Synchrocyclotron for extracting beams of various energies

A synchrocyclotron for extracting charged particles accelerated to an extraction energy includes a magnetic unit comprising N valley sectors and N hill sectors, and configured for creating z-component of a main magnetic characterized by a radial tune of the successive orbits. The synchrocyclotron includes a first instability coil unit and a second instability coil unit configured for creating a field bump of amplitude increasing radially. The amplitude of the field bump may be varied to reach the value of the offset amplitude at the average instability onset radius. The offset amplitude may be the minimal amplitude of the field bump at the average instability onset radius required for sufficiently offsetting the center of the orbit of average instability onset radius to generate a resonance instability to extract the beam of charged particle at the average instability onset radius.