Comparative analytical and numerical investigation of the plasma density in atmospheric air generated by nanosecond laser pulses

Energy deposition via laser-induced breakdown (LIB) in gases or other media and its accompanying secondary light and sound radiative processes are nowadays increasingly deployed in scientific and technological applications. The modeling and control of the breakdown and radiative processes occurring by the interactions of the free electrons with the heavy particles in the partially ionized medium, requires precise spatio-temporal description of the generated free electron density. This work presents an analysis of a free electron rate model describing the free electron density in air plasmas produced by nanosecond laser pulses. The model accounts for multiphoton and cascade ionization, and for electron diffusion, recombination, and attachment. A closed-form expression of the rate model is derived and validated by comparison with experimentally validated numerical solutions, showing very good agreement in a wide range of parameters. Simulation results are presented for different laser pulses and focal spot sizes and analysis is carried out regarding the dependence of the air plasma on the various laser radiation parameters. The presented approach is particularly useful for complex multi-scale models calculating the electron and ion temperature evolution, the thermoelastic expansion and the shock-wave following LIB of gases.