Optical breakdown and filamentation of femtosecond laser pulses propagating in air at a kHz repetition rate

We report the experiments on the optical breakdown and filamentation of femtosecond laser pulses propagating in air at a kHz repetition rate and with several hundreds micro-joule-energy. A 10m-long filament and its breakup and merging at the nonlinear focal region produced by modulational instability of femtosecond laser pulses in air are observed. A simple model based on the nonlinear Schr?dinger equation coupled with multiphoton ionization law is presented to explain the several experimental results.