## 3 Results
It is important to note that higher densities of free electrons cause the phase mismatch between the driving and harmonics waves for overheated and strongly ionized plasmas, which plays a destructive role in HHG. The moderate fluencies of nanosecond pulses also increased the lifetime of the targets and provided better survival of the original nanostructures being ablated and spread in the plasma plume without their destruction. It was demonstrated that, in the case of laser ablation of C\({}_{60}\), MW CNT, CNF, and DN [25] at the experimental conditions similar to ours, the transmission electron microscopy analysis of deposited debris has shown that laser-produced plumes contained the original nanostructures. Figure 3 shows the harmonic spectra in different plasmas at variable delays between heating and driving pulses in the 100-600 ns range. The dependences of the harmonic yield on the delay are plotted in Figure 4a. The left column of Figure 3 compares the harmonics generated from 9 th to 25 th order from bulk C (blue curve) and C\({}_{60}\) (red curve). The maximal harmonic yields for both samples were observed at \(\sim\)200 ns delay from the beginning of the ablation. Meanwhile, the delay dependence for C\({}_{60}\) (Figure 4a, red line with empty squares) demonstrates higher integrated harmonics signal, as well as it is extended up to longer delays (\(\sim\)1 \(\mu\)s). In the case of bulk C (Figure 4a, black line with filled squares) we observed a pronounced single maximum at 200 ns, which can be interpreted as the moment of arriving of the largest amount of elemental emitters to the interaction area with DP. The estimation for the velocity of the main part of emitters shows that it equals 1.2 \(\times\) 10\({}^{3}\) m/s, which is close to our HHG-based measurements in the case of DP propagation at 0.2 mm distance from the target surface (\(\sim\)(1-2) \(\times\) 10\({}^{3}\) m/s). The delay dependence in the case of C\({}_{60}\) (Figure 4a) demonstrates a weak decay between 200 and 600 ns, which can be interpreted as a gradual passing of C\({}_{60}\) and its different fragments through the interaction area at the velocities slightly varying from 1 \(\times\) 10\({}^{3}\) m/s. As one can see (left column of Figure 3), in the case of harmonic spectrum from C\({}_{60}\) their yield gradually increased and maintained almost equal for the 9 th to 17 th orders in the range of 200 to 500 ns delays. Figure 4b shows the saturated images of harmonics collected by CCD camera from the phosphorous screen of the microchannel plate of XUV spectrometer at the optimal delays of each studied sample. The images are shown in log scale and normalized to 1. The purpose of such presentation of harmonics distribution is to define the maximal order of generated harmonics, i.e., harmonic cutoff, and better view the difference in harmonic intensities from various species. In this figure, an emission is observable on the right side of 9H in the first five spectra, which is a second-order diffraction related with strong emission from 17 th order. One can also see the weak second-order diffraction related to the 19H (see third panel from the top in the case of MW CNT), which is seen on the left side of 9H. Similar pattern is seen in some panels of Figure 3 showing the lineouts of the harmonic spectra. Figure 3: High-order harmonic generation (HHG) spectra generated from the plasmas produced on the bulk C and C\({}_{60}\) (left column), CNT and CNF (middle column), GR and DN (right column) at the HP-DP delays ranging from 100 ns to 600 ns. The contribution to HHG spectra from different components of ablated plume spreading with almost similar velocities is shown. For bulk C and C\({}_{60}\) we notice a difference in the harmonic cutoffs. From all six samples, ablated bulk C allowed the generation of the highest cutoff at similar conditions of experiments (25 th order; we also observed very weak 27 th harmonic, however, its signal was close to the sensitivity limit of our detection system).