  In this Snowmass 2021 white paper, we summarise the Conceptual Design of the
European Spallation Source neutrino Super Beam (ESSvSB) experiment and its
synergies with the possible future muon based facilities, e.g. a Low Energy
nuSTORM and the Muon Collider. The ESSvSB will benefit from the high power, 5
MW, of the European Spallation Source (ESS) LINAC in Lund-Sweden to produce the
world most intense neutrino beam, enabling measurements to be made at the
second oscillation maximum. Assuming a ten-year exposure, physics simulations
show that the CP-invariance violation can be established with a significance of
5 sigma over more than 70% of all values of delta CP and with an error in the
measurement of the delta CP angle of less than 8 degree for all values of delta
CP.
  However, several technological and physics challenges must be further studied
before achieving a final Technical Design. Measuring at the 2nd oscillation
maximum necessitates a very intense neutrino beam with the appropriate energy.
For this, the ESS proton beam LINAC, which is designed to produce the world's
most intense neutron beam, will need to be upgraded to 10 MW power, 2.5 GeV
energy and 28 Hz beam pulse repetition rate. An accumulator ring will be
required for the compression of the ESS LINAC beam pulse from 2.86 ms to 1.3
mus. A high power target station facility will be needed to produce a
well-focused intense (super) mu-neutrino beam. The physics performance of that
neutrino Super Beam in conjunction with a megaton underground Water Cherenkov
neutrino far detector installed at a distance of either 360 km or 540 km from
the ESS, the baseline, has been evaluated.
