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A method for obtaining self-potentials and fields of charged particle beams called the template potential algorithm has been developed. The approach stems from the analytical Green's function formulation and is based on a discrete representation by auxiliary macroelements or templates of the charge density distribution. Superposition of the potentials and fields including image forces for each template is used to reproduce the total potential and field of the original charge distribution within a conducting boundary. The technique is especially useful when the Poisson solver is being used repeatedly as with the simulation of charged particle beam dynamics in accelerators. Numerical results are presented and limitations of the method are discussed.

Fast Poisson Solver for Space Charge Dominated Beam Simulation Based on the Template Potential Technique