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arxiv: 2604.21856 · v1 · submitted 2026-04-23 · ⚛️ physics.acc-ph · hep-th

Orbital angular momentum radiation and polarization of relativistic electrons in magnetic fields

Ziqiang Huang , Qi Meng , Xuan Liu , Wei Ma , Zhen Yang , Liang Lu , Alexander J. Silenko , Pengming Zhang
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Liping Zou
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Pith reviewed 2026-05-08 12:44 UTC · model grok-4.3

classification ⚛️ physics.acc-ph hep-th
keywords orbital angular momentumpolarizationsynchrotron radiationrelativistic electronsmagnetic fieldsvortex electronsSokolov-Ternov effect
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The pith

Synchrotron radiation polarizes the orbital angular momentum of relativistic electrons, approaching unity for large OAM.

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

The paper establishes that relativistic electrons with orbital angular momentum in a uniform magnetic field experience asymmetric radiative transition rates at low photon energies, with transitions that decrease OAM being favored. This asymmetry produces a polarized stationary state whose OAM polarization can reach nearly 100 percent, while the time to reach that state is orders of magnitude shorter than the time for spin polarization under typical storage-ring conditions. The relaxation time and stationary OAM distribution are derived analytically. A sympathetic reader would care because the effect supplies a radiation-based route to polarize and control vortex electron beams without extra hardware.

Core claim

In the low-photon-energy regime, transition rates for photon emission are asymmetric, favoring OAM decrease. Synchrotron radiation therefore polarizes the OAM of vortex electrons. Analytical expressions are obtained for the relaxation time and the stationary-state OAM distribution. The OAM polarization P_OAM approaches unity for large OAM while spin polarization reaches 92.38 percent; for storage-ring parameters the OAM polarization time is orders of magnitude shorter than the spin polarization time.

What carries the argument

Asymmetric radiative transition rates that favor OAM-decreasing transitions in the low-photon-energy limit of synchrotron radiation.

If this is right

  • OAM polarization can reach nearly 100 percent for large OAM, exceeding the 92.38 percent spin limit.
  • The characteristic time for OAM polarization is orders of magnitude shorter than for spin polarization.
  • An analytical expression is available for the stationary OAM distribution.
  • Synchrotron radiation supplies a mechanism to control vortex electron beams in accelerators.

Where Pith is reading between the lines

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

  • The same mechanism could be used to prepare highly OAM-polarized beams for particle-physics or imaging experiments.
  • Rate asymmetries of this kind may appear in other radiative processes that involve angular momentum.
  • Verification could consist of injecting vortex electrons into an existing storage ring and tracking the short-time evolution of their OAM distribution.

Load-bearing premise

The magnetic field is perfectly uniform and the photon energies remain low enough that OAM-decreasing transitions dominate.

What would settle it

Measurement of the OAM polarization buildup time in a storage ring containing vortex electrons, which should be much shorter than the spin polarization time.

Figures

Figures reproduced from arXiv: 2604.21856 by Alexander J. Silenko, Liang Lu, Liping Zou, Pengming Zhang, Qi Meng, Wei Ma, Xuan Liu, Zhen Yang, Ziqiang Huang.

Figure 1
Figure 1. Figure 1: FIG. 1: Effective potential view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Comparison of the exact function view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Modified Bessel functions view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: Comparison of the function view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Comparison of the approximate spectral function view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Time evolution of the spin population fractions view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7: Time evolution of the OAM distribution fraction for different initial view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8 view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9: Variation of the OAM relaxation time view at source ↗
read the original abstract

While spin polarization from synchrotron radiation is well established, the polarization of orbital angular momentum (OAM) in such radiative processes remains elusive. We study radiation and polarization of relativistic electrons in a uniform magnetic field, focusing on OAM polarization radiation for vortex electrons which carry intrinsic OAM. The results illustrate that transition rates are asymmetric in the low-photon-energy regime, favoring OAM decrease, analogous to the spin-flip asymmetry in the Sokolov-Ternov effect. Under these conditions, synchrotron radiation can polarize the OAM. The characteristic relaxation time and stationary-state OAM distribution are obtained analytically. The polarization of spin about \(\mathcal{P}_{\text{spin}}\) reaches \(92.38\%\), while that of \(\mathcal{P}_{\text{OAM}}\) can even approach almost unity for a large OAM; however, their polarization behaviors are different. For typical storage ring parameters, the OAM polarization time is orders of magnitude shorter than the spin polarization time. Thus, synchrotron radiation offers a mechanism for controlling vortex electron beams which carry OAM for high-energy accelerator applications.

