Towards Cavity-Based X-ray Free-Electron Lasers: Milestones and Challenges

Abstract

Cavity-based X-ray free-electron lasers (CBXFELs) could advance X-ray science by delivering fully coherent radiation with high spectral brightness and enhanced pulse control, addressing the limitations of conventional self-amplified spontaneous emission paradigms. Recent experiments at the European XFEL have demonstrated spectral narrowing and proof-of-concept multi-pass amplification, marking the first experimental signature of the tightly coupled three-body interaction between relativistic electron beams, FEL gain dynamics, and high-finesse Bragg cavities. This review consolidates advances in CBXFEL theory built on this framework, global R$\&$D efforts, and outstanding technical challenges arising from the coupled system. CBXFELs support applications in X-ray spectroscopy, quantum optics, and precision metrology. Future directions prioritize CBXFEL stabilization, X-ray comb generation, and applications in coherent quantum control of nuclear transitions.