In the future, a new superconducting (SC) continuous wave (CW) high intensity heavy ion HElmholtz LInear ACcelerator (HELIAC) should provide ion beams with maximum beam energy above the Coulomb barrier for the Super Heavy Element program at GSI (Gesellschaft für Schwerionenforschung, in Engl.: Association for Heavy Ion Research). The HELIAC consists of a SC main accelerator supplied by a normal conducting injector, which comprises an electron cyclotron resonance ion source, a radio-frequency quadrupole, and two separate interdigital H-mode drift-tube linear accelerator cavities, based on an Alternating Phase Focusing (APF) scheme. Together, both cavities will accelerate ions from 300 to 1400 keV/u with only one external quadrupole triplet for transverse focusing in between. Due to the demanding requirements of the APF concept on the voltage distribution along the beam axis on the one hand and the CW operation on the other hand, the optimization of each cavity concerning RF, mechanical, and thermal properties is crucial for the successful operation of the HELIAC injector.