(\[eqn:fappfasi\]) or Eq. (\[eqn:fappAmp\]), we introduce the kinetic coherence indicator defined as the ratio of the variance of the initial beam over the variance of the distribution function after a given integration time. The number of particles, the integration time and the initial conditions are equal to the ones used in the previous section.

![Kinetic coherence versus the phase introduced in the approximate control term given by Eq. (\[eqn:fappfasi\]). 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. The overlap parameter is $s=1.27$.[]{data-label="fig:kin_fase"}](Fig6.eps){width="7.9cm" height="7.0cm"}

In Fig. \[fig:kin\_fase\] we show the kinetic coherence as a function of the phase of the approximate control term for the strongly chaotic regime $s=1.27$. We notice that $\varphi$ or $-\varphi$ will give the same velocity distribution function for symmetry reason. Therefore we only consider the range $\varphi\in[0,\pi]$. The efficiency of the approximated control term is very sensitive with respect to the phase. In fact an error of $5^{\mathrm o}-6^{\mathrm o}$ causes a decrease of the kinetic coherence of about $50\%$ and with an error greater than $30^{\mathrm o}$ the kinetic coherence drops in the range of values of 