## 4 Discussion
With the increasing of the delay, the 11 th to 15 th harmonics also enhanced (Figure 3, right column, red solid lines), while up to 500 ns delay the harmonic spectral shape and cutoff located at 25 th order remained the same (Figure 4b). The observed peculiarities of HHG spectra from GR and DN plasmas can be explained by the presence of the small-sized carbon molecules and clusters having uniform distribution of velocities. The latter assumption can explain the flattened delay curves with the same HHG cutoffs (23 rd and 25 th orders). The cutoff positions for all studied samples were, to some extent, close to each other except for graphene (Figure 3). Though the ionization potentials were almost similar, the studied plasmas were distinguished from each other by the harmonic yield rather than by cutoff energy. Below, we address the importance of considering the above delay-dependent experiments for understanding the dynamics of plasma propagation. The signature, indicating the presence of specific emitters, is the increase in the output of harmonics at certain specific delays from the beginning of ablation. We can assume that the same average kinetic energy E = mv\({}^{2}\)/2 could characterize all plasma components containing the same basic atom, in our case carbon. Accordingly, the same average arrival time could be expected for carbon clusters of different sizes. The duration for cluster propagation from the target surface to the optical axis of the femtosecond pulse propagation corresponds to the optimal delay between HP and DP. Our results show that small carbon clusters enter the area of interaction with the femtosecond beam much earlier than expected, assuming only kinetic consideration when it is assumed that the components reach thermodynamic equilibrium during expansion. Alternatively, we can suppose that all carbon clusters acquire the same kinetic energy from the very beginning and propagate from the surface at speed approximately similar to that of a single carbon ablated from bulk material. The arrival times of particles consisting of a single carbon atom, 60 atoms (fullerene), 10\({}^{6}\) atoms (diamond nanoparticles), 10\({}^{9}\) atoms (CNT and CNF), and even much larger species, such as parts of graphene sheets, were comparable to each other (200-400 ns). Thus, the role of the cluster's atomic weight in HHG becomes questionable if only a simple kinetic energy mechanism is considered. In other words, from the very beginning, all the atoms in the clusters acquire the same kinetic energy and propagate from the surface at speed approximately equal to that of a single carbon atom. When we use the term \"heating\" for the laser ablation, we do not merely suppose the thermal evaporation of the target. It is not a simple thermal evaporation induced plasma formation. This process depends on the level of target excitation that is used for laser ablation. The creation of nonlinear medium above the target surface is not based on the simple heating of the target surface and steady-state processes of melting, evaporation, and spreading of the particles with the velocities defined from the thermodynamic relations. This relation refers to cw heating. In this case the velocity of the C\({}_{60}\) molecule at 1000 K is in the range of 1.5 \(\times\) 10\({}^{2}\) m s\({}^{-1}\). Correspondingly, during the first few hundred nanoseconds (\(\sim\)200 ns corresponding to our observation of maximal yield of harmonics) the fullerene molecules will move only 30 \(\upmu\)m above the surface. Notice that femtosecond driving pulse propagates at the distance of \(\sim\)0.2 mm above the target's surface. If one assumes that plasma creation by laser pulses is defined by this slow process, then no harmonics at all should be observed in such experimental configuration for any of our targets, be it C\({}_{60}\), CNT, CNF, graphene, or DN.