Propagation properties of the electron circular vortex beam based on the butterfly catastrophe

In this paper, an alternative kind of electron circle butterfly vortex beam (ECBVB) based on the butterfly catastrophe is introduced, and its propagation characteristics in free space and constant magnetic field are numerically discussed. In free space, the ECBVB exhibits autofocusing and self-healing properties, and the probability flow density vector and cross-section intensity distribution are also analyzed. Compared to that in the free space, the focusing intensity of the ECBVB in the magnetic field increases by two orders of magnitude. By changing the distribution factor, the magnetic flux density, and the second-order chirp factor, the autofocusing properties of the ECBVB can be adjusted flexibly. In addition, adjusting the topological charges and the initial transverse velocity of the ECBVB is conducive to obtaining the desired propagation behavior of the ECBVB.