Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation
Abstract In typical numerical simulations, the space-charge force is calculated by slicing a beam into many longitudinal segments and by solving the two-dimensional Poisson equation in each segment. This method neglects longitudinal leakage of the space-charge force to nearby segments owing to its l...
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2018-08-01
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Online Access: | https://doi.org/10.1038/s41598-018-30960-2 |
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doaj-af5083b9063347019724fa276082aca42020-12-08T04:10:01ZengNature Publishing GroupScientific Reports2045-23222018-08-018111910.1038/s41598-018-30960-2Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equationYoshihiro Shobuda0Yong Ho Chin1JAEAKEK, High Energy Accelerator Research OrganizationAbstract In typical numerical simulations, the space-charge force is calculated by slicing a beam into many longitudinal segments and by solving the two-dimensional Poisson equation in each segment. This method neglects longitudinal leakage of the space-charge force to nearby segments owing to its longitudinal spread over 1/γ. By contrast, the space-charge impedance, which is the Fourier transform of the wake function, is typically calculated directly in the frequency-domain. So long as we follow these approaches, the longitudinal leakage effect of the wake function will remain to be unclear. In the present report, the space-charge wake function is calculated directly in the time domain by solving the three-dimensional Poisson equation for a longitudinally Gaussian beam. We find that the leakage effect is insignificant for a bunch that is considerably longer than the chamber radius so long as the segment length satisfies a certain condition. We present a criterion for how finely a bunch should be sliced so that the two-dimensional slicing approach can provide a good approximation of the three-dimensional exact solution.https://doi.org/10.1038/s41598-018-30960-2 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Yoshihiro Shobuda Yong Ho Chin |
spellingShingle |
Yoshihiro Shobuda Yong Ho Chin Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation Scientific Reports |
author_facet |
Yoshihiro Shobuda Yong Ho Chin |
author_sort |
Yoshihiro Shobuda |
title |
Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation |
title_short |
Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation |
title_full |
Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation |
title_fullStr |
Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation |
title_full_unstemmed |
Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation |
title_sort |
rigorous formulation of space-charge wake function and impedance by solving the three-dimensional poisson equation |
publisher |
Nature Publishing Group |
series |
Scientific Reports |
issn |
2045-2322 |
publishDate |
2018-08-01 |
description |
Abstract In typical numerical simulations, the space-charge force is calculated by slicing a beam into many longitudinal segments and by solving the two-dimensional Poisson equation in each segment. This method neglects longitudinal leakage of the space-charge force to nearby segments owing to its longitudinal spread over 1/γ. By contrast, the space-charge impedance, which is the Fourier transform of the wake function, is typically calculated directly in the frequency-domain. So long as we follow these approaches, the longitudinal leakage effect of the wake function will remain to be unclear. In the present report, the space-charge wake function is calculated directly in the time domain by solving the three-dimensional Poisson equation for a longitudinally Gaussian beam. We find that the leakage effect is insignificant for a bunch that is considerably longer than the chamber radius so long as the segment length satisfies a certain condition. We present a criterion for how finely a bunch should be sliced so that the two-dimensional slicing approach can provide a good approximation of the three-dimensional exact solution. |
url |
https://doi.org/10.1038/s41598-018-30960-2 |
work_keys_str_mv |
AT yoshihiroshobuda rigorousformulationofspacechargewakefunctionandimpedancebysolvingthethreedimensionalpoissonequation AT yonghochin rigorousformulationofspacechargewakefunctionandimpedancebysolvingthethreedimensionalpoissonequation |
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