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Performance degradation in laser-driven inertial confinement fusion (ICF) implosions is caused by several effects, one of which is Rayleigh–Taylor instability growth. Defects in ICF targets, such as internal voids and surface roughness, create instability seeds in the shell as shocks propagate through the target. A comprehensive understanding of seeding mechanisms is essential to characterize the impact of target defects on inflight shell integrity and mass injection into the central, lower-density vapor region. An analysis of early-time behavior of both single-mode shell mass modulations and isolated voids is performed by examining the evolution of the acoustic waves launched by these target imperfections. A systematic study of localized perturbation growth as a function of defect placement and size is presented. The use of low-density ablator materials (such as foams) is suggested as a potential mitigation strategy to improve target robustness against the impact of defect-initiated growth.

International audience; A novel approach to efficiently model 3-D laser plasma interactions at fluid scales is presented. This method, implemented in the IFRIIT propagation code developed at CELIA, relies on inverse ray tracing to compute laser fields at arbitrary locations in a plasma. This enables to describe the fields at high order in space compared to standard forward ray tracing approaches. In addition, inverse ray tracing enables the use of etalon integral methods to reconstruct caustic fields and greatly speeds up calculations of cross-beam energy transfer by decoupling the ray amplitude and ray phase calculations. A comparison of the inverse and forward methods for 3-D calculations of fields in presence or not of cross-beam energy transfer illustrates the significant advantages of the inverse method. Conversely, while the inverse method is well suited to most spherical plasma profiles, it currently cannot treat concave profiles or target holders. The coupling of IFRIIT with the 3-D ASTER radiative hydrodynamics code developped at the Laboratory for Laser Energetics is then presented. ASTER and IFRIIT resolve their respective equations on separate grids which communicate through interpolation. As such, IFRIIT uses a dedicated laser grid adapted to the computations at play, which also allows to use different parallelization methods for both codes: block decomposition for the hydrodynamics versus domain duplication for the laser. Applications to direct-drive implosions for inertial confinement fusion are presented, for which a geodesic icosahedron grid is implemented in IFRIIT. The performances of the ASTER/IFRIIT coupling is demonstrated by conducting simulations of cryogenic implosions performed on the OMEGA laser system, in presence of various sources of 3-D effects; laser port geometry, cross-beam energy transfer, beam imbalance and target mis-alignment. Comparison with neutron data, measured through bang-time, for a cryogenic implosion experiment shows an excellent agreement for the laser-plasma coupling.

Focusing laser light onto a very small target can produce the conditions for laboratory-scale nuclear fusion of hydrogen isotopes. The lack of accurate predictive models, which are essential for the design of high-performance laser-fusion experiments, is a major obstacle to achieving thermonuclear ignition. Here we report a statistical approach that was used to design and quantitatively predict the results of implosions of solid deuterium-tritium targets carried out with the 30-kilojoule OMEGA laser system, leading to tripling of the fusion yield to its highest value so far for direct-drive laser fusion. When scaled to the laser energies of the National Ignition Facility (1.9 megajoules), these targets are predicted to produce a fusion energy output of about 500 kilojoules-several times larger than the fusion yields currently achieved at that facility. This approach could guide the exploration of the vast parameter space of thermonuclear ignition conditions and enhance our understanding of laser-fusion physics.

Refraction-enhanced x-ray radiography (REXR) is used to infer shock-wave positions of more than one shock wave, launched by a multiple-picket pulse in a planar plastic foil. This includes locating shock waves before the shocks merge, during the early time and the main drive of the laser pulse that is not possible with the velocity interferometer system for any reflector. Simulations presented in this paper of REXR show that it is necessary to incorporate the refraction and attenuation of x rays along with the appropriate opacity and refractive-index tables to interpret experimental images. Simulated REXR shows good agreement with an experiment done on the OMEGA laser facility to image a shock wave. REXR can be applied to design multiple-picket pulses with a better understanding of the shock locations. This will be beneficial to obtain the required adiabats for inertial confinement fusion implosions.

A thin-glass-shell, D3He-filled exploding-pusher inertial confinement fusion implosion at the National Ignition Facility (NIF) has been demonstrated as a proton source that serves as a promising first step toward development of a monoenergetic proton, alpha, and triton backlighting platform at the NIF. Among the key measurements, the D3He-proton emission on this experiment (shot N121128) has been well-characterized spectrally, temporally, and in terms of emission isotropy, revealing a highly monoenergetic ( Δ E / E ∼ 4 % ) and isotropic source (~3% proton fluence variation and ~0.5% proton energy variation). On a similar shot (N130129, with D2 fill), the DD-proton spectrum has been obtained as well, illustrating that monoenergetic protons of multiple energies may be utilized in a single experiment. These results, and experiments on OMEGA, point toward future steps in the development of a precision, monoenergetic proton, alpha, and triton source that can readily be implemented at the NIF for backlighting a broad range of high energy density physics (HEDP) experiments in which fields and flows are manifest, and also utilized for studies of stopping power in warm dense matter and in classical plasmas.

