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Article in advance; International audience; Thermal protection systems experience severe thermal load during atmospheric reentry of hypersonic vehicles. Inherent to the ablation process, roughness and blowing effects may appear, affecting the performance of the heat shield. The modeling and the simulation of these effects in the hypersonic regime are challenging and rarely compared to experimental data. In this paper, Reynolds-averaged Navier–Stokes simulations of hypersonic turbulent boundary layers with roughness and blowing wall conditions are performed on Holden’s experimental configurations (“Studies of Surface Roughness and Blowing Effects on Hypersonic Turbulent Boundary Layers over Slender Cones,” 27th Aerospace Sciences Meeting, AIAA Paper 1989-0458, 1989). Using the k–ω shear stress transport model. Four experimental configurations, characterized by different levels of turbulence compressibility, are considered. A detailed discussion is proposed about the behavior of equivalent sand grain corrections and blowing corrections in combination with turbulence compressibility corrections. The predictions of skin-friction coefficients and Stanton numbers are in good agreement with Holden’s experimental data. These results show that the combination of the Zeman compressibility correction and roughness/blowing wall corrections is promising for the simulation of hypersonic boundary layers over rough walls with blowing.

International audience; A new modeling strategy adapted to Reynolds-Averaged Navier-Stokes (RANS) turbulence models is proposed to predict combined effects of roughness and blowing boundary conditions. First, an analysis of experimental data is presented, leading to a specific description of the velocity profile in the logarithmic region of transpired turbulent boundary layers over rough walls. This analysis points out the deficiencies of existing roughness corrections to predict the effect of blowing in the presence of surface roughness. Indeed, these corrections tend to underestimate skin friction coefficients and Stanton numbers with addition of blowing. The failure of existing models derives from an inaccurate estimation of the velocity shift of the logarithmic law given by roughness corrections. Concretely, roughness corrections underestimate the apparent velocity shift of the logarithmic law with blowing. To recover the expected law of the wall, an additional contribution on the velocity shift, characterizing blowing/roughness interactions, is integrated to standard roughness corrections. To that end, a modification of the equivalent sand grain height, adapted to k − ω based turbulence models, is proposed to take blowing effects into account. Furthermore, an extension of Aupoix's thermal correction [B. Aupoix, International Journal of Heat and Fluid Flow 56, 160 (2015)] to blowing is presented to predict combined thermal effects of roughness and blowing. The assessment of the proposed corrections is performed using k − ω Shear Stress Transport (SST) model on a large set of experimental data and proves the relevance of the strategy for incompressible and compressible turbulent boundary layers.

Laser-produced high-energy-density plasmas may contain strong magnetic fields that affect the energy transport, which can be nonlocal. Models which describe the magnetized nonlocal transport are formally complicated and based on many approximations. This paper presents a more straightforward approach to the description of the electron transport in this regime, based on the extension of a reduced entropic model. The calculated magnetized heat fluxes are compared with the known asymptotic limits and applied for studying of a magnetized nonlocal plasma thermalization.

The European High Power laser Energy Research (HiPER) project aims at demonstrating the feasibility of high gain inertial confinement fusion (ICF) using the fast ignitor approach. A baseline target has been recently developed by Atzeni et al. [Phys. Plasmas 14, 052702 (2007)]. The radiative transport have a minor effect on the peak areal density but decreased by 20% the peak density. We have found that with 95 kJ of absorbed laser energy one can assemble the fuel with a peak density around 500 g/cm3 and a peak areal density of 1.2 g/cm2. This implies a total target gain of about 60.

Hydrodynamic simulations of high-energy-density plasmas require a detailed description of energy fluxes. For low and intermediate atomic number materials, the leading mechanism is the electron transport, which may be a nonlocal phenomenon requiring a kinetic modeling. In this paper, we present and test the results of a nonlocal model based on the first angular moments of a simplified Fokker-Planck equation. This multidimensional model is closed thanks to an entropic relation (the Boltzman H-theorem). It provides a better description of the electron distribution function, thus enabling studies of small scale kinetic effects within the hydrodynamic framework. Examples of instabilities of electron plasma and ion-acoustic waves, driven by the heat flux, are presented and compared with the classical formula.

This paper deals with ablation front instabilities simulations in the context of direct drive ICF. A simplified DT target, representative of realistic target on LIL is considered. We describe here two numerical approaches: the linear perturbation method using the perturbation codes Perle (planar) and Pansy (spherical) and the direct simulation method using our Bi-dimensional hydrodynamic code Chic. Numerical solutions are shown to converge, in good agreement with analytical models.

