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

We investigate the interaction between a superintense laser pulse and nitrogen plasmas with electron densities exceeding 10 19cm⁻³ using particle-in-cell simulations. Recent experiments have shown that such dense-plasma configurations can efficiently generate highly charged few-MeV electron beams, even exceeding 10snC per shot with ∼1J, tens-of-femtosecond laser pulses—a significant step toward high-average-current laser–plasma accelerators and related applications. Through a systematic study varying laser energy and plasma density, we analyze the effects of laser self-focusing on beam propagation and wakefield formation. Our results reveal empirical scaling laws describing beam diffraction, wakefield amplitude, and plasma structures, including the formation of a massive channel-like cavity. These findings provide new insights into the strongly nonlinear interaction regime of laser–plasma dynamics at high plasma densities.