## 1 Introduction
The pulses of the sequence are interdependent because of accumulation of heat in the target and because the gas parameters near the evaporating surface depend on the previous pulses [3]. If the inter-pulse separation time increases, the ablation depth decreases while the ignition of laser plasma becomes less probable [3]. The time of gas-phase relaxation after a laser pulse is shorter than that of target relaxation. Therefore, at high inter-pulse separation, the only mechanism of pulse interaction is the accumulation of heat in the target. For example, at modeling the sequences of millisecond pulses with inter-pulse separation of the order of 100 ms [2], the mutual influence of pulses through the gas phase was reasonably neglected. [PERSON] et al. [4] studied surface heat treatment by laser pulses of 1064 nm wavelength, 210 ns duration and the inter-pulse separation of the order of 10 \(\upmu\)s. A rigorous model of conductive heat transfer in the target was proposed [4]. The dynamics of vapor and ambient gas was not considered in detail while simple models for evaporation and vapor ionization were used to take into account the shielding of the target by laser plasma. The model was validated by comparison with experimental results. The models with rigorous gas dynamics are known [3; 15] but they were applied to nanosecond laser pulses. A strong interdependence between heat transfer in the target and gas dynamics of vapor and ambient gas at laser-matter interaction was clearly realized back in the 1990s. The first models of heat transfer coupled with gas dynamics indicated the importance of the boundary conditions at the interface between the target and the gas phase [10; 11]. Under the conditions of strong overheating and intensive evaporation, the near-boundary region of the gas phase (Knudsen layer) is highly non-equilibrium. Thus, the key issue is not gas dynamics but kinetic processes in the gas phase. In the first models,the kinetic description of the gas phase was used in the framework of DSMC [12; 13]. Such an approach has been successfully applied to nanosecond laser ablation up to now [3]. However, the DSMC computation becomes extremely time consuming at small Knudsen numbers. This is why it is not applied in the recent models for sub-microsecond [4] and millisecond [3] laser pulses. The present work implements a rigorous but less time-consuming computation model where the interface region of the Knudsen layer is considered explicitly [15]. It concerns modeling the sequences of CO\({}_{2}\)-laser pulses with 10.7 \(\upmu\)m wavelength, the duration of 300 ns, and inter-pulse separation of 10 \(\upmu\)s, which are promising for high-efficiency surface heat treatment [28]. Estimation of the ionization degree [27] and especially modeling the optical breakdown [4; 16] require strong assumptions. To obtain conclusions that are more general, we restrict our consideration to qualitative effects of laser-plasma interaction. The calculation results obtained are rigorous before plasma ignition only. Note that both experiments and modeling [4; 16] indicate that plasma ignition instantly interrupts the laser beam. It should be avoided at laser processing. The goals of the present study are to estimate the threshold of evaporation, the parameters of the vapor important for plasma ignition, and the physical mechanisms governing the mutual influence of the pulses in the multipulse sequences. The fraction of laser energy absorbed in the gas phase depends on its optical thickness. This is why the probability of plasma ignition is assessed by the optical thickness.