Hydrodynamic instabilities play an important role in the target compression for inertial confinement fusion (ICF). We present the analytical solution of a perturbed isentropic implosion. We compare the analytical solution to the results obtained with perturbation and bi-dimensional Lagrangian hydrodynamic codes. We also compare results from bi-dimensional code and perturbation code on an ICF like test case.

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.

This study deals with the hydrodynamic stability of a planar target in the context of direct drive ICF. Recently, different schemes have been proposed in order to reduce ablative Rayleigh-Taylor growth. They are based on the target adiabat shaping in the ablation zone. In this work, we consider an adiabat shaping scheme by relaxation: a prepulse is followed by a relaxation period where the laser is turned off. A numerical study is performed with a perturbation code dedicated to the linear stability analysis. The simulations show stabilizing effects of the relaxation scheme on the linear Rayleigh-Taylor growth rate. Influence of the picket parameters is also discussed.

International audience; The mechanisms of laser imprint reduction on a surface of a planar foil performed using an underdense foam are presented. The consequences on the Rayleigh–Taylor instability growth at the ablation front when the foil is accelerated are studied. The analysis is based on numerical simulations using a chain of codes: the electromagnetic paraxial code Parax provides the modifications of the intensity perturbation spectrum while the laser beam is crossing the foam. Two-dimensional axially symmetric simulations with the radiation hydrodynamic code CHIC describe the foam expansion and the foil dynamics. Finally, the perturbed flow calculations and the instability growth are investigated with the two-dimensional CHIC version in the planar geometry by using the initial and smoothed perturbation spectra. The dominant role of temporal laser smoothing during the time of foam crossing by the laser beam is demonstrated. Applications to the direct drive targets for inertial confinement fusion are discussed.

Reducing the detrimental effect of the Rayleigh-Taylor (RT) instability on the target performance is a critical challenge. In this purpose, the use of targets coated with low density foams is a promising approach to reduce the laser imprint. This article presents results of ablative RT instability growth measurements, performed on the OMEGA laser facility in direct-drive for plastic foils coated with underdense foams. The laser beam smoothing is explained by the parametric instabilities developing in the foam and reducing the laser imprint on the plastic (CH) foil. The initial perturbation pre-imposed by the means of a specific phase plate was shown to be smoothed using different foam characteristics. Numerical simulations of the laser beam smoothing in the foam and of the RT growth are performed with a suite of paraxial electromagnetic and radiation hydrodynamic codes. They confirmed the foam smoothing effect in the experimental conditions.

The linear and non-linear sensitivity of the 180 kJ baseline HiPER target to high-mode perturbations, i.e. surface roughness, is addressed using two-dimensional simulations and a complementary analysis by linear and non-linear ablative Rayleigh–Taylor models. Simulations provide an assessment of an early non-linear stage leading to a significant deformation of the ablation surface for modes of maximum linear growth factor. A design using a picket prepulse evidences an improvement in the target stability inducing a delay of the non-linear behavior. Perturbation evolution and shape, evidenced by simulations of the non-linear stage, are analyzed with existing self-consistent non-linear theory.

Recently, a European collaboration has proposed the High Power Laser Energy Research (HiPER) facility, with the primary goal of demonstrating laser driven inertial fusion fast ignition. HiPER is expected to provide 250 kJ in multiple, 3ω (wavelength λ = 0.35 µm), nanosecond beams for compression and 70 kJ in 10–20 ps, 2ω beams for ignition. The baseline approach is fast ignition by laser-accelerated fast electrons; cones are considered as a means to maximize ignition laser–fuel coupling. Earlier studies led to the identification of an all-DT shell, with a total mass of about 0.6 mg as a reference target concept. The HiPER main pulse can compress the fuel to a peak density above 500 g cm−3 and an areal density ρR of about 1.5 g cm−2. Ignition of the compressed fuel requires that relativistic electrons deposit about 20 kJ in a volume of radius of about 15 µm and a depth of less than 1.2 g cm−2. The ignited target releases about 13 MJ. In this paper, additional analyses of this target are reported. An optimal irradiation pattern has been identified. The effects on fuel compression of the low-mode irradiation non-uniformities have been studied by 2D simulations and an analytical model. The scaling of the electron beam energy required for ignition (versus electron kinetic energy) has been determined by 2D fluid simulations including a 3D Monte Carlo treatment of relativistic electrons, and agrees with a simple model. Integrated simulations show that beam-induced magnetic fields can reduce beam divergence. As an alternative scheme, shock ignition is studied. 2D simulations have addressed optimization of shock timing and absorbed power, means to increase laser absorption efficiency and the interaction of the igniting shocks with a deformed fuel shell.

