- Letter
- Open Access
Coherent attosecond x-ray pulses from beam-driven relativistic plasma mirrors
Phys. Rev. Research 8, L022009 – Published 10 April, 2026
DOI: https://doi.org/10.1103/w9yj-4hh5
Abstract
We propose a compact source of coherent attosecond x-ray pulses based on laser reflection from nonlinear plasma waves driven by relativistic charged particle beams. Analytical theory and particle-in-cell simulations show that such beams can excite strongly nonlinear plasma waves acting as relativistic mirrors. The reflection of millijoule-level laser pulses from such mirrors in micron-scale plasmas can produce coherent few-attosecond x-ray pulses with pulse duration, peak intensity, and spectral brightness potentially surpassing those of state-of-the-art coherent x-ray sources, all within a significantly reduced footprint. Laser intensification by up to 2 orders of magnitude is demonstrated. The resulting coherent attosecond pulses open avenues for probing ultrafast dynamics of atoms, molecules, and even electrons, enabling transformative applications across atomic physics, chemistry, materials science, and structural biology.
Physics Subject Headings (PhySH)
See Also
Theory of beam-driven nonlinear plasma wake and interior waves
Article Text
Supplemental Material
References (49)
- A. Einstein, Zur elektrodynamik bewegter körper, Ann. Phys. 4, 891 (1905).
- S. V. Bulanov, T. Esirkepov, and T. Tajima, Light intensification towards the Schwinger limit, Phys. Rev. Lett. 91, 085001 (2003).
- S. V. Bulanov, T. Z. Esirkepov, M. Kando, A. S. Pirozhkov, and N. N. Rosanov, Relativistic mirrors in plasmas–novel results and perspectives, Phys. Usp. 56, 429 (2013).
- T. Z. Esirkepov and S. V. Bulanov, Luminal mirror, Phys. Rev. E 109, L023202 (2024).
- F. Krausz and M. Ivanov, Attosecond physics, Rev. Mod. Phys. 81, 163 (2009).
- R. Neutze, R. Wouts, D. Van der Spoel, E. Weckert, and J. Hajdu, Potential for biomolecular imaging with femtosecond X-ray pulses, Nature (London) 406, 752 (2000).
- P. G. O’Shea and H. P. Freund, Free-electron lasers: Status and applications, Science 292, 1853 (2001).
- S. Boutet, P. Fromme, and M. S. Hunter, X-ray Free Electron Lasers (Springer, London, 2018).
- S. Bulanov, T. Z. Esirkepov, M. Kando, J. Koga, K. Kondo, and G. Korn, On the problems of relativistic laboratory astrophysics and fundamental physics with super powerful lasers, Plasma Phys. Rep. 41, 1 (2015).
- G. A. Mourou, T. Tajima, and S. V. Bulanov, Optics in the relativistic regime, Rev. Mod. Phys. 78, 309 (2006).
- P. Chen and G. Mourou, Accelerating plasma mirrors to investigate the black hole information loss paradox, Phys. Rev. Lett. 118, 045001 (2017).
- C. Pellegrini, A. Marinelli, and S. Reiche, The physics of x-ray free-electron lasers, Rev. Mod. Phys. 88, 015006 (2016).
- M. Kando, T. Z. Esirkepov, J. K. Koga, A. S. Pirozhkov, and S. V. Bulanov, Coherent, short-pulse X-ray generation via relativistic flying mirrors, Quantum Beam Sci. 2, 9 (2018).
- U. Teubner and P. Gibbon, High-order harmonics from laser-irradiated plasma surfaces, Rev. Mod. Phys. 81, 445 (2009).
- M. Kando, Y. Fukuda, A.S. Pirozhkov, J. Ma, I. Daito, L. M. Chen, T. Z. Esirkepov, K. Ogura, T. Homma, Y. Hayashi, H. Kotaki, A. Sagisaka, M. Mori, J. K. Koga, H. Daido, S. V. Bulanov, T. Kimura, Y. Kato, and T. Tajima, Demonstration of laser-frequency upshift by electron-density modulations in a plasma wakefield, Phys. Rev. Lett. 99, 135001 (2007).
- A. Pirozhkov, J. Ma, M. Kando, T. Z. Esirkepov, Y. Fukuda, L.-M. Chen, I. Daito, K. Ogura, T. Homma, Y. Hayashi, et al., Frequency multiplication of light back-reflected from a relativistic wake wave, Phys. Plasmas 14, 123106 (2007).
