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  1. Context. Aims. We systematically search for magnetic flux rope structures in the solar wind to within the closest distance to the Sun of ~0.13 AU, using data from the third and fourth orbits of the Parker Solar Probe. Methods. We extended our previous magnetic helicity-based technique of identifying magnetic flux rope structures. The method was improved upon to incorporate the azimuthal flow, which becomes larger as the spacecraft approaches the Sun. Results. A total of 21 and 34 magnetic flux ropes are identified during the third (21-day period) and fourth (17-day period) orbits of the Parker Solar Probe, respectively. Wemore »provide a statistical analysis of the identified structures, including their relation to the streamer belt and heliospheric current sheet crossing.« less