  The European Spallation Source, currently under construction in Lund, Sweden,
is a multidisciplinary international laboratory. Once completed to full
specifications, it will operate the world's most powerful pulsed neutron
source. Supported by a 3 million Euro Research and Innovation Action within the
EU Horizon 2020 program, a design study (HighNESS) has been completed to
develop a second neutron source located below the spallation target. Compared
to the first source, designed for high cold and thermal brightness, the new
source has been optimized to deliver higher intensity, and a shift to longer
wavelengths in the spectral regions of cold (CN, 2--20\,\AA), very cold (VCN,
10--120\,\AA), and ultracold (UCN, ${>}\,{500}$\,\AA) neutrons. The second
source comprises a large liquid deuterium moderator designed to produce CN and
support secondary VCN and UCN sources. Various options have been explored in
the proposed designs, aiming for world-leading performance in neutronics. These
designs will enable the development of several new instrument concepts and
facilitate the implementation of a high-sensitivity neutron-antineutron
oscillation experiment (NNBAR). This document serves as the Conceptual Design
Report for the HighNESS project, representing its final deliverable.