- M. Kando, A. S. Pirozhkov, K. Kawase, T. Z. Esirkepov, Y. Fukuda, H. Kiriyama, H. Okada, I. Daito, T. Kameshima, Y. Hayashi, et al., Enhancement of photon number reflected by the relativistic flying mirror, Phys. Rev. Lett. 103, 235003 (2009).
- M. Lobet, M. Kando, J. K. Koga, T. Z. Esirkepov, T. Nakamura, A. S. Pirozhkov, and S. V. Bulanov, Controlling the generation of high frequency electromagnetic pulses with relativistic flying mirrors using an inhomogeneous plasma, Phys. Lett. A 377, 1114 (2013).
- H. Moghadasin, A. R. Niknam, D. Komaizi, and M. Banjafar, Attosecond pulse generation by relativistic flying mirrors in laser-plasma interaction: Effect of plasma density and driver amplitude on the generated pulse, Phys. Plasmas 26, 093105 (2019).
- P. Valenta, T. Z. Esirkepov, J. Koga, A. Pirozhkov, M. Kando, T. Kawachi, Y.-K. Liu, P. Fang, P. Chen, J. Mu, et al., Recoil effects on reflection from relativistic mirrors in laser plasmas, Phys. Plasmas 27, 032109 (2020).
- J. Mu, T. Z. Esirkepov, P. Valenta, Y. Gu, T. M. Jeong, A. S. Pirozhkov, J. K. Koga, M. Kando, G. Korn, and S. V. Bulanov, Relativistic flying forcibly oscillating reflective diffraction grating, Phys. Rev. E 102, 053202 (2020).
- S. V. Bulanov, N. Naumova, and F. Pegoraro, Interaction of an ultrashort, relativistically strong laser pulse with an overdense plasma, Phys. Plasmas 1, 745 (1994).
- R. Lichters, J. Meyer-ter Vehn, and A. Pukhov, Short-pulse laser harmonics from oscillating plasma surfaces driven at relativistic intensity, Phys. Plasmas 3, 3425 (1996).
- H. Vincenti, Achieving extreme light intensities using optically curved relativistic plasma mirrors, Phys. Rev. Lett. 123, 105001 (2019).
- F. Quéré and H. Vincenti, Reflecting petawatt lasers off relativistic plasma mirrors: A realistic path to the Schwinger limit, High Power Laser Sci. Eng. 9, e6 (2021).
- L. Chopineau, G. Blaclard, A. Denoeud, H. Vincenti, F. Quéré, and S. Haessler, Sub-laser-cycle control of relativistic plasma mirrors, Phys. Rev. Res. 4, L012030 (2022).
- M. Lamač, K. Mima, J. Nejdl, U. Chaulagain, and S. V. Bulanov, Anomalous relativistic emission from self-modulated plasma mirrors, Phys. Rev. Lett. 131, 205001 (2023).
- V. V. Kulagin, V. A. Cherepenin, M. S. Hur, and H. Suk, Theoretical investigation of controlled generation of a dense attosecond relativistic electron bunch from the interaction of an ultrashort laser pulse with a nanofilm, Phys. Rev. Lett. 99, 124801 (2007).
- D. Kiefer, M. Yeung, T. Dzelzainis, P. Foster, S. Rykovanov, C. L. Lewis, R. Marjoribanks, H. Ruhl, D. Habs, J. Schreiber, et al., Relativistic electron mirrors from nanoscale foils for coherent frequency upshift to the extreme ultraviolet, Nat. Commun. 4, 1763 (2013).
- W. J. Ma, J. H. Bin, H. Y. Wang, M. Yeung, C. Kreuzer, M. Streeter, P. S. Foster, S. Cousens, D. Kiefer, B. Dromey, X. Q. Yan, J. Meyer-ter-Vehn, M. Zepf, and J. Schreiber, Bright subcycle extreme ultraviolet bursts from a single dense relativistic electron sheet, Phys. Rev. Lett. 113, 235002 (2014).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/w9yj-4hh5 for derivation.
- P. Chen, J. M. Dawson, R. W. Huff, and T. Katsouleas, Acceleration of electrons by the interaction of a bunched electron beam with a plasma, Phys. Rev. Lett. 54, 693 (1985).
- T. Katsouleas, Physical mechanisms in the plasma wake-field accelerator, Phys. Rev. A 33, 2056 (1986).
