Chapter Three: Quadrupole potential functions
Peter Hawkes
Abstract
Analog and numerical methods of calculating the potential and field functions of quadrupoles and octopoles are presented. The analytical models that have been found useful are described.
Keywords
Relaxation; Analog methods; Curve-fitting; Models
1: Calculation by analog and numerical methods
All the requisite properties of electron lenses can be calculated once the potential or field functions are known. In the case of round lenses, Φ(z) and B(z) may be obtained either by measurement (Germain, 1967) or by relaxation, since the problem is essentially two-dimensional. For the same reason, such analog devices as the resistance network and the electrolytic tank are very ...
