## 5 Discussion
Using the Comsol software package, it was possible to implement an algorithm for solving the model. We used the constant Newton method of solving linear equations, with a Jacobian update at each time step, to solve the emerging nonlinear equations. The solver parameters were chosen to ensure minimal solution time and acceptable convergence. All parameters were described in Section 2 (Mathematical Model of Plasma Spark Initiation). The system of equations was solved in a multi-threaded mode using PARDISO Solver. The connected Andersen acceleration allowed for a faster and improved solution convergence. The main improvement of this model is the preliminary introduction of boundary conditions and the search for the two-dimensional shape of the heat source. This allowed us to obtain physically correct temperature data, which are confirmed by experimental and literature data. With the selected parameters, the solution time of the model was 22 s. The results of this work will form the basis of the model of plasma spark propagation along the fiber and will be combined with it. The process of plasma spark propagation along the fiber has not been studied within the framework of this work. When using lasers with different wavelengths, different times are needed to initiate the optical breakdown process. This time is shorter the closer the laser wavelength is shifted to the ultraviolet part of the spectrum. This is not surprising because decreasing the wavelength (increasing the frequency) leads to an increase in the energy carried by the radiation quantum. Therefore, laser systems for glass micromachining operating in the ultraviolet or visible range have found wide applications. Due to the high probability of optical breakdown in quartz, there is a limitation associated with the use of full-body quartz optical fibers for the transmission short-wave part of the electromagnetic radiation range beginning with the ultraviolet. Hollow fibers are used to transmit radiation from ultraviolet to \(\upgamma\). In this work, the minimum radiation power required to initiate optical breakdown was estimated. It was shown that this power increases with increasing wavelength. This circumstance suggests that, first, the quartz fiber core has the lowest absorption in the infrared region of the spectrum, and second, the laser radiation more easily ionizes the fiber material when shifting to the ultraviolet region. Thus, the presence of the minimum power required to trigger the fiber fuse effect tells us that there is a red border at the beginning of the process. This fact is confirmed by the publications of other authors. For example, the article by [PERSON] [8] reported that the minimum start time of the breakdown process observed in the experiment was 0.18 s, and the minimum power at which it was possible to start the reaction in the SMF-28 fiber was 0.4 W. In the future, it is planned to investigate the red border of the reaction occurrence and experimentally confirm the simulation results. The maximum temperature \(T_{max}\), which occurs at the center of the optical spark, also has a dependence on laser radiation wavelength. Calculations have shown that \(T_{max}\) increases linearly with increasing optical radiation power and decreases with increasing wavelength. In addition, the growth rate of maximum temperature also depends on the wavelength. According to calculations, temperatures of several tens of thousands or even hundreds of thousands of kelvins occur at the plasma droplet center. For example, for \(\lambda_{0}\) = 1080 nm at a laser radiation power of 10 W, the center of the plasma droplet heats up to temperatures over 500,000 K. However, such high-temperature values are localized in the center of the plasma focus and decrease to 5000 K closer to the fiber core-shell interface. In turn, the outer layers of the fiber are practically not heated via the plasma spark. That is, the optical breakdown area is very small.