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arxiv: 2510.08037 · v2 · submitted 2025-10-09 · 🌌 astro-ph.HE

Acceleration of Ultrahigh Energy Particles from Fast Radio Bursts

Lin Yu , Tianxing Hu , Zhiyu Lei , Xiangyan An , Dong Wu , Suming Weng , Min Chen , Jie Zhang
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Zhengming Sheng
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Pith reviewed 2026-05-18 09:04 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords fast radio burstscosmic raysparticle accelerationplasma sheetsultra-relativistic pulsesPIC simulationsion accelerationwakefield acceleration
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The pith

FRB pulses erode to form plasma sheets that accelerate ions to ultra-high energies in two regimes.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Fast radio bursts emit ultra-relativistic electromagnetic pulses that interact with surrounding electron-positron-ion plasma. The pulse front erodes constantly and produces neutral plasma sheets at ultra-high energies. Ions accelerate either through direct Lorentz force in a piston-like regime or through electric fields from charge separation in a wakefield regime, with the choice depending on field strength and density. Both regimes produce energy scalings that match particle-in-cell simulations and generate a power-law spectrum whose index is close to that observed in cosmic rays. This mechanism would link FRBs to at least some ultra-high-energy particles if the modeled plasma conditions hold near real sources.

Core claim

Ultra-high energy neutral plasma sheets form constantly via the front erosion of an FRB pulse. There are two regimes of ion acceleration depending upon the field strength and the plasma density: the piston regime driven by the Lorentz force of the pulse, and the wakefield regime dominated by charge separation field. The predicted energy scalings align well with particle-in-cell simulations. A power-law energy spectrum with an index close to the CRs naturally emerges during FRBs expansion outward.

What carries the argument

Neutral plasma sheets formed by erosion of the FRB pulse front, which drive ion acceleration in the piston regime via Lorentz force or in the wakefield regime via charge separation.

If this is right

  • Energy scalings in the piston and wakefield regimes match results from particle-in-cell simulations.
  • A power-law energy spectrum with an index close to cosmic rays emerges naturally as the FRB expands.
  • FRBs with extreme field strengths may contribute to the observed population of cosmic rays.
  • Detection of high-energy particles correlated with FRBs would provide new information on FRB origins.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Coordinated searches for radio bursts and particle arrivals could directly test whether FRBs supply a measurable fraction of ultra-high-energy cosmic rays.
  • The same erosion and acceleration process might operate in other relativistic electromagnetic pulses beyond FRBs.
  • Predicted particle spectra and compositions could be compared against existing cosmic-ray data sets to constrain the required FRB rate and plasma parameters.

Load-bearing premise

FRBs possess extreme field strengths near their sources and the modeled electron-positron-ion plasma with chosen densities accurately represents the actual environment around an FRB progenitor.

What would settle it

Absence of any correlation between observed FRB positions and the arrival directions or energies of ultra-high-energy particles, or measured spectra that fail to show the predicted power-law index and regime-dependent scalings.

Figures

Figures reproduced from arXiv: 2510.08037 by Dong Wu, Jie Zhang, Lin Yu, Min Chen, Suming Weng, Tianxing Hu, Xiangyan An, Zhengming Sheng, Zhiyu Lei.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematic of ion acceleration via FRB pulse front [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Two regimes of plasma wake-waves in electron – pro [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The acceleration process in the wakefield regime ob [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The energy spectra of the accelerated protons from [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. The kinetic energy of the protons inside the plasma [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. The distributions of (a) the electric field of FRB [PITH_FULL_IMAGE:figures/full_fig_p008_7.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. The acceleration process in piston regime from PIC [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
read the original abstract

