Core-halo boundary in a sheet beam model

Abstract

In this paper, halo formation in a sheet beam model is investigated. Special attention is given to the core-halo boundary. In particular, a theory to determine the final stationary state achieved by an initially mismatched beam is developed. An interesting property of the theory is that it clearly separates the core and the halo portions of the distribution. Self-consistent numerical simulations are employed to obtain particle distributions for the sheet beam stationary state. Using the maximum Laplacian criteria, the core-halo boundary is evaluated from the numerical data for both one-dimensional projections of the beam distribution as well as the full multi-dimensional phase space. The results are compared to those predicted by the theory.