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Analytical theory of coherent radiation and radiation friction in laser-plasma collisions
Phys. Rev. E 114, 025209 – Published 27 August, 2026
DOI: https://doi.org/10.1103/wv25-1w9h
Abstract
We develop an analytical theory of coherent (scaled quadratically with the number of particles) radiation and coherent radiation friction in a head-on collision of a dense charged particle bunch with an intense laser pulse. We demonstrate that the low-frequency coherent radiation in the forward and backward directions dominates the energy-momentum losses of a mildly relativistic bunch and can result in a substantial enhancement of the overall radiation friction as compared to the incoherent case. We derive the scaling laws for the average momentum losses of the bunch over the collision with respect to laser intensity, pulse duration, and particle bunch parameters, and show their robustness with respect to laser polarization and the shape of the particle distribution in the bunch.
Physics Subject Headings (PhySH)
See Also
Coherently Enhanced Radiation Friction in Laser-Plasma Collisions
Article Text
References (68)
- P. A. M. Dirac, Classical theory of radiating electrons, Proc. A 167, 148 (1938).
- L. D. Landau and I. M. Lifshitz, The Classical Theory of Fields, Course of Theoretical Physics, Vol. 2 (Pergamon Press, London, 1988).
- J. D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 2021).
- J. M. Cole, K. T. Behm, E. Gerstmayr, T. G. Blackburn, J. C. Wood, C. D. Baird, M. J. Duff, C. Harvey, A. Ilderton, A. S. Joglekar, et al., Experimental evidence of radiation reaction in the collision of a high-intensity laser pulse with a laser-wakefield accelerated electron beam, Phys. Rev. X 8, 011020 (2018).
- K. Poder, M. Tamburini, G. Sarri, A. Di Piazza, S. Kuschel, C. D. Baird, K. Behm, S. Bohlen, J. M. Cole, D. J. Corvan, et al., Experimental signatures of the quantum nature of radiation reaction in the field of an ultraintense laser, Phys. Rev. X 8, 031004 (2018).
- E. E. Los, E. Gerstmayr, C. Arran, M. J. Streeter, C. Colgan, C. C. Cobo, B. Kettle, T. G. Blackburn, N. Bourgeois, L. Calvin, et al., Observation of quantum effects on radiation reaction in strong fields, Nat. Commun. 17, 1157 (2026).
- B. Voronin and A. Kolomenskii, The pressure of an intense plane wave on a free charge and on a charge in a magnetic field, Sov. Phys. JETP 20, 1027 (1965).
- Y. B. Zel'Dovich, Interaction of free electrons with electromagnetic radiation, Sov. Phys. Usp. 18, 79 (1975).
- A. D. Piazza, Exact solution of the Landau–Lifshitz equation in a plane wave, Lett. Math. Phys. 83, 305 (2008).
- M. Tamburini, F. Pegoraro, A. Di Piazza, C. H. Keitel, and A. Macchi, Radiation reaction effects on radiation pressure acceleration, New J. Phys. 12, 123005 (2010).
- M. Tamburini, F. Pegoraro, A. Di Piazza, C. H. Keitel, T. V. Liseykina, and A. Macchi, Radiation reaction effects on electron nonlinear dynamics and ion acceleration in laser–solid interaction, Nucl. Instrum. Methods Phys. Res. Sect. A 653, 181 (2011).
- M. Tamburini, T. V. Liseykina, F. Pegoraro, and A. Macchi, Radiation-pressure-dominant acceleration: Polarization and radiation reaction effects and energy increase in three-dimensional simulations, Phys. Rev. E 85, 016407 (2012).
- M. Chen, A. Pukhov, T.-P. Yu, and Z.-M. Sheng, Radiation reaction effects on ion acceleration in laser foil interaction, Plasma Phys. Controlled Fusion 53, 014004 (2011).
- R. Capdessus and P. McKenna, Influence of radiation reaction force on ultraintense laser-driven ion acceleration, Phys. Rev. E 91, 053105 (2015).
- E. Gelfer, A. Fedotov, and S. Weber, Radiation induced acceleration of ions in a laser irradiated transparent foil, New J. Phys. 23, 095002 (2021).
- E. Gelfer, N. Elkina, and A. Fedotov, Unexpected impact of radiation friction: Enhancing production of longitudinal plasma waves, Sci. Rep. 8, 6478 (2018).
- E. Gelfer, A. Fedotov, and S. Weber, Theory and simulations of radiation friction induced enhancement of laser-driven longitudinal fields, Plasma Phys. Controlled Fusion 60, 064005 (2018).
- T. Liseykina, S. Popruzhenko, and A. Macchi, Inverse Faraday effect driven by radiation friction, New J. Phys. 18, 072001 (2016).
- S. Popruzhenko, T. Liseykina, and A. Macchi, Efficiency of radiation friction losses in laser-driven ‘hole boring' of dense targets, New J. Phys. 21, 033009 (2019).
