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.

Rayleigh–Taylor instability occurs when a heavier fluid overlies a lighter fluid, and the two seek to exchange positions under the effect of gravity. We present a linearized theory for arbitrary three-dimensional (3D) initial disturbances that grow in time, and calculate the evolution of the interface for early times. A new spectral method is introduced for the fully 3D nonlinear problem in a Boussinesq fluid, where the interface between the light and heavy fluids is approximated with a smooth but rapid density change in the fluid. The results of large-scale numerical calculation are presented in fully 3D geometry, and compared and contrasted with the early-time linearized theory.

A fundamental problem for the realization of laser fusion through the implosion of a spherical target is Kidder's E−1/6 law, where E is the energy needed for ignition, proportional to the 6th power of the ratio R/R0, where R0 and R are the initial and final implosion radii, respectively. This law implies that the ignition energy is very sensitive to the ratio R0/R, or vice versa, the ratio R0/R is very insensitive to the energy input, with R0/R limited by the Rayleigh–Taylor instability. According to still classified data of the Centurion–Halite experiment at the Nevada Test Site, ignition would require an energy of ${\rm E}\simeq 50\,{\rm MJ}$, 25 times larger than the 2 MJ laser at the National Ignition Facility (NIF) reported in the New York Times. This means that even a tenfold increase from 2 to 20 MJ would only decrease the R/R0 ratio by an insignificant factor of 10−1/6 ≃ 0.7. To overcome this problem, it is proposed that the spherical target is replaced with a hollowed-out, rapidly rotating, cm-size ferromagnetic target, accelerated by a rotating traveling magnetic wave to a rotational velocity of ~1 km/s, at the limit of its tensile strength. In a rotating reference system, the general theory of relativity predicts the occurrence of negative gravitational field masses in the center of rotation, with their source located in the Coriolis force field. The density of this negative gravitational field mass can be larger than the magnitude of the positive mass density of a neutron star. The repulsive gravitational force causes the centrifugal force. For a magnetized plasma placed in the rapidly spinning, hollowed-out target chamber, this repulsive force can be balanced by the magnetic force generated by thermomagnetic currents of the Nernst effect. Such a configuration does not suffer from the Rayleigh–Taylor instability, but becomes a small magnetohydrodynamic generator, amplifying the magnetic field to values about equal to those of the Nernst effect, axially confining the plasma. By placing the spinning target in the center of a lithium vortex, the fusion neutrons absorbed in the vortex can breed tritium, and at the same time remove heat from the target chamber to sustain the Nernst effect. A hot spot is thereby produced in the target chamber, which launches a thermonuclear burn wave into a cylindrical deuterium–tritium configuration. With the stability of a rapidly rotating target greatly increased, and the range of 10 MeV electrons in the wall of the cm-size ferromagnetic target, an intense 10 MeV relativistic electron beam drawn from a 10 MJ Marx generator should be sufficient to implode the target for thermonuclear ignition.

The paper presents a review of dynamic stabilization mechanisms for plasma instabilities. One of the dynamic stabilization mechanisms for plasma instability was proposed in the paper [Kawata, Phys. Plasmas 19, 024503 (2012)], based on a perturbation phase control. In general, instabilities emerge from the perturbations. Normally the perturbation phase is unknown, and so the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superimposition of perturbations imposed actively. Based on this mechanism we present the application results of the dynamic stabilization mechanism to the Rayleigh–Taylor instability (RTI) and to the filamentation instability as typical examples in this paper. On the other hand, in the paper [Boris, Comments Plasma Phys. Control. Fusion 3, 1 (1977)] another mechanism was proposed to stabilize RTI, and was realized by the pulse train or the laser intensity modulation in laser inertial fusion [Betti et al., Phys. Rev. Lett. 71, 3131 (1993)]. In this latter mechanism, an oscillating strong force is applied to modify the basic equation, and consequently the new stabilization window is created. Originally the latter was proposed by Kapitza. We review the two stabilization mechanisms, and present the application results of the former dynamic stabilization mechanism.

