Spherical harmonics bring 2-D into 3-D for imaging fusion implosions

Glimpsing conditions during the crucial stagnation phase of an inertial confinement fusion (ICF) implosion poses immense challenges: Forceful events in the salt grain-sized “hot spot” within a deuterium-tritium fuel target unfold in picoseconds, emitting neutrons, X-rays and gamma rays. These emissions traverse tens of meters, passing through micrometer-sized pinholes before registering on a detector. Gathered from very few lines of sight, the resulting data for reconstructing images are akin to using drinking straws to view a TV from the far end of a football field.

Petr Volegov and his colleagues have come up with a powerful method for rendering accurate 3-D images from a minimal number of 2-D projections. Reported in the Journal of Applied Physics, this method is a major stride toward tomographic imaging of neutron production and distribution of fuel density at maximum compression, key to understanding processes necessary for predicting ignition.

Results of tests using X-ray images collected at the OMEGA laser in Rochester, New York, and neutrons emitted during fusion experiments at the National Ignition Facility (NIF) in Livermore, California, confirm the utility of the image-reconstruction method, an application of spherical harmonics decomposition. In sets of experiments, the team demonstrated that their analysis technique can transform emissions gathered from only a few projection directions into the overall shape and size of the source.

Algorithms for reconstructing an emission source as the sum of spherical harmonics also will allow easier comparison between experimental measurements and models employed to unravel the complex physics of ICF. “Spherical harmonics are a widely used tool. They give us a common language that bridges experiment and theory,” said co-author Verena Geppert-Kleinrath.

Source: “Three-dimensional reconstruction of neutron, gamma-ray, and x-ray sources using spherical harmonic decomposition,” by P. L. Volegov, C. R. Danly, D. Fittinghoff, V. Geppert-Kleinrath, G. Grim, F. E. Merrill, and C. H. Wilde, Journal of Applied Physics (2017). The article can be accessed at https://doi.org/10.1063/1.4986652 .