A system (12) is proposed for the acceleration of ions to treat Atrial Fibrillation (AF), arteriovenous malformations (AVMS) and focal epileptic lesions; this system (12) includes a pulsed ion source (1), a pre-accelerator (3) and one or more linear accelerators or linacs (5, 6, 7) operating at frequencies above 1 GHz with a repetition rate between 1 Hz and 500 Hz. The particle beam coming out of the complex (12) can vary (i) in intensity, (ii) in deposition depth and (iii) transversally with respect to the central beam direction. The possibility of adjusting in a few milliseconds and in three orthogonal directions, the location of each energy deposition in the body of the patient makes that system of accelerators (12) perfectly suited to irradiation of a beating heart.