Coupled lenses and their combinations

摘要

Electric or magnetic quadrupole lenses and their thin lens analogues, or coupled lenses, are examined for double focusing. The compatibility conditions for double focusing are similar to the stability conditions of betatron oscillations. When the double‐focusing conditions are satisfied, a quadrupole lens doublet or a pair of coupled thin cylindrical lenses is equivalent to a single thick converging lens with unequal focal lengths in two orthogonal meridian planes. Specific double‐focusing examples are given and a nomogram is developed for facilitating the calculations when combinations of coupled lenses are considered.