Machine Learning driven beam emittance optimization at EuXFEL

Planned upgrades of the European X-Ray Free Electron Laser (Eu-XFEL) target higher photon energy and a high duty-cycle operation up to CW-operation using a superconducting RF gun with lower gradient. An operation in this regime though critically depends on improvements of the beam slice emittance of the electron gun. Within the OPAL-FEL project, we are addressing this challenge by developing a data-driven optimization framework for longitudinal drive laser shapes to minimize beam emittance, thereby ensuring the delivery of high-quality electron beams. Our approach centers on the application of deep learning techniques to create aninverse model that predicts optimal parameter configurations for the photoin-jector, enabling targeted control of beam emittance. This methodology involvesgenerating synthetic training data through comprehensive beam dynamics sim-ulations and introduces a machine learning-based strategy for temporal pulseshaping, accommodating a broad family of pulse distributions beyond flattopand Gaussian shapes. We present results from trained neural networks with various architectures andestablish a theoretical foundation for the invertibility of the forward model byconnecting our approach to the theory of inverse problems. In particular, wedraw on Whitney’s embedding theorem within the framework of attractor re-construction to validate model invertibility.Leveraging extensive simulations, data-driven modeling and theoretical insights,our approach offers a robust pathway for improved optimization and control ofphotoinjector parameters in CW mode, with potential applications for furtheradvancements in FEL performance.