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The stripping extraction system of a cyclotron is prized by the range and quality of beams it delivers. The gap size of a cyclotron magnet is one of the parameters which significantly influence the design as well as the output characteristics of the stripping extraction system. The vertical dimension of the beam as well as of the extraction system elements placed inside a vacuum chamber is limited by the magnet gap size. Beside this direct influence, the indirect effect of the magnet gap size on stripping extraction occurs through the magnetic field and its impact on the beam dynamics in the extraction region. The performance of the extraction system is optimized by the proper placement of the point of beam exit from the cyclotron. It is shown that the optimal position of the exit point strongly depends on the magnet gap size. The performance of the optimized stripping extraction system for a smaller gap size is found to be somewhat better.