Generation of electron vortex beams using line charges via the electrostatic Aharonov-Bohm effect

It has recently been shown that an electron vortex beam can be generated by the magnetic field surrounding the tip of a dipole-like magnet. This approach can be described using the magnetic Aharonov-Bohm effect and is associated with the fact that the end of a long magnetic rod can be treated approximately as a magnetic monopole. However, it is difficult to vary the magnetisation of the rod in such a setup and the electron beam vorticity is fixed for a given tip shape. Here, we show how a similar behaviour, which has the advantage of easy tuneability, can be achieved by making use of the electrostatic Aharonov-Bohm effect associated with an electrostatic dipole line. We highlight the analogies between the magnetic and electrostatic cases and use simulations of in-focus, Fresnel and Fraunhofer images to show that a device based on two parallel, oppositely charged lines that each have a constant charge density can be used to generate a tuneable electron vortex beam. We assess the effect of using a dipole line that has a finite length and show that if the charge densities on the two lines are different then an additional biprism-like effect is superimposed on the electron-optical phase.