Analytical Study of Electron-Driven Ionization Dynamics and Plasma Formation in Intense Laser Fields

Laser-induced breakdown in water-rich biological media results from the interplay between primary photoionization processes and avalanche amplification of free electrons. Understanding this competition is essential for predicting ablation thresholds under ultrashort-pulse irradiation. In this work, we develop an analytical rate-equation model for the buildup of electron density in water-like biological tissues. It combines photoionization and chromophore ionization into a single seed-generation term, while avalanche ionization is described through a cascade gain factor. This formulation provides a framework for describing cascade electron-impact ionization processes in liquid-like media under strong-field excitation. Our approach gives an analytical expression for the temporal evolution of electron density driven by a Gaussian laser pulse and makes it possible to separate the contributions of direct ionization of water and ionization of chromophore centers. The analytical results are compared with numerical simulations that include carrier diffusion, bimolecular recombination and trapping. The comparison clarifies the roles of seed formation and cascade amplification in the growth of the electron population. The predicted dependence of threshold fluence on pulse duration agrees well with experimental data reported for water-like tissues such as the corneal tissues at a wavelength of 800 nm. The model provides a simple analytical picture of ultrafast plasma formation and electron-driven energy deposition in water-like biological media.