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A numerical study of beam dynamics was performed for two injector systems for the proposed National High Magnetic Field Laboratory at the Florida State University (FSU) Free Electron Laser (FEL) facility. The first considered a system consisting of a thermionic DC gun, two buncher cavities operated at 260 MHz and 1.3 GHz and two TESLA type cavities, and is very similar to the injector of the ELBE...