Efficient prediction of attosecond two-colour pulses from an X-ray free-electron laser with machine learning

Aug 5, 2026

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X-ray free-electron lasers produce coherent, high-intensity X-ray pulses, but stochastic SASE and hard-to-control electron injection lead to strong noise and limited temporal coherence. Conventional diagnostics for two-coloured attosecond pulses are often invasive or expensive, making central photon-energy prediction difficult. This work uses machine learning, including neural networks and decision trees, to predict central photon energies for paired fundamental and second-harmonic pulses from easily recorded single-shot parameters. Real experimental data support feature analysis and model training-time optimization.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages10

Reading Time25 min

AccessFree to download

Background: XFEL pulses and diagnostic challenges

Two-colour and enhanced SASE operation

Machine-learning prediction approach

Input parameters and feature analysis

Model training, validation, testing

Model capabilities and experimental implications

Single-pulse prediction without measuring the other

Applications in time-resolved spectroscopy

[www. nature.com/scientificreports](www. nature.com/scientificreports) OPEN Efficient prediction of attosecond two‑colour pulses from an X‑ray free‑electron laser with machine learning Karim K. Alaa El‑Din1*, Oliver G. Alexander1, Leszek J. Frasinski1, Florian Mintert1,3, Zhaoheng Guo4, Joseph Duris4, Zhen Zhang4, David B. Cesar4, Paris Franz4, Taran Driver4, Peter Walter4, James P. Cryan4, Agostino Marinelli4, Jon P. Marangos1 & Rick Mukherjee1,2* X‑ray free‑electron lasers are sources of coherent, high‑intensity X‑rays with numerous applications in ultra‑fast measurements and dynamic structural imaging. Due to the stochastic nature of the self‑ amplified spontaneous emission process and the difficulty in controlling injection of electrons, output pulses exhibit significant noise and limited temporal coherence. Standard measurement techniques used for characterizing two‑coloured X‑ray pulses are challenging, as they are either invasive or diagnostically expensive. In this work, we employ machine learning methods such as neural networksand decision trees to predict the central photon energies of pairs of attosecond fundamental and second harmonic pulses using parameters that are easily recorded at the high‑repetition rate of a single shot. Using real experimental data, we apply a detailed feature analysis on the input parameters while optimizing the training time of the machine learning methods. Our predictive models are able to make predictions of central photon energy for one of the pulses without measuring the other pulse, thereby leveraging the use of the spectrometer without having to extend its detection window. We anticipate applications in X‑ray spectroscopy using XFELs, such as in time‑resolved X‑ray absorption and photoemission spectroscopy, where improved measurement of input spectra will lead to better experimental outcomes. In recent years, X-ray free-electron lasers (XFELs)1–3 have emerged as a versatile tool for research with applications ranging from damage-free dynamic imaging of molecules4 and proteins5–7, new spectroscopic methods for quantum chemistry8,9 and resonant X-ray spectroscopy of nanostructures in condensed matter10, 11. The versatility ofXFELs is based on their tunability, brightness and very short pulse durations, which make the tracking of ultra-fast dynamics of electrons in matter feasible. XFEL sources generate X-ray pulses by accelerating electron bunches to relativistic speeds in a linear accelerator of radiofrequency (RF) cavities and allowing them to interact with magnetic fields generated by an undulator 1–3, see Fig. 1. An XFEL can emit coherent or partially coherent radiation because of a favourable self-organization of the electrons in a relativistic beam as it passes through an appropriately tuned undulator. Different configurations are chosen that lead to the modulation of the phase space for the electron bunch and lasing. This can be used to generate pulses with different properties. Using an additional pre-modulation of the electron beam energy in a short wiggler section, followed by phase space manipulation to transfer the energy into a very short duration high electron current, leads to so-called enhanced SASE that results in sub-femtosecond pulses ofthe kind studied here12. SASE and enhanced SASE pulse are important techniques in ultrafast science13, where dynamics can be resolved using pump-probe configurations with synchronization to infra-red or optical laser fields6, 14 or by using two-pulse XFEL modes15–17. Despite the versatility of XFELs in creating two-colour pulses in the femtosecond regime18, single-shot variation of the pulse energy is significant; for example, photon energy fluctuation of more than 1% of the mean, pulse energy up to 100% of the mean and bandwidth more than 1Blackett Laboratory, Imperial College London, London SW7 2AZ, UK. 2Center for Optical Quantum Technologies, Department of Physics, University of Hamburg, Luruper Chaussee 149, 2276

FAQs

Why are two-colour attosecond X-ray pulse measurements challenging with XFELs?

XFEL outputs show significant noise and limited temporal coherence due to the stochastic SASE process and difficult electron injection control. Standard two-colour characterization methods are often invasive or diagnostically expensive.

What machine-learning methods are used for predicting central photon energies?

The study employs neural networks and decision-tree models based on a gradient boosting classifier, trained and validated using real experimental data.

How does the proposed method reduce measurement requirements?

Predictive models can estimate the central photon energy of one pulse without measuring the other, enabling use of the spectrometer without extending its detection window.

Aug 5, 2026

Upload by Quinn