## 4 Discussion and Comparison with Experiments
### LFC of Tempered Glass
In stage 2, according to Table 1, we choose the VED of the filament plasma as \(w=\) 270 kJ/cm\({}^{3}\), which corresponds to the fulfilment of the condition (12) \(w\leq w_{1}=\) 336 kJ/cm\({}^{3}\), at which, according to our model, there is a significant suppression of the filament energy losses for thermal emission, thus providing for the driving force and efficiency of the LFC process. To calculate \(w_{mod}^{T}\), we use the heat preservation factor \(\eta=\) 0.76, which, as noted above, corresponds to the choice of the repetition frequency \(f\approx\)\(f_{1}\) in the high-frequency range. The value of the \"low-temperature\" heat capacity is taken as \(C=\)\(C_{2}\approx\) 1.0 J/(g\(\times\)K), which in the indicated high-frequency range according to (60) corresponds to a heating by the value \(\rm T_{i}\))/(1 + \(\eta\)) = 313 \({}^{\circ}\)C, i.e., from \(\rm T_{i}\) = 20 \({}^{\circ}\)C to 333 \({}^{\circ}\)C. When substituting the data \(C\), \(\rm T_{i}\), \(T_{stmin}\) and \(\rho\) into (66), we get \(w_{mod}^{T}\) = 0.76 \(\rm kJ/cm^{3}\). In stage 3, we calculate the energy of the laser pulse in the material \(E_{1}\), which is not directly reported in this experiment [5,6]. From (17), we get \(E_{1}\) = 11.5 \(\upmu\)J, and from (66), \(s_{1 max}\)\(\approx\) 6.6 \(\upmu\)m. To ensure partial overlap of the impact zones, we further select for a certainty the step of filaments following, as noted earlier, \(s_{1}\) = 0.95\({}_{1 max}\), which gives \(s_{1}\)= 5.9 \(\upmu\)m.  
In stage 4, the calculation of the pulse duration according to (21) (for a filament created by only one pulse) at the above \(E_{1}\), \(\Gamma\) and \(P_{c}\) gives \(\tau\) = 1.15-2.3 ps. But If the filament is created by a burst of pulses, for example, from \(N\) = 6 pulses, then the energy of a single pulse from the burst \(E_{0}\) can be estimated approximately as \(E_{0}\)\(\approx\)\(E_{1}\)/\(N\), which gives \(E_{0}\)\(\approx\) 1.92 \(\upmu\)J, and the duration of a single pulse from the burst according to (21) will then be \(\tau_{0}\)\(\approx\)\(\tau\)/\(N\), i.e., \(\tau_{0}\)\(\approx\) 192-384 fs. This estimate is consistent with the experiment under discussion, where, as the authors indicate, pulses with \(\tau\) < 400 fs have been used. For such a ratio \(s_{1}\) /\(s_{1 max}\) = 0.9, i.e., (\(s_{1}\)/\(R\)) = 1.8, the value of the frequency limit \(f_{1}\) according to Table 3 is \(f_{1}\) = 13.3\(\chi\)/\(s_{1}\)\({}^{2}\). When substituting here the above-mentioned \(s_{1}\) and the thermal diffusivity of the silica glass \(\chi\), estimated at high temperatures according to the reference data, as (4-5) \(\times\) 10\({}^{-3}\) cm\({}^{2}\)/s, we get the estimate: \(f_{1}\) = 153-191 kHz. For the LFC throughput, using (93) for the indicated \(s_{1}\), \(H\) and \(E_{1}\), we find \(\Omega\)\(\approx\) 23 \(\upmu\)m\({}^{2}\)/\(\upmu\)J. In stage 5, we choose the PRR as \(f\)\(\approx\)\(f_{1}\), i.e., \(f\) =153-191 kHz. The speed of the relative motion of the beam and the material \(u\) is calculated according to (90), which, when substituting the indicated \(s_{1}\) and \(f\), gives \(u\) = 0.90-1.13 m/s. The average power of pulse -periodic laser radiation in the material \(P\) = \(E_{1}\)\(f\) when using the pulse energy found above in the material \(E_{1}\) and the indicated PRR \(f\) for one set of filaments will be \(P\) = 1.76-2.20 W. With a higher PRR \(f\) = 700 kHz and the same \(s_{1}\) and \(E_{1}\), respectively, we get \(u\) = 4.1 m/s and \(P\) = 8.1 W. The obtained range \(u\) = 0.90-4.1 m/s is consistent with the speeds reported by the authors of the experiment: \(<\)4 m/s. However, a real separation of chemically tempered glass requires the creation of two sets of filaments--one usually is placed near the backside of the plate, and the other closer to the front side.