A Study for Positions and Widths of Image Lines in Ion Optical Systems. I. The First-Order Theory with Ideal Magnetic Fields

Abstract

In ion optical systems which contain ideal uniform sector-shaped magnetic fields, the expressions for positions X and widths W of image lines for arbitrary configurations of a magnet and an ion trajectory are derived using six (or eight) independent variables V_i. When an ion optical system is set in some configuration and if one regards the ideal configuration as the origin for measurements, the differential changes of positions or widths of images can be obtained by the linear combinations of the partial differential coefficients ∂X⁄∂V_i or ∂W⁄∂V_i. Comparing calculations of these changes with experiments following the methods described in this paper, one can estimate the order of magnitude of the effect due to, such as, higher order aberrations, fringing fields, or room temperature fluctuations, which influences to positions and widths of images.