Self-Consistent Field and Motion of Electrons Which Have a Range in Canonical Angular Momentum in a Uniform Magnetic Field

Abstract

The self-consistent theory of relativistic electrons circulating in a uniform impressed magnetic field, the "Astron problem," has been generalized to the extent that a range of canonical angular momentum among monoenergetic electrons has been treated. For simplicity, the density distribution in phase space has been chosen to be uniform over a finite momentum range. Just as in the single-momentum case, field reversal is found, but new field and spatial density configurations appear. The uniform distribution is found to be consistent with isotropic regions of constant spatial density and constant magnetic field. The thickness of transition layer between vacuum and such a region conforms, within limits, to an empirical relation previously found. The limit to the number of electrons per unit axial length of layer still exists. The curves relating the ratio of internal to external field to the layer strength still show multiple values of both ratio and strength in certain ranges. Trajectories have been calculated and plotted for several cases.