beam velocity distribution function for $s=1.27$. (b): final beam velocity distribution function without control term (\[eqn:fTWT\]) (light gray line), with the exact control term (black line) and with the approximate control term (\[eqn:fsimappTWT\]) (dark gray line).[]{data-label="Distr_s1p27"}](Fig5b.eps "fig:"){width="8.0cm" height="7.0cm"}

In Figs. \[Distr\_sp85\] and  \[Distr\_s1p27\], the initial velocity distribution function of a set of $10^4$ particles is compared with the final one obtained by integrating over a time $t=50$, the dynamics governed by Hamiltonian (\[Ham:sim\]) without control terms, plus the exact control term (\[eqn:fsimTWT\]) and plus the approximate control term (\[eqn:fsimappTWT\]). This investigation is performed for the two different values of the Chirikov parameter, $s=0.85$ for Fig. \[Distr\_sp85\] and $s=1.27$ for Fig. \[Distr\_s1p27\]. In the case without any control term the original kinetic coherence of the beam is lost which means that some electrons can have velocities in the whole range in between resonances, $v\in [-0.67,
0.88]$. Adding the exact control term the particles are confined in a selected region of phase space by the reconstructed invariant tori, and the beam recovers a large part of its initial kinetic coherence. For $s=0.85$, velocities of the electrons are now between $0.33$ and $0.79$. The exact control term is also efficient in the fully 