Third-order treatment of combined effects of space charge and external fields on cylindrical ion and electron beams

Abstract

Analytical treatments of the space‐charge spread of cylindrical beams have been based upon a number of restrictive assumptions. Most of them can be removed and a higher accuracy attained with the help of a suitable relation connecting motion and Maxwell's equations. As previous treatments appear as paraxial approximations, third‐order formulas applying to arbitrary field forms have been carried out.