- J. Koga, T. Z. Esirkepov, and S. V. Bulanov, Nonlinear Thomson scattering in the strong radiation damping regime, Phys. Plasmas 12, 093106 (2005).
- A. Di Piazza, K. Z. Hatsagortsyan, and C. H. Keitel, Quantum radiation reaction effects in multiphoton Compton scattering, Phys. Rev. Lett. 105, 220403 (2010).
- N. Neitz and A. Di Piazza, Stochasticity effects in quantum radiation reaction, Phys. Rev. Lett. 111, 054802 (2013).
- A. G. R. Thomas, C. P. Ridgers, S. S. Bulanov, B. J. Griffin, and S. P. D. Mangles, Strong radiation-damping effects in a gamma-ray source generated by the interaction of a high-intensity laser with a wakefield-accelerated electron beam, Phys. Rev. X 2, 041004 (2012).
- F. Sauter, Über das Verhalten eines Elektrons im homogenen elektrischen Feld nach der relativistischen Theorie Diracs, Z. Phys. 69, 742 (1931).
- J. Schwinger, On gauge invariance and vacuum polarization, Phys. Rev. 82, 664 (1951).
- V. I. Ritus, Quantum effects of the interaction of elementary particles with an intense electromagnetic field, J. Russ. Laser Res. 6, 497 (1985).
- A. Di Piazza, C. Müller, K. Z. Hatsagortsyan, and C. H. Keitel, Extremely high-intensity laser interactions with fundamental quantum systems, Rev. Mod. Phys. 84, 1177 (2012).
- C. J. Eliezer, On the classical theory of particles, Proc. A 194, 543 (1948).
- G. Ford and R. O'Connell, Radiation reaction in electrodynamics and the elimination of runaway solutions, Phys. Lett. A 157, 217 (1991).
- D. A. Burton and A. Noble, Aspects of electromagnetic radiation reaction in strong fields, Contemp. Phys. 55, 110 (2014).
- A. Gonoskov, T. G. Blackburn, M. Marklund, and S. S. Bulanov, Charged particle motion and radiation in strong electromagnetic fields, Rev. Mod. Phys. 94, 045001 (2022).
- A. Fedotov, A. Ilderton, F. Karbstein, B. King, D. Seipt, H. Taya, and G. Torgrimsson, Advances in QED with intense background fields, Phys. Rep. 1010, 1 (2023).
- F. V. Hartemann, Stochastic electron gas theory of coherence in laser-driven synchrotron radiation, Phys. Rev. E 61, 972 (2000).
- A. Gonoskov, S. Bastrakov, E. Efimenko, A. Ilderton, M. Marklund, I. Meyerov, A. Muraviev, A. Sergeev, I. Surmin, and E. Wallin, Extended particle-in-cell schemes for physics in ultrastrong laser fields: Review and developments, Phys. Rev. E 92, 023305 (2015).
- E. G. Gelfer, A. M. Fedotov, O. Klimo, and S. Weber, Coherent radiation of an electron bunch colliding with an intense laser pulse, Phys. Rev. Res. 6, L032013 (2024).
- E. G. Gelfer, A. M. Fedotov, O. Klimo, and S. Weber, Collective coherent emission of electrons in strong laser fields and perspective for hard x-ray lasers, Matter Radiat. Extremes 9, 024201 (2024).
- J. Schwinger, On radiation by electrons in a betatron, preprint LBNL–39088, July 1996, in A Quantum Legacy: Seminal Papers of Julian Schwinger (World Scientific, Singapore, 2000).
- F. C. Michel, Intense coherent submillimeter radiation in electron storage rings, Phys. Rev. Lett. 48, 580 (1982).
- C. J. Hirschmugl, M. Sagurton, and G. P. Williams, Multiparticle coherence calculations for synchrotron-radiation emission, Phys. Rev. A 44, 1316 (1991).
- J. Vieira, M. Pardal, J. Mendonça, and R. Fonseca, Generalized superradiance for producing broadband coherent radiation with transversely modulated arbitrarily diluted bunches, Nat. Phys. 17, 99 (2021).
- B. Malaca, M. Pardal, D. Ramsey, J. Pierce, K. Weichman, I. Andriyash, W. Mori, J. Palastro, R. Fonseca, and J. Vieira, Coherence and superradiance from a plasma-based quasiparticle accelerator, Nat. Photon. 18, 39 (2024).
- M. J. Quin, A. Di Piazza, and M. Tamburini, Coherent frequency combs from electrons colliding with a laser pulse, Plasma Phys. Controlled Fusion 67, 055008 (2025).
- M. J. Quin, A. Di Piazza, C. H. Keitel, and M. Tamburini, Effect of interparticle fields and radiation reaction on beam dynamics, Phys. Rev. Res. 7, 023210 (2025).
- E. G. Gelfer, A. M. Fedotov, M. P. Malakhov, O. Klimo, and S. Weber, companion paper, Coherently enhanced radiation friction in laser-Plasma collisions, Phys. Rev. Lett. 137, 095001 (2026).
