A cooling system (10) for an extreme ultraviolet (EUV) grazing incidence collector (GIC) mirror assembly (240) having at least one shell (20) with a back surface (22) is disclosed. The cooling system has a plurality of spaced apart circularly configured cooling lines (30) arranged in parallel planes (PL) that are perpendicular to the shell central axis (AC) and that are in thermal contact with and that run around the back surface. Input and output secondary cooling-fluid manifolds (44, 46) are respectively fluidly connected to the plurality of cooling lines to flow a cooling fluid from the input secondary cooling-fluid manifold to the output cooling secondary fluid manifold over two semicircular paths for each cooling line. Separating the cooling fluid input and output locations reduces thermal gradients that can cause local surface deformations in the shell that can lead to degraded focusing performance.