Correction of Chromatic BetaFunctions at the Tevatron

1
Correction of Chromatic Beta-Functions at the
Tevatron

• A. Valishev, V. Lebedev
• 12/20/05

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Focusing Perturbations

• 1st order effect on betatron tune
• 1st order effect on beta-function
• 2nd order effect on tune

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Sources of Chromatic Perturbations

• Quadrupoles
• Sextupoles

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Consequences of Beta Chromaticity

• Betatron tune spread - at Final Focus
  quads gives 80-90 of second order chromaticity
• Chromatic Beta - Detrimental to beam-beam
  effects (dynamic aperture)
• Considering the working point near ½ increases
  all effects by a factor of 4

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Beta-Function Chromaticity X -Measured
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Beta-Function Chromaticity Y -Measured
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Measured Tune Chromaticity
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Tune Chromaticity
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SF Families - Phase
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SF Families V1
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SD Families - Phase
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SD Families V1
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Correction of Chromatic Betas V1
SF12A SD-32A SF217A SF324A SF4-8A SF512A S
D2-32A SD3-32A SD4-10A SD5-47A
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Beta-Function Chromaticity X Corrected V1
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Beta-Function Chromaticity Y Corrected V1
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Tune Chromaticity Corrected V1
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SF and SD Families V2
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Correction of Chromatic Betas V2
SF12A SD-32A SF27A SF4-13A SF532A SD-32A S
D425A SD5-47A
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Beta-Function Chromaticity X Corrected V2
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Beta-Function Chromaticity Y Corrected V2
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SF and SD Families V3
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Correction of Chromatic Betas V3
SF12A SD-32A SF12A SF4-27A SF618A SD-32A S
D443A SD633A
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Beta-Function Chromaticity X Corrected V3
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Beta-Function Chromaticity Y Corrected V3
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Sextupole Resonance Driving Term V3