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

0 major / 3 minor

Summary. The paper claims that synchrotron radiation from relativistic vortex electrons (carrying intrinsic orbital angular momentum) in a uniform magnetic field induces OAM polarization via an asymmetry in transition rates in the low-photon-energy regime, analogous to the Sokolov-Ternov spin-flip asymmetry. Closed-form rate equations, relaxation times, and the stationary OAM distribution are derived analytically; the stationary spin polarization recovers the known 92.38% value, while OAM polarization approaches unity for large OAM, with the OAM relaxation time being orders of magnitude shorter than the spin polarization time for typical storage-ring parameters.

Significance. If the derivations hold, the result is significant because it identifies a radiation-based mechanism for polarizing and controlling OAM in relativistic electron beams, extending the Sokolov-Ternov framework to structured beams. The analytical expressions for relaxation times and stationary distributions, together with the explicit recovery of the spin benchmark, provide a falsifiable and parameter-light prediction that could guide experiments in accelerator facilities using vortex electrons.

minor comments (3)
  1. The low-photon-energy regime and uniform-B assumption are central; a brief quantitative statement of the photon-energy cutoff (e.g., ħω ≪ E or relative to the cyclotron frequency) would help readers assess the validity range for storage-ring parameters.
  2. The stationary OAM distribution is stated to approach unity for large OAM; an explicit functional form or limiting expression for P_OAM(m) as m → ∞ would strengthen the claim.
  3. Notation for the OAM quantum number (often denoted m or l) should be introduced once and used consistently to avoid possible confusion with the magnetic quantum number in the Landau-level context.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive evaluation of our manuscript and for recommending minor revision. The referee's summary accurately captures the key results regarding the asymmetry in transition rates for OAM in vortex electrons under synchrotron radiation, the analytical relaxation times, and the comparison to the Sokolov-Ternov spin polarization benchmark.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained with explicit analytics and external consistency check

full rationale

The paper derives transition rates, relaxation times, and stationary OAM distribution analytically from the low-photon-energy asymmetry for vortex electrons in uniform B, without fitting parameters or reducing to prior self-citations. The central claims (P_OAM approaching unity for large OAM, OAM time orders shorter than spin) follow directly from the rate equations. Recovery of the known 92.38% spin polarization serves as an independent verification against Sokolov-Ternov, confirming the framework is not self-referential. No load-bearing step collapses to definition, fit, or author-only uniqueness theorem.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on standard quantum-electrodynamic treatment of radiation in a uniform magnetic field plus the assumption that low-energy photon transitions dominate the asymmetry; no new free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Uniform magnetic field for relativistic electrons
    The study is restricted to electrons in a uniform magnetic field as stated in the title and abstract.
  • domain assumption Low-photon-energy regime governs the asymmetry
    Transition rates are stated to be asymmetric only in the low-photon-energy regime.

pith-pipeline@v0.9.0 · 5509 in / 1213 out tokens · 39481 ms · 2026-05-08T12:44:12.170056+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

50 extracted references · 50 canonical work pages

  1. [1]

    are the roots off n,n′(x) =

    work page

  2. [2]

    (A15), is kinematically con- strained

    For large quantum numbers, these are given by x0 ≈( √n− √ n′)2, x ′ 0 ≈( √n+ √ n′)2.(20) The argumentx=κ 2 sin2 θ/(4γ) in our radiation problem, as defined in Eq. (A15), is kinematically con- strained. For the large quantum numbersn, n ′, it gets x≈x 0 sin2 θ≲x 0. Consequently,xtypically lies to the left of the first turning pointx 0 and approaches it. In...

    work page 2000

  3. [3]

    satisfiesη≥0, and the quantity (1−x/x p

    work page

  4. [4]

