Simulation of Femtosecond Laser-Induced Positive Polarity Discharge

Femtosecond lasers with fs-level pulses and TWlevel powers can generate plasma filaments that affect discharge behaviour under external fields. However, the microscopic interaction mechanisms between laser-induced plasma and positive polarity discharge remain insufficiently understood. In this paper, a two-dimensional numerical simulation framework based on laser filament fluid model is developed to investigate the microscopic processes of filament-induced discharge under external electric fields. Based on previous study of filament plasma characteristics, the simulation initializes a filament with a peak electron density of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2.4 \times 10^{21} / \mathrm{m}^{3}$</tex>, a length of 2 mm, and a radius of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$50 \mu ~\mathrm{m}$</tex>, under a background electric field of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2-4.5 \text{kV} / \text{cm}$</tex>. Simulation results show that within 50 ps, the electron density distribution of the filament evolves from an initial Gaussian profile into a stable bimodal distribution, with the peak density rising to <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$3.5 \times 10^{21} / \mathrm{m}^{3}$</tex>. The charge redistribution significantly distorts the surrounding electric field, reaching peak intensities of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$1825 ~\mathrm{V} / \text{cm}$</tex> (anode side) and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$-1750 ~\mathrm{V} / \text{cm}$</tex> (cathode side) under <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$2 \text{kV} / \text{cm}$</tex> field. Besides, simulation results under different background electric fields reveal that a higher applied field <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$(4.5 \text{kV} / \text{cm})$</tex> enhances ionization and diffusion processes on the anode side, maintaining peak electric field intensities of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$80-90 \text{kV} / \text{cm}$</tex> from 400 to 800 ps, and promoting early initiation of positive polarity streamer channels. These findings provide important theoretical insights into the microscopic mechanisms of femtosecond laser-induced positive discharge.