Target studies for the proposed High Power Laser Energy Research (HiPER) facility [M. Dunne, Nature Phys. 2, 2 (2006)] are outlined and discussed. HiPER will deliver a 3ω (wavelength λ=0.35μm), multibeam, multi-ns pulse of about 250kJ and a 2ω or 3ω pulse of 70–100kJ in about 15ps. Its goal is the demonstration of laser driven inertial fusion via fast ignition. The baseline target concept is a direct-drive single shell capsule, ignited by hot electrons generated by a conically guided ultraintense laser beam. The paper first discusses ignition and compression requirements, and presents gain curves, based on an integrated model including ablative drive, compression, ignition and burn, and taking the coupling efficiency ηig of the igniting beam as a parameter. It turns out that ignition and moderate gain (up to 100) can be achieved, provided that adiabat shaping is used in the compression, and the efficiency ηig exceeds 20%. Using a standard ponderomotive scaling for the hot electron temperature, a 2ω or 3ω ...

Understanding and mitigating hydrodynamic instabilities and the fuel mix are the key elements for achieving ignition in Inertial Confinement Fusion. Cryogenic indirect-drive implosions on the National Ignition Facility have evidenced that the ablative Rayleigh-Taylor Instability (RTI) is a driver of the hot spot mix. This motivates the switch to a more flexible higher adiabat implosion design [O. A. Hurricane et al., Phys. Plasmas 21, 056313 (2014)]. The shell instability is also the main candidate for performance degradation in low-adiabat direct drive cryogenic implosions [Goncharov et al., Phys. Plasmas 21, 056315 (2014)]. This paper reviews recent results acquired in planar experiments performed on the OMEGA laser facility and devoted to the modeling and mitigation of hydrodynamic instabilities at the ablation front. In application to the indirect-drive scheme, we describe results obtained with a specific ablator composition such as the laminated ablator or a graded-dopant emulator. In application to the direct drive scheme, we discuss experiments devoted to the study of laser imprinted perturbations with special phase plates. The simulations of the Richtmyer-Meshkov phase reversal during the shock transit phase are challenging, and of crucial interest because this phase sets the seed of the RTI growth. Recent works were dedicated to increasing the accuracy of measurements of the phase inversion. We conclude by presenting a novel imprint mitigation mechanism based on the use of underdense foams. The foams induce laser smoothing by parametric instabilities thus reducing the laser imprint on the CH foil.

The effect of anisotropic diffusion on hydrodynamic instabilities in the context of Inertial Confinement Fusion (ICF) flows is numerically assessed. This anisotropy occurs in indirect-drive when laminated ablators are used to modify the lateral transport (1, 2). In direct-drive, non-local transport mechanisms and magnetic fields may modify the lateral conduction (3). In this work, numerical simulations obtained with the code PERLE (4), dedicated to linear stability analysis, are compared with previous theoretical results (1). In these approaches, the diffusion anisotropy can be controlled by a characteristic coefficient which enables a comprehensive study. This work provides new results on the ablative Rayleigh- Taylor (RT), ablative Richtmyer-Meshkov (RM) and Darrieus-Landau (DL) instabilities.

A linear Rayleigh-Taylor instability theory of double ablation (DA) fronts is developed for direct-drive inertial confinement fusion. Two approaches are discussed: an analytical discontinuity model for the radiation dominated regime of very steep DA front structure, and a numerical self-consistent model that covers more general hydrodynamic profiles behaviours. Dispersion relation results are compared to 2D simulations.

The propagation of an ionization wave through a subcritical foam is studied under inertial confinement fusion conditions. Independent measurements of the ionization wave velocity are compared with hydrodynamic simulations and analytical models. It is shown that simulations of a homogeneous material at equivalent density strongly overestimate the front velocity. The internal foam structure can be accounted for with a simple model of foam homogenization that allows improving agreement between experiment and calculations.

The linear stability analysis of accelerated double ablation fronts is carried out numerically with a self-consistent approach. Accurate hydrodynamic profiles are taken into account in the theoretical model by means of a fitting parameters method using 1D simulation results. Numerical dispersión relation is compared to an analytical sharp boundary model [Yan˜ez et al., Phys. Plasmas 18, 052701 (2011)] showing an excellent agreement for the radiation dominated regime of very steep ablation fronts, and the stabilization due to smooth profiles. 2D simulations are presented to validate the numerical self-consistent theory.

