Optimization of the Two-Baseline Beta-Beam

We propose a $\beta$-Beam experiment with four source ions and two baselines for the best possible sensitivity to $\theta_{13}$, CP violation and mass hierarchy. Neutrinos from $^{18}$Ne and $^6$He with Lorentz boost $\gamma=350$ are detected in a 500 kton water \chr detector at a distance L=650 km from the source. Neutrinos from $^8$B and $^8$Li are detected in a 50 kton magnetized iron detector at a distance L=7000 km from the source. Since a tilt angle $\vartheta=34.5^\circ$ is required to send the beam to the magic baseline, the far end of the ring has a maximum depth of $d=2132$ m. We alleviate this problem by proposing to trade reduction of the decay ring with the increase in the boost factor of the $^8$Li and $^8$B ions up to $\gamma_{^8\mathrm{Li}}=390$ and $\gamma_{^8\mathrm{Li}}=650$, such that the number of events at the detector remains almost the same. We study the sensitivity reach of this two-baseline two-storage ring $\beta$-Beam experiment, and compare it with the corresponding reach of the other proposed facilities.