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The development of compact and efficient low-energy linear accelerators is crucial for advanced scientific and medical applications. While H-mode Drift Tube Linacs (DTL) offer superior shunt impedance compared to conventional Alvarez structures, they traditionally suffer from transverse defocusing and longitudinal instability when operating at a 0$^\circ$ synchronous phase. This paper presents the comprehensive design and beam dynamics study of a Radio-Frequency Focused Interdigital (RFI) H-mode DTL. By modifying the drift tubes to include internal pole tips, transverse quadrupole focusing is achieved directly via the RF fields, eliminating the need for internal magnetic lenses. We evaluate three transverse focusing lattices (FDFD, FFDD, and FFFDDD) using TraceWin, determining the optimal balance between beam transmission and required focusing voltage. Furthermore, to address the inaccuracies of standard simulation tools in handling time-varying RF fringe fields, a customized 3D-field-based longitudinal optimization program was developed.
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