Design of a fifth-order achromat

A repetitive system free of all aberrations up to the fifth order was designed based on a recently developed analytical theory that, in principle, allows the design of such achromats to an arbitrary order (Wan and Berz, Phys. Rev. E, 54 (1996) 2870; Wan, Ph.D. Thesis, Michigan State University, 1995). It serves as an example to show that complete correction of aberrations is possible beyond order three, which is the highest order achieved before (Dragt, Nucl. Instr. and Meth. A 258 (1987) 339; F. Neri, in: Berz, McIntyre (Eds.), Proc. Workshop on High Order Effects). d of repetition of identical cells, which is widely used in achromat design based on normal form theory, we utilize cells which are obtained from the original ones through mirror imaging about the x–y plane, which corresponds to a reversion. In our design, the second half of the ring is the reversion of the first one, and two turns make a fifth-order achromat. A possible application of repetitive high-order achromats being time-of-flight spectroscopy, the resulting ring was analyzed with respect to dynamic aperture and energy resolution using maps of orders nine and higher.