The new component of the “laser–plasma simulation environment” (LPSE) described here is a practical numerical model that solves the coupled vector equations for the propagation of nearly monochromatic, coherent, electromagnetic waves in inhomogeneous unmagnetized plasmas. It operates efficiently in the numerically challenging semiclassical regime where characteristic plasma scale lengths are many times greater than the wavelength of the light and solutions are highly oscillatory. Solutions can be obtained in one, two, or three spatial dimensions and time. The model includes the effects of nonlinear coupling of electromagnetic waves to the low-frequency plasma perturbations (i.e., ion-acoustic response) that are responsible for stimulated Brillouin scattering. Induced plasma perturbations are assumed to be imposed on a prescribed large-scale inhomogeneous background that includes spatially varying plasma density and flow. Our code is directly relevant to the problem of cross-beam energy transfer in laser-driven inertial confinement fusion. It may also be applicable in other areas where eikonal solutions of multicomponent wave equations (or coupled wave equations) are insufficient, such as optical scattering from ultrasound, electron dynamics in quantum devices or in nanoscale light–matter interactions.

Accurate and self-consistent knowledge of material properties under high-energy-density (HED) conditions is crucial to reliably understand and design inertial confinement fusion (ICF) targets through radiation–hydrodynamic simulations. For direct-drive ICF target designs, the fuel deuterium–tritium mixtures and ablator materials can undergo a wide range of density and temperature conditions. Their properties under extreme HED conditions, including the equation of state, thermal conductivity, opacity, and stopping power, are the necessary inputs for ICF simulations. To improve the predictive capability of radiation–hydrodynamic codes for direct-drive ICF simulations, we have performed systematic ab initio studies on the static, transport, and optical properties of deuterium (D2) and ablator materials such as polystyrene (CH), beryllium (Be), and silicon (Si), using first-principles methods. The obtained material properties, being favorably compared with existing experimental data, have been implemented into radiation–hydrodynamic codes. This article gives a brief review on how these microphysics studies affect the 1-D radiation–hydrodynamic predictions of direct-drive ICF implosions on the OMEGA Laser System.

Broad bandwidth, infrared light sources have the potential to revolutionize inertial confinement fusion (ICF) by suppressing laser-plasma instabilities. There is, however, a tradeoff: The broad bandwidth precludes high efficiency conversion from the infrared to the ultraviolet, where laser-plasma interactions are weaker. Operation in the infrared could intensify the role of resonance absorption, an effect long suspected to be the shortcoming of early ICF experiments. Here, we present simulations exploring the effect of the bandwidth on resonance absorption. In the linear regime, the bandwidth has little effect on resonance absorption; in the nonlinear regime, the bandwidth suppresses enhanced absorption resulting from the electromagnetic decay instability. These findings evince that, regardless of the bandwidth, an ICF implosion will confront at least linear levels of resonance absorption.

Polystyrene (CH), commonly known as “plastic,” has been one of the widely used ablator materials for capsule designs in inertial confinement fusion (ICF). Knowing its precise properties under high-energy-density conditions is crucial to understanding and designing ICF implosions through radiation–hydrodynamic simulations. For this purpose, systematic ab initio studies on the static, transport, and optical properties of CH, in a wide range of density and temperature conditions (ρ = 0.1 to 100 g/cm3 and T = 103 to 4 × 106 K), have been conducted using quantum molecular dynamics (QMD) simulations based on the density functional theory. We have built several wide-ranging, self-consistent material-properties tables for CH, such as the first-principles equation of state, the QMD-based thermal conductivity (κQMD) and ionization, and the first-principles opacity table. This paper is devoted to providing a review on (1) what results were obtained from these systematic ab initio studies; (2) how these self-consiste...

