Session PO4: Inertial Confinement Fusion II

Interpreting the peak shape of a neutron spectrum

The width of the DT or DD peak in a neutron spectrum has long been used to measure ion temperature in burning plasmas. We relate the moments of the neutron spectrum observed along a given line of sight to moments of the fluid temperature and velocity distributions. The variance of the spectral peak depends not only on the mean fluid temperature, but also on the variance of the fluid velocity. A mean fluid velocity shifts the peak centroid, correlations between fluid temperature and velocity skew the peak, and the variance of the fluid temperature distribution produces kurtosis in the peak. Hydrodynamic simulations of implosions predict that burn occurs over a broad distribution of fluid temperatures, which should produce observable kurtosis of order 0.25 in typical laser fusion implosions.   

Predicted ICF Neutron Spectrum Corrections from Simulation

Produced neutron spectra have long been used as a diagnostic of ICF implosions. The neutron spectrum width is characteristic of the burn temperature as well as the variance of the burning region's fluid motion.\footnote{H.~Brysk,~\textit{Plasma Phys.}, Vol. 15, pp. 611-617 (1973).}$^,$\footnote{L.~Ballabio, J.~Kallne, G.~Gorini,~\textit{Nuclear Fusion}, Vol. 38, No. 11, (1998).} Corrections to higher moments of the spectrum are thought to be diagnostic as well.\footnote{D.~Munro, manuscript in preparation.} Because of the large neutron fluxes at the NIF, we expect to have the opportunity to measure these corrections and compare with simulation. We will discuss a post-process platform that we have built for extracting these moment corrections as well as many other extensive quantities from the hydrodynamic simulations, and report on the predicted neutron spectrum corrections recently calculated for a large suite of implosion simulations in one, two, and three dimensions with varying drive symmetry and overall convergence ratio. We are particularly interested in the observable effects on the neutron spectrum along different lines of sight from the dimensional symmetry constraint in the simulated hydrodynamics.   

Impact of flows on ion temperatures inferred from neutron spectra produced in NIF DT implosions

Neutron spectrometers on the NIF provide accurate, directional information of the DT and DD neutron spectra from layered DT implosions. Traditionally, ion temperatures ($T_{ion})$, essential for assessing conditions in the hotspot of the implosions, are inferred from the broadening of primary neutron spectra. Directional motion (flow) of the fuel at burn also impacts broadening and may lead to artificially inflated ``$T_{ion}$'' values. We examine NIF neutron spectra to assess the impact of flows on measured $T_{ion}$. Measured DT $T_{ion}$ is consistently higher than measured DD $T_{ion}$, which suggests that significant energy is lost to radial or turbulent kinetic fuel motion at peak burn. However, explaining the full observed $T_{ion}$ difference with fuel motion, as calculated from a Ballabio\footnote{Ballabio et al., Nucl. Fusion \textbf{38}, 1723 (1998).} and Murphy\footnote{Murphy, Phys. Plasmas \textbf{21}, 072701 (2014).} analysis, leads to a thermal $T_{ion}$ too low to explain observed yields. These results have improved our understanding of hotspot formation and the concept of ``stagnation'' in layered NIF implosions.   

Neutron Yield and Ion Temperature from DD and DT Fusion in National Ignition Facility High-Foot Implosions

Simultaneous measures of neutrons emitted from DT fusion implosions are postulated to provide insight into the fuel conditions during neutron emission.\footnote{B. Appelbe and J. Chittenden, Plasma Phys. Control. Fusion \textbf{53}, 045002 (2011).}$^{,}$\footnote{T. J. Murphy, Phys. Plasmas \textbf{21}, 072701 (2014).} Neutron spectral diagnostics of National Ignition Facility ``high-foot'' implosions measure both the DT and DD fusion neutron spectra. Equivalent ion temperature is measured from the width of the DT and DD neutron emission and the respective yields from the peak areas. This work has focused on reasons for differing inferred temperatures from the DT and DD spectra and the yield ratio. Spatial and temporal averages of the DT and DD reactivities as corrections to the homogeneous and static temperature distributions are shown. This material is based upon work supported by the Department of Energy National Nuclear Security Administration under Award Number DE-NA0001944.   

