Chromaticity shift induced by misalignment of Landau Octupole

Chromaticity shift induced by misalignment of Landau Octupole Magnets Neal Anderson LHC Department: BE-ABP Advisor: Rogelio Tomas Mentor: Ewen Maclean

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) Closed Orbit 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. Beta Function Actual Path of a Particle

Beam position (arbitrary units) Tune (Q) – is the number of oscillations (about the closed orbit) per revolution Revolutions Q = 1. 00

Beam position (arbitrary units) Rational tunes result in resonances, which multiply the effect of instabilities Revolutions Q = 0. 33

Resonance Diagram Vertical Tune . Chromaticity Horizontal. Tune Taken from Gluap Chromaticity: Q’ = d. Q/(dp/p)

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

Q’ and Landau Octupole Current vs. Time (Beam 1) Motivation Without Landau Octupoles (Beam 2) With Landau Octupoles

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 Reference Edmond Wilson, “Introduction to Particle Accelerators”

Q = 0. 51 Ideal tune is irrational The beam never returns to the same point twice Instabilities are evenly distributed and their effects are dampened