Growth Of Hydrodynamic Perturbations Research Articles

Stability of ablation flows in inertial confinement fusion: Nonmodal effects.

Fast transient growth of hydrodynamic perturbations due to nonmodal effects is shown to be possible in an ablation flow relevant to inertial confinement fusion (ICF). Likely to arise in capsule ablators with material inhomogeneities, such growths appear to be too fast to be detected by existing measurement techniques, cannot be predicted by any of the methods previously used for studying hydrodynamic instabilities in ICF, yet could cause early transitions to nonlinear regimes. These findings call for reconsidering the stability of ICF flows within the framework of nonmodal stability theory.

Neutrino dark energy—revisiting the stability issue

A coupling between a light scalar field and neutrinos has been widely discussed as amechanism for linking (time varying) neutrino masses and the present energy density andequation of state of dark energy. However, it has been pointed out that the viability of thisscenario in the non-relativistic neutrino regime is threatened by the strong growth ofhydrodynamic perturbations associated with a negative adiabatic sound speedsquared. In this paper we revisit the stability issue in the framework of linearperturbation theory in a model independent way. The criterion for the stability ofa model is translated into a constraint on the scalar–neutrino coupling, whichdepends on the ratio of the energy densities in neutrinos and cold dark matter. Weillustrate our results by providing meaningful examples for both stable and unstablemodels.

Growth of hydrodynamic perturbations in accretion disks: Possible route to non-magnetic turbulence

We study the possible origin of hydrodynamic turbulence in cold accretion disks such as those in star-forming systems and quiescent cataclysmic variables. As these systems are expected to have neutral gas, the turbulent viscosity is likely to be hydrodynamic in origin, not magnetohydrodynamic. Therefore, MRI will be sluggish or even absent in such disks. Although there are no exponentially growing eigenmodes in a hydrodynamic disk because of the non-normal nature of the eigenmodes, a large transient growth in the energy is still possible, which may enable the system to switch to a turbulent state. For a Keplerian disk, we estimate that the energy will grow by a factor of 1000 for a Reynolds number close to a million.

Bypass to Turbulence in Hydrodynamic Accretion Disks: An Eigenvalue Approach

Cold accretion disks with temperatures below ~3000 K are likely to be composed of highly neutral gas. The magnetorotational instability may cease to operate in such disks, so it is of interest to consider purely hydrodynamic mechanisms of generating turbulence and angular momentum transport. With this motivation, we investigate the growth of hydrodynamic perturbations in a linear shear flow sandwiched between two parallel walls. The unperturbed flow is similar to plane Couette flow, but with a Coriolis force included. Although there are no exponentially growing eigenmodes in this system, nevertheless, because of the nonnormal nature of the eigenmodes, it is possible to have a large transient growth in the energy of perturbations. For a constant angular momentum disk, we find that the perturbation with maximum growth is axisymmetric with vertical structure. The energy grows by more than a factor of 100 for a Reynolds number R = 300 and more than a factor of 1000 for R = 1000. Turbulence can be easily excited in such a disk, as found in previous numerical simulations. For a Keplerian disk, on the other hand, similar perturbations with vertical structure grow by no more than a factor of 4, explaining why the same simulations did not find turbulence in this system. However, certain other two-dimensional perturbations with no vertical structure do exhibit modest growth. For the optimum two-dimensional perturbation, the energy grows by a factor of ~100 for R ~ 104.5 and by a factor of 1000 for R ~ 106. Such large Reynolds numbers are hard to achieve in numerical simulations, and so the nonlinear development of these kinds of perturbations is only beginning to be investigated. It is conceivable that these nearly two-dimensional disturbances might lead to self-sustained three-dimensional turbulence, although this remains to be demonstrated. The Reynolds numbers of cold astrophysical disks are much larger even than 106; therefore, hydrodynamic turbulence may be possible in disks through transient growth.

Radiation effects on hydrodynamic perturbation growth due to non-uniform laser irradiation

The initial imprint caused by the spatial non-uniformity of laser intensity which generates a mass perturbation is one of the critical issues for directly driven laser fusion research. To mitigate such laser imprint a foam-hybrid target, which has low-density foam layer and is coated with high- Z material, was proposed. In such targets, the X-ray radiation plays a significant role in the formation of the initial imprint. For short wavelength perturbations, a clear suppression of the perturbation growth is observed in the foam-hybrid target. The perturbation growth is reduced by radiation preheating since the ablation surface is smoothed. Moreover, the emitted X-rays from the coated high- Z material suppresses the hydrodynamic instability at the interface of plastic and foam. However, the ablation structure is sensitive to the opacity model. Thus, it is important to analyze the role different radiation models play in the hydrodynamics. In this work we will compare both CRE and LTE models.

