With the use of multiple longitudinal modes nanosecond laser pulses at 1064 nm, laser damage sites at the exit surface of fused silica clearly and systematically exhibit ring patterns. It has been shown in our previous works that the apparent chronology of rings was closely related to the temporal shape of the laser pulses. This particular correspondence had suggested an explanation of the ring morphology formation based on the displacement of an ionization front in the surrounding air. To provide a former basis for this hypothesis and deeper understanding of ring pattern formation, additional experiments have been performed. First, the impact of fluence has been investigated, revealing that a wide variety of damage sites are produced within a very narrow fluence range; this fact involves the chronology of appearance of a surface plasma during the laser pulse. The sizes of the damage sites are proportional to the fluence of their expansion occurring between the beginning of the plasma and the end of the laser pulse. Second, specific experiments have been carried out at different angles of incidence, resulting in egg-shaped patterns rather than circular ones. This behavior can be explained by our previous hypothesis of creation of a plasma in air, its expansion being tightly conditioned by the illumination angle. This series of experiments, in which the angle of incidence is varied up to 80°, permits us to link quantitatively the working hypothesis of ionization front propagation with theoretical hydrodynamics modeling.