Scaling Laws in Plasma Channels for Laser Wakefield Accelerators

Preformed plasma channels are essential for guiding high-power laser pulses over extended distances in laser wakefield accelerators, enabling the generation of multi-GeV electron beams for applications such as free-electron lasers and particle colliders. Above-threshold ionization heating provides a robust mechanism for creating laser-matched plasma channels across a wide parameter range, owing to its density- and geometry-independent heating effect. Establishing predictive scaling laws between channel parameters and formation conditions is critical for designing channels optimized for electron acceleration across energies spanning hundreds of MeV to tens of GeV. Through combined timescale analysis and numerical simulations, hydrodynamic expansion is identified as the dominant mechanism governing density profile evolution during ATI channel formation. Remarkably, this process maintains effective laser-guiding channel structures across a wide range of initial gas density, as evidenced by the persistent profile similarity observed despite these significant parameter variations. For parabolic channels matched to Gaussian laser drivers, rigorous scaling laws are established that, the on-axis density scales linearly with the initial gas density, while the matching radius has an exponential dependence on both the initial gas density and the ionization laser radius. These findings provide a systematic framework for the predictive design and optimization of plasma channels in high-efficiency and high-energy LWFA applications.