Toward high-gain laser-driven electron undulators

Free-electron laser (FEL) is a powerful tool that provides high-brightness radiation across a wide range of frequencies up to the x-ray spectrum. However, the large size and high cost of FEL facilities have limited their accessibility and widespread adoption. To address this challenge, researchers have explored the possibility of replicating FEL physics using lasers instead of magnetic undulators, but practical implementation has remained unattainable. This study proposes a laser-driven approach for generating high-brightness x-ray radiation. Similar to FELs, the method relies on collective coherent emission, where electrons are bunched through highly nonlinear interactions with the laser and their own radiation. This process enables high-gain undulation, a phenomenon previously exclusive to FEL facilities. We establish the fundamental scaling laws of high-gain laser undulation, identifying the upper limits of radiation peak power and brightness determined by Coulomb repulsion and quantum recoil. Promising operational regimes are highlighted, including extreme ultraviolet and soft x rays (water window) using advanced electron and laser sources, with potential extension to hard x rays through low-gain laser undulation in an oscillator configuration. These findings contribute to the ongoing pursuit of compact sources of high-brightness radiation, paving the way for more accessible and versatile x-ray sources. On the fundamental side, they open previously inaccessible regimes of strong-field electrodynamics, offering new opportunities to explore quantum phenomena in extreme conditions.