Influence of the transverse field on accelerating vortex states in an axisymmetric electric field
Phys. Rev. A 114, 052206 – Published 6 November, 2026
DOI: https://doi.org/10.1103/7lw9-hbt4
Abstract
The relativistic vortex states of massive charged particles propagating in a nonuniform axisymmetric electric field are studied. Starting from the stationary-state equation after the relativistic Foldy-Wouthuysen transformation and employing the Scherzer expansion, a longitudinal Wentzel-Kramers-Brillouin reduction, and the paraxial approximation, the coupled evolution equations for the beam width, wavefront curvature, and Gouy phase are derived. The equations are solved numerically for a quadratic electrostatic potential, an immersion lens, and an einzel lens. The essential influence of the transverse field on beam evolution is demonstrated. The results offer insights into the evolution of accelerated vortex electron beams and may help guide the control of their transverse properties using electrostatic fields.
