## 2 Materials and Methods  
The surrogate debris was synthesized from powder mixtures of Gd\({}_{2}\)O\({}_{3}\), CeO\({}_{2}\), ZrO\({}_{2}\), and Fe\({}_{2}\)O\({}_{3}\) to resemble the nuclear fuel debris. All materials were used as received from the supplier (RARE METALLIC, Tokyo, Japan). The mixtures were prepared so that the mass fractions of Ce, Zr, and Fe conformed to the predicted values for the nuclear fuel debris [3], with the various concentrations of Gd. Each mixture (0.5 g) was compressed under hydrostatic pressure (10 kN) into a pellet with an 8 mm diameter and sintered at 1375 \({}^{\circ}\)C for 5 h. The resulting mass fractions of each element per sample are listed in Table 1.  
Figure 1a presents a schematic of the portable FO-LIBS setup used in this study. This setup was slightly modified from the previous version of our FO-LIBS system [14]: a Q-switched Nd:YAG laser (Minilite II, Amplitude, Milpitas, CA, USA) was mounted for the single-pulse operation, and the Czerny-Turner spectrometer was replaced by an Echelle-type spectrometer (EMU-65, Catalina Scientific, Tucson, AZ, USA) for wide spectral coverage. The configuration was installed in an aluminum frame with dimensions of \(500\times 700\times 880\) (see photograph in Figure 1b). The laser output (1064 nm, 6 ns pulses operating at 5 Hz) was coupled into a high-OH optical fiber (S.1000/1100, Fujikura, Japan; length: 5 m; core diameter: 1 mm; NA: 0.12, OH in the core: \(\sim\)1000 ppm, fluorine in the clad: 4 wt%) using a convex lens (\(f=125\) mm) at a coupling box evacuated to a pressure of 90 kPa. The laser light was then delivered to a home-built probe head. The laser beam (10 m/pulse) was focused  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Sample** & **Ce** & **Zr** & **Fe** & **Gd** \\ \hline
#1 & 44.6 & 24.0 & 8.3 & 0.87 \\
#2 & 44.8 & 24.1 & 8.3 & 0.44 \\
#3 & 44.9 & 24.2 & 8.3 & 0.22 \\
#4 & 45.0 & 24.2 & 8.3 & 0.09 \\
#5 & 45.1 & 24.2 & 8.3 & 0.00 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Elemental composition (wt%) of the surrogate nuclear fuel debris.  
onto the sample surface with \(f=40\) mm and \(f=12.5\) mm lens pairs equipped on the probe head. The diameter of the laser spot was 350 \(\upmu\)m. The optical emission was collected by the same optics for the laser delivery, transported to another optical fiber using a pierced mirror at the fiber coupling box, and fed into the Echelle spectrometer equipped with an electron multiplying charge coupled device (EMCCD) camera (FA285-CL, Raptor Photonics, Larne, UK). Spectral detection was synchronized with the laser pulse using a digital delay generator (Model 9214, Quantum Composers, Bozeman, MT, USA); the EMCCD camera was triggered at a delay of 1 \(\upmu\)s to the laser irradiation, which yielded the best signal-to-background ratio (SBR) for the Gd emission lines. The exposure time was set to 2 \(\upmu\)s; the longer exposure resulted in the emergence of highly complex profiles because optical emissions from the molecular species dominated the spectra. Each spectrum was acquired for 500 laser shots. To gain a calibration curve at a given dose rate, five spectra were recorded for each sample.  
The influence of a given radiation field was investigated at the \({}^{60}\)Co gamma irradiation facility at Takasaki Advanced Radiation Research Institute, National Institutes for Quantum and Radiological Science and Technology (QST) in Japan. The dose rates tested in the present work were 0, 0.8, and 10 kGy/h, which were controlled by adjusting the distance between the \({}^{60}\)Co emitter and the probe head installed on a motorized linear stage. The irradiation was performed in ambient air at room temperature.