Towards the optimal energy of the proton driver for a neutrino factory and muon collider

Cross section data from the HARP experiment for pion production by protons from a tantalum target have been convoluted with the acceptance of the front-end channel for the proposed neutrino factory or muon collider and integrated over the full phase space measured by HARP, to determine the beam-energy dependence of the muon yield. This permits a determination of the optimal beam energy for the proton driver for these projects. The cross section data are corrected for the beam-energy dependent amplification due to the development of hadronic showers in a thick target. The conclusion is that, for constant beam power, the yield is maximum for a beam energy of about 7 GeV, but it is within 10% of this maximum for 4<Tbeam < 11 GeV, and within 20% of the maximum for Tbeam as low as 2 GeV. This result is insensitive to which of the two HARP groups' results are used, and to which pion generator is used to compute the thick target effects.