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  • Open Access

Symplectic machine learning model for fast simulation of space-charge effects

Jinyu Wan1,*, Ji Qiang2, and Yue Hao1,†

  • *Contact author: wan@frib.msu.edu
  • †Contact author: haoy@frib.msu.edu
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Phys. Rev. Accel. Beams 28, 074602 – Published 31 July, 2025

DOI: https://doi.org/10.1103/bhpv-bcqk

Abstract

Symplectic simulation of space-charge effects is crucial for the design and operation of high-intensity particle accelerators. Traditional methods for simulating these effects are often computationally expensive, resulting in significant overhead. In this work, we introduce a generative model based on a U-Net architecture within a generative adversarial network framework to efficiently simulate space-charge effects. The model is trained to predict the transverse multiparticle space-charge Hamiltonian, which can be physically computed using a gridless spectral method. The one-step symplectic transverse transfer map for the particles is then obtained by differentiating the predicted Hamiltonian. Benchmarking results demonstrate that this generative model achieves an order of magnitude higher computational efficiency compared to the spectral method, providing a highly efficient alternative for simulating space-charge effects with a large number of particles. By maintaining symplecticity, the model effectively preserves the phase-space structure and mitigates nonphysical errors in long-term simulations. This model has been integrated into jutrack, a novel autodifferentiable accelerator modeling code developed in the julia programming language.

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Phys. Rev. Accel. Beams 28, 074602– Published 31 July, 2025
  • Received 28 February 2025
  • Accepted 16 July 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

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