Evidence for Gain in Trapped Ions and a Cavity Concept for Future X-ray Laser

Coherent X-ray sources are indispensable tools in probing microstructures, resolving ultrafast dynamics, and investigating related phenomena, yet current technologies suffer from irreconcilable trade-offs between miniaturization, high brightness, high coherence, and high repetition rates---forming a critical bottleneck. Here, to our knowledge, we present the first theoretical validation of a groundbreaking ''non-plasma" X-ray laser gain medium. This approach employs ion trapping and cooling techniques to generate and confine highly charged Neon-like (or Ne-like) ions in an ultra-high vacuum environment, where ion excitation is achieved via collisions with a fixed-direction quasi-monoenergetic electron beam. Through first-principles simulations integrating the fully relativistic Flexible Atomic Code (FAC) and collisional-radiative models (CRM), we first validate our theoretical framework against established plasma-based scenarios, then extended to the ''non-plasma" regime and, rigorously demonstrate that excitation of highly charged Ne-like ions (Kr, Xe, W, U) by a fixed-direction quasi-monoenergetic electron beam can effectively achieve population inversion---establishing its principle feasibility. This analysis identifies a series of potential X-ray laser transitions spanning wavelengths from 0.45 nm to 9.88 nm, with small-signal gain coefficients ranging from 0.005 cm ^-1 to 59 cm ^-1 for electron densities between 1 × 10 ¹⁹ cm ^-3 and 1 × 10 ²² cm ^-3 To realise practical X-ray lasing, we further propose constructing an X-ray cavity using two high-reflectivity Bragg-diffracting crystals with specialised facets and two compound refractive lenses (CRLs), enabling coherent X-ray emission in a ''driver-laser-free" and ''non-plasma" environment. This work provides a critical theoretical foundation for developing compact, high-brightness, highly coherent X-ray lasers with high repetition rates and even continuous-wave operation. It indicates the potential transformation of X-ray lasers from ''big-science'' facilities to standard laboratory platforms, opening new ways for advances in materials science, life sciences, semiconductor lithography, and beyond.