Four cell third order achromats and their application to multi-pass time-of-flight spectrometers

A repetitive third order achromatic system was designed. As an example, we chose the ESR storage ring at GSI. Instead of repetition of cells, which is widely used in achromat design based on normal form theory, we utilize cells which are obtained from the 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 third order achromat. The dynamical aperture was determined by tracking with 11th order maps using COSY INFINITY. The 9th order time-of-flight resolution was calculated statistically with beams of different emittances