ABSTRACT
For the study of transfer maps of particle optical systems, first it is necessary to undertake a classification of the possible fields that can occur. The fields extend throughout the length of the device, and thus provide strong focusing. Different from the case of glass optics, it turns out that the motion cannot be rotationally symmetric anymore. To study the solutions of Laplace’s equations for the electric and magnetic scalar potentials, this chapter presents special cases, each of which will be treated in a coordinate system most suitable for the problem. To make an electrostatic device that produces a quadrupole field, it is best to machine the electrodes along the equipotential surfaces, and utilize the fact that if a sufficient amount of boundary information is specified, the field is uniquely determined, and hence must be as specified by the formula used to determine the equipotential surfaces in the first place.
