Interaction of dielectrics with femtosecond laser pulses: Application of kinetic approach and multiple rate equation

We calculate the transient free-electron density in laser-irradiated dielectrics with two different approaches, both considering the energy distribution of excited electrons. The kinetic approach solves a system of complete Boltzmann collision integrals describing different excitation and relaxation processes in detail. The multiple rate equation (MRE) is an approximative way to keep track of the energy distribution of excited electrons with reduced numerical effort. Both methods are applied to trace dielectric breakdown, considering the changing optical parameters during irradiation with a high-intensity laser pulse. In the MRE approach we include also fast recombination, leading to a delay of the increase of the electronic density and to a decrease of the maximum number of free electrons.