Two extreme events in the universe, fast radio bursts (FRBs) and cosmic rays (CRs), could be correlated, where FRBs with extreme field strength near their sources may contribute to CRs. This study investigates localized particle acceleration driven by FRB-like ultra-relativistic electromagnetic pulses in an electron--positron--ion plasma system. It is found ultra-high energy neutral plasma sheets form constantly via the front erosion of an FRB pulse. There are two regimes of ion acceleration depending upon the field strength and the plasma density: the piston regime driven by the Lorentz force of the pulse, and the wakefield regime dominated by charge separation field. The predicted energy scalings align well with particle-in-cell simulations. A power-law energy spectrum with an index close to the CRs naturally emerges during FRBs expansion outward. Detecting high-energy particles possibly produced by FRBs enables deeper insights into their origins and promotes the development of multi-messenger astronomy.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript examines localized ion acceleration by ultra-relativistic electromagnetic pulses modeling fast radio bursts (FRBs) in an electron-positron-ion plasma. It reports that ultra-high-energy neutral plasma sheets form continuously through front erosion of the FRB pulse. Two acceleration regimes are identified: a piston regime driven by the Lorentz force at higher field strengths and a wakefield regime dominated by charge-separation fields at lower strengths or higher densities. Analytic energy scalings for both regimes are stated to match particle-in-cell (PIC) simulation results, and a power-law ion spectrum with index similar to cosmic rays is found to develop during outward expansion.

Significance. If the assumed extreme field strengths and plasma parameters prove representative of FRB environments, the work would establish a concrete mechanism by which FRBs could contribute to ultra-high-energy cosmic rays, with direct implications for multi-messenger astronomy. The explicit identification of two regimes and the reported emergence of a cosmic-ray-like spectrum constitute potentially falsifiable predictions. The use of PIC simulations to test the scalings is a methodological strength, though the realism of the input parameters remains central to the claim's applicability.

major comments (2)
  1. [Plasma parameters and FRB environment] Section on plasma parameters and FRB environment (likely §2 or §3): the central claim that the piston and wakefield regimes produce the reported energy scalings and neutral-sheet formation requires the chosen extreme B-field amplitudes and specific plasma densities (including ion fraction) to be plausible near an FRB progenitor. No direct observational constraints exist on these quantities at the relevant distances; the manuscript should therefore either explore a broader parameter survey or provide quantitative arguments showing that the scalings remain robust outside the narrow range adopted.
  2. [Results section on energy scalings] Results section on energy scalings (likely §4): the scalings are described as 'predicted' yet stated to align with the same PIC simulations used to identify the two regimes. It is therefore unclear whether the scalings constitute independent analytic derivations or post-hoc fits. The manuscript must supply the explicit analytic expressions, the quantitative comparison metrics (including error bars or goodness-of-fit measures), and the criteria used to declare agreement.
minor comments (2)
  1. [Abstract] Abstract: the statement that the scalings 'align well' with PIC simulations would be strengthened by a brief quantitative statement (e.g., fractional deviation or R² value) rather than a qualitative claim.
  2. [Figures] Figure captions and axis labels: ensure that panels clearly distinguish the piston versus wakefield regimes and that the reported power-law index is indicated on the spectrum plot with its uncertainty.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed report. The comments highlight important aspects of parameter justification and clarity in the analytic derivations. We address each major comment below and will incorporate revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: Section on plasma parameters and FRB environment (likely §2 or §3): the central claim that the piston and wakefield regimes produce the reported energy scalings and neutral-sheet formation requires the chosen extreme B-field amplitudes and specific plasma densities (including ion fraction) to be plausible near an FRB progenitor. No direct observational constraints exist on these quantities at the relevant distances; the manuscript should therefore either explore a broader parameter survey or provide quantitative arguments showing that the scalings remain robust outside the narrow range adopted.

    Authors: We agree that justifying the parameter choices is essential given the lack of direct constraints. In the revised manuscript we will expand the plasma parameters section with quantitative arguments drawn from theoretical FRB progenitor models (e.g., magnetar flare scenarios in the literature) to demonstrate that the adopted field strengths and densities lie within plausible ranges. We will also add results from a limited additional parameter survey varying ion fraction and field amplitude to confirm that the two regimes and associated scalings persist, thereby showing robustness beyond the original narrow set. revision: yes

  2. Referee: Results section on energy scalings (likely §4): the scalings are described as 'predicted' yet stated to align with the same PIC simulations used to identify the two regimes. It is therefore unclear whether the scalings constitute independent analytic derivations or post-hoc fits. The manuscript must supply the explicit analytic expressions, the quantitative comparison metrics (including error bars or goodness-of-fit measures), and the criteria used to declare agreement.

