Dynamics of self-accelerating electron beams in a homogeneous magnetic field

TL;DR

This paper investigates how self-accelerating electron beams, especially Airy and power-law beams, behave in a homogeneous magnetic field, revealing their trajectories and wavefunctions through analytical and numerical methods.

Contribution

It provides closed-form solutions and asymptotic formulas for the trajectories of self-accelerating electron beams in magnetic fields, advancing understanding of their dynamics.

Findings

Closed-form solutions for Airy beam wavefunctions

Asymptotic formulas for beam trajectories

Excellent agreement with numerical simulations

Abstract

We examine the dynamics of electron beams that, in free space, are self-accelerating, in the presence of an additional magnetic field. We focus our attention in the case of Airy beams that follow parabolic trajectories and in generalized classes of beams associated with power-law trajectories. We study the interplay between beam self-acceleration and the circular motion caused by the magnetic field. In the case of Airy beams, using an integral representation, we find closed-form solutions for the electron wavefunction. We also derive asymptotic formulas for the beam trajectories both for Airy beams and for self-accelerating power-law beams. A ray optics description is rather useful for the interpretation of the beam dynamics. Our results are in excellent comparison with direct numerical simulations.