Hydrodynamic perturbation growth in the start-up phase

A simple analytical model is presented to study hydrodynamic perturbation growth in the start-up phase in laser fusion, namely propagation of a rippled shock driven by non-uniform laser ablation induced by initial target roughness or non-uniform laser irradiation. These perturbation growths are very important because they seed the Rayleigh-Taylor (RT) instability in the subsequent acceleration and stagnation phases. We investigate temporal evolutions of the shock front and the ablation surface. In the result, we have found that the shock front ripples oscillate and decay in both cases of uniform laser irradiation on a target with a rippled surface and non-uniform laser irradiation on a smooth target surface. On the other hand, we obtain that there is the asymptotic value of the ablation surface deformation in the former case and the asymptotic growth rate of the ablation surface ripple in the latter case. Approximate formulas expressing both temporal evolutions of the shock front and the ablation surface are obtained in the weak shock limit. These formulas are also applicable in a relatively strong shock. We also investigate the case of oscillating non-uniform laser irradiation with time. The oscillation frequency dependences of the shock front ripple and the growth rate of the ablation surface ripple are discussed.

Rippled shock propagation and hydrodynamic perturbation growth in laser implosion

Abstract A simple analytical model is presented to study hydrodynamic perturbation growth in the start-up phase in laser fusion, namely propagation of a rippled shock driven by nonuniform laser ablation induced by initial target roughness or nonuniform laser irradiation. These perturbation growths are very important, because they seed the Rayleigh–Taylor instability in the subsequent acceleration and stagnation phases. We investigate temporal evolutions of the shock front and the ablation surface. As a result, we have found that the shock front ripples oscillate and decay in both the case of uniform laser irradiation on a target with a rippled surface and that of nonuniform laser irradiation on a smooth target. It was also found that there is an asymptotic value of the ablation surface deformation in the former case and an asymptotic growth rate of the ablation surface ripple in the latter case. Approximate formulae expressing both temporal evolutions of the shock front and the ablation surface are obtained in the weak shock limit. These formulae are also applicable in a relatively strong shock. We also investigate the case of oscillating nonuniform laser irradiation with time. The oscillation frequency dependences of the shock front ripple and the growth rate of the ablation surface ripple are discussed.

Model of hydrodynamic perturbation growth in the start-up phase of laser implosion

A simple analytical model is presented to study hydrodynamic perturbation growths driven by nonuniform laser ablation in the start-up phase in laser fusion. Propagation of a rippled shock and deformation of an ablation surface are studied for cases of initial target roughness and nonuniform laser irradiation. The study of the perturbation growth in the start-up phase is very important because it seeds the Rayleigh-Taylor instability in the subsequent acceleration and stagnation phases. Analytical solutions are obtained for temporal evolutions of the shock front ripple and the ablation surface deformation. As a result, it is seen that the shock front ripples oscillate and decay in both cases. On the other hand, there is an asymptotic amplitude of the ablation surface deformation in the case of uniform laser irradiation on a target with a rippled surface, and an asymptotic growth rate of the ablation surface ripple in the case of nonuniform laser irradiation on a smooth target. In both cases, it can be shown that a high intensity of laser irradiation causes the ablation surface to distort, and a short wavelength laser inhibits its deformation. Approximate formulas expressing the temporal behaviors of the shock front and the ablation surface are obtained in the weak shock limit. Those formulas are also applicable to a relatively strong shock. Analytical results agree quite well with recent experimental data for the shock front ripple and the areal mass density perturbation in the initial target roughness case. The behaviors of the shock front ripple and the ablation surface deformation are also investigated in the case where the nonuniformity of the laser irradiation oscillates with time. It can be seen that the deformation of the ablation surface is inhibited for a high oscillation frequency of the laser nonuniformity.

