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Geometry-enabled radiation from structured paraxial electrons

M. S. Epov, I. E. Shenderovich, and S. S. Baturin*

  • School of Physics and Engineering, ITMO University, St. Petersburg 197101, Russia

  • *Contact author: s.s.baturin@gmail.com
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Phys. Rev. A 114, L020801 – Published 3 August, 2026

DOI: https://doi.org/10.1103/lq8m-fn3q

Abstract

We present a microscopic calculation of spontaneous photon emission by twisted (paraxial) electrons propagating through inhomogeneous, axisymmetric magnetic fields. We construct exact electron states that incorporate transverse mode structure and wave-front curvature by combining the Foldy-Wouthuysen transformation with a geometric framework based on Lewis-Ermakov invariants and metaplectic transformations. We show that the evolution of such structured states corresponds to an open path in the space of quadratic forms, giving rise to a geometric contribution to the emission amplitude that cannot be eliminated by gauge choice or adiabatic arguments. The inverse radius of curvature of the electron wave front controls a finite-window boundary contribution to the emission amplitude in regions where the external magnetic field vanishes locally; this contribution vanishes when the observation window is extended to infinity. The mechanism presented generalizes Landau-level radiation to nonasymptotic, structured electron states and establishes a direct connection between noncyclic geometric evolution and photon emission.

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Phys. Rev. A 114, L020801– Published 3 August, 2026
  • Received 9 February 2026
  • Accepted 20 July 2026
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