Algebraic theory of beam-beam interaction in the thin lens model

Technical Report · Thu Aug 01 00:00:00 EDT 1985

DOI:https://doi.org/10.2172/7019665· OSTI ID:7019665

Forest, E; Furman, M

In this paper we will set up a general model for the study of beam-beam interactions. First, we described the ring as made of N generalized interaction points (or GIP). These GIP's could be single IP or clustered IP's. They are equally spaced. Then we assign to the i{sup th} GIP two generalized bunches (or GB) {l brace}{rvec {phi}}{sup i}, {rvec {psi}}{sup i}{r brace}. These two GB are colliding at the center of the i{sup th} GIP. The GB can contain many bunches. This allows for the study of long range effect as well as clustered IP's within the GP. Finally, we adopt the Eulerian point of the view of hydrodynamic. The label i'' in {rvec {phi}}{sup i} or {rvec {psi}}{sup i} denotes the GB's at the i{sup th} GIP. If {rvec {phi}}{sup i} moves toward the right and {rvec {psi}}{sup i} toward the left, we see that one collision later {rvec {phi}}{sup i} is made of bunches previously at the (i{minus}l){sup th} GIP while {sub {rvec {psi}}}{sup i} originates from the (i+l){sup th} GIP.

• Research Organization: Lawrence Berkeley Lab., CA (USA). SSC Central Design Group
• Sponsoring Organization: DOE/ER
• DOE Contract Number: AC02-89ER40486
• OSTI ID: 7019665
• Report Number(s): SSC-32; ON: DE90014102; TRN: 90-023103
• Country of Publication: United States
• Language: English

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