Empirical scaling laws for self-focused laser pulses in nitrogen plasmas

We investigate the interaction between a superintense laser pulse and a nitrogen plasma with densities exceeding $10^{19}\,$cm$^{-3}$, using particle-in-cell simulations. Such configurations have recently demonstrated the capability to produce highly charged electron beams (i.e., $>10\,$nC) with $1\,$J-class lasers, a significant step toward high-average-current laser-plasma accelerators. Our study focuses on analyzing the impact of laser self-focusing on laser dynamics, leading to scaling laws that characterize beam diffraction, wakefield amplitude and plasma structures, providing important insights of this interaction regime.