Orbit and optics distortion in a muon FFAG accelerator

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Orbit and optics distortion in a muon FFAG
accelerator

• Shinji Machida
• ASTeC/STFC/RAL
• 3 October, 2007
• http//www.astec.ac.uk/intbeams/users
• /machida/doc/othertalks/machida_20071003.pdf ppt

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Contents

• Neutrino Factory and a nonscaling FFAG as an
  introduction.
• Tracking results of integer (and half-integer)
  tune crossing.
• Random walk model and its limitations.
• Orbit and optics distortion in FFAG muon
  accelerators by S. Machida and D. J.
  Kelliher, submitted to Phys. Rev. ST AB.
• http//prst-ab.aps.org/

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Neutrino factory and FFAG
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Neutrino factory and FFAG (1)Schematic view
neutrino factory complex

• Neutrino Factory 20 to 50 GeV muon beam.
• c.f. Muon Collider a few TeV muon beam.
• Accelerators are the most costly part of the
  machine complex.
• FFAG as the most cost effective option.

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Neutrino factory and FFAG (2) FFAG in one word

• FFAG is a Fixed Field Alternating Gradient
  accelerator.
• It separates the guiding field from the
  acceleration process. No synchronization.
• Quick acceleration is possible. The rate only
  depends on voltage.
• Nonscaling FFAG looks as a storage ring.
• Lattice with ordinary dipoles and quadrupoles.
• Dispersion function is small enough to give large
  momentum acceptance.
• Orbit shift from injection to extraction is small.

lattice functions of 10 to 20 MeV electron model
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Neutrino factory and FFAG (3) nonscaling and
scaling

• Constant gradient magnets give a focusing force
  inversely proportional to a particle momentum.
• With acceleration, the machine
• tune decreases.
• gt Nonscaling FFAG
• Field nonlinearities can make
• the tune constant.
• gt Scaling FFAG

Scaling FFAG
Nonlinear field profile cancel chromaticity.
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Neutrino factory and FFAG (4) why nonscaling for
muon?

• Magnets of a nonscaling FFAG are expected to be
• smaller because of smaller orbit shift,
• simpler because of no nonlinearities.
• However, the machine tune changes a lot during
  acceleration.
• Crossing of resonance becomes a big concern.
• Only plausible argument is that a muon does not
  stay long.

Tune excursion from 10 to 20 GeV/c muon ring.
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Tracking results
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Tracking results (1)source of resonances

• resonance is excited by various kinds of
  machine errors.
• Integer tune by alignment and gradient errors.
• Half-integer tune by gradient errors.

• Track a particle with reasonable amount of
  errors, and see how orbit and optics change when
  a particle crosses integer and half-integer tunes.

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Tracking results (2)orbit distortion with
alignment and gradient errors

• Distribution of maximum horizontal orbit
  distortion out of 501 different alignment errors.
• Distribution of maximum horizontal orbit
  distortion out of 501 different gradient errors.

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Tracking results (3)optics distortion with
gradient errors

• Distribution of maximum optical distortion out of
  501 different gradient errors. Initial emittance
  is 0.003 p.
• Distribution of maximum optical distortion out of
  501 different gradient errors. Initial emittance
  is 30 p.

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Tracking results (4)scaling parameters

• Amplification factor
• Maximum orbit distortion mm / Rms alignment
  errors mm
• 0.1 mm (rms) alignment errors make 10 to 15 mm
  orbit distortion.
• Growth factor
• Relative amplitude growth / Gradient errors
• dG/G1x10-3 (rms) gradient errors make 25
  emittance growth.

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Random walk model
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Random walk model (1) integer resonance width

• Orbit distortion is not necessarily excited when
  a particle cross integer tune with large harmonic
  strength.

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Random walk model (2) half-integer resonance
width

• Optics distortion is not necessarily excited when
  a particle cross half-integer tune with large
  harmonic strength.

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Random walk model (3) another explanation

• Tracking results do not show any resonance
  behavior.
• Since tune changes quickly (one unit per turn),
  dipole and quadrupole errors kick a beam in a
  random way, not excite resonance.

Random walk model (conceptual)
Individual trajectory
rms deviation at each step
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Random walk model (3b) correction

• Kick strength is proportional to 1/momentum.
• Time dependence becomes
  instead of

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Random walk model (4) rms orbit distortion

• rms orbit distortion due to alignment errors
  agrees with random walk model.

• Distortion for different acceleration rate.
• Circles are simulation results.
• Lines are random walk model.

?
tracking
model
17 turns
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Random walk model (5) a limitation of the model

• When the acceleration becomes slower, resonance
  behavior starts appearing.

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Random walk model (6) rms optics distortion

• rms optics distortion due to alignment errors
  agrees with random walk model.

• Distortion for different acceleration rate.
• Circles are simulation results.

?
tracking
model
17 turns
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Random walk model (7) a limitation of the model

• When the acceleration becomes slower, random walk
  model breaks down more quickly for optics
  distortion.

tracking
model
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Conclusions
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• Amplification factor is 100150. Growth factor is
  250.
• Practically important to determine magnet
  aperture.
• Orbit and optics distortion can be rather
  explained by random kick (walk) model, not by
  resonance crossing.
• One of EMMA goals See effects of resonance
  crossing -gt See effects of machine errors
• If we make the acceleration speed slower, 5 times
  or 85 turns for example, resonance behavior
  appears in addition to random kicks. That is the
  mixed regime of resonance and random kicks.