Particle in the Electromagnetic Wave with Cylindrical Symmetry, an Analog of the Volkov Problem

TL;DR

This paper investigates the classical motion of a non-relativistic particle constrained on a cylindrical surface under a cylindrical electromagnetic wave, providing exact solutions using elliptic functions, and drawing an analogy to the Volkov problem.

Contribution

It introduces a cylindrically symmetric analogue of the Volkov problem and derives exact solutions for particle motion in this setting.

Findings

Exact elliptic function solutions for particle trajectories

Analogy established with the classical Volkov problem

Insights into particle dynamics in cylindrical electromagnetic fields

Abstract

Cylindrically symmetric analogue of the Volkov problem is examined. In presence of the field of a cylindrical electromagnetic wave, classical motion of a non-relativistic particle on a cylindrical surface is described exactly in terms of elliptic functions.