Direct-drive inertial confinement fusion (ICF) is expected to demonstrate high gain on the National Ignition Facility (NIF) in the next decade and is a leading candidate for inertial fusion energy production. The demonstration of high areal densities in hydrodynamically scaled cryogenic DT or D2 implosions with neutron yields that are a significant fraction of the “clean” 1-D predictions will validate the ignition-equivalent direct-drive target performance on the OMEGA laser at the Laboratory for Laser Energetics (LLE). This paper highlights the recent experimental and theoretical progress leading toward achieving this validation in the next few years. The NIF will initially be configured for X-ray drive and with no beams placed at the target equator to provide a symmetric irradiation of a direct-drive capsule. LLE is developing the “polar-direct-drive” (PDD) approach that repoints beams toward the target equator. Initial 2-D simulations have shown ignition. A unique “Saturn-like” plastic ring around the equator refracts the laser light incident near the equator toward the target, improving the drive uniformity. LLE is currently constructing the multibeam, 2.6-kJ/beam, petawatt laser system OMEGA EP. Integrated fast-ignition experiments, combining the OMEGA EP and OMEGA Laser Systems, will begin in FY08.

Gradients in the laser-induced electric field introduce ponderomotive terms in the current flow, heat flux, and electric stress tensor. The transport coefficients, previously derived in the limit Z≫1, are obtained for an arbitrary ion charge Z using the Chapman–Enskog method [S. Chapman and T. G. Cowling, The Mathematical Theory of Non-Uniform Gases (Cambridge University Press, Cambridge, 1970)]. It is shown that the ponderomotive terms significantly modify the thermal transport near the laser turning points and the critical surface.

Three recent developments in direct-drive target design have enhanced the possibility of achieving high target gain on the National Ignition Facility (NIF): (1) Laser absorption was increased by almost 50% using wetted-foam targets. (2) Adiabat shaping significantly increased the hydrodynamic stability of the target during the acceleration phase of the implosion without sacrificing target gain. (3) Techniques to reduce laser imprint using pulse shaping and radiation preheat were developed. These design features can be employed for direct-drive-ignition experiments while the NIF is in the x-ray-drive configuration. This involves repointing some of the beams toward the equator of the target to improve uniformity of target drive. This approach, known as polar direct drive (PDD), will enhance the capability of the NIF to explore ignition conditions. PDD will couple more energy to the fuel than x-ray drive. The compressed fuel core can be more easily accessed for high-ρR diagnostic development and for fast-ign...

Layered and characterized cryogenic D2 capsules have been imploded using both low- and high-adiabat (α, the ratio of the electron pressure to the Fermi-degenerate pressure) pulse shapes on the 60-beam OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] at the Laboratory for Laser Energetics (LLE). These experiments measure the sensitivity of the direct-drive implosion performance to parameters such as the inner-ice-surface roughness, the adiabat of the cryogenic fuel during the implosion, the laser power balance, and the single-beam nonuniformity. The goal of the direct-drive program at LLE is to demonstrate a high neutron-averaged fuel ρR at a significant fraction of the predicted one-dimensional (1-D) neutron yield using an energy-scaled, low-adiabat (α∼3) ignition pulse shape driving a hydrodynamically scaled deuterium–tritium ignition capsule. New results are reported from implosions of ∼920-μm-diam, thin (∼5 μm) polymer shells containing 100 μm D2-ice layers with characterized inne...

The effect of a Gaussian prepulse (picket pulse) before a “drive” pulse on the Rayleigh–Taylor (RT) instability growth rate was measured for single-mode, 20-, 30-, and 60-μm-wavelength mass perturbations. These data, from the OMEGA [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] laser system, show that the measured RT growth of mass perturbations was reduced when a picket pulse was used. The picket pulse and subsequent relaxation period, before the drive pulse, cause the foil to expand and rarefy, resulting in higher ablation velocities during the drive pulse and greater ablative stabilization. This effect was examined both computationally and experimentally for different picket-pulse intensities.

Hydrodynamicinstabilities seeded by laser imprint and surface roughness limit the compression ratio and neutron yield in the direct-drive inertial confinement fusion target designs. New improved-performance designs use adiabat shaping to increase the entropy of only the outer portion of the shell, reducing the instability growth. The inner portion of the shell is kept on a lower entropy to maximize shell compressibility. The adiabat shaping is implemented using a high-intensity picket in front of the main-drive pulse. The picket launches a strong shock that decays as it propagates through the shell. This increases the ablation velocity and reduces the Rayleigh–Taylor growth rates. In addition, as shown earlier [T.J.B. Collins and S. Skupsky, Phys. Plasmas 9, 275 (2002)], the picket reduces the instability seed due to the laser imprint. To test the results of calculations, a series of the picket pulse implosions of CH capsules were performed on the OMEGA laser system [T.R. Boehly, D.L. Brown, R.S. Craxton et al., Opt. Commun. 133, 495 (1997)]. The experiments demonstrated a significant improvement in target yields for the pulses with the picket compared to the pulses without the picket. Results of the theory and experiments with adiabat shaping are being extended to future OMEGA and the National Ignition Facility’s [J.A. Paisner, J.D. Boyes, S.A. Kumpan, W.H. Lowdermilk, and M.S. Sorem, Laser Focus World 30, 75 (1994)] cryogenic target designs.

