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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.