Ablative Richtmyer-Meshkov Instability Research Articles

Early-Time Harmonic Generation from a Single-Mode Perturbation Driven by X-Ray Ablation.

X-ray ablation dynamics of the planar foil with preimposed sinusoidal ripples is investigated at the SG 100kJ Laser Facility. A significant fraction of the second harmonics is observed and identified at the beginning of the ablative drive when the amplitude of the perturbation is within the linear regime. With radiation-hydrodynamic simulations and a developed simple model, we can reveal that such a novel phenomenon is due to the fact that a sustained deformation of the ablation front is initiated since the ablation pressure is directed to the normal direction of the perturbation surface. We find that this deformation dominates the early-time perturbation evolution and results in a specific stage in addition to the traditional ablative Richtmyer-Meshkov instability phase. Our results can be applicable to various regions such as implosions in inertial confinement fusion and the dynamics of molecular clouds in astrophysics.

Successive Picket Drive for Mitigating the Ablative Richtmyer–Meshkov Instability**Supported by the National Natural Science Foundation of China under Grant Nos 11675026, 11875091 and 11575034.

The ablative Richtmyer–Meshkov instability (ARMI) is crucial to the successful ignition implosion of the inertial confinement fusion (ICF) because of its action as the seed of the Rayleigh–Taylor instability. In usual ICF implosions, the first shock driven by various foots of the pulses plays a central role in the ARMI growth. We propose a new scheme for refraining from ARMI with a pulse of successive pickets. With the successive-picket pulse design, a rippled capsule surface is compressed by three successive shocks with sequentially strengthening intensities and ablated stabilization, and the ablative Richtmyer–Meshkov growth is mitigated quite effectively. Our numerical simulations and theoretical analyses identify the validity of this scheme.

Stabilization of thin-shell implosions using a high-foot adiabat-shaped drive at the National Ignition Facility

The thin-shell adiabat-shaped implosions proposed in this paper are designed to combine the ablation front stability benefits of the High Foot (HF) pulses with the demonstrated high fuel compressibility of the low foot implosions to reach the alpha-heating regime. This is accomplished by both lowering the drive between the first and second shocks and tailoring the rise-to-peak drive. Two-dimensional radiation hydrodynamics simulations show that while weakening the growth of low-mode number perturbations at the ablation front, this approach also introduces negative lobes to the growth factor spectrum at high mode numbers. A very-high foot picketless drive, characterized by an intermediate fuel adiabat level, is proposed to suppress negative perturbation growth. Moreover, the picketless feature of this design and the shorter duration of the through reduce the hohlraum wall motion allowing us to keep the capsule implosion symmetry under control. Introducing an accurately tuned dopant fraction in the outer ablator suggests that the stabilization of the ablation front may be even further improved. This study has shown that the smaller oscillation amplitude and the frequency of ablative Richtmyer-Meshkov instability reduce the initial perturbation seed at the beginning of the acceleration phase. The combination of a thin-shell design and a very high-foot picketless radiation drive has enlightened the calculated benefits of this intermediate fuel adiabat design: high implosion performance, more predictive low-mode implosion symmetry, and a similar stability at the ablation front than that of HF designs.

Measurement of ablative Richtmyer-Meshkov evolution from laser imprint

Experiments were performed to investigate the ablative Richtmyer-Meshkov (RM) instability in plastic (CH2) foils. The two-dimensional (2-D) perturbations were created by laser imprinting using a special phase plate with a 2-D single mode, ∼70 μm wavelength sinusoidal intensity pattern on the plastic foil. The growth of imprinted perturbations was measured by face-on, X-ray radiography using Sm and Ta backlighters in 30-μm and 50-μm thick plastic foils, respectively. After the initial imprinting phase, the 2-D perturbations grew due to ablative RM instability before the onset of foil acceleration when they were further amplified by Rayleigh-Taylor instability. Experimental results agree reasonably well with 2-D hydrodynamic simulations and analytic models showing that the modulation growth in areal density is due to ablative RM instability.

Effect of bromine-dopant on radiation-driven Rayleigh–Taylor instability in plastic foil

Effects of bromine (Br) dopant on the growth of radiation-driven ablative Rayleigh–Taylor instability (RTI) in plastic foils are studied by radiation hydrodynamics simulations and theoretical analysis. It is found that the Br-dopant in plastic foil reduces the seed of ablative RTI. The main reasons of the reduction are attributed to the smaller oscillation amplitude of ablative Richtmyer–Meshkov instability (RMI) induced by the smaller post-shock sound speed, and the smaller oscillation frequency of ablative RMI induced by the smaller ablation velocity and blow-off plasma velocity. The Br-dopant also decreases the linear growth rate of ablative RTI due to the smaller acceleration. Treating the perturbation growth as a function of foil’s displacement, the perturbation growth would increase in Br-doped foil at the phase of ablative RTI, which is attributed to the decrease of the ablation velocity and the density gradient scale length. The results are helpful for further understanding the influence of high-Z dopant on the radiation-driven ablative RTI.