A novel way for igniting small thermonuclear assemblies by inertial confinement is proposed, by replacing the positive mass of an imploding dense star with the negative mass in the reference frame of a rapidly rotating thermonuclear target. According to Einstein's general theory of relativity, this negative mass can be orders of magnitude larger than the positive mass density of a neutron star. This novel concept also replaces the Plutonium 239 “spark plugs” of large thermonuclear devices with a shell of natural uranium surrounding a target composed of DT or Li6D.

Unlike the ignition by a laser – or particle beam – induced spherical implosion, this configuration, similar to that of an imploding star is not only Rayleigh–Taylor stable, but it can be realized with intense relativistic electron or ion beams, with an energy of about 100 MJ, having a short range in the dense high Z natural uranium shell.

Dynamics and organization of laser-generated three-dimensional (3D) Richtmyer–Meshkov (RMI) and Rayleigh–Taylor instabilities (RMI and RTI) on metal target in the semiconfined configuration are different in the central region (CR) (Lugomer, 2016), near central region (NCR) (Lugomer, 2017) and the near periphery region (NPR) of the Gaussian-like spot. The RMI/RTI in the NPR evolve from the shock and series of reshocks associated with lateral expansion and increase of the vapor density, decrease of the Atwood number and momentum transfer. Scanning electron micrographs show irregular (chaotic) web of the base-plane walls, and mushroom spikes on its nodal points with disturbed two-dimensional (2D) lattice organization. Lattice disturbance is caused by the incoherent wavy motion of background fluid due to fast reshocks, which after series of reflections change their strength and direction. Reconstruction of the disturbed lattice reveals rectangular lattice of mushroom spikes with p2mm symmetry. The splitting (bifurcation) of mushroom diameter distribution on the large and small mushroom spikes increases with radial distance from the center of Gaussian-like spot. Dynamics of their evolution is represented by the orbits or stable periods in 2D phase space. The constant mushroom diameter – stable circulation or the stable periodic orbits – are the limit cycles between the unstable spiral orbits. Those with increasing periods represent supercritical Hopf bifurcation, while those leading to decrease and disappearance represent subcritical Hopf bifurcation. The empirical models of RMI, although predict dependence of the growth rate on radial distance (distance the reshocks travel to reach the interface), show many limitations. More appropriate interpretation of the simultaneous growth and lattice organization of small and large spikes give the fundamental model based on the interference of the perturbation modes depending on their amplitude, relative phase, and the symmetry. The late-time instability in the base-plane evolves into line solitons, vortex filaments and wave–vortex structures with chaotic rather than stochastic features.

Laser-induced three-dimensional (3D) Richtmyer–Meshkov and Rayleigh–Taylor instabilities (RMI and RTI) on metal target in the semi-confined configuration (SCC) show the new paradigm of wave-vortex mixing. The SCC enables extended lifetime of a hot vapor/plasma plume above the target surface and the formation of fast multiple reshocks. This causes – in the central region (CR) of Gaussian-like spot – the evolution of RMI with the spike breakup (Lugomer, 2016b), while in the near CR causes the RMI followed by the RTI. The density interface is transformed into the large-scale broken irregular, quasi-periodic web, which comprises the RTI mushroom-shape spikes and the coherent wave-vortex structures such as the line solitons and vortex filaments. The intensity and direction of reshocks change (due to irregularity of the interface) and cause the formation of domains with the weak and the strong reshocks effects. The weak reshocks affect mushroom-shape spikes only slightly, while the strong ones cause their deformation and symmetry break, bubble collapse, and separation of the horizontal flow into vortex ribbons. Interaction of ribbons with spikes and bubbles causes the ribbon pinning, looping, winding, and formation of knotted and tangled structures. The line solitons, vortex filaments, and ribbons tend to organize into complex large-scale structures with the low wave-vortex turbulent mixing. They represent the new paradigm of 3D RMI and RTI in which the transition to the small-scale turbulent mixing does not appear.