The evolution of shell modulations was measured in targets with titanium-doped layers using differential imaging [B. Yaakobi et al., Phys. Plasmas 7, 3727 (2000)] near peak compression of direct-drive spherical implosions. Inner-shell modulations grow throughout the deceleration phase of the implosion due to the Rayleigh–Taylor instability with relative modulation levels of ∼20% at peak neutron production and ∼50% at peak compression (∼100 ps later) in targets with 1-mm-diam, 20-μm-thick shells filled with 4 atm of D3He gas. In addition, the shell modulations grow up to about 1.5 times due to Bell–Plesset convergent effects during the same period. At peak compression the inner part of the shell has a higher modulation level than other parts of the shell.

A model for the deceleration phase and marginal ignition of imploding capsules is derived by solving a set of ordinary differential equations describing the hot-spot energy balance and the shell dynamics including the return shock propagation. It is found that heat flux leaving the hot spot goes back in the form of internal energy and PdV work of the material ablated off the inner-shell surface. Though the hot-spot temperature is reduced by the heat conduction losses, the hot-spot density increases due to the ablated material in such a way that the hot-spot pressure is approximately independent of heat conduction. For hot-spot temperatures exceeding approximately 7 keV, the ignition conditions are not affected by heat conduction losses that are recycled into the hot spot by ablation. Instead, the only significant internal energy loss is due to the hot-spot expansion tamped by the surrounding shell. The change of adiabat induced by the shock is also calculated for marginally igniting shells, and the relati...

A 16-image Kirkpatrick-Baez (KB)-type x-ray microscope consisting of compact KB mirrors [F. J. Marshall, Rev. Sci. Instrum. 83, 10E518 (2012)] has been assembled for the first time with mirrors aligned to allow it to be coupled to a high-speed framing camera. The high-speed framing camera has four independently gated strips whose emission sampling interval is ∼30 ps. Images are arranged four to a strip with ∼60-ps temporal spacing between frames on a strip. By spacing the timing of the strips, a frame spacing of ∼15 ps is achieved. A framed resolution of ∼6-μm is achieved with this combination in a 400-μm region of laser-plasma x-ray emission in the 2- to 8-keV energy range. A principal use of the microscope is to measure the evolution of the implosion stagnation region of cryogenic DT target implosions on the University of Rochester's OMEGA Laser System [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. The unprecedented time and spatial resolutions achieved with this framed, multi-image KB microscope have made it possible to accurately determine the cryogenic implosion core emission size and shape at the peak of stagnation. These core size measurements, taken in combination with those of ion temperature, neutron-production temporal width, and neutron yield allow for inference of core pressures, currently exceeding 50 Gbar in OMEGA cryogenic target implosions [Regan et al., Phys. Rev. Lett. 117, 025001 (2016)].

Cross-beam energy transfer (CBET) is thought to be responsible for a 30% reduction in hydrodynamic coupling efficiency on OMEGA and up to 50% at the ignition scale for direct-drive (DD) implosions. These numbers are determined by ray-based models that have been developed and integrated within the radiation–hydrodynamics codes LILAC (1-D) and DRACO (2-D). However, ray-based modeling of CBET in an inhomogeneous plasma assumes a steady-state plasma response, does not include the effects of beam speckle, and treats ray caustics in an ad hoc manner. The validity of the modeling for ignition-scale implosions has not yet been determined. To address the physics shortcomings, which have important implications for DD inertial confinement fusion, a new wave-based model has been developed. It solves the time-enveloped Maxwell equations in three dimensions, including polarization effects, plasma inhomogeneity, and open-boundary conditions with the ability to prescribe beams incident at arbitrary angles. Beams can be m...

