Virtual dielectric waveguide mode description of a high-gain free-electron laser I: Theory

TL;DR

This paper develops a theoretical framework using dielectric waveguide modes to analyze the electromagnetic field evolution in high-gain free-electron lasers, incorporating space-charge effects and enabling efficient eigenmode characterization.

Contribution

It introduces a mode-coupled excitation equation approach for FEL analysis, connecting eigenmode properties with free-space propagation and providing a method to find FEL eigenmodes.

Findings

Derived excitation equations for FEL modes including space-charge effects

Established a matrix determinant condition for FEL eigenmodes

Predicted the spot size of the dominant eigenmode in a quadratic index medium

Abstract

A set of mode-coupled excitation equations for the slowly-growing amplitudes of dielectric waveguide eigenmodes is derived as a description of the electromagnetic signal field of a high-gain free-electron laser, or FEL, including the effects of longitudinal space-charge. This approach of describing the field basis set has notable advantages for FEL analysis in providing an efficient characterization of eigenmodes, and in allowing a clear connection to free-space propagation of the input (seeding) and output radiation. The formulation describes the entire evolution of the radiation wave through the linear gain regime, prior to the onset of saturation, with arbitrary initial conditions. By virtue of the flexibility in the expansion basis, this technique can be used to find the direct coupling and amplification of a particular mode. A simple transformation converts the derived coupled differential excitation equations into a set of coupled algebraic equations and yields a matrix determinant equation for the FEL eigenmodes. A quadratic index medium is used as a model dielectric waveguide to obtain an expression for the predicted spot size of the dominant system eigenmode, in the approximation that it is a single gaussian mode.