Particle Focusing Properties of the Prolate Spheroidal Magnetic Field and of the Superposed Spheroidal and Uniform Fields

Abstract

In the first part of the paper values of transmission T and resolution W are computed for prolate spheroidal field magnetic spectrometers with various positions of the source. A value of 15% of 4π has been found for T with W = 1%. The aberration due to size of source has been estimated by computing trajectories from non-axial points. Envelopes and caustics formed by monoenergetic families of rays are mapped for several magnetic rigidities. The second part considers the focusing of particles in superpositions in various ratios of a prolate spheroidal and a uniform field with a common axis. It appears that the position of a point image I of an axial point object O is unrestricted except to the extent that O and I must lie between the foci of the spheroids on the axis and that a narrow zone of angles of emission is used. A β spectrometer using one such ratio is found to give a poorer aperture aberration but an improved source size aberration when compared with the pure spheroidal field instrument. In each case the luminosity is similar to that of the uniform field lens spectrometer.