Higher order modes at FELs: a machine interpretation

In X-ray Free-Electron Lasers (FELs), intense and coherent pulses are generated via amplification of the undulator radiation from micro-bunched electron pulses. The initial radiation is spontaneous and intrinsically stochastic, thus causing shot-to-shot fluctuations in the intensity, pointing, and spatiotemporal profile of the X-ray beam. In this work, we use deep neural networks to investigate the fluctuations in X-ray beam profiles, thereby obtaining statistical information on the lasing process. A supervised model was built to classify X-ray images, and an unsupervised one to study the distribution of beam profiles. We have found that round-shaped profiles appear more often with increasing monochromator bandwidth, suggesting that some round-shaped images can be superpositions of higher-order modes. Our results also suggest that the X-ray beam continues to evolve past the FEL saturation length towards a round-shaped beam profile.