- Physical Review Journals
All JournalsPhysics Magazine

Physical Review D

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Transition from diffusion to drift-dominated cosmic ray transport and the origin of the knee

Luis E. Espinosa Castro*, Carmelo Evoli†, and Pasquale Blasi‡

  • *Contact author: luis.espinosacastro@gssi.it
  • †Contact author: carmelo.evoli@gssi.it
  • ‡Contact author: pasquale.blasi@gssi.it
PDF

Phys. Rev. D 114, 063060 – Published 28 September, 2026

DOI: https://doi.org/10.1103/975j-ysz9

Abstract

In a magnetic field with a complex topology, as can be the Galactic magnetic field, cosmic ray transport cannot simply be described by diffusion parallel and perpendicular to magnetic field lines, because the gradients and curvature of the large-scale magnetic field induce drift motions. These effects become especially important at high energies. Here we revisit the possibility that the competition between diffusion and drifts may lead to a knee in the cosmic ray spectrum. We carry out test-particle simulations of cosmic ray transport in a mock Galactic magnetic field made of a regular large scale component, with a nontrivial topology and a homogeneous and isotropic turbulent magnetic field, with a spectrum that is assumed to be Kolmogorov-like in the basic setup. These simulations are used to infer the escape time and the grammage accumulated by cosmic rays with energy in the TeV–10 PeV energy range. In the case of a large scale magnetic field with a purely azimuthal structure, the drift due to the curvature of magnetic field lines produces a knee in the PeV range, but the model fails to reproduce the grammage, due to the exceedingly low value of the perpendicular diffusion coefficient. If the large scale magnetic field acquires a component perpendicular to the Galactic disc, the parallel diffusion coefficient becomes quickly dominant in terms of particle escape, and drifts are unable to compete. A knee structure does not appear in such a scenario. However, if the parallel diffusion coefficient becomes energy independent at E≳1  TeV, a knee may arise around PeV energies due to drift dominance. We discuss two cases in which this situation may occur.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (77)

