scale chaos occurs in phase space. As a consequence, the particle can have an arbitrary velocity in between the two phase velocities of the waves ($\omega_2/k_2$ and $\omega_1/k_1$). In this TWT, such typical chaotic behavior has been observed directly [@Macor1]. This chaotic diffusion of the particles in phase space can be reduced by using an apt control term which consists here as an additional wave (or more generally a set of waves) of small amplitude. The characteristics of this additional wave are computed explicitly, and then the wave is injected in addition to the two others. The results presented in this article were announced in Ref. [@c18].

The paper is organized as follows : The control method is briefly recalled in Sec. \[loc:method\] and its application to the considered Hamiltonian is presented in Sec. \[loc:computation\]. Numerical investigations of the effect of the control term and its robustness are reported in Secs. \[loc:simulation\] and \[loc:robust\]. In Sec. \[experiment:setup\], a description of the experimental set-up precedes the results of the implementation of the control term shown in Sec. \[experiment:implementation\] as well as its robustness in Sec. \[experiment:robust\].

Local control method applied to a two wave model {#loc:control}
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The Hamiltonian of an 