The properties of the neutrino provide a unique window on physics beyond that described by the standard model. The study of subleading effects in neutrino oscillations, and the race to discover CP-invariance violation in the lepton sector, has begun with the recent discovery that θ 13 >0 . The measured value of θ 13 is large, emphasizing the need for a facility at which the systematic uncertainties can be reduced to the percent level. The neutrino factory, in which intense neutrino beams are produced from the decay of muons, has been shown to outperform all realistic alternatives and to be capable of making measurements of the requisite precision. Its unique discovery potential arises from the fact that only at the neutrino factory is it practical to produce high-energy electron (anti)neutrino beams of the required intensity. This paper presents the conceptual design of the neutrino factory accelerator facility developed by the European Commission Framework Programme 7 EUROν Design Study consortium. EUROν coordinated the European contributions to the International Design Study for the Neutrino Factory (the IDS-NF) collaboration. The EUROν baseline accelerator facility will provide 10 21 muon decays per year from 12.6 GeV stored muon beams serving a single neutrino detector situated at a source-detector distance of between 1 500 km and 2 500 km. A suite of near detectors will allow definitive neutrino-scattering experiments to be performed.