor (RT) instability is enhanced by magnetic fields self-generated by the Biermann battery mechanism; a scaling for this effect with perturbation height and wavelength is proposed and validated with extended-magnetohydrodynamic simulations. The magnetic flux generation rate around a single RT spike is found to scale with the spike height. The Hall parameter, which quantifies electron magnetization, is found to be strongly enhanced for short-wavelength spikes due to Nernst compression of the magnetic field at the spike tip. The impact of the magnetic field on spike growth is through both the suppressed thermal conduction into the unstable spike and the Righi-Leduc heat flow deflecting heat from the spike tip to the base. Righi-Leduc is found to be the dominant effect for small Hall parameters, while suppressed thermal conduction dominates for large Hall parameters. These results demonstrate the importance of considering magnetic fields in all perturbed inertial confinement fusion hot spots.

Effect of ablation on the nonlinear spike growth for the single-mode ablative Rayleigh–Taylor instability

The effect of ablation on the nonlinear spike growth of single-mode ablative Rayleigh–Taylor instability (RTI) is studied by two-dimensional numerical simulations. It is shown that the ablation can reduce the quasi-constant velocity and significantly suppress the reacceleration of the spike in the nonlinear phase. It is also shown that the spike growth can affect the ablation-generated vorticity inside the bubble, which further affects the nonlinear bubble acceleration. The vorticity evolution is found to be correlated with the mixing width (i.e., the sum of the bubble and spike growths) for a given wave number and ablation velocity. By considering the effects of mass ablation and vorticity, an analytical model for the nonlinear bubble and spike growth of single-mode ablative RTI is developed in this study. It is found that the nonlinear growth of the mixing width, induced by the single mode, is dominated by the bubble growth for small-scale ablative RTI, whereas it is dominated by the spike growth for classical RTI.

Shock-Augmented Ignition Approach to Laser Inertial Fusion

Shock ignition enables high gain at low implosion velocity, reducing ablative Rayleigh-Taylor instability growth, which can degrade conventional direct drive. With this method, driving a strong shock requires high laser power and intensity, resulting in inefficiencies in the drive and the generation of hot electrons that can preheat the fuel. A new "shock-augmented ignition" pulse shape is described that, by preconditioning the ablation plasma before launching a strong shock, enables the shock ignition of thermonuclear fuel, but importantly, with substantially reduced laser power and intensity requirements. The reduced intensity requirement with respect to shock ignition limits laser-plasma instabilities, such as stimulated Raman and Brillouin scatter, reducing the risk of hot-electron preheat and restoring the laser coupling advantages of conventional direct drive. Simulations indicate that, due to the reduced power requirements, high gain (∼100) ignition of large-scale direct drive implosions (outer radius ∼1750 μm, deuterium-tritium ice thickness ∼165 μm) may be possible within the power and energy limits of existing facilities such as the National Ignition Facility. Moreover, this concept extends to indirect drive implosions, which exhibit substantial yield increases at reduced implosion velocity. Shock-augmented ignition expands the viable design space of laser inertial fusion.

Mitigation of the ablative Rayleigh–Taylor instability by nonlocal electron heat transport

The effects of electron nonlocal heat transport (NLHT) on the two-dimensional single-mode ablative Rayleigh–Taylor instability (ARTI) up to the highly nonlinear phase are reported for the first time through numerical simulations with a multigroup diffusion model. It is found that as well as its role in the linear stabilization of ARTI growth, NLHT can also mitigate ARTI bubble nonlinear growth after the first saturation to the classical terminal velocity, compared with what is predicted by the local Spitzer–Härm model. The key factor affecting the reduction in the linear growth rate is the enhancement of the ablation velocity Va by preheating. It is found that NLHT mitigates nonlinear bubble growth through a mechanism involving reduction of vorticity generation. NLHT enhances ablation near the spike tip and slows down the spike, leading to weaker vortex generation as the pump of bubble reacceleration in the nonlinear stage. NLHT more effectively reduces the nonlinear growth of shorter-wavelength ARTI modes seeded by the laser imprinting phase in direct-drive laser fusion.

Thin-shell effects on nonlinear bubble evolution in the ablative Rayleigh–Taylor instability

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.

Self-generated magnetic field in ablative Rayleigh–Taylor instability

Self-generated magnetic fields in single-mode ablative Rayleigh–Taylor instability (ARTI) relevant to the acceleration phase of inertial confinement fusion (ICF) implosions are studied via two dimensional simulations. In ARTI, ∼100 T magnetic fields can be generated via the Biermann battery source without considering the Nernst effect. The Nernst effect significantly compresses the magnetic field against the electron temperature gradient and amplifies the peak value by more than three times. A scaling law for the magnetic flux is obtained, and it well predicts the evolution of the magnetic field from linear to deeply nonlinear phases of ARTI. The self-generated magnetic field reduces the ablation near the spike and reduces the width of bubbles by magnetizing the electron heat flows, which results in higher magnitude vorticity inside the bubble and enhances the nonlinear ARTI bubble penetration velocity for short-wavelength modes. The bubble velocity boosting due to self-generated magnetic field indicates the larger impact of the short-wavelength ARTI modes on ICF implosion performance than previously expected.

Diffuse interface relaxation model for two-phase compressible flows with diffusion processes

The paper addresses a two-temperature model for simulating compressible two-phase flow taking into account diffusion processes related to the heat conduction and viscosity of the phases. This model is reduced from the two-phase Baer-Nunziato model in the limit of complete velocity relaxation and consists of the phase mass and energy balance equations, the mixture momentum equation, and a transport equation for the volume fraction. Terms describing effects of mechanical relaxation, temperature relaxation, and thermal conduction on volume fraction evolution are derived and demonstrated to be significant for heat conduction problems. The thermal conduction leads to instantaneous thermal relaxation so that the temperature equilibrium is always maintained in the interface region with meeting the entropy relations. A numerical method is developed to solve the model governing equations that ensures the pressure-velocity-temperature (PVT) equilibrium condition in its high-order extension. We solve the hyperbolic part of the governing equations with the Godunov method with the HLLC approximate Riemann solver. The non-linear parabolic part is solved with an efficient Chebyshev explicit iterative method without dealing with large sparse matrices. To verify the model and numerical methods proposed, we demonstrate numerical results of several numerical tests such as the multiphase shock tube problem, the multiphase impact problem, and the planar ablative Rayleigh–Taylor instability problem.