This splinter session is intended as follow-up of the oral session ST 1.3, that is scheduled 1330-1500. The goal of the splinter is to deepen the discussion started in the oral session on the different acceleration mechanisms and to concentrate on discussing difference and similarities between them. This comparative approach is the key aspect of the session ST 1.3 and it cannot be performed during the oral session due to time limitation. The splinter session is also very important as preparation for the following poster session of ST 1.3, 1730-1900, to stimulate among the participants an active comparison between the results of the different posters. All this is crucial for obtaining the best outcome from the ST 1.3 session, since this session is intended to be multi-disciplinary.