A linear stability theory of double ablation fronts is developed for direct-drive inertial confinement fusion targets. The so-called electron radiative ablation front [S. Fujioka et al., Phys. Rev. Lett. 92, 195001 (2004)] is studied with a self-consistent model. Numerical results are presented as well as an analytical approach for the radiation dominated regime of very steep double ablation front structure. Dispersion relation formula is tackled by means of a sharp boundary model.

The dynamics of double ablation front (DAF) structures is studied for planar targets with moderate atomic number ablators. These structures are obtained in hydrodynamic simulations for various materials and laser intensities and are qualitatively characterized during the acceleration stage of the target. The importance of the radiative transport for the DAF dynamics is then demonstrated. Simulated hydrodynamic profiles are compared with a theoretical model, showing the consistency of the model and the relevant parameters for the dynamics description. The stability of DAF structures with respect to two-dimensional perturbations is studied using two different approaches: one considers the assumptions of the theoretical model and the other one a more complete physics. The numerical simulations performed with both approaches demonstrate good agreement of dispersion curves.

Shock ignition of a pre-compressed deuterium tritium fuel is considered here. When properly timed, a converging shock launched in the target prior to stagnation time strongly enhances the hot spot pressure. This allows ignition to be reached in a nonisobaric configuration. We show in this work that the igniting mechanism is pressure amplification by shock convergence and shock collision. The shock ignition applied to the HiPER target allows one to study the robustness of this method. It is shown that the spike energy is not a critical parameter and that the spike power delivered on the target depends mainly on the shell implosion velocity. Finally, a family of homothetic targets ignited with a shock wave is studied.

The one-dimensional theory of double ablation fronts is developed for direct-drive inertial confinement fusion targets. The theory is based on the subsonic ablation front approximation and includes the effects of both radiation and electron heat fluxes. It is found that the structure of the ablation front is determined by two dimensionless parameters: the Boltzmann number and the effective mean free path. The Boltzmann number represents the ratio of the convective thermal and radiation energy fluxes, while the effective mean free path is the ratio between the characteristic plasma temperature gradient conduction scale length and the radiation mean free path. The development of a double ablation front is determined based on the range of the above dimensionless parameters. Temperature and density profiles in double ablation fronts are derived from a simplified analytic model and compared with the results of numerical simulations.

Hydrodynamics and robustness of three high yield targets within the HiPER project are presented. Using realistic illumination nonuniformity configuration, hydrodynamic perturbations sensitivity analysis is carried out. A rather simple hydrodynamic perturbation modeling sequence is validated thanks to 2D simulations. 1D simulations post-processed with such a modeling sequence provide a good estimation of the thermonuclear burn. First estimates of hydrodynamic safety factor are given.

The European High Power laser Energy Research (HiPER) project aims at demonstrating the feasibility of high gain inertial confinement fusion using the fast ignitor approach. A baseline target has been recently developed by Atzeni et al (2007 Phys. Plasmas 14 052702). We study here the robustness of this target during the compression phase and define pulse shape tolerances for a successful fuel assembly. The comparison between a standard and a relaxation pulse shows that the latter allows one to reduce both the laser power contrast and the growth of perturbations due to Rayleigh?Taylor instability. We have found that with 95?kJ of absorbed laser energy one can assemble the fuel with a peak density around 500?g?cm?2 and a peak areal density of 1.2?g?cm?2. This implies a total target gain of about 60.

The hydrodynamic stability of a planar target is considered for the conditions of the direct drive inertial confinement fusion. It has been recently proposed to reduce the ablative Rayleigh-Taylor instability growth by using the adiabat shaping in the ablation zone. In this work, we consider the relaxation adiabat shaping scheme [K. Anderson and R. Betti, Phys. Plasmas 11, 5 (2004); R. Betti, K. Anderson, J. P. Knauer, T. J. B. Collins, R. L. McCrory, P. W. McKenty, and S. Skupsky, Phys. Plasmas 12, 042703 (2005)]. In this scheme, a prepulse (“picket”) is followed by a relaxation period, when the laser is turned off. A parametric study of picket parameters is performed with a code dedicated to the linear stability analysis on the basis of spherical realistic simulations including full physics. The influence of the picket parameters is investigated numerically. Simulations show that the set picket/relaxation time mainly determines the target stability and that the adiabat shaping scheme modifies the pertur...