The beam dynamics design of the low energy DTL section of a fusion driver linac based on the IH-structure is presented. The acceleration of a 209Bi1+ beam by an IH-DTL operated at 27 MHz (54 MHz) is investigated for two specific injection energies at 60 A keV and at 200 A keV, respectively. Both cases are optimized separately, with the goal to find out the maximum achievable acceleration gradient, beam current, as well as the most attractive field strength range of the quadrupole lenses. Calculations are performed on one beamlet, but the results can be applied to build up multibeam cavities. H-mode cavities are very well suited for this purpose and provide high acceleration efficiency, especially at low particle velocity. In addition, the “Combined 0° structure” (“Kombinierte Null Grad Struktur–KONUS”) beam dynamics concept allows grouping into modular units consisting of short, simple rf cavities and of multiaperture quadrupole triplet lenses located in the intertank sections.