## 4 Discussion
This value appears to be approximately the same for the single laser pulse with \(I_{\text{max}}=15\) MW/cm\({}^{2}\) and for the sequence of three weaker pulses with \(I_{\text{max}}=10\) MW/cm\({}^{2}\) (see Figure 9). It is slightly greater than one micron. However, the parameters of vapor are quite different. Table 4 compares the parameters at 200 ns after the beginning of the single pulse with \(I_{\text{max}}=15\) MW/cm\({}^{2}\) (\(t=0.2\) us in Figure 4) and the third pulse of the sequence with \(I_{\text{max}}=10\) MW/cm\({}^{2}\) (\(t=20.2\) us in Figure 7). In both cases, the vapor temperature is about 3000 K. The vapor pressure at 15 MW/cm\({}^{2}\) is four times the pressure at 10 MW/cm\({}^{2}\). The thickness of the vapor domain at 15 MW/cm\({}^{2}\) is four times its thickness at 10 MW/cm\({}^{2}\). In summary, at the multipulse laser processing, vapor is considerably less dense and occupies a considerably thinner domain. Metallic vapor is expected to be slightly ionized at the temperature of 3000 K. The source of charges is thermoelectric and thermoion emission from the target surface [27]. Modeling [27] revealed the Knudsen layer and the sheath fused together at the interface between an evaporating surface and slightly ionized vapor. It was shown that the electronic temperature is around the surface temperature and the ionization degree is around the equilibrium one at the electronic temperature [27]. The last row of Table 4 shows the calculated surface temperature estimating the electronic temperature of the vapor. One can see that the electronic temperature is greater for the single pulse with \(I_{\text{max}}=15\) MW/cm\({}^{2}\). According to the Saha Equation [31], the ionization degree sharply grows with the electronic temperature. Therefore, the ionization degree can be considerably greater at 15 MW/cm\({}^{2}\). The principal mechanism of the absorption of infrared radiation in ionized gas is inverse bremsstrahlung [31]. The absorption coefficient is proportional to the concentration of electrons [31]. \begin{table}
\begin{tabular}{l l l} \hline Maximum absorbed intensity, \(I_{\text{max}}\) (MW/cm\({}^{2}\)) & 15 & 10 \\ \hline Time \(t\), (us) & 0.2 & 20.2 \\ \hline Position of the contact surface, \(z\) (\(\mu\)m) & 75 & 18 \\ \hline Vapor pressure, \(p\) (atm.) & \(\sim\)8 & \(\sim\)2 \\ \hline Vapor temperature, \(T\) (K) & \(\sim\)3000 & \(\sim\)3000 \\ \hline Target surface temperature, (K) & 4200 & 3400 \\ \hline \end{tabular}
\end{table} 
Table 4: Calculated parameters of vapor. The probability of optical breakdown in the vapor can be assessed from the optical thickness, which is roughly the vapor layer thickness (optical path) multiplied by the absorption coefficient of the vapor. Compare, for example, the distributions of vapor density at the end of the single laser pulse (see Figure 4, \(t=0.3\)\(\upmu\)s) and at the end of the third pulse in the sequence (see Figure 7, \(t=20.3\)\(\upmu\)s). The thickness of the vapor domain is about 140 \(\upmu\)m in the former case and only 30 \(\upmu\)m in the latter case. Thus, the optical path through vapor considerably reduces at the multipulse laser processing. One can see from these figures that the vapor density is around the density of the ambient gas in the former case and approximately a quarter of the ambient gas density in the latter case. The electron temperature and the ionization degree in the vapor are lower at the multipulse laser processing (see above). The electron density is the vapor density multiplied by the ionization degree. Therefore, the electron density along with the absorption coefficient considerably reduces at the multipulse laser processing. Finally, the optical thickness of the vapor considerably reduces too. The absorption initiates optical breakdown and the ignition of plasma shielding the target from laser radiation.