Intelligent multi-objective optimization for high-performance betatron radiation sources

Hansheng Ye; Jiaxing Wen; Feng Wan; Song Li; Sijie Fan; Genbai Chu; Sixin Wu; Shaoyi Wang; Minghai Yu; Yue Yang; Tiankui Zhang; Wentao Wang; Yuqiu Gu; Weiming Zhou; Zongqing Zhao

doi:10.1063/5.0325710

Volume 11 Issue 5

Sep. 2026

Turn off MathJax

Article Contents

Article Navigation > Matter and Radiation at Extremes > 2026 > 11(5): 057206

Hansheng Ye, Jiaxing Wen, Feng Wan, Song Li, Sijie Fan, Genbai Chu, Sixin Wu, Shaoyi Wang, Minghai Yu, Yue Yang, Tiankui Zhang, Wentao Wang, Yuqiu Gu, Weiming Zhou, Zongqing Zhao. Intelligent multi-objective optimization for high-performance betatron radiation sources[J]. Matter and Radiation at Extremes, 2026, 11(5): 057206. doi: 10.1063/5.0325710

Citation:

Hansheng Ye, Jiaxing Wen, Feng Wan, Song Li, Sijie Fan, Genbai Chu, Sixin Wu, Shaoyi Wang, Minghai Yu, Yue Yang, Tiankui Zhang, Wentao Wang, Yuqiu Gu, Weiming Zhou, Zongqing Zhao. Intelligent multi-objective optimization for high-performance betatron radiation sources[J]. Matter and Radiation at Extremes, 2026, 11(5): 057206. doi: 10.1063/5.0325710

Citation:

Hansheng Ye, Jiaxing Wen, Feng Wan, Song Li, Sijie Fan, Genbai Chu, Sixin Wu, Shaoyi Wang, Minghai Yu, Yue Yang, Tiankui Zhang, Wentao Wang, Yuqiu Gu, Weiming Zhou, Zongqing Zhao. Intelligent multi-objective optimization for high-performance betatron radiation sources[J]. Matter and Radiation at Extremes, 2026, 11(5): 057206. doi: 10.1063/5.0325710

PDF( 7376 KB)

Intelligent multi-objective optimization for high-performance betatron radiation sources

doi: 10.1063/5.0325710

1.
National Key Laboratory of Plasma Physics, Laser Fusion Research Center (LFRC), China Academy of Engineering Physics (CAEP), Mianyang 621900, China
2.
Ministry of Education Key Laboratory for Nonequilibrium Synthesis and Modulation of Condensed Matter, Shaanxi Province Key Laboratory of Quantum Information and Quantum Optoelectronic Devices, School of Physics, Xi’an Jiaotong University, Xi’an 710049, China
3.
State Key Laboratory of Ultra-intense Laser Science and Technology, Shanghai Institute of Optics and Fine Mechanics (SIOM), Chinese Academy of Sciences (CAS), Shanghai 201800, China
4.
Shanghai Institute of Laser Plasma, China Academy of Engineering Physics (CAEP), Shanghai 201800, China

More Information

Corresponding author: a)Author to whom correspondence should be addressed: zhaozongqing99@caep.cn
Received Date: 2026-02-01
Accepted Date: 2026-06-03

Available Online: 2026-09-28

Publish Date: 2026-09-01

Abstract

Abstract

Betatron radiation, generated by electrons undergoing transverse oscillations in laser wakefield acceleration, represents a promising compact X-ray source. It features micrometer-scale source size, femtosecond pulse duration, and high peak brightness comparable to that of third-generation synchrotron facilities. These properties make it highly suitable for phase-contrast imaging and ultrafast dynamic probing. However, betatron radiation sources still need improvements in photon number, critical energy, and source size, and optimization is challenging owing to the complex coupling and trade-offs among these key performance parameters. Traditional single-objective optimization strategies often fail to achieve a global optimum. This paper proposes a multi-objective Bayesian optimization framework integrated with particle-in-cell simulations to address this challenge. By systematically tuning critical parameters including laser focal position, plasma density, and plasma length, our method efficiently navigates the parameter space and identifies the Pareto front within 90 iterations. Results demonstrate that photon number and critical energy can be simultaneously optimized, while the source size is the primary limiting factor. The established predictive model further aids in physical analysis and application-specific source design, paving the way for intelligent, closed-loop control of high-performance betatron radiation sources.

