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

TL;DR

The problem addressed is non-destructive wall-thickness metrology for ICF target capsules, especially when optical techniques fail for opaque materials. The paper introduces frequency-domain laser ultrasound (FreDomLUS) to excite and detect zero-group velocity (ZGV) resonances in a spherical shell and uses time-gating to isolate ZGV resonances from circumferential modes, enabling local thickness mapping. On a 2 mm diameter, ~80 µm thick high-density carbon capsule, the method yields a ~1% equatorial thickness variation that agrees with infrared interferometry, and a second ZGV around ~203 MHz provides a Poisson's ratio estimate ν ≈ 0.16, consistent with doping-induced property changes; the ZGV frequencies follow the inverse-thickness scaling, allowing thickness inferences via Δf_ZGV / f_ZGV = - Δh / h. The work demonstrates a scalable, non-destructive approach applicable to opaque target materials and suggests future use of circumferential resonances and dispersion fitting for comprehensive elastic characterization of ICF capsules.

Abstract

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.

Figures (7)

• Figure 1: (a) Close-up of the HDC-capsule in front of the microscope objective and a sketch showing its geometry and dimensions (inset). (b) Sketch of the FreDomLUS-Setup used for thermoelastic excitation and detection of the ultrasonic frequency response of an HDC-capsule. The capsule is placed on a manual rotation stage for point-wise measurements along its circumference.
• Figure 2: (a) Sketch of a finite element model of a HDC-capsule. (b) Snapshot of the radial displacement field on 80µm thick HDC-capsule. An animation can be found online as supplementary in Sec. \ref{['sec:suppl']}.
• Figure 3: (a) Calculated elastic-wave dispersion (GEWtool) of a non-curved 80µm thick HDC-plate. The fundamental mode (A$_0$) is marked with an arrow, and the first two ZGV-resonances (ZGV1 & ZGV2) with red dots. The dashed line corresponds to the Rayleigh surface acoustic wave (RW) of a semi-infinite half-space of the same material. (b,c,d,f) HDC-shell radial elastic response spectra from FreDomLUS-measurements (black solid lines) and FEM-simulations (red solid lines). (b) Broadband response spectra up to a frequency of 250MHz (FEM-trace is offset by a constant value), and time-gated versions of the same traces (shifted semi-transparent lines in the upper region of the graph). (c) Spectra up to 110MHz showing multiple fundamental mode circumferential resonance peaks. Extracted resonance peak frequencies from the FreDomLUS spectrum are indicated by grey arrows. (d) Zoomed view of circumferential resonance peaks (frequency range is marked as grey area in (c)). (e) Calculated group velocity curves (GEWtool) of guided plate modes in a straight 80µm thick HDC-plate. The grey (FreDomLUS) and black (FEM) data-points are group-velocities calculated from extracted circumferential resonance peaks. (f) Zoom to the frequency region around the ZGV1-resonance (marked as grey areas in (a,b,c,e)).
• Figure 4: Elastic wave dispersion curves. (a) Calculated for a HDC-plate ($h\!=\!80µm$) with the GEWtool. (b,c) For a HDC shell ($R\!=\!1.127mm$, $h\!=\!80µm$) obtained from a FEM simulation. In (c) the plate dispersion from (a) is superimposed as red family of lines. (d) Dispersion of a solid HDC sphere ($R\!=\!1.127mm$) obtained from a FEM simulation. The $y$-axis are identical in each graph and have been omitted in (b-d) for space saving reasons.
• Figure 5: (a) Narrow-band FreDomLUS-measured acoustic response spectra in the range of the ZGV1-resonance, recorded along the HDC-shell equator. The spectra are normalized to their maximum magnitudes (black solid line). (b) Example spectrum recorded at a rotation angle of $\phi\!=\!220°$. (c) Time-signal of the spectrum in (b), obtained by inverse fast Fourier transformation. The shaded red area indicates the fraction of the signal which is selected prior back-transformation. The time-gated spectrum is plotted as red solid line in (b). (d) Time-gated acoustic response spectra as function of rotation angle $\phi$. The black solid line indicates the extracted ZGV1-resonance frequency. The sequence of the applied data-processing steps is indicated by the numbers ➊ -- ➍.