Simulation of instability growth rates on the front and back of laser accelerated planar targets

The ability of an inertial confinement fusion target to achieve ignition and burn depends critically upon controlling the growth of hydrodynamic perturbations originating on the outer ablator surface and the inner deuterium–tritium (DT) ice. The MIMOZA-ND code [Sofronov et al., Voprosy Atomnoy Nauki i Tehniki 2, 3 (1990)] was used to model perturbation growth on both sides of carbon foils irradiated by 0.35 μm light at 1015 W/cm2. When an initial perturbation was applied to a laser irradiated surface, the computational instability growth rates agreed well with the existing theoretical estimates. Perturbations applied to the rear side of the target for wavelengths that are large compared to the thickness (d/Λ≪1) behave similarly to the perturbations at the ablation front. For d/Λ⩾1, the shorter the wave length is, the faster the decrease of the growth rate of the amplitudes at the interface (and the mass flows) as compared to the perturbations at the ablation front. This is due to the Richtmyer–Meshkov instability-induced transverse velocity component. The time of Rayleigh–Taylor instability transition to the nonlinear phase depends on the initial amplitude and is well modeled by an infinitely thin shell approximation. The transverse velocity generated by the Richtmyer–Meshkov instability causes the interaction of Λ=10 μm and Λ=2 μm wavelength modes to differ qualitatively when the perturbations are applied to the ablation front or to the rear side of target.

Hydrodynamic perturbation growth in start-up phase in laser implosion

Nonuniform laser ablation caused by nonuniform laser irradiation and initial target roughness induces ripples of shock and ablation surfaces in laser implosion. Hydrodynamic perturbation growth before the shock breakout is investigated by using an analytical model and two-dimensional simulations. The model agrees well with simulation and experimental results. Areal mass density perturbations and growth rate of the Richtmyer–Meshkov instability are estimated for an ignition target. The thermal smoothing in the ablation layer is also studied for perturbations with a wavelength longer than the layer thickness. A large increase of temperature and density perturbations is shown instead of the smoothing for such a wavelength.

Fusion neutrons from the gas–pusher interface in deuterated-shell inertial confinement fusion implosions

The first measurements and numerical simulations of fusion neutrons from the gas–pusher interface of indirectly-driven inertial confinement fusion implosions have been performed using hydrogen-filled capsules made with a deuterated inner layer. Nonlinear saturation of the growth of hydrodynamic perturbations in high linear growth factor (≃325) implosions was varied by adjusting the initial surface roughness of the capsule. The neutron yields are in quantitative agreement with the direct simulations of perturbation growth, and also with a linear mode superposition and saturation model including enhanced thermal loss in the mixed region. Neutron spectra from these capsules are broader than expected for the calculated ion temperatures, suggesting the presence of nonthermal broadening from mass motion during the fusion burn.

Rippled Shock Propagation and Hydrodynamic Perturbation Growth in Laser Implosion.

Abstract A simple analytical model is presented to study hydrodynamic perturbation growth in the start-up phase in laser fusion, namely propagation of a rippled shock driven by nonuniform laser ablation induced by initial target roughness or nonuniform laser irradiation. These perturbation growths are very important, because they seed the Rayleigh–Taylor instability in the subsequent acceleration and stagnation phases. We investigate temporal evolutions of the shock front and the ablation surface. As a result, we have found that the shock front ripples oscillate and decay in both the case of uniform laser irradiation on a target with a rippled surface and that of nonuniform laser irradiation on a smooth target. It was also found that there is an asymptotic value of the ablation surface deformation in the former case and an asymptotic growth rate of the ablation surface ripple in the latter case. Approximate formulae expressing both temporal evolutions of the shock front and the ablation surface are obtained in the weak shock limit. These formulae are also applicable in a relatively strong shock. We also investigate the case of oscillating nonuniform laser irradiation with time. The oscillation frequency dependences of the shock front ripple and the growth rate of the ablation surface ripple are discussed.

Propagation of a Rippled Shock Wave Driven by Nonuniform Laser Ablation

A simple analytical model is presented to study hydrodynamic perturbation growth in the start-up phase in laser fusion, namely propagation of a rippled shock driven by nonuniform laser ablation induced by initial target roughness or nonuniform laser irradiation. Analytical results agree quite well with experimental data for the rippled shock propagation in the case of uniform irradiation on a rough surface. Approximate formulas expressing both the time evolution of the shock front and the asymptotic behavior of the ablation front are obtained in the weak shock limit. {copyright} {ital 1997} {ital The American Physical Society}