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Stabilizing a wave amplified by a beam of particles with test-waves

Romain Bachelard, Cristel Chandre, Duccio Fanelli, Xavier Leoncini, Michel Vittot
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
(using the residue method) 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 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 control parameter which is able to strongly decrease the
oscillations of the intensity without reducing its mean-value.
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