Characterization of thick cryogenic fuel layers using convergent-beam interferometry: A numerical investigation

The inner-surface roughness of thick cryogenic-fuel layers in inertial confinement fusion (ICF) targets plays a critical role in determining the overall success of an ICF capsule implosion. Imperfections at this surface affect the growth of Raleigh–Taylor hydrodynamic instabilities during both the acceleration and deceleration phases of the implosion. Characterization of this surface is performed using a Mach–Zehnder interferometer that illuminates the target with a wavefront that is convergent to a point near the targets’ rear focal point, thereby reducing the strong negative-lens effects of the thick cryogenic fuel layer. The construction of this interferometer is described in the text. Phase-shifting interferometry is utilized to acquire the perturbed wavefronts that have passed through the target. These wavefronts are subsequently sampled around the target perimeter and decomposed into a one-dimensional Fourier spectrum, which is Abel transformed into a two-dimensional (2D) spectrum. The validity of convergent-beam interferometry is demonstrated by analyzing numerically generated perturbed wavefronts. The wavefronts are analyzed, and the (2D) spectrum obtained is compared to the actual spectrum imposed on the interior of the ice surface of the target model. Agreement between these spectra is >80% for Legendre modes between 2 and 50.