Relativistic Quantum-Mechanical Description of Acceleration of Charged Vortex Particles by a Uniform Electric Field

Abstract Stationary wave eigenfunctions of a charged Laguerre–Gauss beam accelerated in a uniform electric field are rigorously derived in the framework of relativistic quantum mechanics. The evolution of beam parameters during acceleration is calculated in detail. The simple classical model of this evolution is proposed. The acceleration extraordinary suppresses transverse spreading of the beam. Our results show that vortex particle beams can be accelerated without destroying their intrinsic vortex properties.