  This conceptual design report provides a detailed account of the European
Spallation Source neutrino Super Beam (ESS$\nu$SB) feasibility study. This
facility has been proposed after the measurements reported in 2012 of a
relatively large value of the neutrino mixing angle $\theta_{13}$, which raised
the possibility of observing potential CP violation in the leptonic sector with
conventional neutrino beams. The measured value of $\theta_{13}$ also
privileges the $2^{nd}$ oscillation maximum for the discovery of CP violation
instead of the more typically studied $1^{st}$ maximum. The sensitivity at this
$2^{nd}$ oscillation maximum is about three times higher than at the $1^{st}$
one, which implies a reduced influence of systematic errors. Working at the
$2^{nd}$ oscillation maximum requires a very intense neutrino beam with an
appropriate energy. The world's most intense pulsed spallation neutron source,
the European Spallation Source (ESS), will have a proton linac operating at
5\,MW power, 2\,GeV kinetic energy and 14~Hz repetition rate (3~ms pulse
duration, 4\% duty cycle) for neutron production. In this design study it is
proposed to double the repetition rate and compress the beam pulses to the
level of microseconds in order to provide an additional 5~MW proton beam for
neutrino production. The physics performance has been evaluated for such a
neutrino super beam, in conjunction with a megaton-scale underground water
Cherenkov neutrino detector installed at a distance of 360--550\,km from ESS.
The ESS proton linac upgrades, the accumulator ring required for proton-pulse
compression, the target station design and optimisation, the near and far
detector complexes, and the physics potential of the facility are all described
in this report. The ESS linac will be operational by 2025, at which point the
implementation of upgrades for the neutrino facility could begin.
