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| WEP157 |
An Implementation of the Fast Multipole Method for High Accuracy Particle Tracking of Intense Beams |
1782 |
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- E.W. Nissen, B. Erdelyi
Northern Illinois University, DeKalb, Illinois, USA
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We implement a single level version of the fast multipole method in the software package COSY Infinity. This algorithm has been used in other physics fields to determine high accuracy electrostatic potentials, and is implemented here for charged particle beams. The method scales like NlogN with the particle number and has a priori error estimates, which can be reduced to essentially machine precision if multipole expansions of high enough order are employed, resulting in a highly accurate algorithm for simulation of intense beams without averaging such as encountered in PIC methods. In order to further speed up the algorithm we use COSY Infinity’s innate differential algebraic methods to help with the expansions inherent in this system. Differential algebras allow for fast and exact numerical differentiation of functions that carries through any mathematical transformations performed, and can be used to quickly create the expansions used in the fast multipole method. This can then be combined with moment method techniques to extract transfer maps which include space charge within distributions that are difficult to approximate.
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