A model for the deceleration phase of imploding inertial confinement fusion capsules is derived by solving the conservation equations for the hot spot. It is found that heat flux leaving the hot spot goes back in the form of internal energy and pdV work of the material ablated off the inner shell surface. Though the hot-spot temperature is reduced by the heat conduction losses, the hot-spot density increases due to the ablated material in such a way that the hot-spot pressure is approximately independent of heat conduction. For direct-drive National Ignition Facility-like capsules, the ablation velocity off the shell inner surface is of the order of tens μm/ns, the deceleration of the order of thousands μm/ns2, and the density-gradient scale length of the order a few μm. Using the well-established theory of the ablative Rayleigh–Taylor instability, it is shown that the growth rates of the deceleration phase instability are significantly reduced by the finite ablative flow and the unstable spectrum exhibits a cutoff for mode numbers of about l≈90.

This paper reviews the current direct-drive ignition capsule designed for the National Ignition Facility (NIF) [M. D. Campbell and W. J. Hogan, Plasma Phys. Control. Fusion 41, B39 (1999)]. The ignition design consists of a cryogenic deuterium–tritium (DT) shell contained within a very thin CH shell. To maintain shell integrity during the implosion, the target is placed on an isentrope approximately three times that of Fermi-degenerate DT (α=3). One-dimensional studies show that the ignition design is robust. Two-dimensional simulations examine the effects on target performance due to laser imprint, power imbalance, and inner- and outer-target-surface roughness. Results from these studies indicate that the capsule gain can be scaled to the ice/vapor surface deformation at the end of the acceleration stage of the implosion. The physical reason for gain reduction as a function of increasing nonuniformities is examined. Simulations show that direct-drive target gains in excess of 30 can be achieved for an inner-ice-surface roughness of 1 μm rms, an on-target power imbalance of 2% rms, and by using the beam-smoothing technique SSD with 1 THz and two color cycles.

Irradiation nonuniformities in direct-drive (DD) inertial confinement fusion experiments generate, or “imprint,” surface modulations that degrade the symmetry of the implosion and reduce the target performance. To gain physical insight, an analytical model of imprint is developed. The model takes into account the hydrodynamic flow, the dynamics of the conduction zone, and the mass ablation. The important parameters are found to be the time scale for plasma atmosphere formation and the ablation velocity. The model is validated by comparisons to detailed two-dimensional (2D) hydrocode simulations. The results of the model and simulations are in good agreement with a series of planar-foil imprint experiments performed on the OMEGA laser system [T.R. Boehly, D.L. Brown, R.S. Craxton et al., Opt. Commun. 133, 495 (1997)]. Direct-drive National Ignition Facility’s [J.A. Paisner, J.D. Boyes, S.A. Kumpan, W.H. Lowdermilk, and M.S. Sorem, Laser Focus World 30, 75 (1994)] cryogenic targets are shown to have gains l...

The results from a series of single-mode, Rayleigh–Taylor (RT) instability growth experiments performed on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] using planar targets are reported. Planar targets with imposed mass perturbations were accelerated using five or six 351 nm laser beams overlapped with total intensities up to 2.5×1014 W/cm2. Experiments were performed with both 3 ns ramp and 3 ns flat-topped temporal pulse shapes. The use of distributed phase plates and smoothing by spectral dispersion resulted in a laser-irradiation nonuniformity of 4%–7% over a 600 μm diam region defined by the 90% intensity contour. The temporal growth of the modulation in optical depth was measured using throughfoil radiography and was detected with an x-ray framing camera for CH targets. Two-dimensional (2-D) hydrodynamic simulations (ORCHID) [R. L. McCrory and C. P. Verdon, in Inertial Confinement Fusion (Editrice Compositori, Bologna, 1989), pp. 83–124] of the growth of 20, 31, and 60 ...

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.

A simple procedure is developed to determine the Froude number Fr, the effective power index for thermal conduction ν, the ablation-front thickness L0, the ablation velocity Va, and the acceleration g of laser-accelerated ablation fronts. These parameters are determined by fitting the density and pressure profiles obtained from one-dimensional numerical simulations with the analytic isobaric profiles of Kull and Anisimov [Phys. Fluids 29, 2067 (1986)]. These quantities are then used to calculate the growth rate of the ablative Rayleigh–Taylor instability using the theory developed by Goncharov et al. [Phys. Plasmas 3, 4665 (1996)]. The complicated expression of the growth rate (valid for arbitrary Froude numbers) derived by Goncharov et al. is simplified by using reasonably accurate fitting formulas.

