Wakefields in Collimators

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Wakefields in Collimators

• Roger Barlow
• Adriana Bungau
• Adina Toader

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What were doing

• Collimator wakefields
• Wakefields in Merlin
• Geometric and resisitive wakes
• BDS studies
• Wakefields in Placet

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ILC collimators
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Why these are different

• Collimators are not dominated by resonance
  structure
• High order modes may matter

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Invalid approximations

• Cant just consider dipole mode
• Cant assume ???
• Axial wakes matter as well as radial ones
• Bunches are not Gaussian
• Luminosity is lost by emittance growth and jitter

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Basic Formalism

• Single particle wake
• wx??mmWm(s)rm rm-1
• cos(m-1)?cosm?sin(m-1)?sinm?
• wy??mmWm(s)rm rm-1
• -sin(m-1)?cosm?cos(m-1)?sinm?
• Slice wake
• wx??mWm(s) rm-1 Cmcos(m-1)?Smsin(m-1)?
• wy??mWm(s)rm-1 Smcos(m-1)?-Cmsin(m-1)?
• where
• Cm ?rm cos(m?) Sm ?rm sin(m?)

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Whats all that for

• Wake due to slice is sum of terms like Cm Wm(s)
  rm-1 cos(m-1)?

Mnumber of modes considered
Particle
Slice
Aperture
Avoid N(N-1)/2 calculations Find Cm, Sm for all
slices Sum 2M terms for each of N particles
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Implementation

• Particle by particle wake calculations are
  possible (avoid Gaussian assumption)
• All done in a couple of for loops

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Merlin

• Framework adaptable
• Consider Wx and Wy, not just WT
• Done by defining new classes inheriting from
  (almost) standard Merlin
• SpoilerWakeFieldProcessWakefieldProcess
• SpoilerWakePotentialsWakepotentials
• SpoilerWakeFieldProcess does the sums
• SpoilerWakePotentials is pure virtual functions
  Wtrans(s,m), Wlong(s,m)

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Geometric wakes

• TaperedCollimatorSpoilerWakePotentials
• Raimondi formula
• Wm(s)2(1/a2m-1/b2m)e-ms/a

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Results

• Simple setup
• Increasing offset
• More modes
• Note distortion

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Resistive wakes

• Different Wtrans, Wlong
• Work in progress (AB)

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Application to BDS

• Studies done (AB) showing small emittance growth
  for reasonable offsets
• Large emittance growth for unreasonable offsets

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Other apertures

• Can use numerical simulations (Echo2D, GdfidL)to
  compute bunch wakes
• Split into modes (automatic for Echo2D, needs
  work for GdfidL)
• Extract delta wakes using Fourier deconvolution

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Bunch to Delta wakes
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Contrast Raimondi formula
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Where next

• Still some problems with FT artefacts that need
  to be sorted
• Can then use these values in interpolation table
  for Merlin etc

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Wakes in PLACET

• Includes wakefields although
• Only up to 2nd order
• Not generally extendable
• Uses some very-short-wake approximation.
  Wakefields only within slice
• But they do handle square apertures which our
  formalism doesnt (yet)

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PLACET studies (AT)

• Comparisons with Merlin predictions
• Investigate effects of wakefields on Frank
  Jacksons improved ILC BDS collimator
  arrangements

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Summary and Outlook

• Lots being done
• Lots still to do
• Interesting problems and potentially useful
  results