- The role is investigated numerically in the companion Letter [44]; see also [42].
- L. I. Schiff, Production of particle energies beyond 200 MeV, Rev. Sci. Instrum. 17, 6 (1946).
- A. G. R. Thomas, Algorithm for calculating spectral intensity due to charged particles in arbitrary motion, Phys. Rev. ST Accel. Beams 13, 020702 (2010).
- M. Boca and V. Florescu, Nonlinear Compton scattering with a laser pulse, Phys. Rev. A 80, 053403 (2009).
- D. Seipt and B. Kämpfer, Nonlinear Compton scattering of ultrashort intense laser pulses, Phys. Rev. A 83, 022101 (2011).
- F. V. Hartemann, A. L. Troha, N. C. Luhmann, Jr., and Z. Toffano, Spectral analysis of the nonlinear relativistic Doppler shift in ultrahigh intensity Compton scattering, Phys. Rev. E 54, 2956 (1996).
- D. Seipt and B. Kämpfer, Nonlinear Compton scattering of ultrahigh-intensity laser pulses, Laser Phys. 23, 075301 (2013).
- V. Y. Kharin, D. Seipt, and S. G. Rykovanov, Temporal laser-pulse-shape effects in nonlinear Thomson scattering, Phys. Rev. A 93, 063801 (2016).
- Note that to make the angular distribution wider and better pronounced these plots were made by choosing both . This, however, is worse for the accuracy of our approximation (see below), so that the figure actually corresponds to a worse scenario.
- M. Malakhov, T. Benahmed, E. Gelfer, A. Fedotov, O. Klimo, S. Weber, and S. Rykovanov, Analytical calculation of the spectrum of nonlinear Compton scattering beyond local approximations, arXiv:2606.22427.
- D. Seipt and B. Kämpfer, Asymmetries of azimuthal photon distributions in nonlinear Compton scattering in ultrashort intense laser pulses, Phys. Rev. A 88, 012127 (2013).
- Note that the structure of Eq. (28) resembles the notion of a momentum-transfer cross section that typically arises in considerations of momentum transfer in particle collisions.
- F. Salehi, M. Le, L. Railing, M. Kolesik, and H. M. Milchberg, Laser-accelerated, low-divergence 15-MeV quasimonoenergetic electron bunches at 1 kHz, Phys. Rev. X 11, 021055 (2021).
- Y.-Y. Chang, J. C. Cabadağ, A. Debus, A. Ghaith, M. LaBerge, R. Pausch, S. Schöbel, P. Ufer, U. Schramm, and A. Irman, Reduction of the electron-beam divergence of laser wakefield accelerators by integrated plasma lenses, Phys. Rev. Appl. 20, L061001 (2023).
- D. Storey, C. Zhang, P. San Miguel Claveria, G. J. Cao, E. Adli, L. Alsberg, R. Ariniello, C. Clarke, S. Corde, T. N. Dalichaouch, et al., Wakefield generation in hydrogen and lithium plasmas at FACET-II: Diagnostics and first beam-plasma interaction results, Phys. Rev. Accel. Beams 27, 051302 (2024).
- V. Yakimenko, S. Meuren, F. Del Gaudio, C. Baumann, A. Fedotov, F. Fiuza, T. Grismayer, M. J. Hogan, A. Pukhov, L. O. Silva, and G. White, Prospect of studying nonperturbative QED with beam-beam collisions, Phys. Rev. Lett. 122, 190404 (2019).
- FACET II beam parameters, https://facet-ii.slac.stanford.edu/facility/beam-parameters.
- Y. Shi, D. Blackman, D. Stutman, and A. Arefiev, Generation of ultrarelativistic monoenergetic electron bunches via a synergistic interaction of longitudinal electric and magnetic fields of a twisted laser, Phys. Rev. Lett. 126, 234801 (2021).
- Y. Shi, D. R Blackman, and A. Arefiev, Electron acceleration using twisted laser wavefronts, Plasma Phys. Controlled Fusion 63, 125032 (2021).
- Y. Shi, D. R. Blackman, P. Zhu, and A. Arefiev, Electron pulse train accelerated by a linearly polarized Laguerre–Gaussian laser beam, High Power Laser Sci. Eng. 10, e45 (2022).
- D. R. Blackman, Y. Shi, S. R. Klein, M. Cernaianu, D. Doria, P. Ghenuche, and A. Arefiev, Electron acceleration from transparent targets irradiated by ultra-intense helical laser beams, Commun. Phys. 5, 116 (2022).
- E. Esarey, S. K. Ride, and P. Sprangle, Nonlinear Thomson scattering of intense laser pulses from beams and plasmas, Phys. Rev. E 48, 3003 (1993).
- Note that there is a typo in the expression for for this case in Ref. [35], where should be replaced with .
- For example, for and the accuracy of Eq. (A4) is better than 6%.