The Paths of Ions and Electrons in Non-Uniform Magnetic Fields

Abstract

The integration of the Lorentz force equations to give electron or ion paths has been reduced to simple quadratures for systems in which the electric field is zero and the magnetic field is a function of one Cartesian or cylindrical coordinate. For several interesting types of magnetic field variation the quadrature can be carried through analytically; and even for complicated magnetic fields, or such as are known only empirically, the numerical integration can be effected without difficulty. From general considerations of the functions involved, it is possible to determine the extension and periodicity of the orbits for any set of initial conditions. The representation used is also convenient for obtaining information regarding the dispersion and focusing characteristics of the trajectories, some of which have unique properties of promise for use in specific instrument design such as mass spectrometers, beta-ray spectrographs, etc. Schematic designs of such instruments are proposed, and a discussion is given of their advantages and special properties.