ALIGNMENT SENSITIVITY STUDIES FOR

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• ALIGNMENT SENSITIVITY STUDIES FOR
• THE ILC DAMPING RINGS
• Kosmas Gr. Panagiotidis

The Cockcroft Institute
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Contents

• Overview of the ILC
• Luminosity and Emittance
• Generation of Emittance in a Storage Ring
• Sensitivity Studies
• Future Work

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The International Linear Collider
30km
Figure 1Schematic layout of ILC

• The International Linear Collider (ILC) is a
  proposed facility for future studies of
  fundamental particle physics.
• ILC will be designed to collide electrons and
  positrons at centre of mass energies of 500GeV or
  more, in order to make precision measurements of
  new phenomena, such as the Higgs boson and
  supersymmetry.
• The baseline configuration of the ILC1 has been
  determined by the Global Design Effort.

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Luminosity

• A fixed target has a high density of target
  particles, resulting in a good probability for
  interaction. Therefore, the intensity and
  emittance of the incident beam are not usually a
  major concern in fixed target experiments. In
  contrast, the density of a colliding beam target
  is extremely small compared to that of a solid
  target.
• The luminosity of a collider is determined by the
  density of the colliding bunches and the
  collision rate. For a linear collider concerning
  two colliding bunches of particles n1 and n2
  colliding at a repetition rate f, the luminosity
  is given by
• where sx and sy are the horizontal and
  vertical beam sizes.
• Practical issues limit the charge per bunch and
  the repetition rate. Therefore, to enhance
  luminosity, one needs to reduce the beam sizes
  (and hence the emittances) as much as possible.

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Emittance
Figure 2 Phase-space ellipse

• The emittance is a measure of the phase space
  area (the area on a plot of momentum vs
  coordinate) occupied by particles in the beam,
  and is invariant in the absence of effects like
  radiation and acceleration.
• Thus, to get a small beam size at the IP, we need
  both very strong focusing (which is provided by
  the final focus magnets) and a very small
  emittance.
• The job of the damping rings is to use radiation
  effects to produce a beam with very small
  emittance.  The lowest emittance ever achieved in
  a storage ring is 4.5 pm to produce the design
  luminosity, the damping rings have to achieve a
  vertical emittance of 2 pm.

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The ILC Damping Rings

• The two damping rings (one for the electron beam
  and one for the positron beam), situated
  coaxially around the Interaction Point (IP), form
  a major component of the ILC.
• Their purpose is to reduce the emittance of the
  beam, since, when created, neither the electron
  nor the positron bunches are compact enough to
  yield the high luminosity essential for the
  physics programme.

Figure 3 Footprint of ILC positron ring and
important parameters
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Types of Magnets used in the Damping Ring

• Dipole Magnets
• They are used to bend the beam.
• Quadrupole Magnets
• Their purpose is to focus the beam.
• Sextupole Magnets
• They are used to correct the chromaticity.

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Particle Trajectory and Steering Errors
Dipole field error
Closed Orbit
Reference Trajectory
Figure 4 Illustration of a dipole field error

• A dipole field error causes a distortion of the
  closed orbit and particles crossing the field
  error region get a vertical kick, as
  illustrated in figure 4.
• Depending on the sensitivity of the particular
  lattice, even a small error can lead to a large
  orbit distortion and this in turn means that in
  order to achieve successful operation of the
  ring, the alignments tolerances of magnetic
  components become very demanding.

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Generation of emittance in a storage ring

• In storage ring operation the vertical emittance
  is typically dominated by magnet misalignments.
• Betatron coupling results in direct transfer of
  horizontal emittance into the vertical plane.
• The distortion on the closed orbit, resulting
  from this steering together with vertical
  sextupole misalignments, leads to a vertical beam
  offset in the sextupoles with respect to their
  magnetic center. Consequently, betatron coupling
  is introduced .
• Vertical misalignments in the sextupoles
  introduce a vertical kick to the beam that is
  dependent on the horizontal coordinate. This
  leads to each particle experiencing a different
  force in respect to their horizontal position in
  the bunch and consequently this also leads to
  vertical emittance growth.
• Rotations of quadrupoles around the beam axis
  have a similar effect to vertical misalignments
  of the sextupoles.

