Eur. Phys. J. D 42, 125-132 (2007)
https://doi.org/10.1140/epjd/e2006-00276-x

Stabilizing the intensity of a wave amplified by a beam of particles

¹ Centre de Physique Théorique (Unité Mixte de Recherche (UMR 6207) du CNRS, et des universités Aix-Marseille I, Aix-Marseille II et du Sud Toulon-Var; Laboratoire affilié à la FRUMAM (FR 2291); Laboratoire de Recherche Conventionné du CEA (DSM-06-35).) , CNRS Luminy, Case 907, 13288 Marseille Cedex 9, France
² Dipartimento di Energetica and CSDC, Università di Firenze, INFN, via S. Marta, 3, 50139 Firenze, Italy
³ Department of Cell and Molecular Biology, Karolinska Institute, 17177 Stockholm, Sweden
⁴ Physique des Interactions Ioniques et Moléculaires, CNRS-Université de Provence, Centre de St Jérôme, 13397 Marseille, France

Corresponding author: ^a bachelard@cpt.univ-mrs.fr

Received: 11 September 2006
Published online: 22 December 2006

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 re-shaping the macro-particle. This strategy involves the study of the linear stability (using the residue method) of selected periodic orbits of a mean-field model. As parameters of an additional perturbation are varied, bifurcations occur in the system which have drastic effect on the modification of the self-consistent dynamics, and in particular, of the macro-particle. We show how to obtain an appropriate tuning of the parameters which is able to strongly decrease the oscillations of the intensity without reducing its mean-value.