  1. O. Adriani, G. C. Barbarino, G. A. Bazilevskaya et al., Science 332, 69 (2011).
  2. Y. S. Yoon, H. S. Ahn, P. S. Allison et al., Astrophys. J. 728, 122 (2011).
  3. M. Aguilar, D. Aisa, B. Alpat et al., Phys. Rev. Lett. 114, 171103 (2015).
  4. Y. S. Yoon, T. Anderson, A. Barrau et al., Astrophys. J. 839, 5 (2017).
  5. Q. An, R. Asfandiyarov, P. Azzarello et al., Sci. Adv. 5, eaax3793 (2019).
  6. M. Aguilar, L. Ali Cavasonza, G. Ambrosi et al., Phys. Rep. 894, 1 (2021).
  7. F. Alemanno, Q. An, P. Azzarello et al., Phys. Rev. Lett. 126, 201102 (2021).
  8. O. Adriani, Y. Akaike, K. Asano et al., Phys. Rev. Lett. 129, 101102 (2022).
  9. O. Adriani, Y. Akaike, K. Asano et al., Phys. Rev. Lett. 130, 171002 (2023).
  10. T. Antoni, W. D. Apel, A. F. Badea et al., Astropart. Phys. 24, 1 (2005).
  11. W. D. Apel, J. C. Arteaga-Velázquez, K. Bekk et al., Phys. Rev. Lett. 107, 171104 (2011).
  12. W. D. Apel, J. C. Arteaga-Velázquez, K. Bekk et al., Astropart. Phys. 47, 54 (2013).
  13. M. Amenomori, X. J. Bi, D. Chen et al., Astrophys. J. 678, 1165 (2008).
  14. M. G. Aartsen, M. Ackermann, J. Adams et al., Phys. Rev. D 100, 082002 (2019).
  15. N. M. Budnev, A. Chiavassa, O. A. Gress et al., Astropart. Phys. 117, 102406 (2020).
  16. R. U. Abbasi, M. Abe, T. Abu-Zayyad et al., Astrophys. J. 865, 74 (2018).
  17. Z. Cao, F. Aharonian, Axikegu et al., Phys. Rev. Lett. 132, 131002 (2024).
  18. Z. Cao, F. Aharonian et al. (The LHAASO Collaboration), Sci. Bull. 70, 4173 (2025).
  19. Z. Cao, F. Aharonian, Y. X. Bai et al., Phys. Rev. Lett. 136, 121001 (2026).
  20. B. Peters, Nuovo Cimento (1955–1965) 22, 800 (1961).
  21. J. R. Hörandel, Astropart. Phys. 21, 241 (2004).
  22. P. Cristofari, P. Blasi, and E. Amato, Astropart. Phys. 123, 102492 (2020).
  23. F. Aharonian, R. Yang, and E. de Oña Wilhelmi, Nat. Astron. 3, 561 (2019).
  24. S. Kaci, G. Giacinti, F. Aharonian et al., arXiv:2510.01369.
  25. B. T. Zhang and S. Yu, arXiv:2602.08940.
  26. G. Cocconi, Nuovo Cimento (1955–1965) 3, 1433 (1956).
  27. D. De Marco, P. Blasi, and T. Stanev, J. Cosmol. Astropart. Phys. 06 (2007) 027.
  28. G. Giacinti, M. Kachelrieß, and D. V. Semikoz, Phys. Rev. D 91, 083009 (2015).
  29. P. Subedi, W. Sonsrettee, P. Blasi et al., Astrophys. J. 837, 140 (2017).
  30. A. Dundovic, O. Pezzi, P. Blasi, C. Evoli, and W. H. Matthaeus, Phys. Rev. D 102, 103016 (2020).
  31. V. S. Ptuskin, S. I. Rogovaya, V. N. Zirakashvili et al., Astron. Astrophys. 268, 726 (1993).
  32. P. A. Isenberg and J. R. Jokipii, Astrophys. J. 234, 746 (1979).
  33. J. Candia, E. Roulet, and L. N. Epele, J. High Energy Phys. 12 (2002) 033.
  34. J. Candia and E. Roulet, J. Cosmol. Astropart. Phys. 10 (2004) 007.
  35. C. Evoli, D. Grasso, and L. Maccione, J. Cosmol. Astropart. Phys. 06 (2007) 003.
  36. J. Giacalone and J. R. Jokipii, Astrophys. J. 520, 204 (1999).
  37. J. R. Jokipii, Astrophys. J. 146, 480 (1966).
  38. P. Blasi, Proc. Int. Sch. Phys. “Enrico Fermi” 208, 41 (2024).
  39. R. C. Tautz and A. Shalchi, Astrophys. J. 744, 125 (2012).
  40. B. Rossi and S. Olbert, Introduction to the physics of space (McGraw-Hill, New York, 1970).