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Simulation Codes

• The studies presented here were performed using
  specialized codes for the modeling of accelerator
  systems, namely MAD (Methodical Accelerator
  Design 2 (version 8.23dl), and Merlin 3.
• The simulations run with the aforementioned codes
  investigated the effect of magnet misalignments
  on specific beam parameters, namely on the
  vertical closed orbit, the dispersion and the
  vertical emittance ey.
• A definition file for the present baseline
  damping ring lattice, referred to as the OCS6
  lattice, is available in the standard format used
  by MAD. This file describes the sequence of all
  elements that comprise the ring, but cannot be
  read directly by Merlin. Instead, MAD is used to
  produce a file that contains a detailed
  description of the lattice in a simplified format
  that can be recognized by Merlin. The simulations
  are then performed using Merlin.
• Using Merlin we are able to apply a random set of
  misalignments to a particular types of families
  of magnets and then calculate the effects of
  these misalignments on various properties of the
  beam.

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Sensitivity of the yrms closed orbit to
Quadrupole misalignments
Figure 5

• Figure 5 illustrates the closed orbit distortion
  for rms quadrupole vertical misalignments up to
  10µm. The blue points show the average over 100
  sets of errors with a given rms. The error bars
  indicate the 5th and 95th percentiles of each set
  of errors.

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Sensitivity of the Vertical Emittance ey to
Quadrupole tilts
Figure 6

• The above figure shows how the emittance is
  affected by quadrupole tilts (rotation of the
  magnet in respect to the reference trajectory).
  The error bars indicate the 5th and 95th
  percentiles of each set of errors

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Sensitivity of the Vertical Emittance ey to
Sextupole misalignments
Figure 7

• Figure 7 illustrates the effect of vertical
  sextupole misalignments to the vertical
  emittance The error bars indicate the 5th and
  95th percentiles of each set of errors.

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Conclusions

• The calculations based on the simulated data
  appear to be in reasonable agreement with theory
  and present acceptable errors.
• The simulations predict very accurately the trend
  of the effect to the lattice sensitivity in
  respect to each misalignment error, as expected
  by the theoretical formulae each case. Knowing
  these trends provides a clear understanding of
  how the machine responds to the different types
  of errors that are always present in everyday
  operation.
• A vertical emittance of 2pm (nominal
  specification for the ILC damping rings) is
  generated by vertical sextupole misalignments of
  the order of 60µm. An equal amount of vertical
  emittance is generated by quadrupole tilts of the
  order of 70 to 80µrad. It is unrealistic to
  expect that this level of precision can be
  achieved during commissioning of the machine.
  This effectively means that the machine will have
  to be tuned to the desired vertical emittance
  levels after construction and after successful
  beam circulation has been achieved.

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Future Work

• The performed simulations took into account only
  one type of error each time.
• Of course, in reality all types of possible
  errors come into play simultaneously. To evaluate
  a simulation where all types of errors have been
  introduced into the model, one needs to be able
  to account for the effect of each type of error
  separately and that information is provided by
  the current studies.
• The next step of these studies is to try and
  simulate a more realistic model of the damping
  ring lattice, where all types of misalignment
  errors are present and evaluate it based on the
  knowledge acquired so far.
• Simulate the tuning procedure to achieve the
  necessary beam quality.

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• References
• ILC Baseline Configuration Document,
  http//www.linearcollider.org/wiki/docu.php?idbcd
  bcd_home
• http//mad.web.cern.ch/mad/
• http//www.desy.de/merlin/
• A.W.Chao, M.Tigner, Handbook of Accelerator
  Physics and Engineering, World Scientific
  Publishing (Jun 1999)
• S.Y. Lee, Accelerator Physics, World Scientific
  Publishing 2Rev Ed edition (26 Jan 2005)
• A.Wolski, J.Gao, S.Guiducci, Configuration
  Studies and Recommendations for the ILC Damping
  Rings, Lawrence Berkeley National Laboratory,
  February 4, 2006 , http//repositories.cdlib.org/l
  bnl/LBNL-59449
• A.Wolski, Linear Dynamics for Particle
  Accelerators, The Cockcroft Institute, Autumn
  Lecture Courses 2006, http//www.cockcroft.ac.uk/e
  ducation.htm
• A.Wolski, J.Jones, Damping Rings Design and
  Physics Issues, USPAS January 2007, Houston,
  Texas, http//www.cockcroft.ac.uk/education.htm
• Hans Grote, F. Cristoph Iselin, The MAD Program,
  Users Reference Manual, CERN/SL/90-13 (AP) Rev.
  5, Geneva, Switzerland 1996

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• End of Presentation
• Thank you for your attention !