An axial type impinging receiver has been developed for a solar dish-Brayton system. By using selective reflection cavity surfaces as a secondary concentrator, the solar irradiation is reflected and concentrated on a cylindrical absorber that is located in the center of the cavity. A modified inverse design method was applied for quickly finding possible cavity receiver designs, and a numerical conjugate heat transfer model combined with a ray-tracing model was utilized for studying the detailed performance of the impinging receivers. The ray-tracing results show that the flux distribution on the cavity and absorber surfaces can be efficiently adjusted to meet the design requirements by changing the absorber diameter, the cavity diameter, the cavity length and the offset length. A candidate receiver design was selected for detailed numerical studies, and the results show that the average outlet air temperature and the radiative-to-thermal efficiency can reach 801.1 degrees C and 82.8% at a DNI level of 800 W/m(2). The temperature differences on the absorber can be controlled within 122.7 degrees C for DNI level of 800 W/m(2), and 126.4 degrees C for DNI level of 1000 W/m(2). Furthermore, the structure is much simpler than a typical radial impinging design. (C) 2018 Elsevier Ltd. All rights reserved.