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