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A multi-stage program for the development of a heavy ion superconducting (sc) continuous wave (cw) linac is in progress at HIM (Mainz, Germany) and GSI (Darmstadt, Germany) under support of IAP (Frankfurt, Germany). In 2017 the first section of the CW-Linac has been successfully commissioned at GSI. Beam acceleration at the CWLinac is foreseen to be performed by twelve multi-gap Crossbar H-type (CH) cavities. The linac should provide the beam for physics experiments, smoothly varying the output particle energy from 3.5 to 7.3 MeV/u, simultaneously keeping high beam quality. Due to a wide variation of the input and output beam energy for each cavity, a longitudinal beam matching to every cavity is of high importance. An advanced algorithm for an optimization of matched beam parameters under variable rf-voltage and rf-phase of each cavity has been developed. The description of the method and the obtained results are presented . INTRODUCTION The design, construction and operation of continuous wave (cw) proton and ion linacs is a crucial goal of worldwide accelerator technology development. Also a high energy cw linac is an essential part of a large scale research facility, as an accelerator driven system or a spallation neutron source [1-3]. A cw linac in the medium energy range could be used for several applications, as high productivity isotope generation, material science and boron-neutron capture therapy. The compactness of such cw facilities, accomplished by the use of superconducting (sc) elements, is a modern trend for the development of high intensity ion linacs [48]. Therefore the elaboration and optimization of a cw linac, as well as progress in elaboration of the superconducting technology, is of high relevance. Figure 1: Conceptual layout of heavy ion superconducting CW-Linac with warm injector.

Advanced Approach for Beam Matching along the Multi-Cavity SC CW Linac at GSI