A new approach to solving the radiation field problem of an extended helical undulator

TL;DR

This paper introduces an exact series expansion method for calculating the radiation field of a particle moving along an infinite helical path, improving precision over approximate solutions and enabling optimization of radiation characteristics.

Contribution

The paper presents a novel exact solution for the radiation field of a helical particle trajectory using cylindrical multipole series expansion, with applications to optimization.

Findings

Derived exact relationships for the Doppler effect.

Compared exact solution with approximate models.

Showed continuous transition to circular motion expressions.

Abstract

A new method is applied to construct an exact solution for the radiation field of a particle moving along an infinite helical trajectory. The solution is obtained in the form of a series expansion in cylindrical multipoles. The obtained solution is compared with the existing approximate solution and, using the derived exact relationships for the Doppler effect, is used to construct integral and angular characteristics of the radiation field. The possibility of a continuous transition from expressions for a helical trajectory of a particle to expressions describing the motion of a particle along a closed circle is shown. Optimization criteria are introduced and the possibility of optimizing the radiation characteristics by several parameters is considered.