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

Highlights: • The frequency equation of isotropic multi-layer hollow spheres was derived using three-dimension (3D) elasticity theory and transfer matrix method. • The natural frequencies of the capsules with a millimeter-sized diameter are determined experimentally using resonant ultrasound spectrum (RUS) system. • The predicted natural frequencies of the frequency equation accord well with the observed results. • The theoretical and experimental investigation has proved the potential applicability of RUS to both metallic and non-metallic capsules. - 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.