To investigate the effectiveness of a simple analytic model for the calculation of electrostatic fields and optical properties of particle beams in accelerator tubes.
The analytic model is derived by superimposing the solution obtained from two co‐axial circular apertures. Potentials and fields derived from the model are compared to solutions based on finite element analysis together with first, third, and fifth order optical parameters and aberration. More realistic models are also compared.
It is shown that the model is capable of capturing many of the ion optical effects produced in small electrostatic accelerator tubes. Even for more realistic tube models the basic optical parameters, first and third order, are sufficiently accurate to allow a preliminary design to be achieved.
The work demonstrates that the first stages of the optical design of accelerator tubes can be rapidly achieved by analytic means which then provide good starting parameters for a fuller optimisation carried out by advanced numerical methods. The results also serve as a benchmark for numerical methods.
