Sub-nanometer free electrons with topological charge

The holographic mask technique is used to create freely moving electrons with quantized angular momentum. With electron optical elements they can be focused to vortices with diameters below the nanometer range. The understanding of these vortex beams is important for many applications. Here we present a theory of focused free electron vortices. The agreement with experimental data is excellent. As an immediate application, fundamental experimental parameters like spherical aberration and partial coherence are determined.