Perturbations of axisymmetric systems described by 2-D solution methods

It is often desirable to know how small displacements of a structure from its ideally symmetrical form alter the electric fields, and possibly also the tracks of charged particles, within the structure. This information is useful both for deciding what tolerances are required in manufacture, and for testing small variations to see whether they improve some behaviour of the system. In many cases we would like to know how a system that was originally axisymmetric is affected by perturbations that make it no longer strictly axisymmetric. The effects of small perturbations can be found by a modification of the standard method for solution by use of finite elements. Many types of perturbation can be modelled; they include, for individual electrodes, (a) axial displacement of an electrode; (b) change of diameter of an aperture; (c) transverse displacement of an electrode; (d) tilt of an electrode relative to the axis; and (e) ellipticity or triangularity of an aperture