Halbach Magnets for CBETA

Abstract

A principle of the non-scaling Fixed Field Alternating Gradient (NS-FFAG) is that different energy beam has orbit oscillations Δx around the central circular orbit in both positive and negative direction within a small radial aperture as: Δx=D x *δp/p. For the central circular orbit Δx=0, or for the combined function magnets the field is equal to Bo (B (x) = B o + G* x). The smallest orbit offsets Δx are obtained when the defocusing magnet provides most of the bending for the central energy, while the focusing magnet could be even the regular quadrupole with the central orbit in the middle. Stable orbits for a very large energy range [in the case of CBETA this is 4 times in energy], is obtained using opposite polarity magnets producing linear magnetic fields, small dispersion, and very strong focusing.