Particle and guiding-center orbits in crossed electric and magnetic fields

TL;DR

This paper examines charged-particle trajectories in crossed electric and magnetic fields, comparing exact particle motion with guiding-center approximations, especially under nonuniform electric fields, and provides explicit Hamiltonian formulations.

Contribution

It extends guiding-center theory to arbitrary radial electric fields and offers explicit examples for linear electric field cases, enhancing understanding of particle dynamics in complex fields.

Findings

Guiding-center approximation validity is assessed against exact dynamics.

Explicit Hamiltonian formulations for linear radial electric fields are derived.

The theory accommodates nonuniform electric fields in crossed-field configurations.

Abstract

The problem of the charged-particle motion in crossed electric and magnetic fields is investigated, and the validity of the guiding-center representation is assessed in comparison with the exact particle dynamics. While the magnetic field is considered to be straight and uniform, the (perpendicular) radial electric field is nonuniform. The Hamiltonian guiding-center theory of charged-particle motion is presented for arbitrary radial electric fields, and explicit examples are provided for the case of a linear radial electric field.