At Tektronix, two classes of non-rotationally symmetric electrostatic lenses which lead to significant three-dimensional-field problems are currently under investigation. Extensive interactive computer programs have been developed to study these lens structures.
The first class is referred to as Klemperer lipped lenses; the accelerating quadrupole being the most important. Klemperer lenses are formed from shaped concentric cylindrical electrodes and employ two or three independent voltages. These lenses are predominantly of quadrupole type, but possess higher multipoles to correct for geometry distortion.
The second class of lenses, referred to as wafer-lenses, consists of lenses formed from spaced sequences of metal wafer electrodes with varying apertures and two planes of symmetry. Typical lenses formed in this manner include quadrupoles, octopoles, slot-lenses, stigmators and solid quadrupoles with exit field shaping.
The primary method of calculation used here is three-dimensional relaxation in either a rectangular or cylindrical coordinate mesh representing one quadrant of the field. The three-dimensional relaxation is followed by multipole decomposition of the core field using Fast Fourier Trans-forms (FFTs). Numerous graphical methods are used for program diagnostics and to display lens distortions. The electrodes are described by simple shape parameters and the computer program does the complete analysis of the boundary conditions. Program setup time for a complex lens can be less than one half hour. Large fields can be segmented if necessary.
"Computer Programs for Analyzing Certain Classes of 3-D Electrostatic Fields with Two Planes of Symmetry,"
Scanning Electron Microscopy: Vol. 3
, Article 12.
Available at: https://digitalcommons.usu.edu/electron/vol3/iss1/12