## 5 Conclusions
This requires the dominance of the thermal mechanism in the formation of the impact zone radius, but not of the alternative shockwave or thermal deformation mechanisms, which just lead to scattered cracking formation in the solid material, excluding thus a smooth separation after irradiation. As the model shows, the dominance of the thermal mechanism occurs when two dimensionless criteria for material and radiation parameters are met simultaneously. It requires the use of a specific class of materials--tempered glasses, which corresponds to experimental observations of smooth cutting for these materials. On the other hand, these criteria are not met for sapphire and non-tempered glasses. In experiments, a smooth separation in LFC for these materials really is not observed. Materials with a fairly long de-excitation time, \(t_{E}>>t_{P2}\) (that is, \(t_{E}>>\) 0.4-0.8 ns according to the estimates of the pressure confinement time \(t_{P2}\) made in Section 3.1 for \(\tau_{f}=0.25\)-0.5 \(\upmu\)m) may also provide the dominance of the thermal mechanism--see the inequality (48). For such \(t_{E}\), a significant decrease in the amplitude of the shock wave and a corresponding decrease in the radius \(R_{SW}\) of modification zone due to the shock-wave mechanism is expected, which is preferable for obtaining a smoother separation. The model searches for a set of four indicated parameters (\(E_{1}\), \(\tau\), \(s_{1}\) and \(f\)) that allow us to fulfil all these necessary conditions for obtaining a smoother separation. In practice, these four parameters are sufficient to define completely the LFC process. The LFC process is very complicated to model, as it is an effect of in a total of about 40 radiation and material parameters. We have proposed an algorithm for the sequential calculation of \(E_{1}\), \(\tau\), \(s_{1}\) and \(f\) as a function of these numerous parameters. A comparison of the calculation according to this algorithm with the LFC experiments for sapphire and tempered glass shows a good agreement for the entire set of \(E_{1}\), \(\tau\), \(s_{1}\) and \(f\), which indicates the reliability and adequacy of the constructed model. Besides, from this comparison, it is found that the experimental values of VED \(w\) both for sapphire and tempered glass satisfy the inequality \(w<w_{1}\). According to the condition (12) obtained, it corresponds to the practical elimination of the filament energy losses for thermal emission. As a next step, the model is used to predict new modes of LFC that have a positive property in addition to better smoothness. For example, it is shown that the choice of the PRR in the high-frequency range,\(f\geq f_{1}\), and the use of twice shorter laser radiation wavelength as 1.04 \(\upmu\)m, allow obtaining very high cutting speeds--about 1-25 m/s or more, depending on the material. These speeds can be tens or hundreds of times higher than the characteristic cutting speeds of glass, sapphire and other transparent materials by known mechanical methods, and tens of times higher than the characteristic separation speeds by known controlled thermal splitting methods using continuous-wave lasers. On the other hand, it is found that the choice of the PRR in the low-frequency range, mboxemphf \(\leq\) f\({}_{2}\), and the use of the shorter radiation wavelength (0.52 \(\upmu\)m) make possible LFC with an extremely low average laser power--only about one or several hundred mW, which provides a cutting speed of about 0.2 m/s. This value, although not a very high, but nevertheless is acceptable for applications. Besides, LFC modes that are characterised by high throughput are found, i.e., a high ratio of the cut-off area \(s_{1}H\) per pulse to the pulse energy \(E_{1}\). It is shown that here, too, the reduction of the filament radius by almost half due to the use of a shorter wavelength than 1.04 \(\upmu\)m, for example, \(\lambda=0.52\)\(\upmu\)m, provides significant advantages in obtaining a higher LFC throughput.