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Chromaticity shift induced by misalignment of Landau Octupole
Magnets
Neal Anderson
Department: BE-ABPAdvisor: Rogelio TomasMentor: Ewen Maclean
LHC
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Accelerator Optics• Design Orbit – Ideal path for the
beam to follow around the LHC.
• Closed Orbit – Actual path the beam follows around the accelerator. (Differs slightly from ideal path)
• The actual path of a particle oscillates around the closed orbit in both transverse (perpendicular to the beam direction) planes.
• Beta Function – the envelope within which an individual particle path oscillates. It defines the maximum amplitude of oscillation.
Closed Orbit
Beta Function
Actual Path of a Particle
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Tune (Q) – is the number of oscillations (about the closed orbit)
per revolution
Revolutions
Beam
pos
ition
(arb
itrar
y un
its)
Q = 1.00
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Revolutions
Beam
pos
ition
(arb
itrar
y un
its)
Q = 0.33
Rational tunes result in resonances, which multiply the effect of instabilities
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Taken from Gluap
Verti
cal T
une
HorizontalTune
Chromaticity: Q’ = dQ/(dp/p)
Resonance Diagram
.Tune
Chromaticity
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Magnets in the LHC• Dipole Magnets Steer the
beam
• Quadrupoles focus the beam
• Determine Beta Function and Tune
• Sextupoles correct the chromaticity
• Octupoles are used to damp other instabilities. Pictures taken from wikipedia
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Motivation
With Landau Octupoles
Without Landau Octupoles
Q’ and Landau Octupole Current vs. Time (Beam 1)
(Beam 2)
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How do octupoles affect chromaticity?
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My project - Measure systematic closed orbit of Landau Octupoles and study resulting
chromaticity shifts in 2012
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Mean: 1.84 units Median: 1.67 units
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Conclusions
• Landau Octupole effect is larger and more frequent than expected
• Chromaticities caused by the Landau Octupole misalignment are significant enough to cause concerns for operation
• The LHC may decide to actively correct for this effect in the future
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Acknowledgements
Rogelio Tomas, Ewen Maclean, CERN Summer Student Program, U of M REU program
ReferenceEdmond Wilson, “Introduction to Particle Accelerators”
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Q = 0.51
Ideal tune is irrational
The beam never returns to the same
point twiceInstabilities are
evenly distributed and their effects are dampened