    Authors: The energy scalings were derived analytically from the Lorentz force balance in the piston regime and from the charge-separation wake potential in the wakefield regime, prior to running the simulations. In the revision we will explicitly present these derivations together with the closed-form expressions. We will also add quantitative comparisons, including the ratio of simulated to predicted energies with standard deviations obtained from multiple runs, linear-regression slopes and R-squared values on log-log plots, and error bars. Agreement will be defined as the analytic prediction lying within the 1-sigma uncertainty envelope of the simulation data. revision: yes

Circularity Check

1 steps flagged

Energy scalings labeled 'predicted' but aligned with the same PIC simulations used to identify the acceleration regimes

specific steps
  1. fitted input called prediction [Abstract]
    "There are two regimes of ion acceleration depending upon the field strength and the plasma density: the piston regime driven by the Lorentz force of the pulse, and the wakefield regime dominated by charge separation field. The predicted energy scalings align well with particle-in-cell simulations."

    The regimes are presented as discovered findings, after which the energy scalings are called 'predicted' yet stated to align with the PIC simulations. If the scalings were obtained by fitting or measuring the same simulation outputs that identified the regimes, labeling them predictions creates a circular presentation where the 'prediction' is statistically forced by the input data.

full rationale

The abstract states that two regimes are found and that the predicted energy scalings align well with PIC simulations, while the power-law spectrum naturally emerges. This raises the fitted-input-called-prediction pattern because the scalings appear to be extracted from the same numerical experiments that revealed the piston and wakefield regimes rather than derived independently and then validated. No explicit self-definitional equations or load-bearing self-citations are visible in the provided text, so the circularity is partial and does not collapse the entire claim.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The work rests on standard assumptions of relativistic plasma physics and the validity of PIC methods for the chosen parameters; no new entities are postulated.

free parameters (2)
  • FRB field strength
    Varied to delineate piston versus wakefield regimes
  • plasma density
    Varied to delineate piston versus wakefield regimes
axioms (1)
  • domain assumption The FRB pulse can be modeled as an ultra-relativistic electromagnetic pulse propagating in an electron-positron-ion plasma
    Invoked in the description of the simulated system

pith-pipeline@v0.9.0 · 5712 in / 1243 out tokens · 32300 ms · 2026-05-18T09:04:58.803342+00:00 · methodology

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Reference graph

Works this paper leans on

70 extracted references · 70 canonical work pages

  1. [1]

    A typical solution shows in Figs

    pair [56]. A typical solution shows in Figs. 2(a1) - 2(a4) fora 0 = 103. The electrons with lower inertia are pushed by the intense longitudinal Lorentz force−eβ yBof the pulse, piling up to form energetic electron peaks as shown in Fig. 2(a2). In the meanwhile, the background ions are pulled forward by the strong Coulomb force of these elec- tron sheets,...

    work page

  2. [2]

    Electrons and ions simultaneously accumulate un- der the Lorentz force to form a second-harmonic density distribution, which is futher shaped by the electrostatic field of the plasma wave, as shown in Fig. 2(b2). The plasma wave intensifies as the peak densities, Lorentz factors, and electrostatic field strength increase, while its period reduces to less ...

    work page

  3. [3]

    Petroff, J

    E. Petroff, J. W. T. Hessels, and D. R. Lorimer, Fast radio bursts, Astron. Astrophys. Rev.27, 4 (2019)

    work page 2019

  4. [4]

    J. M. Cordes and S. Chatterjee, Fast radio bursts: An extragalactic enigma, Annu. Rev. Astron. Astr.57, 417 (2019)

    work page 2019

  5. [5]

    Petroff, J

    E. Petroff, J. W. T. Hessels, and D. R. Lorimer, Fast radio bursts at the dawn of the 2020s, Astron. Astrophys. Rev.30, 2 (2022)

    work page 2022

  6. [6]

    Zhang, The physics of fast radio bursts, Rev

    B. Zhang, The physics of fast radio bursts, Rev. Mod. Phys.95, 035005 (2023)

    work page 2023

  7. [7]

