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