Nonequilibrium dynamics of laser-generated plasma channels

A time-dependent nonequilibrium kinetics model based upon the time-dependent electron Boltzmann equation coupled with an extensive air chemistry model accounting for gas heating and vibrational kinetics is developed. The model is applied to the temporal evolution of femtosecond laser-generated air plasma channels at atmospheric pressure in an external electric field. The plasma channel dynamics depend upon the initial free electron density, the initial electron energy of the plasma, and upon the externally applied electric field strength. The model predicts an electric breakdown field strength of 5-10 kV/cm with a delay time of hundreds of nanoseconds when the electron density drops to the optimum value of ∼10¹²-10¹³ cm^-3. The experimentally observed breakdown field is ∼5.7 kV/cm with a statistical breakdown delay time of ∼200 ns. The reduction in the breakdown field strength in natural air from ∼30 to 5 kV/cm is attributed to a combination of processes such as enhanced ionization due to relaxation of the initial electron energy distribution function toward a Maxwellian distribution, strong electron detachment, and gas heating. The calculated electron density decay of the laser-generated plasma channel in both pure nitrogen and dry air is in good agreement with the NRL experiments. The derived rate constant for recombination in dry air is b_B^air=3.9x10^-8 cm³ s^-1 and in pure nitrogen it is b_B^N₂=4.4x10^-8 cm³ s^-1. The attachment rate coefficient in dry air is η_B^air=7.5x10⁶ s^-1