Electrons wiggling through an undulator emit coherent X-rays via SASE
In a free electron laser, relativistic electrons pass through a periodic magnet array (undulator). The wiggling motion emits synchrotron radiation at λ = λ_u/(2γ²)·(1+K²/2). SASE (Self-Amplified Spontaneous Emission): radiation bunches the electrons, which then radiate coherently — exponential gain over ~10 gain lengths. FELs reach angstrom wavelengths impossible with conventional lasers.