Very intense neutrino beams and large neutrino detectors will be needed in order to enable the discovery of CP violation in the leptonic sector. We propose to use the proton linac of the European Spallation Source currently under construction in Lund, Sweden to deliver, in parallel with the spallation neutron production, a very intense, cost effective and high performance neutrino beam. The baseline program for the European Spallation Source linac is that it will be fully operational at 5 MW average power by 2022, producing 2 GeV 2.86 ms long proton pulses at a rate of 14 Hz. Our proposal is to upgrade the linac to 10 MW average power and 28 Hz, producing 14 pulses/s for neutron production and 14 pulses/s for neutrino production. Furthermore, because of the high current required in the pulsed neutrino horn, the length of the pulses used for neutrino production needs to be compressed to a few µs with the aid of an accumulator ring. A long baseline experiment using this Super Beam and a megaton underground Water Cherenkov detector located in existing mines 300-600 km from Lund will make it possible to discover leptonic CP violation at 5 σ significance level in up to 50% of the leptonic Dirac CP-violating phase range. This experiment could also determine the neutrino mass hierarchy at a significance level of more than 3 σ if this issue will not already have been settled by other experiments by then. The mass hierarchy performance could be increased by combining the neutrino beam results with those obtained from atmospheric neutrinos detected by the same large volume detector. This detector will also be used to measure the proton lifetime, detect cosmological neutrinos and neutrinos from supernova explosions. Results on the sensitivity to leptonic CP violation and the neutrino mass hierarchy are presented.

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The beams in LHC collide head-on in at most four experimental points. Due to the small bunch spacing, the beams experience more than one hundred 'near-misses' on either side of the collision points. The transverse beam separation at these places, limited by the quadrupole aperture, is in the range of 7 to 13σ. The non-linear part of these 'longrange' interactions appears to be the dominant mechanism for beam blow-up or beam loss in simulation. A simple non-linear model of the long-range interactions can be devised. It shows that the latter may be locally corrected with good accuracy using wires as correcting lenses. The nonlinearity measured by the tune footprint is reduced by one order of magnitude. Pulsing the correcting lenses cancels the so-called PACMAN effect. With a 25 ns bunch spacing, there would be 31 headon collisions per experimental insertion in the absence of the ±150 µrad crossing angle. The aperture of the singlebore low-β quadrupoles does not allow to increase it much above its nominal value. In the high-luminosity proton mode, the beam size is squeezed in two of the four collision points (IP1 and IP5). The larger beam divergence sets the normalized beam separation to 9.5σ on average (Figure 1). In the other two collision points, the normalized separation is much larger. Their contribution to the long-range (LR) beam-beam effect can be neglected. THE LONG-RANGE BEAM-BEAM INTERACTIONS IN LHCThe machine parameters were chosen to limit to 0.01 the tune spread due to the beam-beam effect. This criterion, successfully tested in the SppS for the head-on beam-beam effect, is extended, for LHC to its LR component as well.In spite of the crossing angle, the footprint of the latter is still 65% of that due to the head-on collision.Tracking studies using as a criterion the dynamic aperture Even-though the footprint criterion is fulfilled, losses of particles occurs at 8.5σ and a significant diffusion in amplitude and tune is observed at lower amplitudes. The LR effect acts as the dominant destabilizing mechanism.The alternating crossing angles [6] in IP1 and IP5 minimize the tune footprint by a compensation of the linear detunings. We propose in this paper a correction principle able to cope with the non-linear part as well. MODEL OF THE LONG-RANGE BEAM-BEAM KICKSWe consider a slightly simplified model of the LR beambeam interactions for the design of the correction system. The test of its efficiency is carried out without these simplifications. Only one of the two identical insertions is considered without losing generality. Following the tradition, the sample particle of one beam is called the weak beam. It suffers from the perturbation of the second 'strong' beam. Layout and Strength of the LR EffectDue to the strong focusing of the low-β quadrupoles, the 15 LR kicks experienced by the weak beam on each side of an IP are very close in betatron phase. Their average and rms phase shifts from the IP are 88.5• and 2.0• . For 80% of the kicks, the rms phase difference is 0.4• only. We can therefore l...

The European Spallation Source (ESS), currently under construction in Lund, Sweden, is a research center that will provide, by 2023, the world's most powerful neutron source. The average power of the proton linac will be 5 MW. Pulsing this linac at higher frequency will make it possible to raise the average total beam power to 10 MW to produce, in parallel with the spallation neutron production, a very intense neutrino Super Beam of about 0.4 GeV mean neutrino energy. This will allow searching for leptonic CP violation at the second oscillation maximum where the sensitivity is about 3 times higher than at the first. The ESS neutrino Super Beam, ESSnuSB operated with a 2.0 GeV linac proton beam, together with a large underground Water Cherenkov detector located at 540 km from Lund, will make it possible to discover leptonic CP violation at 5 significance level in 56% (65% for an upgrade to 2.5 GeV beam energy) of the leptonic CP-violating phase range after 10 years of data taking, assuming a 5% systematic error in the neutrino flux and 10% in the neutrino cross section. The paper presents the outstanding physics reach possible for CP violation with ESSnuSB obtainable under these assumptions for the systematic errors. It also describes the upgrade of the ESS accelerator complex required for ESSnuSB.