Scaling laws in plasma channels for laser wakefield accelerators

Preformed plasma channels are essential for guiding driver laser pulses over extended distances in laser wakefield accelerators (LWFAs), enabling the generation of multi-giga-electron volt electron beams for the applications of free-electron lasers and particle colliders. Optical-field ionization (OFI) heating provides a robust approach for creating laser-matched plasma channels across a broad range of parameters, owing to its density- and geometry-independent heating effect. Establishing predictive scaling laws between channel parameters and formation conditions is critical for the design of plasma channels capable of accelerating electrons from energies of hundreds of mega-electron volt up to tens of giga-electron volt. Through a combination of timescale analysis and numerical simulations, hydrodynamic expansion has been identified as the dominant mechanism governing density profile evolution during OFI channel formation, which leads to the similarity in density profiles under normalized conditions. As a result, this method preserves effective laser-guiding channel structures across a wide range of initial gas density (1017–1019 cm−3) and initial ionization radius (10–100 μm). For parabolic channels optimized for Gaussian laser drivers, scaling laws have been established, indicating that the on-axis density scales linearly with the initial gas density, while the matching radius exhibits an exponential dependence on both the initial gas density and the ionization laser radius. These findings provide a systematic framework for the parameter design and optimization of plasma channels in high-efficiency and high-energy LWFA applications.