SNAKES, ROTATORS, SERPENTS, AND THE OCTAHEDRAL GROUPt

Specific configurations of horizontal and vertical bending magnets are given that, when acting on the spin polarization vector of a particle beam, generate a group of 24 operators isomorphic to the group of rotational symmetries of a cube, known as the octahedral group. Some of these configurations have the feature of converting transversely polarized beams to longitudinally polarized beams (or vice versa) at the midpoint of the configuration for, in principle, all beam energies. Since the first-order optical transfer matrix for each half of these configurations is nearly that of a drift region, the external geometry remains unchanged and midpoint dispersion is not introduced. Changing field strengths and/or polarities allows a configuration to serve as either a snake(first or second kind) or a rotator, where in both cases the spin polarization is longitudinal at the midpoint. Practical applications using these configurations for electron or proton beams can be envisioned. The requisite high integrated field strengths will limit these applications for electrons.