Variational Principle for Spontaneous Wiggler and Synchrotron Radiation

TL;DR

This paper introduces a maximum-power variational principle within a Hilbert space framework to model spontaneous electromagnetic radiation from relativistic electron beams, applicable to undulator and synchrotron radiation.

Contribution

It develops a novel variational principle for modeling classical spontaneous radiation, extending its applicability to various radiation sources and structured media.

Findings

The MPVP effectively models undulator radiation with analytical approximations.

Numerical examples demonstrate the principle's application to x-ray generation.

The framework generalizes to different radiation problems beyond undulators.

Abstract

Within the framework of a Hilbert space theory, we develop a maximum-``power'' variational principle (MPVP) applicable to classical spontaneous electromagnetic radiation from relativistic electron beams or other prescribed classical current sources. A simple proof is summarized for the case of three-dimensional fields propagating in vacuum, and specialization to the important case of paraxial optics is also discussed. The techniques have been developed to model undulator radiation from relativistic electron beams, but are more broadly applicable to synchrotron or other radiation problems, and may generalize to certain structured media. We illustrate applications with a simple, mostly analytic example involving spontaneous undulator radiation (requiring a few additional approximations), as well as a mostly numerical example involving x-ray generation via high harmonic generation in sequenced undulators