Second-order achromat design based on FODO cell

Two dipole doglegs are widely used to translate the beam axis horizontally or vertically. Quadrupoles are placed between the two consecutive dipoles to match first-order dispersion and provide betatron focusing. Similarly, a four dipole chicane is usually employed to form a bypass region, where the beam axis is transversely shifted first, then translated back to the original axis. In order to generate an isochronous section, quadrupoles are again needed to tune the first-order transfer matrix element R(56) equaling zero. Usually sextupoles are needed to correct second-order dispersion in the bending plane, for both the dogleg optics and the chicane (with quad) optics. In this paper, an alternative optics design is introduced, which is based on a simple FODO cell and does not need sextupole assistance to form a second-order achromat. It may provide a similar function of either a dogleg or a bypass, by using two or four of such combined supercells.