"Interestingly, the ring structure at the trailing part of the pulse converges with propagation, thus creating the second(weak) maximum in the dependence of the filament energy on the distance (see Figure 1) This convergence occurs because the plasma is confined to the near-axis part of the beam "

Why does the plsama can affect the second energy peak formation along filament?

https://www.osapublishing.org/ol/abstract.cfm?uri=ol-22-5-304