[en] The major goal of this project is to study the effects that lead to emittance growth and limitation of beam current and brightness in periodic focusing systems (including linear accelerators). This problem is of great importance for all accelerator applications requiring high intensity beams with small emittance such as heavy ion fusion, spallation neutron sources and high energy physics. In the latter case, future machines must not only provide higher energies (in the range of 10 to 100 TeV), but also higher luminosities than the existing facilities. This implies considerably higher phase-space density of the particle beam produced by the injector linac, i.e., the detrimental emittance growth and concurrent beam loss observed in existing linacs must be avoided