Effect of high-Z dopant on the laser-driven ablative Richtmyer–Meshkov instability

AbstractThe effects of high-Z dopant on the laser-driven ablative Richtmyer–Meshkov instability (RMI) are investigated by theoretical analysis and radiation hydrodynamics simulations. It is found that the oscillation amplitude of ablative RMI depends on the ablation velocity, the blow-off plasma velocity and the post-shock sound speed. Owing to enhancing the radiation at the plasma corona and increasing the radiation temperature at the ablation front, the high-Z dopant in plastic target can significantly increase the ablation velocity and the blow-off plasma velocity, leading to an increase in oscillation frequency and a reduction in oscillation amplitude of the ablative RMI. The high-Z dopant in plastic target is beneficial to reduce the seed of ablative Rayleigh–Taylor instability. These results are helpful for the design of direct drive inertial confinement fusion capsules.

Strength and Viscosity Effects on Perturbed Shock Front Stability in Metals

Computational modeling and experimental measurements on metal samples subject to a laser-driven, ablative Richtmyer-Meshkov instability showed differences between viscosity and strength effects. In particular, numerical and analytical solutions, coupled with measurements of fed-through perturbations, generated by perturbed shock fronts onto initially flat surfaces, show promise as a validation method for models of deviatoric response in the postshocked material. Analysis shows that measurements of shock perturbation amplitudes at low sample thickness-to-wavelength ratios are not enough to differentiate between strength and viscosity effects, but that surface displacement data of the fed-through perturbations appears to resolve the ambiguity. Additionally, analytical and numerical results show shock front perturbation evolution dependence on initial perturbation amplitude and wavelength is significantly different in viscous and materials with strength, suggesting simple experimental geometry changes should provide data supporting one model or the other.

Stabilization of high-compression, indirect-drive inertial confinement fusion implosions using a 4-shock adiabat-shaped drive

Hydrodynamic instabilities and poor fuel compression are major factors for capsule performance degradation in ignition experiments on the National Ignition Facility. Using a recently developed laser drive profile with a decaying first shock to tune the ablative Richtmyer-Meshkov (ARM) instability and subsequent in-flight Rayleigh-Taylor growth, we have demonstrated reduced growth compared to the standard ignition pulse whilst maintaining conditions for a low fuel adiabat needed for increased compression. Using in-flight x-ray radiography of pre-machined modulations, the first growth measurements using this new ARM-tuned drive have demonstrated instability growth reduction of ∼4× compared to the original design at a convergence ratio of ∼2. Corresponding simulations give a fuel adiabat of ∼1.6, similar to the original goal and consistent with ignition requirements.

Numerical study of the ablative Richtmyer–Meshkov instability of laser-irradiated deuterium and deuterium-tritium targets

The Richtmyer–Meshkov instability (RMI) at the ablation front of laser-irradiated planar targets is investigated by two-dimensional numerical hydrodynamics simulations. The linear evolution of perturbations seeded either by surface roughness or target inhomogeneity is studied for perturbation wavelengths in the range 10≤λ≤400 μm and laser intensity 4×1012≤I≤4×1014 W/cm2 (with laser wavelength λlaser=0.35 μm). Thin and thick cryogenic deuterium or deuterium-tritium (DT) planar targets are considered. For targets irradiated at constant intensity, it is found that perturbations with wavelength below a given threshold perform damped oscillations, while perturbations above such a threshold are unstable and oscillate with growing amplitude. This is qualitatively in agreement with theoretical predictions by Goncharov et al. [Phys. Plasmas 13, 012702 (2006)], according to which ablation related processes stabilize perturbations with kDc⪢1, where Dc is the distance between the ablation front and critical density for laser propagation. For kDc<1 a weakly growing Landau–Darrieus instability (LDI) is instead excited. The stability threshold increases substantially with laser intensity, given the dependence of Dc on laser intensity I (roughly Dc∝I, according to the present simulations). Direct-drive laser fusion targets are irradiated by time-shaped pulses, with a low intensity initial foot. In this case, perturbations with wavelengths below some threshold (about 10 μm, for typical ignition-class all-DT targets) are damped after an initial growth. In a thin target, initial perturbations, either damped or amplified by RMI and LDI, seed the subsequent Rayleigh–Taylor instability. Finally, it is shown that RMI growth of fusion targets can be reduced by using laser pulses including an initial adiabat-shaping picket (originally proposed to reduce the growth of Rayleigh–Taylor instability).

