A comparison of past and present computational methods for shape analysis of double-shell x-ray radiographs.

Implosion symmetry is a key requirement in achieving a robust burning plasma in inertial confinement fusion experiments. In double-shell capsule implosions, we are interested in the shape of the inner shell as it pushes on the fuel. Shape analysis is a popular technique for studying said symmetry during implosion. Combinations of filtering and contour-finding algorithms are studied for their promise in reliably recovering Legendre shape coefficients from synthetic radiographs of double-shell capsules with applied levels of noise. A radial lineout max(slope) method when used on an image pre-filtered with non-local means and a variant of the marching squares algorithm are able to recover p0, p2, and p4 maxslope Legendre shape coefficients with mean pixel discrepancy errors of 2.81 and 3.06, respectively, for the noisy synthetic radiographs we consider. This improves upon prior radial lineout methods paired with Gaussian filtering, which we show to be unreliable and whose performance is dependent on input parameters that are difficult to estimate.

Neural network for 3D inertial confinement fusion shell reconstruction from single radiographs.

In inertial confinement fusion (ICF), x-ray radiography is a critical diagnostic for measuring implosion dynamics, which contain rich three-dimensional (3D) information. Traditional methods for reconstructing 3D volumes from 2D radiographs, such as filtered backprojection, require radiographs from at least two different angles or lines of sight (LOS). In ICF experiments, the space for diagnostics is limited, and cameras that can operate on fast timescales are expensive to implement, limiting the number of projections that can be acquired. To improve the imaging quality as a result of this limitation, convolutional neural networks (CNNs) have recently been shown to be capable of producing 3D models from visible light images or medical x-ray images rendered by volumetric computed tomography. We propose a CNN to reconstruct 3D ICF spherical shells from single radiographs. We also examine the sensitivity of the 3D reconstruction to different illumination models using preprocessing techniques such as pseudo-flatfielding. To resolve the issue of the lack of 3D supervision, we show that training the CNN utilizing synthetic radiographs produced by known simulation methods allows for reconstruction of experimental data as long as the experimental data are similar to the synthetic data. We also show that the CNN allows for 3D reconstruction of shells that possess low mode asymmetries. Further comparisons of the 3D reconstructions with direct multiple LOS measurements are justified.

Shock formation and the ideal shape of ramp compression waves.

We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long-duration ramps are desired.