Charged particle optics without detailed field maps

Abstract

For the initial design of a beam line or charged particle optical system, it is both useful and convenient to be able to describe the components in terms of a small number of parameters. These parameters are used in a calculation of a transfer map which represents the effect of the beam line on a particle trajectory. The transfer map is often expressed as some kind of series expansion. A calculation to first order requires the smallest number of descriptive parameters. Extension of the calculation to higher orders requires a greater number of parameters. From our mathematical backgrounds we have come to have certain expectations as to the characteristics of a series expansion. These expectations may not always be commensurate with the physics of charged particle beam lines. The reconciliation of these expectations will be discussed. The example used will be the program TRANSPORT and its extension to third order. The third‐order expansion may represent the inherent limit of the series representation without numerical integration. We shall explain why we may have reached that limit.