In this paper, the robustness of the dynamic instability mitigation mechanism is first examined, and then the instability mitigation phenomenon is demonstrated in a deuterium–tritium (DT) fuel target implosion by wobbling heavy-ion beams (HIBs). The results presented here show that the mechanism of the dynamic instability mitigation is rather robust against changes in the phase, the amplitude and the wavelength of the wobbling perturbation applied. In general instability would emerge from the perturbation of the physical quantity. Normally the perturbation phase is unknown, so that the instability growth rate is discussed. However, if the perturbation phase is known, the instability growth can be controlled by a superposition of perturbations imposed actively: if the perturbation is induced by, for example, a driving beam axis oscillation or wobbling, the perturbation phase could be controlled and the instability growth is mitigated by the superposition of the growing perturbations. In this paper, we realize the superposition of the perturbation by the wobbling HIBs’ illumination onto a DT fuel target in heavy-ion inertial fusion (HIF). Our numerical fluid implosion simulations present that the implosion non-uniformity is mitigated successfully by the wobbling HIBs illumination in HIF.

In this experimental study, the ablative Richtmyer–Meshkov (RM) and the Rayleigh–Taylor (RT) instabilities were generated by the laser pulse of Gaussian-like power profile. The initial multi-modal perturbation, the inhomogeneous momentum transfer and different Atwood numbers generate different shapes of spikes and bubbles in the central region (CR) and the near-central region (NCR) of the spot. A one-dimensional Gaussian-like power profile causes the formation of the wavy-like rows of aperiodic spikes. The periodic spike segments inside the rows appear due to locally coherent flow. In the NCR, the mushroom-shape spikes tend to the organization on the isotropic square and the anisotropic rhombic lattices. The increase of the lattice periods two, three, or four times indicates formation of superstructures. The growth of sharp asymmetric RM/RT spikes in the CR is fast, uncorrelated and linear, while the growth of the symmetric mushroom-shape ones in the NCR is slow, correlated, and nonlinear.

The effects of polymer additives on Rayleigh–Taylor (RT) instability of immiscible fluids is investigated using the Oldroyd-B viscoelastic model. Analytic results obtained exploiting the phase-field approach show that in polymer solution the growth rate of the instability speeds up with elasticity (but remains slower than in the pure solvent case). Numerical simulations of the viscoelastic binary fluid model confirm this picture.

We present a Rayleigh–Taylor mixing rate simulation with an acceleration rate falling within the range of experiments. The simulation uses front tracking to prevent interfacial mass diffusion. We present evidence to support the assertion that the lower acceleration rate found in untracked simulations is caused, at least to a large extent, by a reduced buoyancy force due to numerical interfacial mass diffusion. Quantitative evidence includes results from a time-dependent Atwood number analysis of the diffusive simulation, which yields a renormalized mixing rate coefficient for the diffusive simulation in agreement with experiment. We also present the study of Richtmyer–Meshkov mixing in cylindrical geometry using the front tracking method and compare it with the experimental results.

The three-dimensional (3D) turbulent mixing zone (TMZ) evolution under Rayleigh–Taylor and Richtmyer–Meshkov conditions was studied using two approaches. First, an extensive numerical study was made, investigating the growth of a random 3D perturbation in a wide range of density ratios. Following that, a new 3D statistical model was developed, similar to the previously developed two-dimensional (2D) statistical model, assuming binary interactions between bubbles that are growing at a 3D asymptotic velocity. Confirmation of the theoretical model was gained by detailed comparison of the bubble size distribution to the numerical simulations, enabled by a new analysis scheme that was applied to the 3D simulations. In addition, the results for the growth rate of the 3D bubble front obtained from the theoretical model show very good agreement with both the experimental and the 3D simulation results. A simple 3D drag–buoyancy model is also presented and compared with the results of the simulations and the experiments with good agreement. Its extension to the spike-front evolution, made by assuming the spikes' motion is governed by the single-mode evolution determined by the dominant bubbles, is in good agreement with the experiments and the 3D simulations. The good agreement between the 3D theoretical models, the 3D numerical simulations, and the experimental results, together with the clear differences between the 2D and the 3D results, suggest that the discrepancies between the experiments and the previously developed models are due to geometrical effects.

