Multi-rate-equation modeling of the energy spectrum of laser-induced conduction band electrons in water

We study the energy spectrum of laser-induced conduction band (CB) electrons in water by multi-rate equations (MRE) with different impact ionization schemes. Rethfeld's MRE model [Phys. Rev. Lett. 92, 187401 (2004)] enables tracking the evolution of the energy distribution of CB electrons during femtosecond breakdown and deriving an asymptotic single-rate equation (SRE) suitable for the calculation of energy deposition at longer (picosecond to nanosecond) pulse durations. However, the impact ionization scheme neglects the excess energy remaining after collisional ionization of valence band electrons. This shortcoming is overcome by an energy splitting scheme introduced by Christensen and Balling [Phys. Rev. B 79, 155424 (2009)], but the corresponding rate equations are computationally very expensive. We introduce a simplified splitting scheme and corresponding rate equations that still agree with energy conservation but enable the derivation of an asymptotic SRE. This approach is well suited for the calculation of energy spectra at long pulse durations and high irradiance, and for combination with spatiotemporal beam propagation/plasma formation models. Using the energy-conserving MREs, we present the time-evolution of CB electron density and energy spectrum during femtosecond breakdown as well as the irradiance dependence of free-electron density, energy spectrum, volumetric energy density, and plasma temperature. These data are relevant for understanding photodamage pathways in nonlinear microscopy, free-electron-mediated modifications of biomolecules in laser surgery, and laser processing of transparent dielectrics in general.