Chromaticity shift induced by misalignment of Landau Octupole
Magnets
Neal Anderson
Department: BE-ABPAdvisor: Rogelio TomasMentor: Ewen Maclean
LHC
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
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
Revolutions
Beam
pos
ition
(arb
itrar
y un
its)
Q = 0.33
Rational tunes result in resonances, which multiply the effect of instabilities
Taken from Gluap
Verti
cal T
une
HorizontalTune
Chromaticity: Q’ = dQ/(dp/p)
Resonance Diagram
.Tune
Chromaticity
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
Motivation
With Landau Octupoles
Without Landau Octupoles
Q’ and Landau Octupole Current vs. Time (Beam 1)
(Beam 2)
How do octupoles affect chromaticity?
My project - Measure systematic closed orbit of Landau Octupoles and study resulting
chromaticity shifts in 2012
Mean: 1.84 units Median: 1.67 units
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
Acknowledgements
Rogelio Tomas, Ewen Maclean, CERN Summer Student Program, U of M REU program
ReferenceEdmond Wilson, “Introduction to Particle Accelerators”
Q = 0.51
Ideal tune is irrational
The beam never returns to the same
point twiceInstabilities are
evenly distributed and their effects are dampened