We report on the development of non-tracking solar concentrator troughs designed subject to the condition that they operate efficiently for diffuse irradiation from all angles during daylight hours. Troughs of the usual compound parabolic form were considered initially. Remarkably however, the most efficient shape for the above requirement turns out to be a trough of simple semi-circular cross-section incorporating a tube of height equal to the circle radius and with a planar absorber plate placed vertically. This trough has a limited concentration ratio of exactly 2.0 but an intercept factor for incident radiation of 100% forallangles of incidence. This desirable feature is explained from the properties of caustics arising from reflection of incident light at the semi-circular trough (SCT) surface. This very simplest of trough design has the clear advantages of small size and low-cost of manufacture. Experimental tests conducted under varying solar irradiation conditions, demonstrate that the simple step of placing an evacuated tube in a SCT can lead to a power output gain of a factor of at least 1.7 on average.