EMMA Horizontal and Vertical Corrector Study

David Kelliher

ASTEC/CCLRC/RAL

14th April, 2007

Introduction

• Ability to move magnets perpendicular to the beamline in the horizontal plane allows horizontal corrections to be made.

• Vertical corrections made using kicker magnets.• There will be 2 BPMs per cell, providing both

horizontal and vertical displacement measurements.

• No BPMs will be placed in those long drifts with an RF cavity.

BPMs and vertical kicker location

Neil Bliss 3/4/07

MADX ‘Correct’ Module

• The CORRECT statement makes a complete closed orbit or trajectory correction using the computed values at the BPMs from the Twiss table.

• There are three corrections modes – MICADO, LSQ, SVD. MICADO is used in this study as it tries to minimise the number of correctors used.

• The MICADO algorithm solves a system of linear equations

• Where b is the vector of BPM measurements, is the correction kick vector and A is the beam response matrix to a set of kicks. The algorithm iteratively minimises the norm of the residual vector r using least squares method. At each iteration it finds the corrector that most effectively lowers r.m.s BPM distortion.

bθ .Ar

Error simulation

• Errors in the magnet horizontal (=50m) and vertical (=25m) position simulated by using the MADX function EALIGN.

• Random errors with a Gaussian distribution, cut-off point at 2

• MADX was run with many instances of such randomly perturbed magnets in order to generate useful statistics.

Error distribution – F magnet

BPM location and Horizontal orbit distortion

Horizontal tune / Horizontal Orbit distortion

1 seed used to simulate random alignment errors

Energy Scan1 seed D F D F

10 MeV50 seeds

D F D F

1 2 3 4

15 MeV50 seeds

D F D F

1 2 3 4

Energy Scan1 seed

D F D F

1 2 3 4

Energy Scan1 seed

D F D F

1 2 3 4

Variation of Corrector strengths

Variation of Corrector strengths

Horizontal Correction - Conclusions

• No optimal position for BPMs can be inferred from this study.

• Outside the vicinity of energies which correspond to integral tunes, the difference in orbit correction accuracy due to BPM position is of the micron order (if all available correctors used).

• Position of BPMs down to engineering considerations.• Corrector strengths were allowed to vary in this study

(not feasible in reality). • How to find corrector strengths, constant over energy

range, which best reduce horizontal orbit distortion?

Number of correctors and vertical orbit distortion

Vertical Tune / Orbit Distortion

1 seed used to simulate random alignment errors

1 Corrector – Variable Strength

1 Corrector – Constant Strength

2 Correctors – Variable Strength

2 Correctors – Constant Strength

Conclusion

• Due to strongly varying phase advance per cell over the energy range, it is difficult to correct with constant corrector strength

• There is no simple way to solve this problem using existing MADX routines.

• A smart interpolation method should be used to find the best set of correctors to reduce both vertical and horizontal orbit distortion over the energy range.