Significant progress has been made in direct-drive inertial confinement fusion research at the Laboratory for Laser Energetics since the 2009 IFSA Conference [R.L. McCrory et al. , J. Phys.: Conf. Ser. 244 , 012004 (2010)]. Areal densities of 300mg/cm2 have been measured in cryogenic target implosions with neutron yields 15% of 1-D predictions. A model of crossed-beam energy transfer has been developed to explain the observed scattered-light spectrum and laser–target coupling. Experiments show that its impact can be mitigated by changing the ratio of the laser beam to target diameter. Progress continues in the development of the polar-drive concept that will allow direct-drive–ignition experiments to be conducted on the National Ignition Facility using the indirect-drive-beam layout.

The linear growth rate of the Rayleigh–Taylor instability is calculated for accelerated ablation fronts with small Froude numbers (Fr≪1). The derivation is carried out self‐consistently by including the effects of finite thermal conductivity (κ∼Tν) and density gradient scale length (L). It is shown that long‐wavelength modes with wave numbers kL0≪1 [L0=νν/(ν+1)ν+1 min(L)] have a growth rate γ≂√ATkg−βkVa, where Va is the ablation velocity, g is the acceleration, AT=1+O[(kL0)1/ν], and 1

The success of ignition target designs in inertial confinement fusion (ICF) experiments critically depends on the ability to maintain the main fuel entropy at a low level while accelerating the shell to ignition-relevant velocities of V imp > 3 ×107 cm/s. The University of Rochester’s Laboratory for Laser Energetics has been implodingcryogenic deuterium and deuterium–tritium targets on the Omega Laser System for over a decade. Fuel entropy is inferred in these experiment by measuring fuel areal density near peak compression. Measured areal densities up to ⟨ρR⟩n ∼ 300 mg/cm2 (larger than 85 % of predicted values) are demonstrated in the cryogenic implosion with V imp approaching 3 ×107 cm/s and peak laser intensities of 8 ×1014 W/cm2. Scaled to the laser energies available at the National Ignition Facility, implosions, hydrodynamically equivalent to theseOmega designs, are predicted to achieve ⟨ρR⟩n > 1. 2 g/cm2, sufficient for ignition demonstration in direct-drive ICF experiments.

Polar-direct-drive experiments at the National Ignition Facility (NIF) are being used to validate direct-drive-implosion models. Energy coupling and fast-electron preheat are the primary issues being studied in planar and imploding geometries on the NIF. Results from backlit images from implosions indicate that the overall drive is well modeled although some differences remain in the thickness of the imploding shell. Implosion experiments to mitigate cross-beam energy transfer and preheat from two-plasmon decay are planned for the next year.

Understanding and designing inertial confinement fusion (ICF) implosions through radiation-hydrodynamics simulations rely on the accurate knowledge of the equation of state (EOS) of the deuterium and tritium fuels. To minimize the drive energy for ignition, the imploding shell of DT fuel must be kept as cold as possible. Such low-adiabat ICF implosions can access to coupled and degenerate plasma conditions, in which the analytical or chemical EOS models become inaccurate. Using the path-integral Monte Carlo (PIMC) simulations we have derived a first-principles EOS (FPEOS) table of deuterium that covers typical ICF fuel conditions at densities ranging from 0.002 to 1596 g/cm3 and temperatures of 1.35 eV to 5.5 keV. We report the internal energy and the pressure, and discuss the structure of the plasma in terms of pair-correlation functions. When compared with the widely used SESAME table and the revised Kerley03 table, discrepancies in the internal energy and in the pressure are identified for moderately coupled and degenerate plasma conditions. In contrast to the SESAME table, the revised Kerley03 table is in better agreement with our FPEOS results over a wide range of densities and temperatures. Although subtle differences still exist for lower temperatures (T < 10 eV) and moderate densities (1 to 10 g/cc), hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table and the Kerley03 table have resulted in similar results for the peak density, areal density ({\rho}R), and neutron yield, which are significantly different from the SESAME simulations., Comment: 15 pages, 18 figures, 1 long table

Accurate knowledge about the equation of state (EOS) of deuterium is critical to inertial confinement fusion (ICF). Low-adiabat ICF implosions routinely access strongly coupled and degenerate plasma conditions. Using the path integral Monte Carlo method, we have derived a first-principles EOS (FPEOS) table of deuterium. It is the first ab initio EOS table which completely covers typical ICF implosion trajectory in the density and temperature ranges of $\ensuremath{\rho}=0.002--1596\text{ }\text{ }\mathrm{g}/{\mathrm{cm}}^{3}$ and $T=1.35\text{ }\text{ }\mathrm{eV}--5.5\text{ }\text{ }\mathrm{keV}$. Discrepancies in internal energy and pressure have been found in strongly coupled and degenerate regimes with respect to SESAME EOS. Hydrodynamics simulations of cryogenic ICF implosions using the FPEOS table have indicated significant differences in peak density, areal density ($\ensuremath{\rho}R$), and neutron yield relative to SESAME simulations.

