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Title: Minimizing the Pacman effect

Abstract

The Pacman bunches will experience two deleterious effects: tune shift and orbit displacement. It is known that the tune shift can be compensated by arranging crossing planes 900 relative to each other at successive interaction points (lPs). This paper gives an analytical estimate of the Pacman orbit displacement for a single as well as for two crossings. For the latter, it can be minimized by using equal phase advances from one IP to another. In the LHC, this displacement is in any event small and can be neglected.

Authors:
 [1]
+ Show Author Affiliations
  1. Stanford University, CA (United States), Chou, W. [Fermi National Accelerator Lab., Batavia, IL (United States)
Publication Date:
Research Org.:
Fermi National Accelerator Lab., Batavia, IL (United States)
Sponsoring Org.:
USDOE Office of Energy Research, Washington, DC (United States)
OSTI Identifier:
563144
Report Number(s):
FNAL-TM-2029
ON: DE98051100; BR: KA HEP; TRN: 98:002590
DOE Contract Number:
AC02-76CH03000
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: Oct 1997
Country of Publication:
United States
Language:
English
Subject:
43 PARTICLE ACCELERATORS; QUADRUPOLAR CONFIGURATIONS; MATHEMATICAL MODELS; EIGENFUNCTIONS; FERMILAB

Citation Formats

Ritson, D. Minimizing the Pacman effect. United States: N. p., 1997. Web. doi:10.2172/563144.
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Ritson, D. Minimizing the Pacman effect. United States. doi:10.2172/563144.
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Ritson, D. Wed . "Minimizing the Pacman effect". United States. doi:10.2172/563144. https://www.osti.gov/servlets/purl/563144.
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@article{osti_563144,
title = {Minimizing the Pacman effect},
author = {Ritson, D.},
abstractNote = {The Pacman bunches will experience two deleterious effects: tune shift and orbit displacement. It is known that the tune shift can be compensated by arranging crossing planes 900 relative to each other at successive interaction points (lPs). This paper gives an analytical estimate of the Pacman orbit displacement for a single as well as for two crossings. For the latter, it can be minimized by using equal phase advances from one IP to another. In the LHC, this displacement is in any event small and can be neglected.},
doi = {10.2172/563144},
journal = {},
number = ,
volume = ,
place = {United States},
year = {Wed Oct 01 00:00:00 EDT 1997},
month = {Wed Oct 01 00:00:00 EDT 1997}
}
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Technical Report:
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DOI:  10.2172/563144
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    In order to find the combined effects of beam-beam interaction (head-on and long-range) and random nonlinear multipoles in dipole magnets, transverse tunes and smears have been calculated as a function of oscillation amplitudes. Two types of particles, ''regular'' and ''Pacman,'' have been investigated using a modified version of tracking code TEAPOT. Regular particles experience beam-beam interactions in all four interaction regions (IR's), both head-on and long range, while pacman particles interact with bunches of the other beam in one medium-beta and one low-beta IR's only. The model for the beam-beam interaction is of weak-strong type and the strong beam ismore » assumed to have a round Gaussian charge distribution. Furthermore, it is assumed that the vertical closed orbit deviation arising from the finite crossing angle of 70 ..mu..rad is perfectly compensated for regular particles. The same compensation applied to pacman particles creates a closed orbit distortion. Linear tunes are adjusted for regular particles to the design values but there are no nonlinear corrections except for chromaticity correcting sextupoles in two families. Results obtained in this study do not show any reduction of dynamic or linear aperture for pacman particles but some doubts exist regarding the validity of defining the linear aperture from the smear alone. Preliminary results are given for regular particles when (..delta..p/p) is modulated by the synchrotron oscillation. For these, fifty oscillations corresponding to 26,350 revolutions have been tracked. A very slow increase in the horizontal amplitude, /approximately/4 /times/ 10/sup /minus/4//oscillation (relative), is a possibility but this should be confirmed by trackings of larger number of revolutions. 11 refs., 18 figs., 2 tabs.« less

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    This note analyses the regions of the tune plane which are occupied in a (nominal) model SSC which has two collision points with {beta}* = 0.5 metres, and two with {beta}* = 10.0 metres. The full crossing angle at each collision point is taken to be {alpha}* = 75 microradians, and the head on tune shift parameter is {xi} = {minus}0.00084, (significantly less than the SPS parameter {xi}{sub SPS} {approx} 0.004). Long range beam-beam interactions take place in the free spaces on either side of the collision point, {plus minus}L = 72 metres for the low beta IRs, and 150more » metres in the high beta IRs, which are assumed for convenience to be pure drifts. Bunches in one beam are longitudinally separated from each other by S{sub B} = 4.8 metres. In one variant of the model the transverse beam separation is vertical in all cases, while in a second variant alternate crossings are vertical and horizontal. In both of these cases the horizontal and vertical tune shifts of a test particle in a nominal bunch, and in a PACMAN bunch, are calculated and plotted as a function of its transverse amplitudes, (a{sub x}, a{sub Y}), which are conveniently measured in units of {sigma}, the rms size of the incident gaussian beam. Similar results to these have also been reported elsewhere.« less

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