@Article{CiCP-17-1,
author = {},
title = {A Differential Algebraic Method for the Solution of the Poisson Equation for Charged Particle Beams},
journal = {Communications in Computational Physics},
year = {2015},
volume = {17},
number = {1},
pages = {47--78},
abstract = {<p style="text-align: justify;">The design optimization and analysis of charged particle beam systems employing
intense beams requires a robust and accurate Poisson solver. This paper presents
a new type of Poisson solver which allows the effects of space charge to be elegantly
included into the system dynamics. This is done by casting the charge distribution
function into a series of basis functions, which are then integrated with an appropriate
Green&#39;s function to find a Taylor series of the potential at a given point within
the desired distribution region. In order to avoid singularities, a Duffy transformation
is applied, which allows singularity-free integration and maximized convergence region
when performed with the help of Differential Algebraic methods. The method is
shown to perform well on the examples studied. Practical implementation choices and
some of their limitations are also explored.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.240813.170614a},
url = {https://global-sci.com/article/80371/a-differential-algebraic-method-for-the-solution-of-the-poisson-equation-for-charged-particle-beams}
}