The key issue of the accelerator part of the European Spallation Source (ESS) is the loss free ring injection. In the transfer line between linac and compressor rings two rf cavities, phased independently, are installed followed by an achromatic collimator. This two-stage system allows an optimum energy spread limitation under varying beam current and energy ramping conditions. The system aims to have less than lo4 particles outside an energy spread of +2 MeV at ring injection. Longitudinal space charge forces are still present and cause an increase of the energy spread and the longitudinal emittance. Multiparticle calculations with varying beam currents are presented for the 130 m long straight transfer line after the linac end.