Aspects of phase space dynamics in spiral inflectors

The equations of motion for paraxial rays in a pseudo cylindrical electrostatic inflector with tilt have been known for some time. Unfortunately the origin of the various components of the electric field expansion are more poorly documented. In this paper we present a physical interpretation for each element of the electric field and then discuss how the resulting field expansion might be implemented in a FORTRAN program that tracks particles in a general magnetic field. Results from such a program are then used together with an acceptance calculations program, to study the question of inflector acceptance as a function of several inflector parameters