Frequency domain laser ultrasound for inertial confinement fusion target wall thickness measurements

In inertial confinement fusion experiments hollow, spherical mm-sized capsules are used as a container for nuclear fuel. To achieve maximum implosion efficiency, a perfect capsule geometry is required. This paper presents a wall thickness measurement method based on zero-group velocity guided elastic wave resonances. They are measured with a non-destructive, contactless frequency domain laser ultrasound microscopy system. Wall thickness measurements along the equator of a high-density carbon capsule with a diameter of around 2 mm and a wall thickness of around 80 $\unicode{x00B5}$m excellently agree with infrared interferometry reference measurements. In addition, the multi-resonant nature of a spherical shell is studied by complementing experimental observations with plate dispersion calculations and finite element wave propagation simulations. The presented method is scalable and can be applied to a broad range of target materials, including metals, or metal-doped targets.

💡 Research Summary

This paper presents a novel, non-destructive method for measuring the wall thickness uniformity of spherical capsules used as fuel containers in inertial confinement fusion (ICF) experiments. Precise geometry, particularly wall thickness uniformity, is critical for achieving efficient implosion and ignition. The proposed technique leverages zero-group velocity (ZGV) resonances of guided elastic waves (Lamb waves) within the capsule wall.

The core technological advancement is the use of a frequency-domain laser ultrasound (FreDomLUS) microscopy system. Unlike conventional pulsed laser ultrasound which generates broadband acoustic frequencies and may require sample ablation for sufficient signal strength, FreDomLUS employs a low-power, intensity-modulated continuous-wave laser for excitation. This allows for highly frequency-selective, phase-sensitive detection of ultrasonic vibrations directly in the frequency domain. This approach is particularly suited for probing narrow resonance bands like ZGV points without damaging fragile micron-scale samples.

ZGV resonances occur at specific frequencies on the Lamb wave dispersion curves where the group velocity is zero, causing wave energy to be trapped locally. The key relationship Δ𝑓_ZGV / 𝑓_ZGV = - Δℎ / ℎ establishes that the relative shift in the ZGV resonance frequency is directly proportional to the relative change in local wall thickness, enabling precise thickness mapping.

The study was conducted on a high-density carbon (HDC) capsule with a ~2 mm diameter and a nominal wall thickness of ~80 µm. FreDomLUS measurements were taken point-by-point along the capsule’s equator. The results showed excellent agreement with reference measurements obtained via infrared interferometry (FTIR), validating the accuracy of the ultrasonic method.

A significant finding was the complex acoustic response spectrum of the spherical shell, which exhibited a dense forest of resonance peaks. The authors complemented experimental observations with two numerical analyses: 1) semi-analytical dispersion curve calculations for a flat HDC plate, identifying theoretical ZGV frequencies, and 2) finite element method (FEM) wave propagation simulations on a 2D axisymmetric model of the spherical shell. The FEM simulation successfully reproduced the complex experimental spectrum. This analysis revealed that the spectrum results from a superposition of local plate-mode ZGV resonances and non-local circumferential resonances, where waves travel multiple times around the shell’s circumference.

To isolate the local ZGV resonances crucial for thickness measurement from the confounding circumferential resonances, the authors implemented a time-domain gating procedure. The measured frequency response was converted to a time-domain signal via an inverse FFT. A time gate was then applied to select only the early-arriving signal components, which primarily contain the local ZGV response. Transforming this gated signal back to the frequency domain yielded a spectrum dominated by the ZGV resonances, effectively filtering out the longer-lasting circumferential modes.

In conclusion, this work successfully demonstrates that ZGV resonance spectroscopy using FreDomLUS is a viable and accurate technique for non-contact wall thickness characterization of ICF target capsules. The method’s scalability and ability to work with opaque materials like metals or metal-doped targets address a critical limitation of optical techniques, paving the way for its application to a broader range of future ICF target designs.