Method of Moments Applied to the Analysis of Precision Spectra from the Neutron Time-of- flight Diagnostics at the National Ignition Facility

The method of moments was introduced by Pearson as a process for estimating the population distributions from which a set of ``random variables'' are measured. These moments are compared with a parameterization of the distributions, or of the same quantities generated by simulations of the process. Most diagnostics processes extract scalar parameters depending on the moments of spectra derived from analytic solutions to the fusion rate, necessarily based on simplifying assumptions of the confined plasma. The precision of the TOF spectra, and the nature of the implosions at the NIF require the inclusion of factors beyond the traditional analysis and require the addition of higher order moments to describe the data. This talk will present a diagnostic process for extracting the moments of the neutron energy spectrum for a comparison with theoretical considerations as well as simulations of the implosions.   

Analysis of fusion neutron spectral widths in high-foot implosions at the National Ignition Facility

We present the latest results of thermal temperature analyses of cryogenically layered deuterium-tritium implosions at the NIF using data from the ``High Foot'' campaign.\footnote{Hurricane, O. et al., Phys. Plasmas, {\bf 21} 056314 (2014)} Data from new analysis methods\footnote{Hatarik R. et al., Hartouni, E. et al. these proc.} and interpreted in the context of new theoretical developments\footnote{Munro D. et al. and Field, J. et al. these proceedings} will be reported. These data will include DD and DT apparent ion temperatures, their uniformity with direction, inferred plasma thermal temperature, as well as the magnitude of non-thermal contributions to the spectral widths.   

Analysis of fusion neutron spectra and the importance of 6 dimensional effects in ``high-foot'' implosions at the National Ignition Facility

High convergence implosions introduce a number of factors having significant effects on the analysis of high precision reactant neutron time-of-flight (TOF) spectra at the NIF. Low mode perturbations of both the spatial and velocity distributions of the hot-spot and the cold-fuel are measurable in this data set. We report on the analysis performed to date including the line-of-sight (LOS) variation of ``standard observables'' (e.g. the yield and ion temperature) as well as new analysis extracting the bulk hot-spot velocity and the hot-spot velocity variance. These observations indicate that the assumption of isotropy of reactant neutrons can no longer provide an accurate description of the data. Preliminary analysis of the NIF ``high foot'' campaign data will be reported. We will describe the direction of future nuclear diagnostic techniques.   

A derivation of bulk-motion insensitive implosion metrics inferred from neutron and high-energy x-ray emission in a series of high yield implosions on the NIF

A suite of nuclear and x-ray data is used to deduce key implosion performance metrics at stagnation including the hotspot pressure, energy, and the role of alpha heating on producing the observed yield. Key to this analysis is a determination of the burn-averaged temperature of the hot plasma so that the nuclear reactivity and yield can then be used to deduce the plasma density and pressure. In this presentation we examine the systematics of both neutron and high-energy x-ray emission (22 keV x-ray monochromator) from a series of high yield implosions on the NIF. The advantage of incorporating high energy x-rays into the analysis is their insignificant attenuation and insensitivity to bulk flows, thus providing insight as to whether these effects complicate the interpretation of the nuclear data, and that a precipitous drop in their production is expected as the thermal temperature is reduced. A dynamic model for hotspot assembly is developed that incorporates thermal conduction, radiative losses, and alpha heating, which simultaneously matches both neutron and x-ray data with nearly identical nuclear and x-ray derived thermal temperatures. *Work performed under the auspices of the USDoE by Lawrence Livermore National Laboratory under contract DE-AC52-07NA273.   

