Saturation of the filament density of ultrashort intense laser pulses in air

We experimentally and numerically characterize multiple filamentation of laser pulses with incident intensities of a few TW/cm(2). Propagating 100 TW laser pulses over 42 m in air, we observe a new propagation regime where the filament density saturates. As also evidenced by numerical simulations in the same intensity range, the total number of filaments is governed by geometric constraints and mutual interactions among filaments rather than by the available power in the beam.