Pro­ton and car­bon ion beams pre­sent ad­van­ta­geous depth-dose dis­tri­bu­tions with re­spect to X-rays. Car­bon ions allow a bet­ter con­trol of "ra­diore­sis­tant" tu­mours due to their high­er bi­o­log­i­cal re­sponse. For deep-seat­ed tu­mours pro­ton and car­bon ion beams of some nA and en­er­gies of about 200 MeV and 400 MeV/u re­spec­tive­ly are need­ed. For these ap­pli­ca­tions TERA pro­posed the "cy­clinac": a high-fre­quen­cy linac which boosts the hadrons ac­cel­er­at­ed by a cy­clotron. The di­men­sions of the com­plex can be re­duced if high­er ac­cel­er­at­ing gra­di­ents are achieved in the linac. To test the max­i­mum achiev­able fields, a 3 GHz cav­i­ty has been built by TERA. The 19 mm-long cell is fore­seen to be ex­cit­ed at 200 Hz by 3 us RF puls­es and should reach a 40 MV/m ac­cel­er­at­ing gra­di­ent, which cor­re­sponds to a peak sur­face elec­tric field Es of 260 MV/m. In a first high-pow­er test per­formed at CTF3 the cell was op­er­at­ed at 50 Hz with a max­i­mum peak power of 1 MW. The max­i­mum Es achieved was above 350 MV/m. The break­down rate at these field val­ues was around 10-1 bpp/m. The max­i­mum value of the mod­i­fied Poynt­ing vec­tor is close to the best val­ues achieved by high gra­di­ent struc­tures at 12 and 30 GHz.