- M. Lamač, P. Valenta, U. Chaulagain, J. Nejdl, D. Čáp, O. Morvai, and S. V. Bulanov, companion paper, Theory of beam-driven nonlinear plasma wake and interior waves, Phys. Rev. E 113, 045209 (2026).
- T. Arber, K. Bennett, C. Brady, A. Lawrence-Douglas, M. Ramsay, N. Sircombe, P. Gillies, R. Evans, H. Schmitz, A. Bell, et al., Contemporary particle-in-cell approach to laser-plasma modelling, Plasma Phys. Controlled Fusion 57, 113001 (2015).
- A. Golovanov and I. Y. Kostyukov, Bubble regime of plasma wakefield in 2D and 3D geometries, Phys. Plasmas 25, 103107 (2018).
- A. F. Lifschitz, X. Davoine, E. Lefebvre, J. Faure, C. Rechatin, and V. Malka, Particle-in-cell modelling of laser–plasma interaction using Fourier decomposition, J. Comput. Phys. 228, 1803 (2009).
- A. Davidson, A. Tableman, W. An, F. S. Tsung, W. Lu, J. Vieira, R. A. Fonseca, L. O. Silva, and W. B. Mori, Implementation of a hybrid particle code with a PIC description in – and a gridless description in into OSIRIS, J. Comput. Phys. 281, 1063 (2015).
- A. Caldwell, K. Lotov, A. Pukhov, and F. Simon, Proton-driven plasma-wakefield acceleration, Nat. Phys. 5, 363 (2009).
- P. Muggli, E. Adli, R. Apsimon, F. Asmus, R. Baartman, A.-M. Bachmann, M. B. Marin, F. Batsch, J. Bauche, V. B. Olsen, et al., AWAKE readiness for the study of the seeded self-modulation of a 400 GeV proton bunch, Plasma Phys. Controlled Fusion 60, 014046 (2018).
- L. Verra, G. Z. Della Porta, J. Pucek, T. Nechaeva, S. Wyler, M. Bergamaschi, E. Senes, E. Guran, J. Moody, M. Kedves, et al., Controlled growth of the self-modulation of a relativistic proton bunch in plasma, Phys. Rev. Lett. 129, 024802 (2022).
- T. Ziegler, I. Göthel, S. Assenbaum, C. Bernert, F.-E. Brack, T. E. Cowan, N. P. Dover, L. Gaus, T. Kluge, S. Kraft, et al., Laser-driven high-energy proton beams from cascaded acceleration regimes, Nat. Phys. 20, 1211 (2024).
- M. Streeter, G. Glenn, S. DiIorio, F. Treffert, B. Loughran, H. Ahmed, S. Astbury, M. Borghesi, N. Bourgeois, C. Curry, et al., Stable laser-acceleration of high-flux proton beams with plasma collimation, Nat. Commun. 16, 1004 (2025).
- C. N. Danson, C. Haefner, J. Bromage, T. Butcher, J.-C. F. Chanteloup, E. A. Chowdhury, A. Galvanauskas, L. A. Gizzi, J. Hein, D. I. Hillier, et al., Petawatt and exawatt class lasers worldwide, High Power Laser Sci. Eng. 7, e54 (2019).
- S. S. Bulanov, V. Y. Bychenkov, V. Chvykov, G. Kalinchenko, D. W. Litzenberg, T. Matsuoka, A. G. R. Thomas, L. Willingale, V. Yanovsky, K. Krushelnick, et al., Generation of GeV protons from 1 PW laser interaction with near critical density targets, Phys. Plasmas 17, 043105 (2010).
- K. V. Lezhnin and S. V. Bulanov, Laser ion acceleration from tailored solid targets with micron-scale channels, Phys. Rev. Res. 4, 033248 (2022).
- J. Li, X. Ren, Y. Yin, K. Zhao, A. Chew, Y. Cheng, E. Cunningham, Y. Wang, S. Hu, Y. Wu, et al., 53-attosecond X-ray pulses reach the carbon K-edge, Nat. Commun. 8, 186 (2017).
- C. Lazzarini, G. Grittani, P. Valenta, I. Zymak, R. Antipenkov, U. Chaulagain, L. Goncalves, A. Grenfell, M. Lamač, S. Lorenz, et al., Ultrarelativistic electron beams accelerated by terawatt scalable kHz laser, Phys. Plasmas 31, 030703 (2024).
- D. Attwood and A. Sakdinawat, X-Rays and Extreme Ultraviolet Radiation: Principles and Applications, 2nd ed. (Cambridge University Press, NY, USA, 2017).