The direct-drive, laser-based approach to inertial confinement fusion (ICF) is reviewed from its inception following the demonstration of the first laser to its implementation on the present generation of high-power lasers. The review focuses on the evolution of scientific understanding gained from target-physics experiments in many areas, identifying problems that were demonstrated and the solutions implemented. The review starts with the basic understanding of laser–plasma interactions that was obtained before the declassification of laser-induced compression in the early 1970s and continues with the compression experiments using infrared lasers in the late 1970s that produced thermonuclear neutrons. The problem of suprathermal electrons and the target preheat that they caused, associated with the infrared laser wavelength, led to lasers being built after 1980 to operate at shorter wavelengths, especially 0.35 μm—the third harmonic of the Nd:glass laser—and 0.248 μm (the KrF gas laser). The main physics areas relevant to direct drive are reviewed. The primary absorption mechanism at short wavelengths is classical inverse bremsstrahlung. Nonuniformities imprinted on the target by laser irradiation have been addressed by the development of a number of beam-smoothing techniques and imprint-mitigation strategies. The effects of hydrodynamic instabilities are mitigated by a combination of imprint reduction and target designs that minimize the instability growth rates. Several coronal plasma physics processes are reviewed. The two-plasmon–decay instability, stimulated Brillouin scattering (together with cross-beam energy transfer), and (possibly) stimulated Raman scattering are identified as potential concerns, placing constraints on the laser intensities used in target designs, while other processes (self-focusing and filamentation, the parametric decay instability, and magnetic fields), once considered important, are now of lesser concern for mainline direct-drive target concepts. Filamentation is largely suppressed by beam smoothing. Thermal transport modeling, important to the interpretation of experiments and to target design, has been found to be nonlocal in nature. Advances in shock timing and equation-of-state measurements relevant to direct-drive ICF are reported. Room-temperature implosions have provided an increased understanding of the importance of stability and uniformity. The evolution of cryogenic implosion capabilities, leading to an extensive series carried out on the 60-beam OMEGA laser [Boehly et al., Opt. Commun. 133, 495 (1997)], is reviewed together with major advances in cryogenic target formation. A polar-drive concept has been developed that will enable direct-drive–ignition experiments to be performed on the National Ignition Facility [Haynam et al., Appl. Opt. 46(16), 3276 (2007)]. The advantages offered by the alternative approaches of fast ignition and shock ignition and the issues associated with these concepts are described. The lessons learned from target-physics and implosion experiments are taken into account in ignition and high-gain target designs for laser wavelengths of 1/3 μm and 1/4 μm. Substantial advances in direct-drive inertial fusion reactor concepts are reviewed. Overall, the progress in scientific understanding over the past five decades has been enormous, to the point that inertial fusion energy using direct drive shows significant promise as a future environmentally attractive energy source.

Effects of temporal density variation and spherical convergence on the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability are studied using an analytical model based on Layzer's theory [Astrophys. J. 122, 1 (1955)]. When the temporal density variation is included, the bubble amplitude in planar geometry is shown to asymptote to (bu(t))U{sub L}(t'){rho}(t')dt'/{rho}(t), where U{sub L}={radical}(g/(C{sub g}k)) is the Layzer bubble velocity, {rho} is the fluid density, and C{sub g}=3 and C{sub g}=1 for the two- and three-dimensional geometries, respectively. The asymptotic bubble amplitude in a converging spherical shell is predicted to evolve as {eta}{approx}{bar {eta}}m{sup -} |r{sub 0}|/{ell}U{sub L}{sup sp}-{bar {eta}}/r{sub 0}, where r{sub 0} is the outer shell radius, {eta}(t)=(bu(t))U{sub L}{sup sp}(t'){rho}(t')r{sub 0}{sup 2}(t')dt{sup '}/{rho}(t)r{sub 0}{sup 2}(t), U{sub L}{sup sp}={radical}(-re{sub 0}(t)r{sub 0}(t)/l), m(t)={rho}(t)r{sub 0}{sup 3}(t), and l is the mode number.

