Session TI1: Ignition Target Design and Laser-Plasma Instabilities

Robustness studies of NIF ignition targets in two dimensions

Inertial confinement fusion capsules are critically dependent on the integrity of their hot spots to ignite. At the time of ignition, only a certain fractional perturbation of the nominally spherical hot spot boundary can be tolerated and the capsule still achieve ignition. The degree to which the expected hot spot perturbation in any given capsule design is less than this maximum tolerable perturbation is a measure of the ignition margin or robustness of that design. Moreover, since there will inevitably be uncertainties in the initial character and implosion dynamics of any given capsule, all of which can contribute to the eventual hot spot perturbation, quantifying the robustness of that capsule against a range of parameter variations is an important consideration in the capsule design. Here, the robustness of the 300 eV indirect drive target design for the National Ignition Facility (NIF) [J. D. Lindl, {\it et. al.}, Phys. Plasmas {\bf 11}, 339 (2004)] is studied in the parameter space of inner ice roughness, implosion velocity, and capsule scale. A suite of two thousand two-dimensional simulations, run with the radiation hydrodynamics code Lasnex, is used as the data base for the study. For each scale, an ignition region in the two remaining variables is identified and the ``ignition cliff'' is mapped. In accordance with the theoretical arguments of W. K. Levedahl and J. D. Lindl [Nucl. Fusion {\bf 37}, 165 (1997)] and R. Kishony and D. Shvarts [Phys. Plasmas {\bf 8}, 4925 (2001)], the location of this cliff is fitted to a power law of the capsule implosion velocity and scale. It is found that the cliff can be quite well represented in this power law form, and, using this scaling law, an assessment of the overall (one- and two-dimensional) ignition margin of the design can be made. The effect on the ignition margin of an increase or decrease in the density of the target fill gas is also assessed.   

Multi-Variable Sensitivity Studies of NIF Ignition Targets

Performance of indirect drive ignition targets planned for the National Ignition Facility has been studied with multi-variable sensitivity studies. Large numbers of simulations are run, in each of which a number of parameters are set from statistical ensembles intended to represent expected variations in the variables describing the target. Parameters varied include target dimensions, compositions, densities, laser pulse variations, variations in the hohlraum parameters as they determine pulse shaping and symmetry variations, surface roughness, intrinsic hohlraum asymmetry, beam-to-beam power imbalance, and pointing errors. Statistical samples are very large (10,000) for variations of the 1D spherical implosion, and large enough for meaningful statistics (a few hundred runs) for the 2D variations. The overall performance trends can be quite well predicted from a model that uses second order Taylor series to calculate the implosion velocity and DT fuel entropy, as functions of the target variables. The statistical variations allow us to address quantitatively questions such as ``What is the distribution function describing the probability of ignition, given expected shot-to-shot variations in the parameters describing the experiment?''   

Ignition Capsule Design with a High-Density Carbon (HDC) Ablator for the National Ignition Facility (NIF)

An ignition capsule with a nano-crystalline, high density, carbon ablator is emerging as a promising alternative target for NIF. There are four main advantages in using the HDC ablator. First, for a given outer radius, the HDC ablator absorbs more hohlraum-driven x-ray energy than for a beryllium ablator. Second, the HDC ablator will have smaller and more uniform crystalline grains than beryllium, enabling more isotropic shock propagation. Third, the higher density reduces the coupling of the DT ice surface and the ablator/ice interface from the unstable ablation front, thereby reducing the growth of the surface perturbations seeded by ice roughness and inner-shell roughness. Fourth, material strength of the HDC can reduce instability growth at early times. Possible - though surmountable - challenges include: (1) The ice surface might in fact be rougher because of differences in the beta-layering in HDC vs Beryllium. (2) The need for smoother outer ablator surfaces because of slightly lower ablation rates, and larger mass perturbations for a given surface roughness. (3) Ensuring that the HDC does not spend time in a partially melted state in which density or velocity variations could seed Rayleigh-Taylor instabilities, the 2nd shock should completely melt the HDC ablator. LASNEX design simulations show good 1-D performance and overall favorable 2-D stability behavior. In particular, the ablator is completely melted upon the arrival of the 2nd shock, the capsule can tolerate about twice as rough a DT ice surface as with Beryllium, and instability growth is reduced by material-strength in the HDC ablator.   