Measuring the stagnation phase of NIF implosions: reproducibility and intentional asymmetry

We report here data from a 5-shot sequence of cryogenic DT layered implosions designed to measure NIF implosion stagnation, the reproducibility of stagnation, and the response of the stagnation phase to intentional perturbation. We emphasize new analysis of the neutron spectral moments. These features provide an experimental measurement of hot spot thermal (temperature) and fluid (residual flow) processes. They also provide strong constraints for code validation. In implosions that were intentionally perturbed by laser drive and DT layer asymmetry, the experimental measurements show clear signs of the damaged stagnation. These signatures also match well our expectations from simulation, reproducing the variation of apparent temperature with line of sight and the down scattered neutron ratio, among others. The suite of implosions provides a demonstration of our ability to measure stagnated flow performance and highlights the several precision diagnostic signatures that are correctly captured by radhydro codes. This work was performed by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344.   

Data driven models of the performance and repeatability of NIF high foot implosions

Recent high foot (HF) inertial confinement fusion (ICF) experiments performed at the national ignition facility (NIF) have consisted of enough laser shots that a data-driven analysis of capsule performance is feasible. In this work we use 20-30 individual implosions of similar design, spanning laser drive energies from 1.2 to 1.8 MJ, to quantify our current understanding of the behavior of HF ICF implosions. We develop a probabilistic model for the projected performance of a given implosion and use it to quantify uncertainties in predicted performance including shot-shot variations and observation uncertainties. We investigate the statistical significance of the observed performance differences between different laser pulse shapes, ablator materials, and capsule designs. Finally, using a cross-validation technique, we demonstrate that 5-10 repeated shots of a similar design are required before real trends in the data can be distinguished from shot-shot variations.   

Implosion Robustness, Time-Dependent Flux Asymmetries and Big Data

Both direct and indirect drive inertial confinement fusion rely on the formation of spherical implosions, which can be a challenge under temporal and spatial drive variations (either from discrete laser beams, a complex hohlraum radiation environment, or both). To that end, we examine the use of large simulation databases of 2D capsule implosions to determine the sensitivity of indirectly driven NIF designs to time-varying low-mode radiation drive asymmetries at varying convergence ratios. In particular, we define and calculate a large number of extensive quantities for the simulations within the database and compare with the equivalent quantities extracted from fully 3D simulations and those used in 1D hydrodynamic models. Additionally, we discuss some of the practical challenges of searching for physical insight in multi-petabyte datasets.   

Quantifying low-mode shell asymmetry as a means to predict ICF implosion performance on the NIF

Low mode fuel and ablator asymmetries are a significant degradation mechanism in NIF indirect drive ICF implosions. These asymmetries are forced by radiation drive asymmetry stemming from asymmetric hohlraum wall illumination. We develop an ensemble of two, three, and four-shock high-density-carbon ablator simulations with varying drive asymmetries and convergence ratios.~We use this ensemble to relate the shell properties prior to its peak implosion velocity to the overall implosion performance and extend this technique to analyze NIF in-flight radiograph (convergent ablator) experimental data.   

Thin Shell Model for NIF capsule stagnation studies

We adapt the thin shell model of Ott, et. al.\footnote{D. Colombant, W. Manheimer, E. Ott, PRL, \textbf{53} (1984) 446.} to asymmetric ICF capsule implosions on NIF. Through much of an implosion, the shell aspect ratio is large so the thin shell approximation is well satisfied. Asymmetric pressure drive is applied using an analytic form for ablation pressure as a function of the x-ray flux, as well as time-dependent 3D drive asymmetry from hohlraum calculations. Since deviations from a sphere are small through peak velocity, we linearize the equations, decompose them by spherical harmonics and solve ODE's for the coefficients. The model gives the shell position, velocity and areal mass variations at the time of peak velocity, near 250 microns radius. The variables are used to initialize 3D rad-hydro calculations with the HYDRA and ARES codes. At link time the cold fuel shell and ablator are each characterized by a density, adiabat and mass. The thickness, position and velocity of each point are taken from the thin shell model. The interior of the shell is filled with a uniform gas density and temperature consistent with the 3/2PV energy found from 1D rad-hydro calculations. 3D linked simulations compare favorably with integrated simulations of the entire implosion. Through generating synthetic diagnostic data, the model offers a method for quickly testing hypothetical sources of asymmetry and comparing with experiment.