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The so-called "compound solar sail", also known as "Solar Photon Thruster" (SPT), is a solar sail design concept, for which the two basic functions of the solar sail, namely light collection and thrust direction, are uncoupled. In this paper, we introduce a novel SPT concept, termed the Advanced Solar Photon Thruster (ASPT). This model does not suffer from the simplified assumptions that have been made for the analysis of compound solar sails in previous studies. We present the equations that describe the force, which acts on the ASPT. After a detailed design analysis, the performance of the ASPT with respect to the conventional flat solar sail (FSS) is investigated for three interplanetary mission scenarios: An Earth-Venus rendezvous, where the solar sail has to spiral towards the Sun, an Earth-Mars rendezvous, where the solar sail has to spiral away from the Sun, and an Earth-NEA rendezvous (to near-Earth asteroid 1996FG3), where a large orbital eccentricity change is required. The investigated solar sails have realistic near-term characteristic accelerations between 0.1 and 0.2mm/s2. Our results show that a SPT is not superior to the flat solar sail unless very idealistic assumptions are made.