Analyses of laser-plasma interactions in National Ignition Facility (NIF) ignition targets

Achieving indirect drive ignition on NIF requires hohlraum targets (high-Z cylinders) that provide good symmetry with acceptable energetics. In these first ignition targets we have elected to optimize ignition hohlraums in a linear regime for laser-plasma interactions (LPI), i.e. where laser light resonantly scatters off linear ion acoustic or electron plasma waves. In this regime we can quantitatively analyze how backscatter affects propagation and deposition of the laser beams within the target. We use pF3D\footnote{R. L. Berger, C. H. Still, E. A. Williams, and A. B. Langdon, \textit{Phys. Plasmas} \textbf{5}, 4337 (1998).} to calculate the reflectivity and deposition profile along a laser beam path in our ignition designs. pF3D is a wave optics beam propagation code designed to model stimulated scatter in the linear regime. It has recently been shown to successfully model NIF-relevant LPI experiments shot on the Omega laser. Unprecedented simulations of whole and near-whole laser beam propagation in ignition targets have been performed. These simulations propagate a realistic laser beam from where it enters the target to the target wall, and include both axial and transverse gradients in the plasma profiles. Such calculations are massively parallel, requiring more than 8000 cpus. We present simulations of 300 eV, 285 eV and 270 eV ignition designs driven at 1 to 1.3 MJ of laser energy at wavelength 351 nm. We discuss the total reflectivity, importance of ensuring good speckle statistics and show the role of re-absorption of the backscattered light on the laser energy deposition rate.   

Predictive modeling of Omega Laser Plasma Interaction Experiment

We have developed a new target platform to study Laser Plasma Interaction in ignition-relevant condition at the Omega laser facility (LLE/Rochester)[1]. By shooting an interaction beam along the axis of a gas-filled hohlraum heated by 15 kJ of heater beam energy, we were able to create a millimeter-scale underdense uniform plasma at electron temperatures above 3 keV. Extensive Thomson scattering measurements allowed to benchmark our hydrodynamic simulations performed with HYDRA [1]. As a result of this effort, we can use with much confidence these simulations as input parameters for our LPI simulation code pF3d [2]. The variety of LPI measurements performed (Stimulated Brillouin and Raman backscattering both in the lens (FABS) and outside (NBI), transmitted light image and energy) allows for a constraining test of our LPI predictive capabilities. We will show that by using accurate hydrodynamic profiles and full three dimensional simulations (see Fig. 1) including a realistic modeling of the laser intensity pattern generated by various smoothing options, linear LPI theory reproduces a variety of measured quantities, including SBS thresholds and absolute reflectivity values, beam spray and the absence of measurable SRS. We will also discuss the effect of beam smoothing techniques (Polarization smoothing, spectral dispersion) on SBS in these targets and compare to experimental data. This good agreement was made possible by the recent increase in computing power routinely available for such simulations, coupled to a detailed description of both plasma and laser parameters. \newline \newline [1] Phys. Plasmas \textbf{14}, 056304~(2007); Phys. Plasmas \textbf{14}, 055705 (2007) \newline [2] Phys. Plasmas 5, 4337 (1998)   

Suppression of Stimulated Brillouin Scattering in multiple-ion species inertial confinement fusion Hohlraum Plasmas.

Understanding and control of laser coupling into high-electron temperature hohlraums is important for the success of the indirect-drive approach to inertial confinement fusion (ICF). Parametric instabilities such as stimulated Brillouin scattering (SBS) and stimulated Raman scattering (SRS) can backscatter the incident laser light reducing the total drive energy and affecting radiation symmetry. Consequently, recent hohlraum designs for indirect-drive ignition on the National Ignition Facility investigate wall liner material options so that the linear gain for parametric instabilities will be below threshold for the onset SBS. Increasing the Landau damping of acoustic waves by employing multiple-ion species plasmas offers the perspective of controlling SBS. Although the effect of two-ion species plasmas on Landau damping has been directly observed with Thomson scattering, early experiments on SBS in these plasmas have suffered from competing non-linear effects or laser beam filamentation. In this study, a reduction of SBS in multiple-ion species hohlraum plasmas to below the percent level has been demonstrated. By adding a low-mass ion species (Hydrogen) to a CO2 hohlraum gas fill, the SBS reflectivity was reduced by 3 orders of magnitude. The reduction in the total backscattered energy resulted in an increase of the hohlraum radiation temperature indicating improved coupling of the heater beams. These observations may be scaled to the plasma conditions within ignition scale hohlraums and support employing multiple-ion species plasmas in target designs for the first attempt at ignition on the National Ignition Facility.