## 3 Results and Discussion  
### View Factor Evaluation According to the Shape of Plasma  
Figure 5 shows a photograph of the laser-induced plasma taken with a high-speed camera. The shape, diffusion, and extinction of the plasma could be confirmed. Figure 5a shows a symmetrical shape with no flow, and the generation and extinction of plasma. Figure 5b shows the shape of plasma with N\({}_{2}\) gas flowing at a rate of 350 cm\({}^{3}\)/s from left to right. The plasma was affected by the gas flow; the shape was not symmetrical and appeared somewhat unstable. It is clear that the plasma was affected by the flow pressure. In this case, the shape of the plasma was inclined in the flow direction; if it matched the direction of the signal detector, it could be expected that the magnitude of the plasma signal would change according to the observation direction.  
[PERSON] et al. reported that the size and shape of laser-induced plasma are affected by ambient atmospheric pressure [4]. Plasma generated on the surface of a material by a laser goes through the stages of generation, diffusion, and extinction. In previous studies, the size of plasma was represented schematically (as shown in Figure 6) according to time and ambient pressure [4]. In this study, the shape of plasma after 0.1 us had elapsed under atmospheric pressure was used as a model, and for simplicity of calculation, the plasma was assumed to be a cylinder with a diameter of 1 mm and height of 10 mm.  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Gas**} & **Ar, N\({}_{2}\), He** \\ \hline Azimuth of an inlet port (degree) & Every 30 \\ \hline Flow rates (cm\({}^{3}\)/s) & 300 – 430 \\ \hline Target material & Mg alloy \\ \hline \hline \end{tabular}
\end{table}
Table 3: Experimental parameters.  
Figure 4: Graph of LIBS spectral line for a magnesium target.  
The effect of ambient gas flow on plasma can be predicted by numerically simplifying its effect on plasma signal measurements. In LIBS, a plasma signal is acquired from plasma received by a signal detector. This process can predict interactions of the radiator and signal detector through simplified modeling, and these results can be compared in a limited manner with experimental values. The radiation of the plasma surface can be measured by the signal detector, and the signal acquired by the signal detector varies according to the shape or projected area of the plasma surface. To apply this principle, the plasma is assumed to have a simple hemispherical, elliptical, or cylindrical shape. If the change in strength of the radiation measured on the simplified surface is verified, it is possible to predict the change in the strength of the signals from the detector with respect to the change in plasma shape.  
In terms of radiation, the ratio between the amount of the surface of the radiator and surface of the absorber that can be viewed in the observation direction is called the view factor (Figure 7). The view factor can be expressed as a function of the projected area of the surfaces where radiation occurs and the distance between the two bodies. The shape factor depends on the geometry of the body, or on the irradiation and radiation on the surface of  
Figure 5: (**a**) Formation and extinction of plasma in the absence of gas flow. (**b**) Plasma generation and annihilation geometry when nitrogen gas flow is 350 cm\({}^{3}\)/s.  
Figure 6: Schematic of various shapes of laser-induced plasma with respect to the ambient pressure.