Charged particles in crossed and longitudinal electromagnetic fields and beam guides

TL;DR

This paper analyzes the motion of charged particles in complex electromagnetic fields, identifies configurations that act as beam guides, and provides exact solutions to quantum wave equations in these fields, expanding theoretical understanding.

Contribution

It introduces new exact solutions to Klein-Gordon and Dirac equations in combined electromagnetic fields and identifies conditions for effective beam guiding.

Findings

Certain field configurations serve as effective beam guides.

Exact solutions to quantum equations are derived and shown to be complete and orthogonal.

New theoretical tools for analyzing particle motion in complex fields are developed.

Abstract

We consider a class of electromagnetic fields that contains crossed fields combined with longitudinal electric and magnetic fields. We study the motion of a classical particle (solutions of the Lorentz equations) in such fields. Then, we present an analysis that allows one to decide which fields from the class act as a beam guide for charged particles, and we find some time-independent and time-dependent configurations with beam guiding properties. We demonstrate that the Klein-Gordon and Dirac equations with all the fields from the class can be solved exactly. We study these solutions, which were not known before, and prove that they form complete and orthogonal sets of functions.