The authors have no conflicts to disclose.
Conflict of Interest
Hansheng Ye: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Methodology (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Jiaxing Wen: Conceptualization (equal); Methodology (equal); Supervision (equal); Writing – review & editing (equal). Feng Wan: Formal analysis (equal); Methodology (equal); Writing – review & editing (equal). Song Li: Conceptualization (equal); Methodology (equal). Sijie Fan: Conceptualization (equal); Methodology (equal); Writing – review & editing (equal). Genbai Chu: Writing – review & editing (equal). Sixin Wu: Project administration (equal); Supervision (equal). Shaoyi Wang: Conceptualization (equal); Resources (equal). Minghai Yu: Formal analysis (equal); Writing – original draft (equal). Yue Yang: Conceptualization (equal); Investigation (equal); Supervision (equal). Tiankui Zhang: Writing – review & editing (equal). Wentao Wang: Supervision (equal); Writing – review & editing (equal). Yuqiu Gu: Conceptualization (equal); Methodology (equal); Supervision (equal). Weiming Zhou: Supervision (equal). Zongqing Zhao: Resources (equal).
Author Contributions
The data that support the findings of this study are available from the corresponding author upon reasonable request.

FullText(HTML)

References(55)

References

[1]	L. Mino, E. Borfecchia, J. Segura-Ruiz, C. Giannini, G. Martinez-Criado et al., “Materials characterization by synchrotron x-ray microprobes and nanoprobes,” Rev. Mod. Phys. 90, 025007 (2018).10.1103/revmodphys.90.025007
[2]	F. Albert and A. G. R. Thomas, “Applications of laser wakefield accelerator-based light sources,” Plasma Phys. Controlled Fusion 58, 103001 (2016).10.1088/0741-3335/58/10/103001
[3]	F. Albert, M. E. Couprie, A. Debus, M. C. Downer, J. Faure et al., “2020 roadmap on plasma accelerators,” New J. Phys. 23, 031101 (2021).10.1088/1367-2630/abcc62
[4]	T. Tajima and J. M. Dawson, “Laser electron accelerator,” Phys. Rev. Lett. 43, 267–270 (1979).10.1103/physrevlett.43.267
[5]	J. Faure, Y. Glinec, A. Pukhov, S. Kiselev, S. Gordienko et al., “A laser-plasma accelerator producing monoenergetic electron beams,” Nature 431, 541–544 (2004).10.1038/nature02963
[6]	W. Lu, C. Huang, M. Zhou, W. B. Mori, and T. Katsouleas, “Nonlinear theory for relativistic plasma wakefields in the blowout regime,” Phys. Rev. Lett. 96, 165002 (2006).10.1103/physrevlett.96.165002
[7]	X. Wang, R. Zgadzaj, N. Fazel, Z. Li, S. A. Yi et al., “Quasi-monoenergetic laser-plasma acceleration of electrons to 2 GeV,” Nat. Commun. 4, 1988 (2013).10.1038/ncomms2988
[8]	A. J. Gonsalves, K. Nakamura, J. Daniels, C. Benedetti, C. Pieronek et al., “Petawatt laser guiding and electron beam acceleration to 8 GeV in a laser-heated capillary discharge waveguide,” Phys. Rev. Lett. 122, 084801 (2019).10.1103/physrevlett.122.084801
[9]	S. Corde, K. Ta Phuoc, G. Lambert, R. Fitour, V. Malka et al., “Femtosecond x rays from laser-plasma accelerators,” Rev. Mod. Phys. 85, 1–48 (2013).10.1103/revmodphys.85.1
[10]	K. Ta Phuoc, E. Esarey, V. Leurent, E. Cormier-Michel, C. G. R. Geddes et al., “Betatron radiation from density tailored plasmas,” Phys. Plasmas 15, 063102 (2008).10.1063/1.2918657