  41. V. Ptuskin, V. Zirakashvili, and E.-S. Seo, Astrophys. J. 718, 31 (2010).
  42. K. M. Schure and A. R. Bell, Mon. Not. R. Astron. Soc. 435, 1174 (2013).
  43. D. Caprioli, Proc. Int. Sch. Phys. “Enrico Fermi” 208, 143 (2024).
  44. R. Alves Batista, J. Becker Tjus, J. Dörner et al., J. Cosmol. Astropart. Phys. 09 (2022) 035.
  45. M. Haverkorn, J. C. Brown, B. M. Gaensler, and N. M. McClure‐Griffiths, Astrophys. J. 680, 362 (2008).
  46. M. Iacobelli, M. Haverkorn, E. Orrú et al., Astron. Astrophys. 558, A72 (2013).
  47. F. Casse, M. Lemoine, and G. Pelletier, Phys. Rev. D 65, 023002 (2001).
  48. M. Kuhlen, P. Mertsch, and V. H. M. Phan, Astrophys. J. 992, 11 (2025).
  49. M. Kuhlen, P. Mertsch, and V. H. M. Phan, Astrophys. J. 992, 10 (2025).
  50. J. W. Bieber and W. H. Matthaeus, Astrophys. J. 485, 655 (1997).
  51. C. Evoli and U. Dupletsa, Proc. Int. Sch. Phys. “Enrico Fermi” 208, 257 (2024).
  52. L. Tibaldo, S. W. Digel, J. M. Casandjian et al., Astrophys. J. 807, 161 (2015).
  53. C. Evoli, G. Morlino, P. Blasi, and R. Aloisio, Phys. Rev. D 101, 023013 (2020).
  54. N. Weinrich, M. Boudaud, L. Derome, Y. Génolini, J. Lavalle, D. Maurin, P. Salati, P. Serpico, and G. Weymann-Despres, Astron. Astrophys. 639, A74 (2020).
  55. K. Ferrière, Mem. Soc. Astron. Ital. 82, 824 (2011).
  56. M. Unger and G. R. Farrar, Astrophys. J. 970, 95 (2024).
  57. M. Haverkorn, arXiv:2606.02149.
  58. J. L. Han, AIP Conf. Proc. 609, 96 (2002).
  59. M. S. Pshirkov, P. G. Tinyakov, P. P. Kronberg, and K. J. Newton-McGee, Astrophys. J. 738, 192 (2011).
  60. J. Xu and J. L. Han, Astrophys. J. 966, 240 (2024).
  61. A. Shalchi, Astrophys. J. Lett. 881, L27 (2019).
  62. B. Schroer, C. Evoli, and P. Blasi, Phys. Rev. D 103, 123010 (2021).
  63. G. Giacinti, M. Kachelrieß, and D. V. Semikoz, J. Cosmol. Astropart. Phys. 07 (2018) 051.
  64. Dampe Collaboration, Sci. Bull. 67, 2162 (2022).
  65. V. Grebenyuk, D. Karmanov, I. Kovalev et al., Adv. Space Res. 64, 2559 (2019).
  66. S. Recchia and S. Gabici, Astron. Astrophys. 692, A20 (2024).
  67. A. Ambrosone, C. Evoli, B. Schroer, and P. Blasi, Astron. Astrophys. 698, L18 (2025).
  68. R. Yang and F. Aharonian, Phys. Rev. D 111, 083040 (2025).
  69. S. Sridhar and P. Goldreich, Astrophys. J. 432, 612 (1994).
  70. P. Goldreich and S. Sridhar, Astrophys. J. 438, 763 (1995).
  71. M. Lemoine, J. Plasma Phys. 89, 175890501 (2023).
  72. P. Kempski, D. B. Fielding, E. Quataert, A. K. Galishnikova, M. W. Kunz, A. A. Philippov, and B. Ripperda, Mon. Not. R. Astron. Soc. 525, 4985 (2023).
  73. P. Kempski, D. Li, D. B. Fielding, E. Quataert, E. S. Phinney, M. W. Kunz, D. L. Jow, and A. A. Philippov, Astrophys. J. Lett. 990, L18 (2025).
  74. O. Pezzi and P. Blasi, Mon. Not. R. Astron. Soc. 529, L13 (2024).
  75. A. J. Farmer and P. Goldreich, Astrophys. J. 604, 671 (2004).
  76. P. Blasi, E. Amato, and P. D. Serpico, Phys. Rev. Lett. 109, 061101 (2012).
  77. S. S. Cerri, D. Gaggero, A. Vittino, C. Evoli, and D. Grasso, J. Cosmol. Astropart. Phys. 10 (2017) 019.

Outline

Information

Phys. Rev. D 114, 063060– Published 28 September, 2026
  • Received 4 July 2026
  • Accepted 11 September 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation