Putting it together

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LECTURE 17
COURSE SUMMARY A Design Study of a Compressor
ring for A Neutrino Factory MT 2009 E. J.
N. Wilson
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Putting it together

• The SPS Design Committee get down to business
  (1971)

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SPL
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SPL Output Parameters for the neutrino factory
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Neutrino Factory Demands
Specifications (from R. Palmers conclusion at
ISS meeting in RAL on Thursday 27, April 2006)
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Accumulate and Compress Scenario
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Space charge Q shift

• Radial force
• equals rate of change of momentum

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Smooth approx. - choosing No. of periods
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Period geometry

• Everything must add up for the ring

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Phase advance per cell

• The beta at the F quadrupole which defines the
  scale of the apertures goes through a minimum at
  about 70 deg/cell.
• Other considerations which might lead to close to
  90 degrees per cell are
• Sensitivity to closed orbit errors
• Ease of locating correctors
• Schemes for correcting the chromaticity in the
  arcs without exciting resonances

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Basic Cell of the C0mpressor
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Insertion for 3 Bunch Compressor
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Compressor Lattice

• Your Christmas Present!

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Correction of chromaticity

• Parabolic field of a 6 pole is really a gradient
  which rises linearly with x
• If x is the product of momentum error and
  dispersion
• The effect of all this extra focusing cancels
  chromaticity
• Because gradient is opposite in v plane we must
  have two sets of opposite polarity at F and D
  quads where betas are different

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Parameters of the Magnets of the Compressor
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Magnet design
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Various coil and yoke designs

• ''C' Core
• Easy access
• Less rigid
• H core
• Symmetric
• More rigid
• Access problems.
• ''Window Frame'
• High quality field
• Major access problems
• Insulation thickness

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RF Cavity

• constraint is Voltage per meter and MW of power
  (Shunt impedance and Q)
• pressure from need to provide a good acceleration
  rate or large bucket (e.g. for bunch rotation)

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Rf frequency (injection)

• At injection, in order to use the Keil Schnell
  criterion to combat instabilites we must have
  enough voltage to reach a threshold value of

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Rf frequency(in collision))

• When colliding bunches, we want a short bunch
• either
  or
• If h is small, the bucket area must be much
  bigger
• Hence

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Synchrotron motion (continued)

• This is a biased rigid pendulum
• For small amplitudes
• Synchrotron frequency
• Synchrotron tune

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The bunch and bucket at start of rotation
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Intensity and impedance

• Local enlargement in the beam tube which can
  resonate like a cavity
• Voltage experienced has same form as the current
  which excites it
• Impedance
• Relates force on particles to the Fourier
  component of the beam current which excites the
  force.
• A complex quantity
• - REAL if the voltage and current are in phase
• - IMAGINARY if 90 degrees or "i" between voltage
  and current (L , C )
• - different from r.f. wave by 90 degrees!

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Instability

• Keil Schnell stability criterion

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Some parameters of accumulator and compressor
Table 6 Main parameters of the accumulator and
compressor for a neutrino factory
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LHC parameters
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ORGANISATION OF DESIGN
1. Keep a parameter list
A. Lattice Working Group Rossbach ,J.
and Schmüser, P. (1992). Basic course on
accelerator optics. Proceedings of the 1986 CERN
Accelerator School, Jycaskyla, Finland, CERN
87-1 http//doc.cern.ch/yellowrep/2005/2005-012/p5
5.pdf 2. Choose a lattice http//doc.cern.ch/ye
llowrep/2005/2005-012/p55.pdf 3. Decide phase
advance per cell 4. Calculate beta max and min 5.
Decide period geometry 6. Calculate beta max and
min 7. Calculate dispersion 8. Calculate
transition energy B. Errors
and corrections http//preprints.cern.ch/cgi-bin/s
etlink?basecernrepcategYellow_Reportid95-06_v
1 9. Identify sources of orbit distortion 10.
Correction of chromaticity 11. Effect of
errors 12. Identify sources of orbit
distortion 13. Acceptance required
C. Magnet and power supply http//preprints.c
ern.ch/cgi-bin/setlink?basecernrepcategYellow_R
eportid92-05 14. The magnet aperture - the most
expensive component 15. Calculating magnet stored
energy 16. Resonant power supply design
D. RF http//preprints.cern.ch/cernrep/2
005/2005-003/2005-003.html 17. RF Cavity tuning
(frequency swing) 18. Choice of RF frequency
(scaling) 19. Choice of RF voltage
(injection) 20. Bucket size for capture and
acceleration E. Collective
effects 21. Instability thresholds http//doc.cern
.ch/yellowrep/2005/2005-012/p139.pdf
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THE MOMENT OF TRUTH

• Adams, waiting for the first beam in the SPS,
  asks his team if they have remembered everything.