A metamodeling approach for studying ignition target robustness in a highly dimensional parameter space

Abstract

Inertial confinement fusion targets must be carefully designed to ignite their central hot spots and burn. Changes in the optimal implosion could reduce the fusion energy or even prevent ignition. Since there are unavoidable uncertainties due to technological defects and not perfect reproducibility from shot to shot, the fusion energy will remain uncertain. The degree with which a target can tolerate larger specifications than specified, and the probability with which a particular yield is exceeded, are possible measures of the robustness of that design. This robustness must be assessed in a very high-dimensional parameter space whose variables include every characteristics of the given target and of the associated laser pulse shape, using high-fidelity simulations. Therefore, these studies would remain computationally very intensive. In this paper we propose an approach which consist first of constructing an accurate metamodel of the yield on the whole parameter space with a reasonable data set of simulations. Then the robustness is very quickly assessed for any set of specifications with this surrogate. The yield is approximated by a neural network, and an iterative method adds new points in the data set by means of D-optimal experimental designs. The robustness study of the baseline Laser Mégajoule target against one-dimensional defects illustrates this approach. A set of 2000 simulations is sufficient to metamodel the fusion energy on a large 22-dimensional parameter space around the nominal point. Furthermore, a metamodel of the robustness margin against all specifications has been obtained, providing guidance for target fabrication research and development.

Progress on LMJ targets for ignition

“…Exhaustive robustness studies [8,9] have been conducted on this target to estimate the yield sensitivity to target fabrication, modeling uncertainties and experimental tuning. The various 1D sources of uncertainties have been combined in order to give a net error budget.…”