Richtmyer–Meshkov instability: theory of linear and nonlinear evolution

A theoretical framework to study linear and nonlinear Richtmyer-Meshkov instability (RMI) is presented. This instability typically develops when an incident shock crosses a corrugated material interface separating two fluids with different thermodynamic properties. Because the contact surface is rippled, the transmitted and reflected wavefronts are also corrugated, and some circulation is generated at the material boundary. The velocity circulation is progressively modified by the sound wave field radiated by the wavefronts, and ripple growth at the contact surface reaches a constant asymptotic normal velocity when the shocks/rarefactions are distant enough. The instability growth is driven by two effects: an initial deposition of velocity circulation at the material interface by the corrugated shock fronts and its subsequent variation in time due to the sonic field of pressure perturbations radiated by the deformed shocks. First, an exact analytical model to determine the asymptotic linear growth rate is presented and its dependence on the governing parameters is briefly discussed. Instabilities referred to as RM-like, driven by localized non-uniform vorticity, also exist; they are either initially deposited or supplied by external sources. Ablative RMI and its stabilization mechanisms are discussed as an example. When the ripple amplitude increases and becomes comparable to the perturbation wavelength, the instability enters the nonlinear phase and the perturbation velocity starts to decrease. An analytical model to describe this second stage of instability evolution is presented within the limit of incompressible and irrotational fluids, based on the dynamics of the contact surface circulation. RMI in solids and liquids is also presented via molecular dynamics simulations for planar and cylindrical geometries, where we show the generation of vorticity even in viscid materials.

Basic hydrodynamics of Richtmyer–Meshkov-type growth and oscillations in the inertial confinement fusion-relevant conditions

In inertial confinement fusion (ICF), the possibility of ignition or high energy gain is largely determined by our ability to control the Rayleigh-Taylor (RT) instability growth in the target. The exponentially amplified RT perturbation eigenmodes are formed from all sources of the target and radiation non-uniformity in a process called seeding. This process involves a variety of physical mechanisms that are somewhat similar to the classical Richtmyer-Meshkov (RM) instability (in particular, most of them are active in the absence of acceleration), but differ from it in many ways. In the last decade, radiographic diagnostic techniques have been developed that made direct observations of the RM-type effects in the ICF-relevant conditions possible. New experiments stimulated the advancement of the theory of the RM-type processes. The progress in the experimental and theoretical studies of such phenomena as ablative RM instability, re-shock of the RM-unstable interface, feedout and perturbation development associated with impulsive loading is reviewed.

Classical and ablative Richtmyer–Meshkov instability and other ICF-relevant plasma flows diagnosed with monochromatic x-ray imaging

In inertial confinement fusion (ICF) and high-energy density physics (HEDP), the most important manifestations of the hydrodynamic instabilities and other mixing processes involve lateral motion of the accelerated plasmas. In order to understand the experimental observations and to advance the numerical simulation codes to the point of predictive capability, it is critically important to accurately diagnose the motion of the dense plasma mass. The most advanced diagnostic technique recently developed for this purpose is the monochromatic x-ray imaging that combines large field of view with high contrast, high spatial resolution and large throughput, ensuring high temporal resolution at large magnification. Its application made it possible for the experimentalists to observe for the first time important hydrodynamic effects that trigger compressible turbulent mixing in laser targets, such as ablative Richtmyer–Meshkov (RM) instability, feedout, interaction of an RM-unstable interface with shock and rarefaction waves. It also helped to substantially improve the accuracy of diagnosing many other important plasma flows, ranging from laser-produced jets to electromagnetically driven wires in a Z-pinch, and to test various methods suggested for mitigation of the Rayleigh–Taylor instability. We will review the results obtained with the aid of this technique in ICF-HEDP studies at the Naval Research Laboratory and the prospects of its future applications.

Multimode evolution of the ablative Richtmyer-Meshkov and Landau-Darrieus instability in laser imprint of planar targets

A mode-coupling model is developed to treat the multimode evolution of the ablative Richtmyer-Meshkov (RM) and Landau-Darrieus (LD) instability in the laser imprint of planar targets. Using this mode coupling model, the multimode power spectrum of the RM and LD instability is computed. For the RM instability, mode-coupling effects lead to a broadening of the oscillatory minima found in linear RM theory. For the LD instability, mode-coupling effects generate an inverse power law spectrum.

