For future experiments with heavy ions near the coulomb barrier within the super-heavy element (SHE) research project a multi-stage R&D program of GSI/HIM and IAP is currently in progress. It aims for developing a supercon-ducting (sc) continuous wave (CW) LINAC with multiple CH cavities as key components downstream the High Charge State Injector (HLI) at GSI. The LINAC design is challenging due to the requirement of intense beams in CW mode up to a mass-to-charge ratio of 6, while covering a

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... while covering a broad output energy range from 3.5 to 7.3 MeV/u with unchanged minimum energy spread. Testing of the first CH-cavity in 2016 demonstrated a promising maximum accelerating gradient of E_{a} = 9.6 MV/m; the worldwide first beam test with this sc multi-gap CH-cavity in 2017 was a milestone in the R&D work of GSI/HIM and IAP. In the light of experience gained in this research so far, the beam dynamics layout for the entire LINAC has recently been updated and optimized.