EMMA Horizontal and Vertical Corrector Study

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EMMA Horizontal and Vertical Corrector Study

• David Kelliher
• ASTEC/CCLRC/RAL
• 14th April, 2007

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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.

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BPMs and vertical kicker location
Neil Bliss 3/4/07
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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, q 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.

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Error simulation

• Errors in the magnet horizontal (?50mm) and
  vertical (?25mm) position simulated by using the
  MADX function EALIGN.
• Random errors with a Gaussian distribution,
  cut-off point at 2s.
• MADX was run with many instances of such randomly
  perturbed magnets in order to generate useful
  statistics.

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Error distribution F magnet
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BPM location and Horizontal orbit distortion
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Horizontal tune / Horizontal Orbit distortion
1 seed used to simulate random alignment errors
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Energy Scan 1 seed
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10 MeV 50 seeds
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15 MeV 50 seeds
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Energy Scan 1 seed
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Energy Scan 1 seed
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Variation of Corrector strengths
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Variation of Corrector strengths
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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?

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Number of correctors and vertical orbit distortion
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Vertical Tune / Orbit Distortion
1 seed used to simulate random alignment errors
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1 Corrector Variable Strength
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1 Corrector Constant Strength
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2 Correctors Variable Strength
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2 Correctors Constant Strength
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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.