[11]	A. Rousse, K. T. Phuoc, R. Shah, A. Pukhov, E. Lefebvre et al., “Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction,” Phys. Rev. Lett. 93, 135005 (2004).10.1103/physrevlett.93.135005
[12]	X.-L. Zhu, M. Chen, S.-M. Weng, T.-P. Yu, W.-M. Wang et al., “Extremely brilliant GeV γ-rays from a two-stage laser-plasma accelerator,” Sci. Adv. 6, eaaz7240 (2020).10.1126/sciadv.aaz7240
[13]	Y. Lu, G.-B. Zhang, J. Zhao, Y.-T. Hu, H. Zhang et al., “Ultra-brilliant GeV betatronlike radiation from energetic electrons oscillating in frequency-downshifted laser pulses,” Opt. Express 29, 8926–8940 (2021).10.1364/oe.419761
[14]	S. Kneip, C. McGuffey, J. L. Martins, S. F. Martins, C. Bellei et al., “Bright spatially coherent synchrotron X-rays from a table-top source,” Nat. Phys. 7, 737 (2011).10.1038/nphys2093
[15]	H. Zhang, Z. Deng, H. Jiang, S. Wang, J. Wei et al., “High-brightness betatron X-ray source driven by the SULF-1 PW laser,” High Power Laser Sci. Eng. 13, e31 (2025).10.1017/hpl.2025.17
[16]	J. Cikhardt, M. Gyrdymov, S. Zähter, P. Tavana, M. M. Günther et al., “Characterization of bright betatron radiation generated by direct laser acceleration of electrons in plasma of near critical density,” Matter Radiat. Extremes 9, 027201 (2024).10.1063/5.0181119
[17]	Y. Zhao, H. Lu, C. Zhou, and J. Zhu, “Overcritical electron acceleration and betatron radiation in the bubble-like structure formed by re-injected electrons in a tailored transverse plasma,” Matter Radiat. Extremes 8, 014403 (2023).10.1063/5.0121558
[18]	R. Rakowski, P. Zhang, K. Jensen, B. Kettle, T. Kawamoto et al., “Transverse oscillating bubble enhanced laser-driven betatron X-ray radiation generation,” Sci. Rep. 12, 10855 (2022).10.1038/s41598-022-14748-z
[19]	U. Chaulagain, M. Lamač, M. Raclavský, K. P. Khakurel, K. H. Rao et al., “ELI gammatron beamline: A dawn of ultrafast hard X-ray science,” Photonics 9, 853 (2022).10.3390/photonics9110853
[20]	S. Fourmaux, E. Hallin, U. Chaulagain, S. Weber, and J. C. Kieffer, “Laser-based synchrotron X-ray radiation experimental scaling,” Opt. Express 28, 3147–3158 (2020).10.1364/oe.383818
[21]	F. Galdenzi, M. P. Anania, A. Balerna, R. J. Bean, A. Biagioni et al., “The EuAPS betatron radiation source: Status update and photon science perspectives,” Condens. Matter 9, 30 (2024).10.3390/condmat9030030
[22]	B. Guo, X. Zhang, J. Zhang, J. Hua, C.-H. Pai et al., “High-resolution phase-contrast imaging of biological specimens using a stable betatron X-ray source in the multiple-exposure mode,” Sci. Rep. 9, 7796 (2019).10.1038/s41598-019-42834-2
[23]	J. M. Cole, D. R. Symes, N. C. Lopes, J. C. Wood, K. Poder et al., “High-resolution μCT of a mouse embryo using a compact laser-driven X-ray betatron source,” Proc. Natl. Acad. Sci. U. S. A. 115, 6335–6340 (2018).10.1073/pnas.1802314115
[24]	V. Tomkus, V. Girdauskas, J. Dudutis, P. Gečys, V. Stankevič et al., “Laser wakefield accelerated electron beams and betatron radiation from multijet gas targets,” Sci. Rep. 10, 16807 (2020).10.1038/s41598-020-73805-7
