NUMERICAL-ANALYSIS OF TRAJECTORIES AND ABERRATIONS OF A WIEN FILTER INCLUDING THE EFFECT OF FRINGING FIELDS

Trajectory equations of a stigmatic Wien filter including the effects of unmatched fringing fields are formulated, and an optimum shape with minimum geometrical aberrations is described. A low-aberration Wien filter is realized under the following conditions: (1) electric and magnetic fields satisfy the orthogonal relation even in the off-axial region, and (2) gap lengths between electrodes and magnetic poles are the same for achieving the balancing condition of electric and magnetic forces in fringing regions. The former condition can be realized by both fields with finite but the same hexapole components; this fact enables us to design a filter with simplified geometry that fulfills the latter condition simultaneously. It is shown that a large deflection of trajectories and resultant aberrations appear if the gap lengths are set to be different. © 1990.