Compact coherent x-ray sources have been the focus of extensive research efforts over the past decades. As a result, several novel schemes like optical and nano-undulators for generating x-ray emissions in "table-top" setups are proposed, developed, and assessed. Despite the extensive efforts in the past decades, there exists as yet no operational free-electron laser (FEL) based on optical or electromagnetic undulators. In this paper, by combining the particle confinement capability of optical cavities with wiggling motion inside an optical undulator, we propose a new concept for making a compact coherent x-ray source. The full-wave solution of first-principle equations based on finite-difference time-domain and particle-in-cell (FDTD/PIC) is performed to simulate inverse-Compton scattering (ICS) of both free and confined electrons. We show that the strong space-charge effect in a low-energy (5 MeV) electron beam is the main obstacle to acquisition of coherent gain through the ICS mechanism with a 10-mm laser. Subsequently, it is shown that confinement of the electron beam at the field nodes of an optical cavity allows the space-charge effect to be compensated, and, additionally, the ultrahigh charge density enables high FEL gain at the confinement spots. Full-wave numerical simulations predict enhancement of about three orders of magnitude in the radiation efficiency when ICS is carried out with confined electrons compared to free electrons. These theoretical results show the promising potential of transverse confinement of electron beams as a novel scheme for implementation of a compact coherent x-ray source.
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