Dynamics of relativistic vortex electrons in external laser fields

Investigating the interactions of vortex electrons with electromagnetic fields is crucial for advancing particle acceleration techniques, scattering theory in background fields, and developing novel electron beams for material diagnostics. In this work, we systematically study the dynamics of relativistic vortex electrons during their head-on collisions with linearly polarized (LP) and circularly polarized (CP) laser pulses, as well as their superposition. We develop a theoretical framework using Volkov-Bessel wave functions to describe the spatiotemporal characteristics of vortex electrons in these external fields. We show that the beam center of the vortex electron follows the classical trajectory of a point-charge electron while maintaining the transverse structure of both vortex eigenstates and superposition states. Specifically, CP laser pulses cause the beam center to rotate, while LP laser pulses induce a lateral shift. The combined effect of LP and CP laser pulses in a two-mode field results in a twisted spiral pattern. Our findings demonstrate the potential for versatile control of vortex electron beams using various laser modes, providing a foundation for future experimental and theoretical studies. This work serves as a benchmark reference for investigations into the manipulation of vortex electron beams using more realistic laser or other types of external fields.