Conceptual design report for the LUXE experiment. - Abramowicz, H.; Acosta, U.; Altarelli, M.; Aßmann, R.; Bai, Z.; Behnke, T.; Benhammou, Y.; Blackburn, T.; Boogert, S.; Borysov, O.; Borysova, M.; Brinkmann, R.; et al. (European Physical Journal: Special Topics, 2021)