First-principles equation of state of polystyrene and its effect on inertial confinement fusion implosions.

Obtaining an accurate equation of state (EOS) of polystyrene (CH) is crucial to reliably design inertial confinement fusion (ICF) capsules using CH/CH-based ablators. With first-principles calculations, we have investigated the extended EOS of CH over a wide range of plasma conditions (ρ=0.1to100g/cm(3) and T=1000 to 4,000,000 K). When compared with the widely used SESAME-EOS table, the first-principles equation of state (FPEOS) of CH has shown significant differences in the low-temperature regime, in which strong coupling and electron degeneracy play an essential role in determining plasma properties. Hydrodynamic simulations of cryogenic target implosions on OMEGA using the FPEOS table of CH have predicted ∼30% decrease in neutron yield in comparison with the usual SESAME simulations. This is attributed to the ∼5% reduction in implosion velocity that is caused by the ∼10% lower mass ablation rate of CH predicted by FPEOS. Simulations using CH-FPEOS show better agreement with measurements of Hugoniot temperature and scattered light from ICF implosions.

First-principles opacity table of warm dense deuterium for inertial-confinement-fusion applications.

Accurate knowledge of the optical properties of a warm dense deuterium-tritium (DT) mixture is important for reliable design of inertial confinement fusion (ICF) implosions using radiation-hydrodynamics simulations. The opacity of a warm dense DT shell essentially determines how much radiation from hot coronal plasmas can be deposited in the DT fuel of an imploding capsule. Even for the simplest species of hydrogen, the accurate calculation of their opacities remains a challenge in the warm-dense matter regime because strong-coupling and quantum effects play an important role in such plasmas. With quantum-molecular-dynamics (QMD) simulations, we have derived a first-principles opacity table (FPOT) of deuterium (and the DT mixture by mass scaling) for a wide range of densities from ρ(D)=0.5 to 673.518g/cm(3) and temperatures from T=5000K up to the Fermi temperature T(F) for each density. Compared with results from the astrophysics opacity table (AOT) currently used in our hydrocodes, the FPOT of deuterium from our QMD calculations has shown a significant increase in opacity for strongly coupled and degenerate plasma conditions by a factor of 3-100 in the ICF-relevant photon-energy range. As conditions approach those of classical plasma, the opacity from the FPOT converges to the corresponding values of the AOT. By implementing the FPOT of deuterium and the DT mixture into our hydrocodes, we have performed radiation-hydrodynamics simulations for low-adiabat cryogenic DT implosions on the OMEGA laser and for direct-drive-ignition designs for the National Ignition Facility. The simulation results using the FPOT show that the target performance (in terms of neutron yield and energy gain) could vary from ∼10% up to a factor of ∼2 depending on the adiabat of the imploding DT capsule; the lower the adiabat, the more variation is seen in the prediction of target performance when compared to the AOT modeling.

Exploration of the transition from the hydrodynamiclike to the strongly kinetic regime in shock-driven implosions.

Clear evidence of the transition from hydrodynamiclike to strongly kinetic shock-driven implosions is, for the first time, revealed and quantitatively assessed. Implosions with a range of initial equimolar D3He gas densities show that as the density is decreased, hydrodynamic simulations strongly diverge from and increasingly overpredict the observed nuclear yields, from a factor of ∼2 at 3.1 mg/cm3 to a factor of 100 at 0.14 mg/cm3. (The corresponding Knudsen number, the ratio of ion mean-free path to minimum shell radius, varied from 0.3 to 9; similarly, the ratio of fusion burn duration to ion diffusion time, another figure of merit of kinetic effects, varied from 0.3 to 14.) This result is shown to be unrelated to the effects of hydrodynamic mix. As a first step to garner insight into this transition, a reduced ion kinetic (RIK) model that includes gradient-diffusion and loss-term approximations to several transport processes was implemented within the framework of a one-dimensional radiation-transport code. After empirical calibration, the RIK simulations reproduce the observed yield trends, largely as a result of ion diffusion and the depletion of the reacting tail ions.

First-principles thermal conductivity of warm-dense deuterium plasmas for inertial confinement fusion applications.