An analytical model of the nonlinear bubble evolution of single-mode, classical Rayleigh-Taylor instability at arbitrary Atwood numbers $({A}_{T})$ is presented. The model is based on an extension of Layzer's theory [Astrophys. J. 122, 1 (1955)] previously applied only to the fluid-vacuum interfaces $({A}_{T}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1)$. The model provides a continuous bubble evolution from the earlier exponential growth to the nonlinear regime when the bubble velocity saturates at ${U}_{b}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}\sqrt{{2A}_{T}/({1+A}_{T})({g/C}_{g}k)}$, where $k$ is the perturbation wave number, $g$ is the interface acceleration, and ${C}_{g}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3$ and ${C}_{g}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1$ for the two-dimensional and three-dimensional geometries, respectively.

The evolution of shell modulations near peak compression of direct-drive spherical-target implosions has been measured using the 60-beam, 30-kJ UV OMEGA laser system. The spatial size and amplitude of shell-areal-density modulations decrease during the target compression, then increase during its decompression as expected. The shell uniformity at peak compression has been increased by reducing single-beam, laser-drive nonuniformity.

Radiative hydrodynamic simulations of implosion experiments on the OMEGA laser system [Boehly et al., Opt. Commun. 133, 495 (1997)] show that energy transfer between crossing laser beams can reduce laser absorption by 10%–20%. A new quantitative model for the crossed-beam energy transfer has been developed, allowing one to simulate the coupling of multiple beams in the expanding corona of implosion targets. Scattered-light and bang-time measurements show good agreement with predictions of this model when nonlocal heat transport is employed. The laser absorption can be increased by narrowing laser beams and/or employing two-color light, which both reduce the crossed-beam energy transfer.

This paper examines the Krook model as a means of quantifying the problem of nonlocal transport of electron energy in laser produced plasmas. The result is an expression for the nonlocal electron energy flux q. The roles of both flux limitation and preheat are clearly delineated. Furthermore, it develops a test for the validity of this model. This is a physics based, “first principles” model that can be economically incorporated into a fluid simulation.

Shock ignition is a two-step inertial confinement fusion concept where a strong shock wave is launched at the end of the laser pulse to ignite the compressed core of a low-velocity implosion. Initial shock-ignition technique experiments were performed at the OMEGA Laser Facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] using 40-μm-thick, 0.9-mm-diam, warm surrogate plastic shells filled with deuterium gas. The experiments showed a significant improvement in the performance of low-adiabat, low-velocity implosions compared to conventional “hot-spot” implosions. High areal densities with average values exceeding ∼0.2g∕cm2 and peak areal densities above 0.3g∕cm2 were measured, which is in good agreement with one-dimensional hydrodynamical simulation predictions. Shock-ignition technique implosions with cryogenic deuterium and deuterium-tritium ice shells produced areal densities close to the 1D prediction and achieved up to 12% of the predicted 1D fusion yield.

Excessive increase in the shell entropy and degradation from spherical symmetry in inertial confinement fusion implosions limit shell compression and could impede ignition. The entropy is controlled by accurately timing shock waves launched into the shell at an early stage of an implosion. The seeding of the Rayleigh-Taylor instability, the main source of the asymmetry growth, is also set at early times during the shock transit across the shell. In this paper we model the shock timing and early perturbation growth of directly driven targets measured on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)]. By analyzing the distortion evolution, it is shown that one of the main parameters characterizing the growth is the size of the conduction zone Dc, defined as a distance between the ablation front and the laser deposition region. Modes with kDc>1 are stable and experience oscillatory behavior [V. N. Goncharov, Phys. Rev. Lett. 82, 2091 (1999)]. The model shows that the main stabiliz...

Multidimensional hydrodynamic properties of high-adiabat direct-drive plastic-shell implosions on the OMEGA laser system [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] are investigated using the multidimensional hydrodynamic code, DRACO [D. Keller et al., Bull. Am. Phys. Soc. 44, 37 (1999)]. Multimode simulations including the effects of nonuniform illumination and target roughness indicate that shell stability during the acceleration phase plays a critical role in determining target performance. For thick shells that remain integral during the acceleration phase, target yields are significantly reduced by the combination of the long-wavelength (l

The performance of triple-picket deuterium-tritium cryogenic target designs on the OMEGA Laser System [T. R. Boehly, Opt. Commun. 133, 495 (1997)] is reported. These designs facilitate control of shock heating in low-adiabat inertial confinement fusion targets. Areal densities up to 300 mg/cm2 (the highest ever measured in cryogenic deuterium-tritium implosions) are inferred in the experiments with an implosion velocity approximately 3x10(7) cm/s driven at peak laser intensities of 8x10(14) W/cm2. Extension of these designs to ignition on the National Ignition Facility [J. A. Paisner, Laser Focus World 30, 75 (1994)] is presented.