A Differential Algebraic Method for the Solution of the Poisson Equation for Charged Particle Beams (Communications in Computational Physics, 2018)
The design optimization and analysis of charged particle beam systems employingintense beams requires a robust and accurate Poisson solver. This paper presentsa new type of Poisson solver which allows the effects of space charge to be elegantlyincluded into the system dynamics. This is done by casting the charge distributionfunction into a series of basis functions, which are then integrated with an appropriateGreen's function to find a Taylor series of the potential at a given point withinthe desired distribution region. In order to avoid singularities, a Duffy transformationis applied, which allows singularity-free integration and maximized convergence regionwhen performed with the help of Differential Algebraic methods. The method isshown to perform well on the examples studied. Practical implementation choices andsome of their limitations are also explored.