has been a growing interest in controlling chaos which here means to reduce it when and where it is undesirable and to increase it when it is useful.

The sensitivity of chaotic systems to small perturbations triggered a strong interdisciplinary effort to control chaos [@c1; @c2; @c3; @c4; @c5; @c6; @c7; @c8]. After the seminal work on optimal control by Pontryagin [@c9], efficient methods were proposed for controlling chaotic systems by nudging targeted trajectories [@c10; @c11; @c12; @c13; @c14]. However, for many body experiments such methods are hopeless due to the high number of trajectories to deal with simultaneously.

It was recently proposed a local control method [@chan06] which aims at building barriers in phase space and hence confines all the trajectories rather than following them individually. These barriers are stable structures in phase space like for instance invariant tori, which are generically broken by the perturbation. The reduction of chaotic behaviors is achieved by using a small apt perturbation of the system which keeps its Hamiltonian structure.

In this article, we consider a traveling wave tube (TWT) specially designed to study wave particle interaction which is used to investigate experimentally the control method and its robustness. The dynamics in 