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The analyses and developments presented here would not have been possible without the CERN Directorate and other laboratories, universities, and groups that supported this study. We admire the skills of the technicians who successfully built the first 802 MHz SC cavity. We thank many of our colleagues for their interest in this work and a supportive attitude when time constraints could have resulted in reduced understanding. Special thanks are also due to the members and Chair of the International Advisory Committee for their attention to, and guidance of this project. From the beginning of the LHeC study, it has been supported by ECFA and its chairs, which was a great help and stimulus in the undertaking of this study, which was performed outside our usual duties. During this time, a number of students in master's and PhD courses have made essential contributions to this project, for which we are especially grateful. This also extends to colleagues with whom we have been working closely but who meanwhile left this development, perhaps temporarily, or who work at non-particle-physics institutions while wishing LHeC success. The current state of particle physics reminds us of the potential we have when resources and prospects are combined, to which this study is considered to be a contribution. The authors would like to thank the Institute of Particle Physics Phenomenology (IPPP) at Durham for the award of an IPPP Associateship to support this work, and gratefully acknowledge the support of the state of Baden-Wurttemberg through High Performance Computing in Baden-Wurttemberg (bwHPC) and the German Research Foundation (DFG) through GrantNo. INST 39/963-1 FUGG. The financial support of the Ministerio de Ciencia e Innovaci ' on of Spain under project FPA2017-83814-P, the Unidad de Excelencia Maria deMaetzu under projectMDM-2016-0692, theXunta deGalicia (projectED431C 2017/07 and Centro singular de investigaci ' on de Galicia accreditation 2019-2022), and the EuropeanUnion (EuropeanRegionalDevelopment Fund (ERDF)) is gratefully acknowledged. This study was performed within the framework of COST Action CA 15213 `Theory of hot matter and relativistic heavy-ion collisions' (THOR), MSCA RISE 823947 `Heavy ion collisions: collectivity and precision in saturation physics' (HIEIC), and has received funding from the European Union's Horizon 2020 research and innovation programme under Grant Agreement No. 824093.; Agostini , P , Aksakal , H , Alekhin , S , Allport , P P , Andari , N , Andre , K D J , Angal-Kalinin , D , Antusch , S , Aperio Bella , L , Apolinario , L , Apsimon , R , Apyan , A , Arduini , G , Ari , L , Armbruster , A , Armesto , N , Auchmann , B , Aulenbacher , K , Azuelos , G , Backovic , S , Bailey , L B , Bailey , S , Balli , F , Behera , S , Behnke , O , Ben-Zvi , Benedikt , M , Bernauer , J , Bertolucci , S , Biswal , S S , Bluemlein , J , Bogacz , A , Bonvini , M , Boonekamp , M , Bordry , F , Boroun , G R , Bottura , L , Bousson , S , Bouzas , A O , Bracco , C , Bracinik , J , Britzger , D , Brodsky , S J , 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