Three Dimensional Simulation of Large-Aspect-Ratio Ellipse-Shaped Charged-Particle Beam Propagation

A new equilibrium theory for a large-aspect-ratio ellipse-shaped charged-particle beam in a non-axisymmetric periodic permanent magnet focusing field has been developed recently [1]. A periodic beam equilibrium solution is obtained numerically from a set of generalized envelope equations. It is shown that the beam edges are well confined in both transverse directions, and that the equilibrium beam exhibits a periodic small-amplitude twist as it propagates. A two-dimensional particle-in-cell (PIC) code, PFB2D and a three-dimensional trajectory code, OMNITRAK [2] are used to verify the theoretical predictions in the paraxial limit. The influence of the beam image charge due to a conducting wall is assessed via both sets of simulations.