    Xuet al., Blinkverse: A database of fast radio bursts, Universe9, 330 (2023)

    J. Xuet al., Blinkverse: A database of fast radio bursts, Universe9, 330 (2023)

    work page 2023

  8. [8]

    Y. K. Zhang, D. Li, Y. Feng, P. Wang, C. H. Niu, S. Dai, J. M. Yao, and C. W. Tsai, The arrival time and energy of FRBs traverse the time-energy bivariate space like a brownian motion, Sci. Bull. (Beijing)69, 1020 (2024)

    work page 2024

  9. [9]

    Nimmoet al., Magnetospheric origin of a fast radio burst constrained using scintillation, Nature637, 48–51 (2025)

    K. Nimmoet al., Magnetospheric origin of a fast radio burst constrained using scintillation, Nature637, 48–51 (2025)

    work page 2025

  10. [10]

    A. B. Pearlmanet al., Multiwavelength constraints on the origin of a nearby repeating fast radio burst source in a globular cluster, Nat. Astron.9, 111–127 (2025)

    work page 2025

  11. [11]

    McKinvenet al., A pulsar-like polarization angle swing from a nearby fast radio burst, Nature637, 43–47 (2025)

    R. McKinvenet al., A pulsar-like polarization angle swing from a nearby fast radio burst, Nature637, 43–47 (2025)

    work page 2025

  12. [12]

    Platts, A

    E. Platts, A. Weltman, A. Walters, S. P. Tendulkar, J. E. B. Gordin, and S. Kandhai, A living theory cat- alogue for fast radio bursts, Phys. Rep.821, 1 (2019)

    work page 2019

  13. [13]

    Zhang, The physical mechanisms of fast radio bursts, Nature587, 45 (2020)

    B. Zhang, The physical mechanisms of fast radio bursts, Nature587, 45 (2020)

    work page 2020

  14. [14]

    Iwamoto, Y

    M. Iwamoto, Y. Matsumoto, T. Amano, S. Matsukiyo, and M. Hoshino, Linearly polarized coherent emission from relativistic magnetized ion-electron shocks, Phys. Rev. Lett.132, 035201 (2024)

    work page 2024

  15. [15]

    Vanthieghem and A

    A. Vanthieghem and A. Levinson, Fast radio bursts as precursor radio emission from monster shocks, Phys. Rev. Lett.134, 035201 (2025)

    work page 2025

  16. [16]

    Huang and Z.-G

    Y.-C. Huang and Z.-G. Dai, The extreme faraday effect in fast radio bursts, Astrophys. J. Lett.983, L24 (2025)

    work page 2025

  17. [17]

    Bhandari and C

    S. Bhandari and C. Flynn, Probing the universe with fast radio bursts, Universe7, 85 (2021)

    work page 2021

  18. [18]

    Connoret al., A gas-rich cosmic web revealed by the partitioning of the missing baryons, Nat

    L. Connoret al., A gas-rich cosmic web revealed by the partitioning of the missing baryons, Nat. Astron.9, 1226–1239 (2025)

    work page 2025

  19. [19]

    Zhang and B

    Z.-L. Zhang and B. Zhang, Cosmological parameter es- timate from persistent radio sources of fast radio bursts, Astrophys. J. Lett.984, L40 (2025)

    work page 2025

  20. [20]

    Glowacki and K.-G

    M. Glowacki and K.-G. Lee, Cosmology with fast-radio bursts, inEncyclopedia of Astrophysics (First Edition), edited by I. Mandel (Elsevier, Oxford, 2026) p. 448

    work page 2026

  21. [21]

    C. D. Bochenek, V. Ravi, K. V. Belov, G. Hallinan, J. Kocz, S. R. Kulkarni, and D. L. McKenna, A fast radio burst associated with a galactic magnetar, Nature587, 59 (2020)

    work page 2020

  22. [22]

    Aharonianet al.(H.E.S.S

    F. Aharonianet al.(H.E.S.S. Collaboration), H.e.s.s. pro- gramme searching for vhe gamma rays associated with frbs, J. Cosmol. Astropart. Phys.2025, 086

    work page 2025

  23. [23]