Thermal conductivity (κ) of both the ablator materials and deuterium-tritium (DT) fuel plays an important role in understanding and designing inertial confinement fusion (ICF) implosions. The extensively used Spitzer model for thermal conduction in ideal plasmas breaks down for high-density, low-temperature shells that are compressed by shocks and spherical convergence in imploding targets. A variety of thermal-conductivity models have been proposed for ICF hydrodynamic simulations of such coupled and degenerate plasmas. The accuracy of these κ models for DT plasmas has recently been tested against first-principles calculations using the quantum molecular-dynamics (QMD) method; although mainly for high densities (ρ > 100 g/cm3), large discrepancies in κ have been identified for the peak-compression conditions in ICF. To cover the wide range of density-temperature conditions undergone by ICF imploding fuel shells, we have performed QMD calculations of κ for a variety of deuterium densities of ρ = 1.0 to 673.518 g/cm3, at temperatures varying from T = 5 × 103 K to T = 8 × 106 K. The resulting κQMD of deuterium is fitted with a polynomial function of the coupling and degeneracy parameters Γ and θ, which can then be used in hydrodynamic simulation codes. Compared with the "hybrid" Spitzer-Lee-More model currently adopted in our hydrocode lilac, the hydrosimulations using the fitted κQMD have shown up to ∼20% variations in predicting target performance for different ICF implosions on OMEGA and direct-drive-ignition designs for the National Ignition Facility (NIF). The lower the adiabat of an imploding shell, the more variations in predicting target performance using κQMD. Moreover, the use of κQMD also modifies the shock conditions and the density-temperature profiles of the imploding shell at early implosion stage, which predominantly affects the final target performance. This is in contrast to the previous speculation that κQMD changes mainly the inside ablation process during the hot-spot formation of an ICF implosion.

Laser-beam zooming to mitigate crossed-beam energy losses in direct-drive implosions.

Spherically symmetric direct-drive-ignition designs driven by laser beams with a focal-spot size nearly equal to the target diameter suffer from energy losses due to crossed-beam energy transfer (CBET). Significant reduction of CBET and improvements in implosion hydrodynamic efficiency can be achieved by reducing the beam diameter. Narrow beams increase low-mode perturbations of the targets because of decreased illumination uniformity that degrades implosion performance. Initiating an implosion with nominal beams (equal in size to the target diameter) and reducing the beam diameter by ∼ 30%-40% after developing a sufficiently thick target corona, which smooths the perturbations, mitigate CBET while maintaining low-mode target uniformity in ignition designs with a fusion gain ≫ 1.

Mitigating laser imprint in direct-drive inertial confinement fusion implosions with high-Z dopants.

Nonuniformities seeded by both long- and short-wavelength laser perturbations can grow via Rayleigh-Taylor (RT) instability in direct-drive inertial confinement fusion, leading to performance reduction in low-adiabat implosions. To mitigate the effect of laser imprinting on target performance, spherical RT experiments have been performed on OMEGA using Si- or Ge-doped plastic targets in a cone-in-shell configuration. Compared to a pure plastic target, radiation preheating from these high-Z dopants (Si/Ge) increases the ablation velocity and the standoff distance between the ablation front and laser-deposition region, thereby reducing both the imprinting efficiency and the RT growth rate. Experiments showed a factor of 2-3 reduction in the laser-imprinting efficiency and a reduced RT growth rate, leading to significant (3-5 times) reduction in the σ(rms) of shell ρR modulation for Si- or Ge-doped targets. These features are reproduced by radiation-hydrodynamics simulations using the two-dimensional hydrocode DRACO.

Strong coupling and degeneracy effects in inertial confinement fusion implosions.

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 ρ=0.002-1596 g/cm3 and T=1.35 eV-5.5 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 (ρR), and neutron yield relative to SESAME simulations.

Demonstration of the highest deuterium-tritium areal density using multiple-picket cryogenic designs on OMEGA.

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.

Validation of thermal-transport modeling with direct-drive, planar-foil acceleration experiments on OMEGA.

We present for the first time the experimental validation of the nonlocal thermal-transport model for a National Ignition Facility relevant laser intensity of approximately 10(15) W/cm(2) on OMEGA. The measured thin target trajectories are in good agreement with predictions based on the nonlocal model over the full range of laser intensities from 2 x 10(14) to 10(15) W/cm(2}) The standard local thermal-transport model with a constant flux limiter of 0.06 disagrees with experimental measurements at a high intensity of approximately 10(15) W/cm(2) but agrees at lower intensities. These results show the significance of nonlocal effects for direct-drive ignition designs.

