Instability of motion of relativistic charged particles in non-uniform stationary electromagnetic fields

It is well established that a sufficiently large gradient of the electric field causes instability of the motion of charged particles in mutually perpendicular electric and magnetic fields. This instability leads to an effective energization of the particles by electrostatic electric fields. The minimum value of the electric field gradient required for this instability to occur for non-relativistic particles depends on the strength of the magnetic field but is independent of both the particle velocity and the local electric field strength. This paper describes an instability caused by non-uniformity of the electric field for relativistic particles and demonstrates that its threshold in the relativistic case depends, in addition to the magnetic field intensity, on the speed of the particle and the local strength of the electric field. Larger particle speeds and larger electric fields reduce the gradient of the electric field required to make the particle motion unstable. (c) 2024 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution-NonCommercialNoDerivs 4.0 International (CC BY-NC-ND) license (https://creativecommons.org/licenses/by-nc-nd/4.0/). https://doi.org/10.1063/5.0220994