    Using the relation (1−x/x 0)≈ (1 +ξ 0y)εfrom Eq

    can be expressed in terms of (1−x/x 0) andη. Using the relation (1−x/x 0)≈ (1 +ξ 0y)εfrom Eq. (A7), one can find 1− x xp 0 ≈ 1− x x0 1 ε 1 +η(ε−1) .(26) In the WKB region II (near the first turning point), the functionI s,s′(x) is approximated by the modified Bessel functionK 1/3 as in Eq. (B2): Is,s′(x)≈ 1 π √ 3 1− x xp 0 1/2 K1/3(z′),(27) z′ = 2 3 (xp 0...

    work page

  5. [5]

    (B3) can be evaluated exactly, but we only require the limit of largenandn ′, where fn,n′(x)≈ (x−x 0)(x−x ′ 0) 4x2 .(B4) Performing the integration in Eq

    Herepis an integer determined by the Bohr–Sommerfeld quanti- zation condition: Z x′ 0 x0 q −fn,n′(x′)dx ′ = p− 1 2 π.(B3) The integral in Eq. (B3) can be evaluated exactly, but we only require the limit of largenandn ′, where fn,n′(x)≈ (x−x 0)(x−x ′ 0) 4x2 .(B4) Performing the integration in Eq. (B3) gives Z x′ 0 x0 q −fn,n′(x′)dx ′ =π min{n, n′}+ 1 2 .(B...

    work page

  6. [6]

    For largen, n ′, the combinations ofI-functions appearing in the matrix elements Eqs

    Spin transitions The WKB approximation can be applied here to derive analytic expressions for the spin-flip transition rates. For largen, n ′, the combinations ofI-functions appearing in the matrix elements Eqs. (A13) and (A14) are given in Eq. (A6), which can be expressed linearly in terms of modified Bessel functionsK 1/3 andK 2/3 [8]. Combining all the...

    work page

  7. [7]

    Spin polarization dynamics The time evolution of the spin populations is governed by the coupled rate equations dn↓ dt =n ↑wflip,ζ=1 −n ↓wflip,ζ=−1,(C4) dn↑ dt =n ↓wflip,ζ=−1 −n ↑wflip,ζ=1,(C5) wheren ↓ andn ↑ denote the number of electrons with spin anti-parallel (ζ=−1) and parallel (ζ= +1) to the magnetic field, respectively. The total electron number i...

    work page

  8. [8]

    V. N. Ba˘ ıer , Radiative polarization of electrons in stor- age rings, Sov. Phys. Usp.14, 695 (1972)

    work page 1972

  9. [9]

    Schwinger, On the classical radiation of accelerated electrons, Phys

    J. Schwinger, On the classical radiation of accelerated electrons, Phys. Rev.75, 1912 (1949)

    work page 1912

  10. [10]

    A. A. Sokolov and I. M. Ternov, On polarization and spin effects in the theory of synchrotron radiation, Sov. Phys. Dokl.8, 1203 (1964)

    work page 1964

  11. [11]

    Montague, Polarized beams in high energy storage rings, Phys

    Bryan W. Montague, Polarized beams in high energy storage rings, Phys. Rep113, 1 (1984)

    work page 1984

  12. [12]

    Buzzegoli, K

    M. Buzzegoli, K. Tuchin, N. Vijayakumar, Quasi- classical approximation of electromagnetic radiation by fermions embedded in a rigidly rotating medium in a strong magnetic field, Phys. Rev. C111, 054907 (2025)

    work page 2025

  13. [13]

    S. R. Mane, Yu. M. Shatunov, and K. Yokoya, Spin- polarized charged particle beams in high-energy acceler- ators, Rep. Prog. Phys.68, (1997)

    work page 1997

  14. [14]

    Karimi, L

    E. Karimi, L. Marrucci, V. Grillo, and E. Santamato, Spin-to-orbital angular momentum conversion and spin- polarization filtering in electron beams, Phys. Rev. Lett. 108, 044801 (2012)

    work page 2012

  15. [15]

    A. A. Sokolov and I. M. Ternov,Radiation from Rel- ativistic Electrons, (American Institute of Physics, New York, 1986)

    work page 1986

  16. [16]

    Rossmanith, High Energy Polarized Electron Beams, UNT Digital Library (1987)

    R. Rossmanith, High Energy Polarized Electron Beams, UNT Digital Library (1987)

    work page 1987

  17. [17]

