Issues

 / 

2026

 / 

April

←  →

Methodological notes


Synchrotron radiation in nonuniform magnetic field

†  a, b,  a, b,  a, b,  a, b
a Lebedev Physical Institute, Russian Academy of Sciences, Leninsky prosp. 53, Moscow, 119991, Russian Federation
b Moscow Institute of Physics and Technology (National Research University), Institutskii per. 9, Dolgoprudny, Moscow Region, 141700, Russian Federation

The distortion of the spectrum of synchrotron radiation received by a distant observer due to magnetic field inhomogeneity is discussed. It is shown that for single-particle radiation, a noticeable difference in the integrated spectrum from the case of a uniform magnetic field occurs only for observation times significantly exceeding the observer's departure from the beam pattern, and only for subrelativistic particles, when the radiation arrives from regions with significantly different magnetic fields during the observation time. For shorter observation times, field inhomogeneity leads only to small-scale distortions (smaller or comparable in frequency to the gyrofrequency &omegaB) and does not manifest itself in the averaged spectrum. For the case of a particle ensemble, which is of interest for astrophysical applications, the difference in the integrated spectrum becomes negligible.

Fulltext pdf (244 KB)
Fulltext is also available at DOI: 10.3367/UFNe.2025.09.040039
Correspondence should be addressed to
Keywords: synchrotron radiation, inhomogeneous magnetic fields, active galactic nuclei
PACS: 41.60.Ap, 98.62.En, 98.62.Js (all)
DOI: 10.3367/UFNe.2025.09.040039
URL: https://ufn.ru/en/articles/2026/4/g/
001764602900007
2-s2.0-105046712102
2026PhyU...69..406B
Citation: Beskin V S, Istomin A Yu, Kniazev F A, Khalilov T I "Synchrotron radiation in nonuniform magnetic field" Phys. Usp. 69 406–414 (2026)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Received: 5th, September 2025, 15th, September 2025

Оригинал: Бескин В С, Истомин А Ю, Князев Ф А, Халилов Т И «Синхротронное излучение в неоднородном магнитном поле» УФН 196 436–445 (2026); DOI: 10.3367/UFNr.2025.09.040039

References (38) ↓ Similar articles (20)

