The influence of the transverse electric field on accelerating vortex state in the axisymmetric electric field

• URL: http://arxiv.org/abs/2607.03747v1
• Date: Sat, 04 Jul 2026 07:40:06 GMT
• Title: The influence of the transverse electric field on accelerating vortex state in the axisymmetric electric field
• Abstract summary: relativistic vortex states of massive charged particles propagating in non-uniform axisymmetric electric field are studied.<n> coupled evolution equations for the beam width, wavefront curvature, and Gouy phase are derived.<n>Results provide a relativistic quantum framework for controlling accelerated vortex particle beams using electrostatic fields.
• Score: 40.36826185009178
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The relativistic vortex states of massive charged particles propagating in non-uniform axisymmetric electric field are studied. Starting from the stationary-state equation after the relativistic Foldy-Wouthuysen (FW) transformation and employing 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 provide a relativistic quantum framework for controlling accelerated vortex particle beams using electrostatic fields.

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