Inertial Confinement Fusion and Applied Mathematics David Starinshak

Inertial Confinement Fusion and Applied Mathematics David Starinshak Ph. D Student, Applied Mathematics University of Michigan Department of Mathematics Advisor: Brian Spears Lawrence Livermore National Laboratory

Outline Background – National Ignition Facility – Inertial Confinement Fusion (ICF) My Project in a Nutshell – Problem Statement – Geometric Interpretation Other Projects Relevant to AIM

National Ignition Facility Multi-billion dollar program by Department of Energy to achieve world’s first fusion reaction

National Ignition Facility

Inertial Confinement Fusion • Millimeter-sized capsule of frozen deuterium and tritium (DT) • X-ray energy compresses capsule by factor of 30 • Temperatures exceed 10, 000 Kelvin • Pressure reaches 1 billion atmospheres • DT fuses into helium, releasing ~18 MJ of energy • All happens in < 20 nanoseconds

Problem Statement X-ray Image Features Experimental Parameters Target radius - Laser power Peak width - Capsule roughness - Doping concentration … … Contour RMS {velocity, mass} Nuclear Features Quantities like implosion velocity, mass, entropy, and temperature can characterize a successful experiment HOWEVER Such quantities cannot be measured directly from observations 1. Can we understand the state of an experiment from observations? 2. Which observations are most informative in making a distinction?

Problem Statement X-ray Image Features Experimental Parameters Target radius - Laser power Peak width - Capsule roughness - Doping concentration … … Contour RMS {velocity, mass} Nuclear Features Scaled Problem 3 parameters instead of 200+ – Capsule thickness – Ablator density – Ablator opacity

Problem Statement X-ray Image Features Experimental Parameters Target radius - Laser power Peak width - Capsule roughness - Doping concentration … … Contour RMS {velocity, mass} Nuclear Features Scaled Problem 1 D simulations – Unclassified hydrodynamic code HYDRA – Simulates laser-driven implosion and (possible) nuclear burn – 4000+ runs

Problem Statement X-ray Image Features Experimental Parameters Target radius - Laser power Peak width - Capsule roughness - Doping concentration … … Contour RMS {velocity, mass} Scaled Problem Yorick Postprocessing – Images simulated using Abel Transform – Images processed into discrete set of features – Nuclear features calculated Nuclear Features

Geometric Interpretation Important Questions • Do different classifications cluster in the space of observations? • Can classifications be separated in feature space? • How many features are needed? • Which are the most informative?

Image Processing Problems • Extracting information from noisy X-ray radiograms • Implementing fast variational methods to filter, de-noise, and detect edges • Reconstruct 3 D picture of imploding capsule from multiple, time-resolved 2 D images

Fluid Dynamics Problems • Numerical approximations for extreme plasma dynamics • Theoretical and applied analysis of turbulent mixing • Fluid interface instability problems (Rayleigh-Taylor and Kelvin-Helmholtz) • Nonlinear analysis of dynamic instabilities

Theoretical and Applied CS • Machine learning algorithms – Data mining and Bayesian analysis – Feature selection and feature engineering • Efficient numerical methods for non-conservation problems – diffusion, convection, neutron transport, etc Training Data BT < 18. 4 ns 18. 4 < BT < 18. 8 BT > 18. 8 ns Im_max < 4 Min_var = 0 Min_var ≠ 0 4 < Im_max < 6 6 < Im_max < 8 Min_var = 0 Min_var ≠ 0 Im_max > 8