[25]	J. M. Cole, J. C. Wood, N. C. Lopes, K. Poder, R. L. Abel et al., “Laser-wakefield accelerators as hard x-ray sources for 3D medical imaging of human bone,” Sci. Rep. 5, 13244 (2015).10.1038/srep13244
[26]	J. Wenz, S. Schleede, K. Khrennikov, M. Bech, P. Thibault et al., “Quantitative X-ray phase-contrast microtomography from a compact laser-driven betatron source,” Nat. Commun. 6, 7568 (2015).10.1038/ncomms8568
[27]	S. Fourmaux, S. Corde, K. T. Phuoc, P. Lassonde, G. Lebrun et al., “Single shot phase contrast imaging using laser-produced betatron x-ray beams,” Opt. Lett. 36, 2426–2428 (2011).10.1364/ol.36.002426
[28]	A. Döpp, L. Hehn, and J. Götzfried, “Quick X-ray microtomography using a laser-driven betatron source,” Optica 2, 199–203 (2018).10.1364/OPTICA.5.000199
[29]	W. Jiaxing, G. Hang, W. Sixin, Z. Tao, Z. Gaojie et al., “In-situ characterization of metal laser additive manufacturing using a laser-driven X-ray source,” High Power Laser Part. Beams 37, 071001 (2025).10.11884/HPLPB202537.250191.
[30]	B. Mahieu, N. Jourdain, K. Ta Phuoc, F. Dorchies, J. P. Goddet et al., “Probing warm dense matter using femtosecond X-ray absorption spectroscopy with a laser-produced betatron source,” Nat. Commun. 9, 3276 (2018).10.1038/s41467-018-05791-4
[31]	C. I. Hojbota, M. Mirzaie, D. Y. Kim, T. G. Pak, M. Rezaei-Pandari et al., “High-energy betatron source driven by a 4-PW laser with applications to non-destructive imaging,” Eur. Phys. J. A 59, 247 (2023).10.1140/epja/s10050-023-01159-5
[32]	M. Schnell, A. Sävert, I. Uschmann, M. Reuter, M. Nicolai et al., “Optical control of hard X-ray polarization by electron injection in a laser wakefield accelerator,” Nat. Commun. 4, 2421 (2013).10.1038/ncomms3421
[33]	B. Guo, Z. Cheng, S. Liu, X. N. Ning, J. Zhang et al., “Enhancement of laser-driven betatron x-rays by a density-depressed plasma structure,” Plasma Phys. Controlled Fusion 61, 035003 (2019).10.1088/1361-6587/aaf613
[34]	M. Kozlova, I. Andriyash, J. Gautier, S. Sebban, S. Smartsev et al., “Hard X rays from laser-wakefield accelerators in density tailored plasmas,” Phys. Rev. X 10, 011061 (2020).10.1103/physrevx.10.011061
[35]	J. Chen, S. Xu, N. Tang, S. Wang, and Z. Li, “Enhanced soft x-ray betatron radiation from a transversely oscillating laser plasma wake,” Opt. Express 29, 13302–13313 (2021).10.1364/oe.420150
[36]	C. Yu, J. Liu, W. Wang, W. Li, R. Qi et al., “Enhanced betatron radiation by steering a laser-driven plasma wakefield with a tilted shock front,” Appl. Phys. Lett. 112, 133503 (2018).10.1063/1.5019406
[37]	J. Ferri, S. Corde, A. Döpp, A. Lifschitz, A. Doche et al., “High-brilliance betatron γ-ray source powered by laser-accelerated electrons,” Phys. Rev. Lett. 120, 254802 (2018).10.1103/physrevlett.120.254802
[38]	Z. H. He, B. Hou, V. Lebailly, J. A. Nees, K. Krushelnick et al., “Coherent control of plasma dynamics,” Nat. Commun. 6, 7156 (2015).10.1038/ncomms8156
[39]	S. J. D. Dann, C. D. Baird, N. Bourgeois, O. Chekhlov, S. Eardley et al., “Laser wakefield acceleration with active feedback at 5 Hz,” Phys. Rev. Accel. Beams 22, 041303 (2019).10.1103/physrevaccelbeams.22.041303
