the non-controlled case.

![Kinetic coherence versus $\delta$ for the approximate control term given by Eq. (\[eqn:fappAmp\]). The red dash-dotted line indicates the kinetic coherence value for the non-controlled case and the dotted line the kinetic coherence value for the approximate control term given by Eq. (\[eqn:fsimappTWT\]).The overlap parameter is $s=1.27$.[]{data-label="fig:kin_amp"}](Fig7.eps){width="8.3cm" height="7.2cm"}

Concerning the robustness with respect to an error on the amplitude of the approximate control term, we plot on Fig. \[fig:kin\_amp\] the behavior of the kinetic coherence as a function of the $\delta$-factor which multiplies the amplitude of the approximate control term. We notice that around the reference value of $\delta=1$ (no error) there is a region ($\delta\in[1,1.3]$) where the approximate control term is very efficient in confining the beam of test particles with a kinetic coherence in between $[0.096,0.12]$. On the other hand reducing the amplitude of the control term, i.e. its energy, there is a region where one has still a confining effect on the beam particle. For example for $\delta=0.6$ the kinetic coherence is larger by $50\%$ of the value of the non-controlled case.

Experimental tests {#experiment}
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Experimental set-up {#experiment:setup}
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The experimental implementation of the control term is performed in a long traveling wave 