Fundamental scaling laws of water-window X-rays from free-electron-driven van der Waals structures

Water-window X-rays are crucial in medical and biological applications, enabling the natural-contrast imaging of biological cells without external staining. However, water-window X-ray sources with bespoke photon energies—needed in high-contrast imaging—remain challenging to obtain, except at large synchrotron facilities. Here we address this challenge by demonstrating tabletop, water-window X-ray generation from free-electron-driven van der Waals materials, enabling the continuous tuning of photon energies across the entire water-window regime. Additionally, we present a truly predictive theoretical framework combining first-principles electromagnetism with Monte Carlo simulations to accurately predict the photon flux and brightness in absolute quantities. We obtain fundamental scaling laws for the tunable photon flux, matching the experimental results and providing a way to design powerful emitters based on free-electron-driven quantum materials. We show that we can potentially achieve photon fluxes needed for imaging and spectroscopy applications (over 10⁸ photons s^–1 on the sample—verified by our framework based on our experimentally achieved fluxes of about 10³ photons s^–1 using ~50 nA current). Importantly, our theory highlights the critical role played by the large mean free paths and interlayer atomic spacings unique to van der Waals structures, showing the latter’s advantages over other materials in generating water-window X-rays.