    Luo and B

    J.-W. Luo and B. Zhang, Time-integrated constraint on neutrino flux of chime fast radio burst sources with 10- yr icecube point-source data, Mon. Not. R. Astron. Soc. 534, 70 (2024)

    work page 2024

  24. [24]

    Qiang, Z.-Q

    D.-C. Qiang, Z.-Q. You, S. Yang, Z.-H. Zhu, and T.- W. Chen, 3d localization of frb 20190425a for its poten- tial host galaxy and implications, Astrophys. J.979, 95 (2025)

    work page 2025

  25. [25]

    Burke-Spolaor, Multiple messengers of fast radio bursts, Nat

    S. Burke-Spolaor, Multiple messengers of fast radio bursts, Nat. Astron.2, 845 (2018)

    work page 2018

  26. [26]

    Nicastro, C

    L. Nicastro, C. Guidorzi, E. Palazzi, L. Zampieri, M. Tu- ratto, and A. Gardini, Multiwavelength observations of fast radio bursts, Universe7, 76 (2021)

    work page 2021

  27. [27]

    Zhang, Multiwavelength and multimessenger counter- parts of fast radio bursts, Annu

    B. Zhang, Multiwavelength and multimessenger counter- parts of fast radio bursts, Annu. Rev. Astron. Astr.74, 89 (2024)

    work page 2024

  28. [28]

    Marcowithet al., The microphysics of collisionless shock waves, Rep

    A. Marcowithet al., The microphysics of collisionless shock waves, Rep. Prog. Phys.79, 046901 (2016)

    work page 2016

  29. [29]

    A. R. Bell, The acceleration of cosmic rays in shock fronts – I, Mon. Not. R. Astron. Soc.182, 147 (1978)

    work page 1978

  30. [30]

    A. R. Bell, A. T. Araudo, J. H. Matthews, and K. M. Blundell, Cosmic-ray acceleration by relativistic shocks: limits and estimates, Mon. Not. R. Astron. Soc.473, 2364 (2018)

    work page 2018

  31. [31]

    J. H. Matthews, A. R. Bell, K. M. Blundell, and A. T. Araudo, Ultrahigh energy cosmic rays from shocks in the lobes of powerful radio galaxies, Mon. Not. R. Astron. Soc.482, 4303 (2019)

    work page 2019

  32. [32]

    Colemanet al., Ultra high energy cosmic rays The in- tersection of the Cosmic and Energy Frontiers, Astropart

    A. Colemanet al., Ultra high energy cosmic rays The in- tersection of the Cosmic and Energy Frontiers, Astropart. Phys.149, 102819 (2023)

    work page 2023

  33. [33]

    Caoet al.(LHAASO Collaboration), Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 gamma-ray galactic sources, Nature594, 33 (2021)

    Z. Caoet al.(LHAASO Collaboration), Ultrahigh-energy photons up to 1.4 petaelectronvolts from 12 gamma-ray galactic sources, Nature594, 33 (2021)

    work page 2021

  34. [34]

    Caoet al.(LHAASO Collaboration), Peta-electron volt gamma-ray emission from the Crab Nebula, Science 373, 425 (2021)

    Z. Caoet al.(LHAASO Collaboration), Peta-electron volt gamma-ray emission from the Crab Nebula, Science 373, 425 (2021)

    work page 2021

  35. [35]

    Luan and P

    J. Luan and P. Goldreich, Physical constraints on fast radio bursts, Astrophys. J. Lett.785, L26 (2014)

    work page 2014

  36. [36]

    Y. P. Yang and B. Zhang, Fast radio bursts as strong waves interacting with the ambient medium, Astrophys. J. Lett.892, L10 (2020)

    work page 2020

  37. [37]

    Pukhov, Z

    A. Pukhov, Z. M. Sheng, and J. Meyer-ter Vehn, Particle acceleration in relativistic laser channels, Phys. Plasmas 6, 2847 (1999)

    work page 1999

  38. [38]

    O. N. Rosmejet al., High-current laser-driven beams of relativistic electrons for high energy density research, Plasma Phys. Control. Fusion62, 115024 (2020)

    work page 2020

  39. [39]