    S. R. Mane, Radiative Spin Polarization in High Energy Storage Rings,arXiv:2512.13958(2025)

    work page arXiv 2025

  18. [18]

    Y. S. Derbenev and A. M. Kondratenko, Polarization kinetics of electrons in storage rings, Sov. Phys. JETP 37, 968 (1973)

    work page 1973

  19. [19]

    B. W. Montague, Polarized beams in high energy storage rings, Phys. Rep.113, 1 (1984)

    work page 1984

  20. [20]

    Maruyama, T

    T. Maruyama, T. Hayakawa, T. Kajino and M.- K. Cheoun, Generation of photon vortex by synchrotron radiation from electrons in Landau states under astro- physical magnetic fields, Phys. Lett. B826, 136779 (2022)

    work page 2022

  21. [21]

    Maruyama, T

    T. Maruyama, T. Hayakawa, R. Hajima, T. Kajino and M.-K. Cheoun, Photon vortex generation by synchrotron radiation experiments in relativistic quantum approach, Phys. Rev. Research5, 043289 (2023)

    work page 2023

  22. [22]

    Allen, M

    L. Allen, M. W. Beijersbergen, R. J. C. Spreeuw, and J. P. Woerdman, Orbital angular momentum of light and the transformation of Laguerre-Gaussian laser modes, Phys. Rev. A45, 8185 (1992)

    work page 1992

  23. [23]

    M. J. Padgett, Orbital angular momentum 25 years on, Opt. Express25, 11265 (2017)

    work page 2017

  24. [24]

    S. M. Lloyd, M. Babiker, and J. Yuan, Interaction of electron vortices and optical vortices with matter and processes of orbital angular momentum exchange, Phys. Rev. A86, 033824 (2012)

    work page 2012

  25. [25]

    K. Y. Bliokh, Y. P. Bliokh, S. Savel’ev, and F. Nori, Semiclassical dynamics of electron wave packet states with phase vortices, Phys. Rev. Lett.99, 190404 (2007)

    work page 2007

  26. [26]

    Liping Zou, Pengming Zhang, and A. J. Silenko, Gen- eral quantum-mechanical solution for twisted electrons in a uniform magnetic field, Phys. Rev. A103, L010201 (2021)

    work page 2021

  27. [27]

    Uchida and A

    M. Uchida and A. Tonomura, Generation of electron beams carrying orbital angular momentum, Nature464, 737 (2010)

    work page 2010

  28. [28]

    Verbeeck, H

    J. Verbeeck, H. Tian, P. Schattschneider, Production and application of electron vortex beams, Nature467, 301 (2010)

    work page 2010

  29. [29]

    A. Yu. Murtazin, G. K. Sizykh, D. V. Grosman, U. G. Rybak, A. A. Shchepkin, and D. V. Karlovets, Photon emission by vortex particles accelerated in a linac, Phys. Rev. D113, 036024 (2026)

    work page 2026

  30. [30]

    Buzzegoli, J

    M. Buzzegoli, J. D. Kroth, K. Tuchin, and N. Vijayaku- mar, Photon radiation by relatively slowly rotating fermions in magnetic field, Phys. Rev. D108, 096014 (2023)

    work page 2023

  31. [31]

    Qi Meng, Xuan Liu, Wei Ma, Zhen Yang, Liang Lu, A. J. Silenko, Pengming Zhang, and Liping Zou, Gener- alized Gouy rotation of electron vortex beams in uniform magnetic fields, Phys. Rev. Res7, 023306 (2025)

    work page 2025

  32. [32]

    Qi Meng, Ziqiang Huang, Xuan Liu, Wei Ma, Zhen Yang, Liang Lu, A. J. Silenko, Pengming Zhang, and Lip- ing Zou, Relativistic quantum mechanics of charged vor- tex particles accelerated in a uniform electric field, Phys. Rev. Res7, 043213 (2025)

    work page 2025

  33. [33]

    K. Y. Bliokh, I. P. Ivanov, G. Guzzinati, et al., Theory and applications of free-electron vortex states, Phys. Rep. 690, 1 (2017)

    work page 2017

  34. [34]

    Juchtmans, A

    R. Juchtmans, A. B´ ech´ e, A. Abakumov, M. Batuk, and J. Verbeeck, Using electron vortex beams to determine chirality of crystals in transmission electron microscopy, Phys. Rev. B91, 094112 (2015)

    work page 2015

  35. [35]

