Enhancement of solar intensity is achieved through concentrator which focuses direct normal irradiance to a smaller area. Such redirection necessitates aligned movement of the whole assembly along the apparent motion of the sun. The motion of a bulky system consumes significant power during the operation, thereby reducing the effective energy collection efficiency. Therefore, a static geometry which does not require tracking the sun is desirable as concentrating optics. Here, we propose such a novel static concentrator based on cylindrical Fresnel lens. Only the absorber is given a single axis tracking motion. A systematic optimization is performed to select the geometrical parameters which maximize the solar intensity and minimize the intensity-non-uniformity. For a Silicone glass cylinder of 20 cm diameter, we find an absorber of width 5 cm, placed at a distance of 11 cm from the axis of the concentrator provides the maximum intensity and the minimum intensity-non-uniformity when the vertex angle of the Frensel lens is 37 degrees. The study demonstrates that the procedure to perform such geometry optimization is straightforwardly extendable. We demonstrate that the annual average intensity on the absorber can be enhanced by over similar to 50% with lower operational cost and a meagre increase in the initial cost. (C) 2020 Elsevier Ltd. All rights reserved.