A mandrel (104) for processing a composite structure (102), comprises a tooling surface (106) on which a composite layup (152) is configured to be supported; and a mandrel vacuum channel (108) formed in the tooling surface (106), wherein the tooling surface (106) is configured such that a vacuum seal (190) is formed between the tooling surface (106) and an edge portion (116) of a vacuum-bag assembly (202), if placed over the composite layup (152) and the mandrel (104), in response to a vacuum applied to the mandrel vacuum channel (108); and such that a sealed vacuum chamber (184) that encloses the composite layup (152) is formed by the mandrel (104), the vacuum-bag assembly (202), and the vacuum seal (190).