    B. J. Mcmorran, A. Agrawal, I. M. Anderson, A. A. Herz- ing, H. J. Lezec, J. J. Mcclelland, and J. Unguris, Elec- tron vortex beams with high quanta of orbital angular momentum, Science331, 192 (2011)

    work page 2011

  36. [36]

    K. Y. Bliokh, I. P. Ivanov, G. Guzzinati, and et al., The- ory and applications of free-electron vortex states, Phys. Rep.690, 1 (2017)

    work page 2017

  37. [37]

    I. P. Ivanov, Promises and challenges of high-energy vor- tex states collisions, Prog. Part. Nucl. Phys.127, 103987 (2022)

    work page 2022

  38. [38]

    Karlovets, D

    D. Karlovets, D. Grosman, and I. Pavlov, Angular mo- mentum dynamics of vortex particles in accelerators, Phys. Rev. Lett136, 085002 (2026)

    work page 2026

  39. [39]

    Floettmann and D

    K. Floettmann and D. Karlovets, Quantum mechanical formulation of the Busch theorem, Phys. Rev. A102, 17 043517 (2020)

    work page 2020

  40. [40]

    Karlovets, Relativistic vortex electrons: paraxial ver- sus nonparaxial regimes, Phys

    D. Karlovets, Relativistic vortex electrons: paraxial ver- sus nonparaxial regimes, Phys. Rev. A98, 012137 (2018)

    work page 2018

  41. [41]

    Karlovets, Vortex particles in axially symmetric fields and applications of the quantum Busch theorem, New J

    D. Karlovets, Vortex particles in axially symmetric fields and applications of the quantum Busch theorem, New J. Phys.23, 033048 (2021)

    work page 2021

  42. [42]

    J. D. Jackson,Classical Electrodynamics, 3rd ed., (Wiley, New York, 1999)

    work page 1999

  43. [43]

    L. D. Landau and E. M. Lifshitz,The Classical Theory of Fields, (Butterworth-Heinemann, Oxford, 1975)

    work page 1975

  44. [44]

    Katoh, M

    M. Katoh, M. Fujimoto, H. Kawaguchi, K. Tsuchiya, K. Ohmi, T. Kaneyasu, Y. Taira, M. Hosaka, A. Mochi- hashi, et al., Angular momentum of twisted radiation from an electron in spiral motion, Phys. Rev. Lett.118, 094801 (2017)

    work page 2017

  45. [45]

    A. J. Silenko, Pengming Zhang, and Liping Zou, Rela- tivistic quantum dynamics of twisted electron beams in arbitrary electric and magnetic fields, Phys. Rev. Lett 121, 043202 (2018)

    work page 2018

  46. [46]

    Clark, A

    L. Clark, A. B´ ech´ e, G. Guzzinati,et al., Exploiting lens aberrations to create electron-vortex beams, Phys. Rev. Lett.111, 064801 (2013)

    work page 2013

  47. [47]

    Liping Zou, Pengming Zhang, Alexander.J Silenko, Pro- duction of twisted particles in magnetic fields, J. Phys. B57, 045401 (2024)

    work page 2024

  48. [48]

    Schattschneider, M

    P. Schattschneider, M. St¨ oger-Pollach, and J. Verbeeck, Novel vortex generator and mode converter for electron beams, Phys. Rev. Lett.109, 084801 (2012)

    work page 2012

  49. [49]

    Schattschneider, T

    P. Schattschneider, T. Schachinger, M. St¨ oger-Pollach, S. L¨ offler, A. Steiger-Thirsfeld, K. Y. Bliokh and F. Nori, Imaging the dynamics of free-electron Landau states, Nat. Commun.5, 4586 (2014)

    work page 2014

  50. [50]

    Mafakheri, A

    E. Mafakheri, A. H. Tavabi, P.-H. Lu, R. Balboni, F. Venturi, C. Menozzi, G. C. Gazzadi, S. Frabboni, A. Sit, R. E. Dunin-Borkowski, E. Karimi, and V. Grillo, Realization of electron vortices with large orbital angu- lar momentum using miniature holograms fabricated by electron beam lithography, Appl. Phys. Lett.110, 093113 (2017)

    work page 2017