Momentum transmission of a diaphragmed magnetic spectrometer: I. Analysis and definitions

An experimental device consisting of a plane source of charged particles and of a magnetic spectrometer equipped with horizontal and vertical diaphragms is considered. An analysis intended to achieve an exact analytical expression to connect the observed particle flux to the source emission and spectrometer transmission characteristics is developed. An analytical expression for the average value of the source brightness that is actually obtained from corpuscular flux measurements is also given. The effectiveness of the diaphragms in defining the domains of the initial conditions of the particles is also emphasized and general definitions of these domains are introduced. These definitions are stated for exact optical transformations, i.e., accounting for geometric and chromatic aberrations, and for general positions of the diaphragms along the optical axis as well as for symmetrical or asymmetrical apertures of the same. The results obtained and the introduced definitions will be used in Part II of this work. The important case of a thick source is considered in Appendix A.