  1. ’G’?’?’?’?’?’?с ’B ’e (’dт’?. р’?’?.) ’K’?’?’?’?’?’?’? т’?’?’?’?ыkh с’?’?’?’? ’? ф’?’?’?’?’? с’?’?’?’?ch’?’?’? ’?’?т’?’?’?’?ст’? (’i’?’?’?: ’O’?’?’?т’?’?, 1982)
  2. "’F 85-’?’?т’?yu с’? ’?’?ya р’?zh’?’?’?’?ya ’l.’R. ’lыр’?’?’?тс’?’?’?’? (’v’?уch’?’?ya с’?сс’?ya ’dт’?’?’?’?’?’?ya ф’?’?’?ch’?с’?’?kh ’?’?у’? ’i’?сс’?’?с’?’?’? ’?’?’?’?’?’?’?’? ’?’?у’?, 26 ’?’?ya 2010 ’?.)" Usp. Fiz. Nauk 180 973 (2010); "Commemoration of the 85th birthday of S I Syrovatskii (Scientific session of the Physical Sciences Division of the Russian Academy of Sciences, 26 May 2010)" Phys. Usp. 53 933 (2010)
  3. ’O’?’?’?’?ы’? ’’ ’a ’? ’?р Usp. Fiz. Nauk 180 973 (2010); Zelenyi L M et al Phys. Usp. 53 933 (2010)
  4. ’sр’?’?’? ’B ’I Usp. Fiz. Nauk 180 982 (2010); Frank A G Phys. Usp. 53 941 (2010)
  5. ’Fу’?’?’?ts’?’? ’E ’K Usp. Fiz. Nauk 180 988 (2010); Kuznetsov V D Phys. Usp. 53 947 (2010)
  6. ’l’?’?’?’? ’G ’E Usp. Fiz. Nauk 180 997 (2010); Somov B V Phys. Usp. 53 954 (2010)
  7. ’zтус’?’?’? ’E ’l Usp. Fiz. Nauk 180 1000 (2010); Ptuskin V S Phys. Usp. 53 958 (2010)
  8. "’F’?с’?’?ch’?с’?’?ya ф’?’?’?’?’? ’? ф’?’?’?’?’? ’?’?’?’?’?ы (’? 100-’?’?т’?yu с’? ’?’?ya р’?zh’?’?’?’?ya ’l.’R. ’lыр’?’?’?тс’?’?’?’?, ’v’?уch’?’?ya с’?сс’?ya ’dт’?’?’?’?’?’?ya ф’?’?’?ch’?с’?’?kh ’?’?у’? ’i’?сс’?’?с’?’?’? ’?’?’?’?’?’?’?’? ’?’?у’?, 5 ’?’?рт’? 2025 ’?.)" Usp. Fiz. Nauk 195 793 (2025); "Space physics and plasma physics (on the 100th anniversary of S.I. Syrovatskii’s birth, Scientific session of the Physical Sciences Division of the Russian Academy of Sciences, March 5, 2025)" Phys. Usp. 68 745 (2025)
  9. ’R’?ь’?’? ’B ’l ’? ’?р Usp. Fiz. Nauk 195 794 (2025); Il’yn A S et al Phys. Usp. 68 747 (2025)
  10. ’O’?’?’?’?ы’? ’’ ’a ’? ’?р Usp. Fiz. Nauk 195 807 (2025); Zelenyi L M et al Phys. Usp. 68 759 (2025)
  11. ’Gы’?’?’? ’B ’a Usp. Fiz. Nauk 195 835 (2025); Bykov A M Phys. Usp. 68 785 (2025)
  12. ’Fу’?’?’?ts’?’? ’E ’K Usp. Fiz. Nauk 195 85 (2025); Kuznetsov V D Phys. Usp. 68 807 (2025)
  13. ’sр’?’?’? ’B ’I Usp. Fiz. Nauk 195 875 (2025); Frank A G Phys. Usp. 68 823 (2025)
  14. ’I’?’?’?’?ур’? ’E ’’ ’l’?’?р’?’?’?’?’?’?ya ’?стр’?ф’?’?’?’?’? (’a.: ’v’?у’?’?, 1970)
  15. Sh’?’?’?’?с’?’?’? ’R ’l ’l’?’?рkh’?’?’?ы’? ’?’?’?’?’?ы ’? с’?ya’?’?’?’?ы’? с ’?’?’?’? ’?р’?’?’?’?’?ы 2-’? ’?’?’?. (’a.: ’v’?у’?’?, 1976)
  16. ’I’?’?’?’?ур’? ’E ’’, ’lыр’?’?’?тс’?’?’? ’l ’R Usp. Fiz. Nauk 87 65 (1965); Ginzburg V L, Syrovatskii S I Sov. Phys. Usp. 8 674 (1966)
  17. ’I’?’?’?’?ур’? ’E ’’, ’l’?’?’?’?’?’? ’E ’v, ’lыр’?’?’?тс’?’?’? ’l ’R Usp. Fiz. Nauk 94 63 (1968); Ginzburg V L, Sazonov V N, Syrovatskii S I Sov. Phys. Usp. 11 34 (1968)
  18. ’I’?’?’?’?ур’? ’E ’’, ’lыр’?’?’?тс’?’?’? ’l ’R ’zр’?’?сkh’?zh’?’?’?’?’? ’?’?с’?’?ch’?с’?’?kh ’?уch’?’? (’a.: ’R’?’?-’?’? ’B’v ’l’l’l’i, 1963); ’z’?р. ’?’? ’?’?’?’?. ya’?., Ginzburg V L, Syrovatskii S I The Origin Of Cosmic Rays (Oxford: Pergamon Press, 1964)
  19. Ginzburg V L, Syrovatskii S I Annu. Rev. Astron. Astrophys. 3 297 (1965)
  20. ’I’?’?’?’?ур’? ’E ’’ ’n’?’?р’?т’?ch’?с’?’?ya ф’?’?’?’?’? ’? ’?стр’?ф’?’?’?’?’?. ’K’?’?’?’?’?’?т’?’?ь’?ы’? ’?’?’?’?ы (’a.: ’v’?у’?’?, 1987); ’z’?р. ’?’? ’?’?’?’?. ya’?., Ginzburg V L Applications Of Electrodynamics In Theoretical Physics And Astrophysics (New York: Gordon and Breach Science Publ., 1989)
  21. ’z’?kh’?’?ьch’?’? ’B ’I ’i’?’?’?’?’?стр’?ф’?’?’?’?’?. ’v’?т’?’?’?’?’?ы’? ’?р’?ts’?ссы ’? ’?’?’?’?’?т’?ch’?с’?’?kh ’? ’?’?’?’?’?’?’?’?т’?ch’?с’?’?kh ’?ст’?ch’?’?’?’?kh (’a.: ’a’?р, 1973); ’z’?р. с ’?’?’?’?. ya’?., Pacholczyk A G Radio Astrophysics. Nonthermal Processes In Galactic And Extragalactic Sources (San Francisco, CA: W H Freeman and Co., 1970)
  22. ’’’?’?’?’?у ’’ ’K, ’’’?фsh’?ts ’M ’a ’n’?’?р’?ya ’?’?’?ya (1993); ’z’?р. ’?’? ’?’?’?’?. ya’?., Landau L D, Lifshitz E M The Classical Theory Of Fields (Oxford: Pergamon Press, 1975)
  23. Thorne K S Astrophys. J. Suppl. 8 1 (1963)
  24. Cavallo G, Horstman H M, Muracchini A Astron. Astrophys. 86 36 (1980)
  25. Lieu R, Axford W I Astrophys. J. 447 302 (1995)
  26. Medvedev M V Astrophys. J. 540 704 (2000)
  27. Cheng K S, Zhang J L Astrophys. J. 463 271 (1996)
  28. Viganò D et al Mon. Not. R. Astron. Soc. 447 1164 (2015)
  29. Kelner S R, Prosekin A Yu, Aharonian F A Astron. J. 149 33 (2015)
  30. ’F’?’?’?’?’?’? Yu ’B, ’a’?kh’?’?’?уts’? ’E ’z Astron. Zh. 57 696 (1980); Kovalev Yu A, Mikhailutsa V P Sov. Astron. 24 400 (1980)
  31. The Event Horizon Telescope Collab., Akiyama K et al Astrophys. J. Lett. 875 L1 (2019)
  32. Lister M L et al Astrophys. J. 874 43 (2019)
  33. Zamaninasab M et al Nature 510 126 (2014)
  34. Mertens F et al Astron. Astrophys. 595 A54 (2016)
  35. ’Fу’?рya’?ts’?’? ’’ ’K ’Fурс ’?’?т’?’?’?т’?ch’?с’?’?’?’? ’?’?’?’?’?’?’? Т. 2 (’a.: ’Eысsh’?ya sh’?’?’?’?, 1988)
  36. Baldwin D E Rev. Mod. Phys. 49 317 (1977)
  37. Comisso L, Sironi L Astrophys. J. 886 122 (2019)
  38. Comisso L, Jiang B Astrophys. J. 959 137 (2023)

© 1918–2026 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions