NOVELTY - A space-based concentrator has a first stage comprising a rectilinear entrance, a rectilinear exit, and four sides joining the entrance and the exit and including inner mirrored surface between the entrance and the exit; and a second stage having mirrored inner surfaces, a rectilinear entrance, a rectilinear exit, and four sides joining the entrance and the exit.    USE - For concentrating solar energy on a solar cell.    ADVANTAGE - The invention provides high concentration with reduced focal distance (f-numbers about 1), hence exhibiting very low profile; high performance with low weight (good specific power); high stowage power density with nesting capability; excellent off-normal performance; negligible chromatic aberration at high concentrations; ability to use conventional flat PV panel mounting the deployment technology; and high stiffness and excellent thermal management with advanced composite system.    DETAILED DESCRIPTION - A space-based concentrator comprises a first stage (64) having a rectilinear entrance, a rectilinear exit, and four sides (34b) joining the entrance and the exit; and a second stage (66) having mirrored inner surfaces, a rectilinear entrance, a rectilinear exit, and four sides joining the entrance and the exit. The four sides of the first stage include inner mirrored surfaces between the entrance and the exit. The inner mirrored surfaces are configured to accept a solar radiation from the entrance and to direct the solar radiation to the exit. The entrance of the second stage abuts the exit of the first stage. The exit of the second stage is adapted to receive the solar cell. Two of the four sides of each of the stages are longer than the other two of the sides of each of the stages. At least the two longer sides comprise optimized Bezier surfaces that approximate a parabolic surface. The concentrator is configured to nest with other concentrators comprising the stages. An INDEPENDENT CLAIM is also included for a panel array, comprising solar cells and space-based concentrators as comprised above.    DESCRIPTION OF DRAWING(S) - The figure shows a cross-sectional view of a single two-stage concentrator.    Sides (34b)    First stage (64)    Second stage (66)