    A. E. Husseinet al., Towards the optimisation of direct laser acceleration, New J. Phys.23, 023031 (2021)

    work page 2021

  40. [40]

    M. M. Gunther, O. N. Rosmej, P. Tavana, M. Gyrdymov, A. Skobliakov, A. Kantsyrev, S. Zahter, N. G. Borisenko, A. Pukhov, and N. E. Andreev, Forward-looking insights in laser-generated ultra-intense gamma-ray and neutron sources for nuclear application and science, Nat. Com- mun.13, 170 (2022)

    work page 2022

  41. [41]

    Z. M. Sheng, K. Mima, Y. Sentoku, M. S. Jovanovic, T. Taguchi, J. Zhang, and J. Meyer-Ter-Vehn, Stochastic heating and acceleration of electrons in colliding laser fields in plasma, Phys. Rev. Lett.88, 055004 (2002)

    work page 2002

  42. [42]

    Tajima and J

    T. Tajima and J. M. Dawson, Laser electron accelerator, Phys. Rev. Lett.43, 267 (1979)

    work page 1979

  43. [43]

    Esarey, C

    E. Esarey, C. B. Schroeder, and W. P. Leemans, Physics of laser-driven plasma-based electron accelerators, Rev. Mod. Phys.81, 1229 (2009)

    work page 2009

  44. [44]

    Tajima, X

    T. Tajima, X. Q. Yan, and T. Ebisuzaki, Wakefield ac- celeration, Rev. Mod. Plasma Phys.4, 7 (2020)

    work page 2020

  45. [45]

    J. E. Gunn and J. P. Ostriker, Acceleration of high- energy cosmic rays by pulsars, Phys. Rev. Lett.22, 728 (1969)

    work page 1969

  46. [46]

    P. Chen, T. Tajima, and Y. Takahashi, Plasma wakefield acceleration for ultrahigh-energy cosmic rays, Phys. Rev. 7 Lett.89, 161101 (2002)

    work page 2002

  47. [47]

    G. B. Huxtable, N. Eltawil, W.-X. Feng, G. Player, W. Wang, T. Tajima, and T. Ebisuzaki, Signatures of wakefield acceleration in astrophysical jets via gamma- rays and uhecrs, Mon. Not. R. Astron. Soc.522, 5402 (2023)

    work page 2023

  48. [48]

    Ebisuzaki, T

    T. Ebisuzaki, T. Tajima, and B. C. Barish, Wakefield acceleration in the universe, Int. J. Mod. Phys. D32, 2330001 (2023)

    work page 2023

  49. [49]

    Zhang and H

    Y. Zhang and H. C. Wu, Upper field-strength limit of fast radio bursts, Astrophys. J929, 164 (2022)

    work page 2022

  50. [50]

    A. M. Beloborodov, Scattering of ultrastrong electromag- netic waves by magnetized particles, Phys. Rev. Lett. 128, 255003 (2022)

    work page 2022

  51. [51]

    A. M. Beloborodov, Can a strong radio burst escape the magnetosphere of a magnetar?, Astrophys. J. Lett.922, L7 (2021)

    work page 2021

  52. [52]

    W. Y. Wang, Y. P. Yang, C. H. Niu, R. X. Xu, and B. Zhang, Magnetospheric curvature radiation by bunches as emission mechanism for repeating fast radio bursts, Astrophys. J.927, 105 (2022)

    work page 2022

  53. [53]

    Kotera and A

    K. Kotera and A. V. Olinto, The astrophysics of ultrahigh-energy cosmic rays, Annu. Rev. Astron. Astr. 49, 119 (2011)

    work page 2011

  54. [54]

    B. M. Gaensler and P. O. Slane, The evolution and struc- ture of pulsar wind nebulae, Annu. Rev. Astron. Astr.44, 17 (2006)

    work page 2006

  55. [55]

    K. M. Ferriere, The interstellar environment of our galaxy, Rev. Mod. Phys.73, 1031 (2001)

    work page 2001

  56. [56]

