Dynamics of Relativistic Vortex Electrons in External Laser Fields

Investigating vortex electron interactions with electromagnetic fields is essential for advancing particle acceleration techniques, scattering theory in background fields, and obtaining novel electron beams for material diagnostics. A systematic investigation into the dynamics of vortex electrons in external laser fields and the exploration of laser-induced vortex modes remains lacking. In this work, we study the propagation of vortex electrons in linearly polarized (LP) and circularly polarized (CP) laser pulses, both separately and in their combined form in two-mode laser pulses. The theoretical formalism is developed by utilizing Volkov-Bessel wave functions, and the four-current density is obtained as a crucial observable quantity. Numerical results illustrate the dynamics of vortex electrons in external lasers, showing that the beam center of the vortex electron follows the classical motion of a point charge electron, while maintaining the probability distribution structure for both vortex eigenstates and superposition modes. The combined effect of LP and CP laser pulses in the two-mode laser field allows for the versatile control of vortex electrons, which is absent with LP or CP lasers alone, at femtosecond and sub-nanometer scales. Our findings demonstrate the versatile control over vortex electrons via laser pulses, with our formalism providing a reference for vortex scattering in laser backgrounds and inspiring the laser-controlled achievement of novel vortex modes as targeted diagnostic probes for specialized materials.