  We perform a systematic study of particle production and neutrino yields for
different incident proton energies $E_p$ and baselines $L$, with the aim of
optimizing the parameters of a neutrino beam for the investigation of
$\theta_{13}$-driven neutrino oscillations in the $\Delta m^2$ range allowed by
Superkamiokande results. We study the neutrino energy spectra in the
``relevant'' region of the first maximum of the oscillation at a given baseline
$L$. We find that to each baseline $L$ corresponds an ``optimal'' proton energy
$E_p$ which minimizes the required integrated proton intensity needed to
observe a fixed number of oscillated events. In addition, we find that the
neutrino event rate in the relevant region scales approximately linearly with
the proton energy. Hence, baselines $L$ and proton energies $E_p$ can be
adjusted and the performance for neutrino oscillation searches will remain
approximately unchanged provided that the product of the proton energy times
the number of protons on target remains constant. We apply these ideas to the
specific cases of 2.2, 4.4, 20, 50 and 400 GeV protons. We simulate focusing
systems that are designed to best capture the secondary pions of the
``optimal'' energy. We compute the expected sensitivities to
$\sin^22\theta_{13}$ for the various configurations by assuming the existence
of new generation accelerators able to deliver integrated proton intensities on
target times the proton energy of the order of ${\cal O}(5\times 10^{23})\rm\
GeV\times\rm pot/year$.
