Stabilizing the intensity for a Hamiltonian model of the FEL

TL;DR

This paper introduces a control strategy to stabilize the intensity in a Free Electron Laser by destabilizing the macro-particle through bifurcation analysis of a mean-field model.

Contribution

It proposes a novel method to reduce intensity oscillations in FELs by tuning external wave amplitude based on stability analysis of a periodic orbit.

Findings

Effective stabilization of intensity oscillations achieved.

Bifurcation analysis reveals control parameter influence.

Macro-particle destabilization reduces oscillations without lowering mean intensity.

Abstract

The intensity of an electromagnetic wave interacting self-consistently with a beam of charged particles, as in a Free Electron Laser, displays large oscillations due to an aggregate of particles, called the macro-particle. In this article, we propose a strategy to stabilize the intensity by destabilizing the macro-particle. This strategy involves the study of the linear stability of a specific periodic orbit of a mean-field model. As a control parameter - the amplitude of an external wave - is varied, a bifurcation occur in the system which has drastic effects on the self-consistent dynamics, and in particular, on the macro-particle. We show how to obtain an appropriate tuning of the control parameter which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.