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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Autores principales:	Yoshihiro Shobuda, Yong Ho Chin
Formato:	article
Lenguaje:	EN
Publicado:	Nature Portfolio 2018
Materias:	Medicine R Science Q
Acceso en línea:	https://doaj.org/article/af5083b9063347019724fa276082aca4
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spelling	oai:doaj.org-article:af5083b9063347019724fa276082aca42021-12-02T11:40:25ZRigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation10.1038/s41598-018-30960-22045-2322https://doaj.org/article/af5083b9063347019724fa276082aca42018-08-01T00:00:00Zhttps://doi.org/10.1038/s41598-018-30960-2https://doaj.org/toc/2045-2322Abstract 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.Yoshihiro ShobudaYong Ho ChinNature PortfolioarticleMedicineRScienceQENScientific Reports, Vol 8, Iss 1, Pp 1-19 (2018)
institution	DOAJ
collection	DOAJ
language	EN
topic	Medicine R Science Q
spellingShingle	Medicine R Science Q Yoshihiro Shobuda Yong Ho Chin Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation
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.
format	article
author	Yoshihiro Shobuda Yong Ho Chin
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 Portfolio
publishDate	2018
url	https://doaj.org/article/af5083b9063347019724fa276082aca4
work_keys_str_mv	AT yoshihiroshobuda rigorousformulationofspacechargewakefunctionandimpedancebysolvingthethreedimensionalpoissonequation AT yonghochin rigorousformulationofspacechargewakefunctionandimpedancebysolvingthethreedimensionalpoissonequation
_version_	1718395665044733952

Rigorous formulation of space-charge wake function and impedance by solving the three-dimensional Poisson equation

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