To keep the ambitious Super Heavy Element (SHE) physics program at GSI competitive a superconducting (sc) continuous wave (cw) high intensity heavy ion LINAC is currently under progress as a multi-stage R&D program of GSI, HIM and IAP*. The baseline linac design consists of a high performance ion source, a new low energy beam transport line, an (cw) upgraded High Charge State Injector (HLI), and a matching line (1.4 MeV/u) which is followed by the new sc-DTL LINAC for post acceleration up to 7.3 MeV/u. In the present design the new cw-heavy ion LINAC comprises constant-beta sc Crossbar-H-mode (CH) cavities operated at 217 MHz. The advantages of the proposed beam dynamics concept applying a constant beta profile are easy manufacturing with minimized costs as well as a straightforward energy variation**. An important milestone will be the full performance test of the first CH cavity (Demonstrator), in a horizontal cryo module with beam. An advanced demonstrator setup comprising a string of cavities and focussing elements is proposed to build from 10 short CH-cavities with 8 gaps. The corresponding simulations and technical layout of the new cw heavy ion LINAC will be presented