Investigation of natural frequencies of laser inertial confinement fusion capsules using resonant ultrasound spectroscopy

Abstract The natural frequency problem of laser inertial confinement fusion (ICF) capsules is one of the basic problems for determining non-destructively the elasticity modulus of each layer material using resonant ultrasound spectroscopy (RUS). In this paper, the frequency equation of isotropic one-layer hollow spheres was derived using three dimension (3D) elasticity theory and some simplified frequency equations were discussed under axisymmetric and spherical symmetry conditions. The corresponding equation of isotropic multi-layer hollow spheres was given employing transfer matrix method. To confirm the validity of the frequency equation and explore the feasibility of RUS for characterizing the ICF capsules, three representative capsules with a millimeter-sized diameter were determined by piezoelectric-based resonant ultrasound spectroscopy (PZT-RUS) and laser-based resonant ultrasound spectroscopy (LRUS) techniques. On the basis of both theoretical and experimental results, it is proved that the calculated and measured natural frequencies are accurate enough for determining the ICF capsules.