Orbit Distortion and Correction

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Orbit Distortion and Correction

• David Kelliher
• ASTeC/STFC/RAL
• Design Review III, Daresbury
• December 10th 11th

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Contents

• PTC model of EMMA
• Orbit distortion - Tolerances
• A new orbit correction scheme
• Vertical corrector magnets

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PTC model of EMMA
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PTC model of EMMA

• PTC is a kick code, allowing symplectic
  integration through all accelerator elements
• Cavities with the appropriate fixed frequency
  included
• Initially, an rbend magnet with a quadrupole
  component was used to simulate the displaced
  quadrupoles
• Displaced quadrupoles have recently been added.
  These have straight field lines (unlike the
  curved field lines in a rbend).
• The fringe fields in the displaced quadrupoles
  have quad symmetry.
• These modifications to PTC carried out by the
  author, E. Forest, KEK.
• Beam Dynamics, E Forest, Harwood Academic
  Publishers, Volume 8, p389
• É Forest and J Milutinovic, Nucl. Inst. and
  Meth. A269 (1988) 474

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Tune comparison with rbend model
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Orbit Distortion
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Tracking with acceleration and misalignment
?misalignment 50 micron
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Horizontal misalignments
Amplification factor gt max orbit distortion/
sigma of misalignment 123 Tolerance (1 mm
distortion) 8 microns

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Vertical misalignments
Amplification factor 98 Tolerance (1 mm
distortion) 10 microns

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Longitudinal misalignments
Amplification factor 13 Tolerance (1 mm
distortion) 80 microns

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Rotation misalignments
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Tolerances
Assuming 1 mm distortion is limit
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Orbit Correction
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Orbit Correction

• Since the betatron tune varies with momentum, the
  phase difference between corrector magnets and
  error sources will change.
• As the corrector strength cannot change during
  the rapid acceleration, it follows that harmonic
  correction of orbit distortion will not work.

• However, local correction of the magnets should
  be possible

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Local Correction

• In horizontal plane there are sliders to enable
  the misalignments to be corrected
• In vertical plane, it is hoped that a once only
  adjustment to the magnets will be sufficient.
• 2 BPMs per cell
• To calculate the misalignments based on the BPM
  measurements, it would be better to run at fixed
  energy.
• A number of turns would allow stochastic BPM
  errors to be averaged out and the tune to be
  calculated.
• However, the error due to BPM misalignments needs
  to be considered when attempting to calculate the
  magnet misalignments

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BPM and Quadrupole misalignments

• Assume these quantities are independently
  misaligned. Not considering other sources we have
  NQNBPM unknowns and NBPM measurements.

• However, we can use a characteristic property
  of the FFAG, namely that the phase shift depends
  on momentum, to generate another set of NBPM
  measurements.
• If we have 2NBPMNQNBPM we can solve the set
  of simultaneous equations. Otherwise some sort of
  least squares fit could be attempted.

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Vertical corrector magnets
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Motivation

• Harmonic correction doesnt work in a EMMA
• Local correction, while possible, may sometimes
  be impractical in the vertical case
• Can we use vertical corrector magnets to reduce
  the accelerated orbit distortion?

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BPMs and vertical kicker location
Neil Bliss 3/4/07
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Accelerated Orbit Distortion

• The accelerated orbit distortion is calculated by
  tracking with PTC from 10-20 MeV.
• Unlike the closed orbit distortion, it is not
  affected by the integer tune resonances.
• In PTC, the initial conditions are given by the
  closed orbit at the initial energy.

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Method

• Vary first corrector strength, run PTC, calculate
  the orbit distortion rms over the full energy
  range, find minimum
• Improve result by varying corrector strength
  about this minimum.
• Repeat for each corrector and find the best one.
• Keeping this optimal corrector, repeat the
  exercise for a second corrector.
• Continue until 16 correctors used.

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Correction with 1 kicker
Vertical orbit distortion rms reduced from 2.67mm
to 0.64mm
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Adding more correctors
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Optimise initial (y,y)
Vertical orbit distortion rms reduced from 2.67mm
to 0.63mm
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Conclusions

• A PTC model of EMMA including displaced
  quadrupoles has been completed
• The simulations predict an amplification factor
  with respect to quadrupole misalignments 100.
  This will place stringent requirements on magnet
  alignment.
• Tolerance levels of various translational and
  rotational errors were calculated.
• Local correction of the misalignments will be
  necessary.
• An new scheme to measure BPM misalignments is
  presented (only available in FFAG).
• Vertical corrector magnets can reduce the
  accelerated orbit distortion. This may be
  equivalent to optimising the initial conditions.

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Future Work

• The scheme to measure BPM errors and quadrupole
  misalignments will be tested.
• Incorporate field maps of the EMMA magnets into
  PTC. This work is well underway with the help of
  Ben Shepherd and Etienne Forest.
• This should allow the beam dynamics, and in
  particular the amplification factor, to be
  determined with more confidence.