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Title: A Symplectic Beam-Beam Interaction with Energy Change

Abstract

The performance of many colliding storage rings is limited by the beam-beam interaction. A particle feels a nonlinear force produced by the encountering bunch at the collision. This beam-beam force acts mainly in the transverse directions so that the longitudinal effects have scarcely been studied, except for the cases of a collision with a crossing angle. Recently, however, high luminosity machines are being considered where the beams are focused extensively at the interaction point (IP) so that the beam sizes can vary significantly within the bunch length. Krishnagopal and Siemann have shown that they should not neglect the bunch length effect in this case. The transverse kick depends on the longitudinal position as well as on the transverse position. If they include this effect, however, from the action-reaction principle, they should expect, at the same time, an energy change which depends on the transverse coordinates. Such an effect is reasonably understood from the fact that the beam-beam force is partly due to the electric field, which can change the energy. The action-reaction principle comes from the symplecticity of the reaction: the electromagnetic influence on a particle is described by a Hamiltonian. The symplecticity is one of the most fundamental requirementsmore » when studying the beam dynamics. A nonsymplectic approximation can easily lead to unphysical results. In this paper, they propose a simple, approximately but symplectic mapping for the beam-beam interaction which includes the energy change as well as the bunch-length effect. In the next section, they propose the mapping in a Hamiltonian form, which directly assures its symplecticity. Then in section 3, they study the nature of the mapping by interpreting its consequences. The mapping itself is quite general and can be applied to any distribution function. They show in Section 4 how it appears when the distribution function is a Gaussian in transverse directions. The mapping is applied to the weak-strong case and some numerical results will be shown in Section 5. The last section is devoted to discussions.« less

Authors:
Publication Date:
Research Org.:
Stanford Linear Accelerator Center, Menlo Park, CA (US)
Sponsoring Org.:
USDOE Office of Science (US)
OSTI Identifier:
813308
Report Number(s):
SLAC-PUB-10055
TRN: US0303848
DOE Contract Number:  
AC03-76SF00515
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: 14 Jul 2003
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; BEAM DYNAMICS; BEAM-BEAM INTERACTIONS; DISTRIBUTION FUNCTIONS; ELECTRIC FIELDS; HAMILTONIANS; LUMINOSITY; PERFORMANCE; STORAGE RINGS

Citation Formats

Moshammer, Herbert. A Symplectic Beam-Beam Interaction with Energy Change. United States: N. p., 2003. Web. doi:10.2172/813308.
Moshammer, Herbert. A Symplectic Beam-Beam Interaction with Energy Change. United States. doi:10.2172/813308.
Moshammer, Herbert. Mon . "A Symplectic Beam-Beam Interaction with Energy Change". United States. doi:10.2172/813308. https://www.osti.gov/servlets/purl/813308.
@article{osti_813308,
title = {A Symplectic Beam-Beam Interaction with Energy Change},
author = {Moshammer, Herbert},
abstractNote = {The performance of many colliding storage rings is limited by the beam-beam interaction. A particle feels a nonlinear force produced by the encountering bunch at the collision. This beam-beam force acts mainly in the transverse directions so that the longitudinal effects have scarcely been studied, except for the cases of a collision with a crossing angle. Recently, however, high luminosity machines are being considered where the beams are focused extensively at the interaction point (IP) so that the beam sizes can vary significantly within the bunch length. Krishnagopal and Siemann have shown that they should not neglect the bunch length effect in this case. The transverse kick depends on the longitudinal position as well as on the transverse position. If they include this effect, however, from the action-reaction principle, they should expect, at the same time, an energy change which depends on the transverse coordinates. Such an effect is reasonably understood from the fact that the beam-beam force is partly due to the electric field, which can change the energy. The action-reaction principle comes from the symplecticity of the reaction: the electromagnetic influence on a particle is described by a Hamiltonian. The symplecticity is one of the most fundamental requirements when studying the beam dynamics. A nonsymplectic approximation can easily lead to unphysical results. In this paper, they propose a simple, approximately but symplectic mapping for the beam-beam interaction which includes the energy change as well as the bunch-length effect. In the next section, they propose the mapping in a Hamiltonian form, which directly assures its symplecticity. Then in section 3, they study the nature of the mapping by interpreting its consequences. The mapping itself is quite general and can be applied to any distribution function. They show in Section 4 how it appears when the distribution function is a Gaussian in transverse directions. The mapping is applied to the weak-strong case and some numerical results will be shown in Section 5. The last section is devoted to discussions.},
doi = {10.2172/813308},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2003},
month = {7}
}

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