Studies of plastic-ablator compressibility for direct-drive inertial confinement fusion on OMEGA.

The compression of planar plastic targets was studied with x-ray radiography in the range of laser intensities of I approximately 0.5 to 1.5x10(15) W/cm2 using square (low-compression) and shaped (high-compression) pulses. Two-dimensional simulations with the radiative hydrocode DRACO show good agreement with measurements at laser intensities up to I approximately 10(15) W/cm2. These results provide the first experimental evidence for low-entropy, adiabatic compression of plastic shells in the laser intensity regime relevant to direct-drive inertial confinement fusion. A density reduction near the end of the drive at a high intensity of I approximately 1.5x10(15) W/cm2 has been correlated with the hard x-ray signal caused by hot electrons from two-plasmon-decay instability.

Role of hot-electron preheating in the compression of direct-drive imploding targets with cryogenic D2 ablators.

The compression of direct-drive, spherical implosions is studied using cryogenic D2 targets on the 60-beam, 351-nm OMEGA laser with intensities ranging from approximately 3x10(14) to approximately 1x10(15) W/cm2. The hard-x-ray signal from hot electrons generated by laser-plasma instabilities increases with laser intensity, while the areal density decreases. Mitigating hot-electron production, by reducing the laser intensity to approximately 3x10(14) W/cm2, results in areal density of the order of approximately 140 mg/cm2, in good agreement with 1D simulations. These results will be considered in future direct-drive-ignition designs.

High-areal-density fuel assembly in direct-drive cryogenic implosions.

The first observation of ignition-relevant areal-density deuterium from implosions of capsules with cryogenic fuel layers at ignition-relevant adiabats is reported. The experiments were performed on the 60-beam, 30-kJUV OMEGA Laser System [T. R. Boehly, Opt. Commun. 133, 495 (1997)10.1016/S0030-4018(96)00325-2]. Neutron-averaged areal densities of 202+/-7 mg/cm2 and 182+/-7 mg/cm2 (corresponding to estimated peak fuel densities in excess of 100 g/cm3) were inferred using an 18-kJ direct-drive pulse designed to put the converging fuel on an adiabat of 2.5. These areal densities are in good agreement with the predictions of hydrodynamic simulations indicating that the fuel adiabat can be accurately controlled under ignition-relevant conditions.

Dependence of shell mix on feedthrough in direct drive inertial confinement fusion.

The mixing of cold, high-density shell plasma with the low-density, hot spot plasma by the Rayleigh-Taylor instability in inertial confinement fusion is experimentally shown to correlate with the calculated perturbation feedthrough from the ablation surface to the inner shell surface. A fourfold decrease in the density of shell material in the mix region of direct drive implosions of gas filled spherical plastic shells having predicted convergence ratios approximately 15 was observed when laser imprint levels were reduced and the initial shell was thicker, corresponding to a reduction in the feedthrough rms level by a factor of 6. Shell mix is also shown to limit the spherical compression of the implosion.

Time-dependent electron thermal flux inhibition in direct-drive laser implosions.

We simulate direct-drive CH target implosions with square laser pulses by a one-dimensional Fokker-Planck solver combined with a hydrodynamic code, and compare the results with those simulated by the flux-limited Spitzer-Härm model. We find that the electron thermal flux inhibition is time dependent, resulting in longer density scale length, larger laser absorption, and smaller growth of Rayleigh-Taylor instability. The time of peak neutron production calculated from Fokker-Planck simulations agrees with experiments for both 1-ns and 400-ps pulses.

Shell mix in the compressed core of spherical implosions.

The Rayleigh-Taylor instability in its highly nonlinear, turbulent stage causes atomic-scale mixing of the shell material with the fuel in the compressed core of inertial-confinement fusion targets. The density of shell material mixed into the outer core of direct-drive plastic-shell spherical-target implosions on the 60-beam, OMEGA laser system is estimated to be 3.4(+/-1.2) g/cm(3) from time-resolved x-ray spectroscopy, charged-particle spectroscopy, and core x-ray images. The estimated fuel density, 3.6(+/-1) g/cm(3), accounts for only approximately 50% of the neutron-burn-averaged electron density, n(e)=2.2(+/-0.4)x10(24) cm(-3).