    Sprangle, E

    P. Sprangle, E. Esarey, and A. Ting, Nonlinear interac- tion of intense laser pulses in plasmas, Phys. Rev. A41, 4463 (1990)

    work page 1990

  57. [57]

    Sprangle, E

    P. Sprangle, E. Esarey, and A. Ting, Nonlinear theory of intense laser-plasma interactions, Phys. Rev. Lett.64, 2011 (1990)

    work page 2011

  58. [58]

    L. F. Shampine and M. W. Reichelt, The MATLAB ode suite, SIAM J. Sci. Comput.18, 1 (1997)

    work page 1997

  59. [59]

    T. D. Arberet al., Contemporary particle-in-cell ap- proach to laser-plasma modelling, Plasma Phys. Control. Fusion57, 113001 (2015)

    work page 2015

  60. [60]

    C. D. Decker, W. B. Mori, K. Tzeng, and T. Katsouleas, The evolution of ultra-intense, short-pulse lasers in un- derdense plasmas, Phys. Plasmas3, 2047 (1996)

    work page 2047

  61. [61]

    Shorokhov and A

    O. Shorokhov and A. Pukhov, Ion acceleration in over- dense plasma by short laser pulse, Laser Part. Beams22, 175 (2004)

    work page 2004

  62. [62]

    A. P. L. Robinson, P. Gibbon, M. Zepf, S. Kar, R. G. Evans, and C. Bellei, Relativistically correct hole-boring and ion acceleration by circularly polarized laser pulses, Plasma Phys. Control. Fusion51, 024004 (2009)

    work page 2009

  63. [63]

    Schlegel, N

    T. Schlegel, N. Naumova, V. T. Tikhonchuk, C. Labaune, I. V. Sokolov, and G. Mourou, Relativistic laser piston model: Ponderomotive ion acceleration in dense plasmas using ultraintense laser pulses, Phys. Plasmas16, 083103 (2009)

    work page 2009

  64. [64]

    L. L. Ji, A. Pukhov, I. Y. Kostyukov, B. F. Shen, and K. Akli, Radiation-reaction trapping of electrons in ex- treme laser fields, Phys. Rev. Lett.112, 145003 (2014)

    work page 2014

  65. [65]

    Duclous, J

    R. Duclous, J. G. Kirk, and A. R. Bell, Monte carlo calcu- lations of pair production in high-intensity laser–plasma interactions, Plasma Phys. Control. Fusion53, 015009 (2011)

    work page 2011

  66. [66]

    V. I. Ritus, Quantum effects of the interaction of ele- mentary particles with an intense electromagnetic field, J. Sov. Laser Res.6, 497 (1985)

    work page 1985

  67. [67]

    C. N. Dansonet al., Petawatt and exawatt class lasers worldwide, High Power Laser Sci. Eng.7, e54 (2019)

    work page 2019

  68. [68]

    Liet al., A bimodal burst energy distribution of a repeating fast radio burst source, Nature598, 267 (2021)

    D. Liet al., A bimodal burst energy distribution of a repeating fast radio burst source, Nature598, 267 (2021)

    work page 2021

  69. [69]

    Aloisio, E

    R. Aloisio, E. Coccia, and F. Vissani,Multiple Messen- gers and Challenges in Astroparticle Physics(Springer International Publishing, 2018). End Matter Appendix A: The wakefield equations—The La- grangians for electron and ion fluids in 1D geometry, L=−mc 2/γ−qΦ +q(v·A y)/c, does not depend on the transverse coordinates, leading to the conservation of tr...

    work page 2018

  70. [70]

    (11) can be rewritten asE(κ) +E(κ, θ), which is the sum of the second kind complete and incomplete elliptic integrals

    For ultra- relativistic electromagnetic waves withα∼0, the right side of Eq. (11) can be rewritten asE(κ) +E(κ, θ), which is the sum of the second kind complete and incomplete elliptic integrals. Differentiating Eq. (11) with respect toξyields dϕ/dξ=−k pa0. From max(sinθ) = 1, we obtain ϕmax =a 2 0(σi −1)/a 2 0 +σ i ≈σ i. So, the electrostatic field satis...

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