Canonical description of a second-order achromat

Charged particle motion in second-order magnetic optical achromat is described using a canonical perturbation theory. Necessary and sufficient conditions for the existence of such a device are presented. Given these conditions, the second-order matrix elements at the end of the achromat are found explicity. It is shown that all geometric matrix elements are equal to zero and all chromatic matrix elements are either also equal to zero or proportional to the corresponding chromaticity. Thus all second-order matrix elements vanish simultaneously when the two chromaticities are made to be equal to zero 13 refs., 1 tab.