Beams Document 5032-v3

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New Formulae for 3DoF Space Charge Field

Document #:
Beams-doc-5032-v3
Document type:
Note
Submitted by:
Yuri Alexahin
Updated by:
Yuri Alexahin
Document Created:
21 Dec 2015, 11:29
Contents Revised:
02 Oct 2017, 02:36
Metadata Revised:
02 Oct 2017, 02:36
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Other Versions:
Beams-doc-5032-v2
22 Dec 2015, 11:15
Beams-doc-5032-v1
21 Dec 2015, 11:29
Abstract:
An alternative to the Basetti-Erskine formula is proposed for calculation of the direct space charge forces in a beam with Gaussian transverse profile. It also gives the longitudinal field depending on the transverse coordinates in such a way that the 3DoF motion remains Hamiltonian. Power expansion is presented that is applicable for transverse amplitudes up to 5 sigma and higher
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Notes and Changes:
Asymptotics added for large particle displacement.
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