Optimized laser wakefield acceleration: Generating stable, high-energy, monoenergetic electron beams and demonstrating extreme-ultraviolet free-electron lasers

Free electron lasers (FELs) are powerful, tunable light sources capable of delivering ultrashort, coherent radiation over a wide spectral range, but their broad scientific and technological impact is limited by the size and cost of large-scale accelerators. Laser wakefield acceleration (LWFA) offers a compact alternative via the ultrahigh accelerating gradients, though achieving FEL gain with such beams remains a major challenge due to the stringent beam-quality requirements. Here, we present a successful demonstration of a laser-plasma accelerator-driven FEL operating at a central wavelength of 40 nm with a highly nonlinear gain. A compact 0.8 J laser system, combined with precise control over the plasma-density profile, injection conditions, and the stability of both laser wave front and gas jet, enabled the generation of high-quality monoenergetic electron beams with excellent shot-to-shot reproducibility. A comprehensive start-to-end simulation framework was established, incorporating beam acceleration, transport, and FEL generation. Each stage of the simulation shows good agreement with the experimental diagnostics. The resulting FEL radiation exhibits clear exponential gain of approximately 20 times. This work highlights a reliable route toward compact, tunable, x-ray FELs driven by LWFA, and represents a significant step toward practical applications of laser-plasma-based light sources.