document: We have developed the theory of electrons carrying quantized orbital angular momentum. To make connection to realistic situations, we considered a plane wave moving along the optic axis of a lens system, intercepted by a round, centered aperture.88In the experiment, this aperture carries the holographic mask. It turns out that the movement along the optic axis can be separated off; the reduced Schrödinger equation operating in the plane of the aperture can be mapped onto Bessel's differential equation. The ensuing eigenfunctions fall into families with discrete orbital angular momentum ℏm along the optic axis where m is a magnetic quantum number. Those vortices can be produced by matching a plane wave after passage through a holographic mask with a fork dislocation to the eigenfunctions of the cylindrical problem. Vortices can be focussed by magnetic lenses into volcano-like charge distributions with very narrow angular divergence, resembling loop currents in the diffraction plane. Inclusion of spherical aberration changes the ringlike shape but does not destroy the central zero intensity of vortices with m≠0. Partial coherence of the incident wave leads to a rise of the central intensity minimum. It is shown that a very small source angle (i.e. a very high coherence) is necessary so as to keep the volcano structure intact. Their small angular width in the far field may allow the creation of nm-sized or smaller electron vortices but the demand for extremely high coherence of the source poses a serious difficulty.
extractive_keyphrases: angular divergence aperture holographic mask incident wave inclusion of spherical aberration lens system magnetic lenses partial coherence plane reduced schrödinger equation vortices
abstractive_keyphrases: creation of nm-sized or smaller electron vortices electrons carrying quantized orbital angular momentum. plane wave round, centered aperture