## 4 Discussion  
Table 1 comprises the optimal conditions of ablation for different targets. Note that earlier studies have demonstrated that neither pulse energy nor pulse intensity can be considered as the definitive parameters responsible for the optimization of plasma formation to produce maximal yield of harmonics. The most important parameter here is the fluence, or energy density, of the heating pulses on the target surface. In this table, we include the optimal fluencies for each studied sample. It was demonstrated in [23; 25; 26] by time-of-flight mass spectroscopy (TOFMS) that LIPs from the graphite surface contain, along with neutral carbon atoms and its ions, different C\({}_{n}\) clusters and their ions. The number of carbon atoms in such clusters varies from \(n=2\) up to \(n=20\), and for strong excitation \(n\) could even reach 100. Earlier, in the case of C\({}_{60}\) ablation at conditions similar to ours, TOFMS demonstrated the presence of preferably C\({}_{26}\)\({}^{+}\) fragments and smaller amount of C\({}_{60}\)\({}^{+}\) ions, alongside the neutral nanoparticles, in LIP [25]. In order to provide a qualitative explanation of the obtained HHG results we use the semiclassical model of HHG in isotropic medium [27]. According to this model, the HHG cutoff is defined by the expression \(N_{c}\approx(I_{p}+3.2U_{p})/\omega\), where \(I_{p}\) is the ionization potential of elemental emitter, \(\omega\) is the laser field frequency, \(U_{p}=I_{l}/(4\omega^{2})\) is the pondermotive potential, and \(I_{l}\) is the laser field intensity. The ionization potential of carbon atom is \(I_{p}\) (Bulk C) = 11.26 eV [28], while the ionization potential for small-sized carbon molecules varies from \(I_{p}\) (C\({}_{2}\)) = 11.35 eV, \(I_{p}\) (C\({}_{3}\)) = 11.5 eV to \(I_{p}\) (C\({}_{9}\)) = 9.4 eV [26] with the tendency to decrease toward bigger molecules. For C\({}_{60}\) \begin{table}
\begin{tabular}{c c c} \hline  & & **F**, \\  & & **J cm\({}^{-2}\)** \\ \hline
1 & Graphite & 3 \\
2 & Fullerenes & 1.4 \\
3 & Carbon nanotubes & 1.2 \\
4 & Carbon nanofiber & 1.2 \\
5 & Diamond nanoparticles & 1.7 \\
6 & Graphene & 1.4 \\ \hline \end{tabular}
\end{table} 
Table 1: Summary of the optimal fluencies of heating pulses for each of studies carbon-containing target. Figure 4: Panel (**a**): dependences of the integrated yield comprising 9 th to 25 th harmonics on the delay between nanosecond heating pulse (HP) and femtosecond driving pulse (DP). Panel (**b**): raw images of the harmonics at the optimal delay for each plasma sample. Images are normalized and logarithmically scaled. For bulk C, the maximal yield of harmonics is shown at a a delay equal to 200 ns. The optimal delays for C\({}_{60}\), MW CNT, CNF, Gr, and DN were 200, 400, 300, 300, and 500 ns, respectively. the ionization potential is correspondingly lower compared to smaller-sized molecules (\(I_{p}\) (C\({}_{60}\)) = 7.6 eV [29]). The application of our experimental parameters in expression for harmonic cutoff gives \(N_{c}\) (bulk C) = 31 and \(N_{c}\) (C\({}_{60}\)) = 29. Note that in the present work the 25 th and 21 st harmonics cutoffs from those species were observed. Thus, we attribute the observed peculiarities of HHG spectra in pair \"bulk C-C\({}_{60}\)\" to the presence of mostly C\({}_{60}\) and its large fragments in the plasma plume, which was indirectly confirmed by our plasma emission spectra (Figure 2, C\({}_{60}\) panel), where the relative intensity of the CI transition line is lower than that of CIII and CIV lines. Larger harmonics cutoff in bulk C targets can be attributed to the presence of mostly neutral and small-sized carbon molecules in LIP. The presence of highly charged ions does not provide sufficient contribution to the extension of HHG cutoff, since the HHG conversion efficiency quickly reduces with increasing ionization potential.