• B. Erdelyi
  Northern Illinois University, DeKalb, Illinois
• S.L. Manikonda
  ANL, Argonne

Most charged particle beams under realistic conditions have Gaussian density distributions in phase space, or can be easily made so. However, for several practical applications, beams with uniform distributions in physical space are advantageous or even required. Liouville’s theorem and the symplectic nature of beam’s dynamic evolution pose constraints on the feasible transformational properties of the density distribution functions. Differential Algebraic methods offer an elegant way to investigate the underlying freedom involving these beam manipulations. Here, we explore the theory, necessary and sufficient conditions, and practicality of the uniformization of Gaussian beams from a rather generic point of view.