
%%%%%%%%% Avant

The horns are designed to focus the $600$~MeV/c pions (see section~\ref{sec:horn}) and the variation of the number of such pion is rather smooth with respect to the beam energy considering a 4MW fixed beam power: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.



%%%%%%%%%%% Apres

The variation of the number of $600$~MeV/c pions is rather smooth with respect to the beam energy (the horns are designed to focus such pions, see section~\ref{sec:horn}). Considering a 4MW fixed beam power, they are: $4.19\times10^{13}\pi$/s for the $2.2$~GeV beam, $4.91\times10^{13}\pi$/s for the $3.5$~GeV beam, $5.14\times10^{13}\pi$/s for the $4.5$~GeV beam, and $4.92\times10^{13}\pi$/s for the $6.5$~GeV beam. The main difference is made by the angular distribution. Figure~\ref{fig:compEner2}(b) shows this distribution for the $\pi^+$ exiting the target with a momentum between $500$~MeV/c and $700$~MeV/c. The acceptance of the horns is limited to the pion below $25^\circ$, and we see that more pions are accepted by the horns for the $3.5$~GeV and $4.5$~GeV proton beams compared to other beam energies.





