Evolution of an accelerated charged vortex particle in an inhomogeneous magnetic lens

We present a detailed analysis of the capture and acceleration of a nonrelativistic charged vortex particle (elec-tron, positron, proton, etc.) with an orbital angular momentum in the field of an axisymmetric electromagnetic lens, typical for a linear accelerator. We account for the acceleration and the inhomogeneity of both electric and magnetic fields that may arise from real-life imperfections. We establish the conditions for this wave packet to be captured and successfully transported through the lens. We describe the transition process and explain how a free Laguerre-Gaussian packet can be captured into the Landau state of the lens and how its structure is preserved for all moments in time. We illustrate the developed formalism with several representative examples.