This article presents a design study of compact and high-performance beam lines for synchrotron-radiation-based x-ray lithography. The optical system is composed of a single toroidal scanning mirror and a movable beryllium window synchronized with the mirror motion. Usually the use of a toroidal scanning mirror tends to cause excessive deformation of beam shape and degradation of the focusing property of the mirror. This problem has been improved by placing the oscillating center of the mirror near the light source. The are-shaped beam forms a concave dose distribution along the scanning centerline. A beryllium window foil with a specified curvature is used to create a uniform dose distribution. A series of analytical studies and computer simulations have been carried out to define the curvature. For example, the design study shows a compact beam line of 7 m length with a brightness of 159 mW/(cm(2) A) within +/-1% of dose uniformity at an exposure field of 50 x 50 mm.