Slow extraction of particles using a thin target for driving for resonance

The slow extraction of particles from the accelerator using parametric resonance of betatron oscillations is investigated. A special feature of the parametric resonance is the absence of separatrix on a phase plane. Therefore frequencies of betatron oscillations of the particles to be extracted at each revolution are to change abruptly. A value of this jump is need to be sufficient to transfer the frequencies of betatron oscillations of these particles inside the band of parametric resonance from the region outside and to ensure the increase of the oscillation amplitude in two revolutions, which is required to throw the particles in a gap of the extraction septum-magnet. It can be achieved through the energy losses of the particles, as ones passes through the thin target, and the use of sextupole lenses. Suggested techniques of the slow extraction can be applied for resonance of the higher order as well