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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 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.

SUBMITTER: Shobuda Y

PROVIDER: S-EPMC6109189 | biostudies-literature | 2018 Aug

REPOSITORIES: biostudies-literature

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

Shobuda Yoshihiro Y Chin Yong Ho YH

Scientific reports 20180824 1

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 a ...[more]

PMID: 30143700

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

Publications

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

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