Intense laser pulses can be employed to generate plasma, carbon aggregates, and nanoparticles. The plasma produced by ns laser pulses impinging on carbon targets in a vacuum generates carbon vapors, atoms nucleation and growth of nano aggregates. Mass quadrupole spectrometry has permitted to analyze the mass of the carbon atoms and molecules produced in a vacuum by laser-generated plasma, discovering that the fullerene C20 and other small carbon aggregates have a high probability of being produced. In this paper, the conditions of C20 aggregate synthetization are presented, and their yield generation is approximately evaluated. It also calculated the process ablation yield, the maximum carbon energy acquired in the plasma, the plasma temperature and density, the adiabatic plasma expansion velocity, and the carbon ion charge state distributions. To this, measurements of time-of-flight (TOF) of ions have been performed using suitable ion collectors and ion energy analyzers.