Inertial Confinement Fusion and Applied Mathematics

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

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

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

4. National Ignition Facility

5. 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

6. Problem Statement X-ray Image Features Experimental Parameters - Laser power - Capsule roughness - Doping concentration Target radius Peak width 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 Can we understand the state of an experiment from observations? Which observations are most informative in making a distinction?

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

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

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

10. 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?

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

12. 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

13. 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 4 < Im_max < 6 6 < Im_max < 8 Im_max > 8 Min_var = 0 Min_var ≠ 0 Min_var = 0 Min_var ≠ 0