Fig. 1. Experimental setup for characterizing the plasma in the filament under different repetition rates using spectroscopy.

Fig. 2. Typical spectra of the O I line generated by the laser filament. (a) Multi-Voigt fit for the O I 777.194 nm, 777.417 nm, and 777.539 nm lines was performed to determine the Stark broadening of the plasma. (b) Multi-Voigt fit for the O I 844.626 nm, 844.636 nm, and 844.676 nm lines. The six O I spectral lines were used to plot Boltzmann plot and determine the temperature of the plasma. The laser pulse energy was 4.5 mJ for filamentation.

Fig. 3. (a) Simulated average electron density of the filament as a function of the propagation distance for 1 Hz, 100 Hz, 500 Hz, and 1000 Hz repetition rates. The electron density is averaged in the range of r < 50 µm (the radius of the filament). (b) Electron density of the laser filament as a function of the laser repetition rate. The red line is the simulated average electron density of the filament zone. The filament zone is defined by specifying the filamentation initiation and termination when the electron density approaches 1 × 10¹⁷ cm⁻³.

Fig. 4. (a) Boltzmann plots for O I lines from 100 Hz and 1000 Hz filaments. (b) Plasma temperature as a function of the laser repetition rate. The red line in (b) is the simulated laser intensity inside the filament for comparison. The laser pulse energy was 4.5 mJ for filamentation.