The European Spallation Source, ESS, uses a linear accelerator to deliver the high intensity proton beam to the target station. The nominal beam power is 5 MW at an energy of 2.5 GeV. The superconducting part covers more than $95\%$ of the energy gain and $90\%$ of the length. The beam dynamics criteria applied to the design of the superconducting part of the linac including the frequency jump at a medium energy of 200 MeV as well as the beam dynamics performance of this structure are described in this paper.