## 1 Introduction
Additionally, fs laser irradiation (120 fs/800 nm/700 uJ) of HOPG in a vacuum (no liquid) showed that mainly polyynes and cumulenes [(=C=C)\({}_{n}\)] were formed at the central ablated area where the fluence was maximum; outside of that area, at the perimeter of the crater corresponding to a lower fluence (due to the Gaussian intensity profile of the laser beam), mainly nanodiamonds (NDs) and some trans-polyacetylenes were formed [13]. The generally accepted polyyne formation mechanism involves the polymerization reaction of single carbon atoms (C\({}_{1}\) or CI or C), carbon dimer radicals (C\({}_{2}\)), or larger radicals (C\({}_{m}\)). This process starts with the addition to a C\({}_{m}\) (for m \(\geq\) 1) of either the direct addition of C\({}_{2}\) or two C\({}_{1}\) atoms sequentially added in two steps of one C\({}_{1}\)[14]. The processes of the addition of C\({}_{2}\) or C\({}_{1}\) to the C\({}_{m}\) (first step of the reaction) have equal probabilities of occurring. Along with the chain elongation that is due to polymerization, there is a competing hydrogenation process that finally terminates the chain growth by its hydrogen or radical (R) end-capping. The carbon radicals needed for the chain growth are supplied by the ablation of the material during the formation of the plasma plume, whereas the hydrogen atoms are supplied by the vaporization or decomposition of water at the plume-water interface because of the high temperature of the plasma plume. It is also believed that the formation of polyynes occurs within the plasma plume [4; 14]. The ultrafast deposition of laser energy into the material in the case of a fs pulse laser ablation results in the ablation of the material via a direct solid-to-gas transition (sublimation) for fluences that are close to the ablation threshold of the material; this is contrary to the case of a ns pulse laser ablation, where the material is ablated via a solid-to-liquid-to-gas transition (melting and vaporization) [15]. However, even in the case of a fs ablation for fluences that are far above the ablation threshold of the material, there is also a contribution to the material's sublimation ablation mechanism in the form of melting and a small percentage of NPs (usually the bigger NPs) corresponding to melted droplets that are directly ejected from the melt pool. Furthermore, the use of fs pulses compared with ns or ps pulses avoids a secondary interaction of the ablating laser pulse with the plasma plume from the material (plasma heating effects), as in this case, the pulse width remains much smaller compared with the plume formation starting time (usually in 1-10 ps time frame); the time interval between successive pulses is much larger than the plume lifetime (usually in the order of a few hundred nanoseconds) in the case of multipulse ablation, even for pulse repetition rates as high as 6 kHz (interval between the pulses \(\approx\) 167 us) (as will be presented later in the paper). However, in the case of a high pulse repetition rate ablation, and depending on the pulse energy, there may be an interaction between the laser pulses and the NPs during their growth, coalescence, and especially ripening within the cavitation bubble (the cavitation bubble lifetime could range from a hundred to a few hundred microseconds) [4].