Electron Trajectories in a Nonuniform Axially Symmetric Magnetic Field

Abstract

Electrons injected along the flux lines of a spatially varying, axially symmetric magnetic field that is increasing in the direction of electron motion will follow approximately helical trajectories about the flux lines. If the field increases too rapidly, the electrons will not be able to penetrate the magnetic field beyond a certain point and will be turned back by the magnetic mirror formed by the increasing field. For more slowly varying fields, the electrons can penetrate the mirror with a large fraction of their energy in axial velocity. The equations of motion for electrons in a sinusoidally varying magnetic field have been solved on a computer, and the results are presented in graphical form. An application of this field configuration as a device for converging a hollow cylindrical electron beam has been tested, and measured area convergences of 15 to 1 have been obtained by photographing a movable carbon screen collector that is heated by the beam. The beam is started out with a conventional parallel flow gun immersed in the magnetic field. As the beam leaves the first accelerating electrode it enters the region of increasing magnetic field. It then shrinks in diameter and thickness, and hence in area, approximately in proportion to the increase in the magnetic field. The actual area convergence will be less than this increase by an amount depending on the length and rate of the magnetic field taper.