Resonant slow extraction in synchrotrons using anti-symmetric sextupole fields

This paper proposes a novel method for resonant slow extraction in synchrotrons by using special anti-symmetric sextupole fields, which can be produced by a special magnet structure. The method has potential in applications demanding very stable slow extraction from synchrotrons. Our studies show that slow extraction at the half-integer resonance by using an anti-symmetric sextupole field has some advantages compared to the standard sextupole field, which is widely used in the slow extraction method. One advantage is that it can work at a more distant tune from the resonance, so that it can reduce significantly the intensity variation of the extracted beam which is mainly caused by the ripples of magnet power supplies. Studies by both the Hamiltonian theory and numerical simulations show that the stable region near the half-integer resonance by anti-symmetric sextupole field is much smaller and flatter than the one by standard sextupole field at the third-order resonance. The particles outside the region will be driven out in two possible directions in quite a short transit time but with spiral steps similar to the third-order resonant extraction. By gradually increasing the field strength, the beam can be extracted with intensity more homogeneous than by the usual third-order resonant method, because of both smaller intensity variation and spike in the beginning spill. With the same field strength and tune distance to the resonance, the change in the stable region area due to the working point variation in the case of the anti-symmetric sextupole is about 1/14 of the one for the standard sextupole. Detailed studies including beam dynamic behaviors near other resonances, expression of the field in polynomial expansion, influence of 2-D field error, half-integer stop-band, and resonant slow extraction using a quadrupole field are also presented.