- Open Access
Performance evaluation of beam breakup instability analysis of energy recovery linac using physics-inspired neural networks
Phys. Rev. Accel. Beams 29, 095101 – Published 17 September, 2026
DOI: https://doi.org/10.1103/9kpd-tlbg
Abstract
Beam breakup (BBU) instability limits the performance of energy recovery linacs (ERLs). This study presents a new approach to estimating the BBU threshold current using a physics-inspired neural network. The application of neural networks to the highly nonlinear beam dynamics of ERLs opens a new paradigm for the development of efficient future particle accelerators. It is found that figure-of-merit-based data can predict the threshold current with higher accuracy than directly feeding the proposed network with raw parameter-based data. This study investigates how embedding such a physically meaningful feature influences predictive performance and generalization. In this work, the effect of the variation in higher-order modes (HOM) parameters due to the geometrical tolerances in the rf cavity fabrication on the BBU threshold current is analyzed with the proposed multilayered bidirectional long short-term memory (BiLSTM) neural network.
Physics Subject Headings (PhySH)
Article Text
References (27)
- L. Merminga, Energy Recovery Linacs, in Synchrotron Light Sources and Free-Electron Lasers, edited by E. Jaeschke, S. Khan, J. Schneider, and J. Hastings (Springer, Cham, 2016), .
- A. Hutton, Energy-recovery linacs for energy-efficient particle acceleration, Nat. Rev. Phys. 5, 708 (2023).
- S. A. Bogacz et al. (PERLE Collaboration), Beam dynamics driven design of powerful energy recovery linac for experiments, Phys. Rev. Accel. Beams. 27, 031603 (2024).
- D. Angal-Kalinin et al., PERLE. Powerful energy recovery linac for experiments. Conceptual design report, J. Phys. G 45, 065003 (2018).
- P. Agostini et al. (LHeC and FCC-he Study Group), The Large Hadron–Electron Collider at the HL-LHC, J. Phys. G 48, 110501 (2021).
- O. Brüning, A. Seryi, and S. Verdú-Andrés, Electron-Hadron Colliders: EIC, LHeC and FCC-eh, Front. Phys. 10, 886473 (2022).
- European Strategy Group, Update of the European strategy for particle physics, CERN, Tech. Rep. CERN-ESU-013, 2020.
- E. Pozdeyev, Regenerative multipass beam breakup in two dimensions, Phys. Rev. ST Accel. Beams 8, 054401 (2005).
- C. D. Tennant, K. B. Beard, D. R. Douglas, K. C. Jordan, L. Merminga, E. G. Pozdeyev, and T. I. Smith, First observations and suppression of multipass, multibunch beam breakup in the Jefferson Laboratory free electron laser upgrade, Phys. Rev. ST Accel. Beams 8, 074403 (2005).
- E. Pozdeyev, C. Tennant, J. J. Bisognano, M. Sawamura, R. Hajima, and T. I. Smith, Multipass beam breakup in energy recovery linacs, Nucl. Instrum. Methods Phys. Res., Sect. A 557, 176 (2006).
- B. C. Yunn, Expressions for the threshold current of multipass beam breakup in recirculating linacs from single cavity models, Phys. Rev. ST Accel. Beams 8, 104401 (2005).
- S. Setiniyaz, R. Apsimon, and P. H. Williams, Implications of beam filling patterns on the design of recirculating energy recovery linacs, Phys. Rev. Accel. Beams 23, 072002 (2020).
- S. Setiniyaz, R. Apsimon, and P. H. Williams, Filling pattern dependence of regenerative beam breakup instability in energy recovery linacs, Phys. Rev. Accel. Beams 24, 061003 (2021).
- S. Setiniyaz, R. Apsimon, M. Southerby, and P. H. Williams, in Proceedings of the 31st International Linear Accelerator Conference (LINAC2022) (JACoW Publishing, Geneva, Switzerland, 2022), p. TUPORI20.
- S. Setiniyaz, R. Apsimon, S. A. Bogacz, R. M. Bodenstein, K. Deitrick, P. H. Williams, I. Bailey et al., Beam breakup instability studies of powerful energy recovery linac for experiments, Phys. Rev. Accel. Beams 28, 011003 (2025).
- A. Edelen and X. Huang, Machine learning for design and control of particle accelerators: A look backward and forward, Annu. Rev. Nucl. Part. Sci. 74, 557 (2024).
- A. Scheinker, F. Cropp, S. Paiagua, and D. Filippetto, An adaptive approach to machine learning for compact particle accelerators, Sci. Rep. 11, 19187 (2021).
- A. L. Edelen, S. G. Biedron, B. E. Chase, D. Edstrom, S. V. Milton, and P. Stabile, Neural networks for modeling and control of particle accelerators, IEEE Trans. Nucl. Sci. 63, 878 (2016).
- A. Hanuka, X. Huang, J. Shtalenkova, D. Kennedy, A. Edelen, Z. Zhang, V. R. Lalchand, D. Ratner, and J. Duris, Physics model-informed Gaussian process for online optimization of particle acceleratorsPhys. Rev. Accel. Beams 24, 072802 (2021).
- O. Convery, L. Smith, Y. Gal, and A. Hanuka, Uncertainty quantification for virtual diagnostic of particle accelerators, Phys. Rev. Accel. Beams 24, 074602 (2021).
- K. Fujita, Physics-informed neural network method for space charge effect in particle accelerators, IEEE Access 9, 164017 (2021).
- A. Ivanov and I. Agapov, Physics-based deep neural networks for beam dynamics in charged particle accelerators, Phys. Rev. Accel. Beams 23, 074601 (2020).
- C. D. Tennant. Studies of energy recovery linacs at Jefferson Laboratory: 1 GeV demonstration of energy recovery at CEBAF and studies of the multibunch, multipass beam breakup instability in the 10 kW FEL upgrade driver, Ph. D. thesis, College of William and Mary, Williamsburg, VA, USA, 2006.
- N. Valles, Pushing the frontiers of superconducting radio frequency science: From the temperature dependence of the superheating field of niobium to higher-order mode damping in very high quality factor accelerating structures, Ph. D. thesis, Cornell University, Ithaca, NY, USA, 2014.
- C. Barbagallo, P. Duchesne, W. Kaabi, G. Olry, F. Zomer, R. A. Rimmer, H. Wang, R. Apsimon, and S. Setiniyaz, HOM-damping studies in a multi-cell elliptical superconducting RF cavity for the multi-turn energy recovery linac PERLE, arXiv:2409.13798.
- C. Barbagallo, Design and optimization of higher order mode couplers for the superconducting cavities of the PERLE energy recovery linac, Ph.d. thesis, University Paris-Saclay, Geneva, Switzerland, 2024.
- The MathWorks, Inc., MATLAB and Deep Learning Toolbox, version: R2025b (The MathWorks, Inc., Natick, Massachusetts, United States, 2025), https://www.mathworks.com.