[40]	P. W. Hatfield, J. A. Gaffney, G. J. Anderson, S. Ali, L. Antonelli et al., “The data-driven future of high-energy-density physics,” Nature 593, 351–361 (2021).10.1038/s41586-021-03382-w
[41]	J. Lin, Q. Qian, J. Murphy, A. Hsu, A. Hero et al., “Beyond optimization-supervised learning applications in relativistic laser-plasma experiments,” Phys. Plasmas 28, 083102 (2021).10.1063/5.0047940
[42]	H. Saberi, J. Burvill, C. Siddle, G. Xia, J. Patrick Farmer et al., “Data-driven beam diagnostics using betatron radiation,” Plasma Phys. Controlled Fusion 68, 025014 (2026).10.1088/1361-6587/ae3eb3
[43]	N. F. Beier, V. Senthilkumaran, E. Kriz, S. Fourmaux, F. Légaré et al., “Deep learning based x-ray spectrometer for high repetition rate characterization of betatron radiation,” Phys. Plasmas 31, 103106 (2024).10.1063/5.0219183
[44]	R. J. Shalloo, S. J. D. Dann, J. N. Gruse, C. I. D. Underwood, A. F. Antoine et al., “Automation and control of laser wakefield accelerators using Bayesian optimization,” Nat. Commun. 11, 6355 (2020).10.1038/s41467-020-20245-6
[45]	S. Jalas, M. Kirchen, P. Messner, P. Winkler, L. Hübner et al., “Bayesian optimization of a laser-plasma accelerator,” Phys. Rev. Lett. 126, 104801 (2021).10.1103/physrevlett.126.104801
[46]	H. Ye, Y. Gu, X. Zhang, S. Wang, F. Tan et al., “Fast optimization for betatron radiation from laser wakefield acceleration based on Bayesian optimization,” Results Phys. 43, 106116 (2022).10.1016/j.rinp.2022.106116
[47]	F. Irshad, C. Eberle, F. M. Foerster, K. v. Grafenstein, F. Haberstroh et al., “Pareto optimization and tuning of a laser Wakefield accelerator,” Phys. Rev. Lett. 133, 085001 (2024).10.1103/physrevlett.133.085001
[48]	B. Shahriari, K. Swersky, Z. Wang, R. P. Adams, and N. de Freitas, “Taking the human out of the loop: A review of Bayesian optimization,” Proc. IEEE 104, 148–175 (2016).10.1109/jproc.2015.2494218
[49]	C. E. Rasmussen and C. K. I. Williams, Gaussian Processes for Machine Learning (MIT, 2005), pp. 1–247.
[50]
[51]	M. Chen, E. Esarey, C. G. R. Geddes, C. B. Schroeder, and W. P. Leemans, “Ionization-induced trapping in laser-plasma accelerators and synchrotron radiation from the betatron oscillation,” in Proceedings of the 2011 Particle Accelerator Conference (JACoW, New York, 2011).
[52]	Y. Ma, D. Seipt, S. J. D. Dann, M. J. V. Streeter, C. A. J. Palmer et al., “Angular streaking of betatron X-rays in a transverse density gradient laser-wakefield accelerator,” Phys. Plasmas 25, 113105 (2018).10.1063/1.5054807
[53]	M. Zeng and K. Seto, “Radiation reaction of betatron oscillation in plasma wakefield accelerators,” New J. Phys. 23, 075008 (2021).10.1088/1367-2630/ac12fa
[54]	M. Schnell, A. Sävert, B. Landgraf, M. Reuter, M. Nicolai et al., “Deducing the electron-beam diameter in a laser-plasma accelerator using x-ray betatron radiation,” Phys. Rev. Lett. 108, 075001 (2012).10.1103/physrevlett.108.075001
[55]	S. M. Lundberg and S.-I. Lee, “A unified approach to interpreting model predictions,” in NIPS’17: Proceedings of the 31st International Conference on Neural Information Processing Systems, Long Beach CA (Curran Associates, Inc., 2017).