Strong shock wave and areal mass oscillations associated with impulsive loading of planar laser targets

When a rippled surface of a planar target is irradiated with a short (subnanosecond) laser pulse, the shock wave launched into the target and the mass distribution of the shocked plasma will oscillate. These oscillations are found to be surprisingly strong compared, for example, to the case when the laser radiation is not turned off but rather keeps pushing the shock wave into the target. Being stronger than the areal mass oscillations due to ablative Richtmyer–Meshkov instability and feedout in planar targets, which have recently been observed at the Naval Research Laboratory (NRL) [Aglitskiy et al., Phys. Plasmas 9, 2264 (2002)], these oscillations should therefore be directly observable with the same diagnostic technique. Irradiation of a target with a short laser pulse represents a particular case of an impulsive loading, a fast release of finite energy in a thin layer near the surface of a target. Renewed interest to the impulsive loading in the area of direct-drive laser fusion is due to the recent proposals of using a short pulse prior to the drive pulse to make the target more resistant to laser imprint and Rayleigh–Taylor growth. Impulsive loading produces a shock wave that propagates into the target and is immediately followed by an expansion wave, which gradually reduces the shock strength. If the irradiated surface is rippled, then, while the shock wave propagates through the target, its modulation amplitude grows, exceeding the initial ripple amplitude by a factor of 2 or more. The oscillating areal mass reaches the peak values that exceed the initial mass modulation amplitude (density times ripple height) by a factor of 5–7 or more, and reverses its phase several times after the laser pulse is over. The oscillatory growth is more pronounced in fluids with higher shock compressibility and is probably related to the Vishniac’s instability of a blast wave. Frequency of the oscillations is determined by the speed of sound in the shocked material, and could be used as a tuning fork to probe its equation of state. The analytical theory and numerical simulations describing such oscillations are reported, and the opportunities available for their experimental observation are discussed.

Direct observation of mass oscillations due to ablative Richtmyer–Meshkov instability and feedout in planar plastic targets

Perturbations that seed Rayleigh–Taylor (RT) instability in laser-driven targets form during the early-time period. This time includes a shock wave transit from the front to the rear surface of the target, and a rarefaction wave transit in the opposite direction. During this time interval, areal mass perturbations caused by all sources of nonuniformity (laser imprint, surface ripple) are expected to oscillate. The first direct experimental observations of the areal mass oscillations due to ablative Richtmyer–Meshkov (RM) instability and feedout followed by the RT growth of areal mass modulation are discussed. The experiments were made with 40–99 μm thick planar plastic targets rippled either on the front or on the rear with a sine wave ripple with either 30 or 45 μm wavelength and with 0.5, 1, or 1.5 μm amplitude. Targets were irradiated with 4 ns long Nike KrF laser pulses at ∼50 TW/cm2. The oscillations were observed with our novel diagnostic technique, a monochromatic x-ray imager coupled to a streak camera. For the ablative RM instability (front side ripple), the mass modulation amplitude was typically observed to grow, reach a peak, and then decrease, after which the exponential RT growth started. In some cases, one phase reversal due to the ablative RM instability was observed. For the feedout geometry (rear side ripple), in all cases two phase reversals were observed: a distinct half-oscillation was followed by the onset of the RT growth, resulting in a second phase reversal.

Direct observation of mass oscillations due to ablative Richtmyer-Meshkov instability in plastic targets.

We report the first direct experimental observation of the ablative Richtmyer-Meshkov instability. It manifests itself in oscillations of areal mass that occur during the shock transit time, which are caused by the "rocket effect" or dynamic overpressure characteristic of interaction between the laser absorption zone and the ablation front. With the 4-ns-long Nike KrF laser pulse and our novel diagnostic technique (monochromatic x-ray imaging coupled to a streak camera) we were able to register a peak and a valley of the areal-mass variation before the observed onset of the Rayleigh-Taylor growth.

Theory of the Ablative Richtmyer-Meshkov Instability

Theory of the ablative Richtmyer-Meshkov instability is presented. It is shown that the main stabilizing mechanism of the ablation-front perturbations during the shock transit time is the dynamic overpressure that causes perturbation oscillations. The amplitude of the oscillation is proportional to ${c}_{s}/\sqrt{{V}_{a}{V}_{\mathrm{bl}}}$ and its frequency is $\ensuremath{\omega}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}k\sqrt{{V}_{a}{V}_{\mathrm{bl}}}$, where $k$ is the wave number, and ${c}_{s}$, ${V}_{a}$, and ${V}_{\mathrm{bl}}$ are sound speed, ablation, and blow-off plasma velocities, respectively.