Acceleration-driven fluid mixing is studied here from a theoretical point of view. Considerable progress has been achieved in the understanding of mix. Theories of the authors are reviewed that allow prediction of the edge of the mixing zone, in agreement with experimental data. Theories that describe the distribution of masses within the mixing region are also reviewed. The theory we present describes a chunk mix regime, in which two phases are mixed at a chunk level, but for which there is no atomic mixing. Thus the two phases are segregated into disjoint regions of space.

We have performed simulations of the evolution of the turbulent Rayleigh–Taylor instability with an arbitrary Lagrange–Eulerian code. The problem specification was defined by Dimonte et al. (2003) for the “alpha group” code intercomparison project. Perfect γ = 5/3 gases of densities 1 and 3 g/cm3 are accelerated by constant gravity. The nominal problem uses a 2562 × 512 mesh with initial random multiwavelength interface perturbations. We have also run three-dimensional problems with smaller meshes and two-dimensional (2D) problems of several mesh sizes. Under-resolution lowered linear growth rates of the seed modes to 5-60% of the analytic values, depending on wavelength and orientation to the mesh. However, the mix extent in the 2D simulations changed little with grid refinement. Simulations without interface reconstruction gave penetration only slightly reduced from the case with interface reconstruction. Energy dissipation differs little between the two cases. The slope of the penetration distance versus time squared, corresponding to the α parameter in h = αAgt2, decreases with increasing time in these simulations. The slope, α, is consistent with the linear electric motor data of Dimonte and Schneider (2000), but the growth is delayed in time.

This article investigates the molecular mixing caused by Rayleigh–Taylor (RT) instability of a gravitationally unstable density interface tilted at a small angle to the horizontal. The mixing is measured by the increase in background potential energy, and the mixing efficiency, or fraction of energy irreversibly lost to fluid motion doing work against gravity, is calculated. Laboratory experiments are carried out using saline and fresh water, and modeled with compressible numerical simulations, with a suitable choice of parameters and initial conditions. The experiments show that the high cumulative efficiency of mixing in RT instability at a horizontal interface is only slightly reduced by an interface tilt of up to 10°, despite the strong overturning that occurs. Instantaneous mixing efficiencies as high as 0.5–0.6 are measured, when RT instability is active, with lower values of about 0.35 during the subsequent overturning. The numerical simulations capture the most unstable scales and the overturning motion well, but generate more mixing than the experiments, with the instantaneous mixing efficiency remaining at 0.5 for most of the run. The difference may be due to restratification at small scales in the high Prandtl number experiments.

The Rayleigh–Taylor instability (RTI) of a laser-accelerated ablative surface of a thin plasma layer in an inertial fusion energy (IFE) target with incompressible electrically conducting plasma in the presence of a transverse magnetic field is investigated using linear stability analysis. A simple theory based on Stokes-lubrication approximation is proposed. It is shown that the effect of a transverse magnetic field is to reduce the growth rate of RTI considerably over the value it would have in the absence of a magnetic field. This is useful in the extraction of IFE efficiently.

Modeling plus simulations using the one-dimensional Lagrangian radiation-hydrodynamics code HYADES are compared with data from classical and ablative Rayleigh–Taylor experiments conducted on the Nova laser. Comparisons between the experiments and modeling for both the gross hydrodynamic motion and the perturbation evolution are made and show good agreement. A third order perturbation analysis is applied to demonstrate the onset of nonlinearity. A simple, physically intuitive saturation model is used to describe the growth further into the nonlinear regime. Finally, we present the first comparison of the Betti ablation front theory with indirect-drive RT data and obtain good agreement.