Spectral control of a cavity-based x-ray free-electron laser via active mode locking

Precise spectral control in the hard x-ray regime remains a long-standing challenge that limits applications in atomic-scale science and ultrafast spectroscopy. We present a proposal and numerical study of an actively mode-locked cavity-based x-ray free-electron laser that achieves deterministic spectral programmability with phase-locked pulse trains and comblike spectra, by coherently modulating the electron-beam energy. Three-dimensional time-dependent simulations predict <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>700</a:mn> <a:mspace width="0.16em"/> <a:mi>μ</a:mi> <a:mi mathvariant="normal">J</a:mi> </a:mrow> </a:math> total energy, <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>30</d:mn> <d:mspace width="0.16em"/> <d:mi mathvariant="normal">G</d:mi> <d:mi mathvariant="normal">W</d:mi> </d:mrow> </d:math> peak power, and frequency-comb spacing of <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mn>1.55</h:mn> <h:mspace width="0.16em"/> <h:mi mathvariant="normal">e</h:mi> <h:mi mathvariant="normal">V</h:mi> </h:mrow> </h:math> set by the modulation frequency. We further develop selective single-line amplification via undulator tapering and absolute frequency positioning through modulation-laser tuning with meV precision. Importantly, stable mode-locked operation persists under &gt;80% peak-to-peak cavity-reflectivity variations, substantially relaxing requirements on x-ray optics. These results establish active mode locking as a practical route to fully coherent, spectrally agile hard x-ray sources and enable opportunities in time-resolved core-level spectroscopy, x-ray quantum optics, and precision metrology.