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COURSE SUMMARY A Design Study of a Compressor ring for A Neutrino Factory MT 2009

This lecture summarizes the design study of a compressor ring for a neutrino factory, including discussions on parameters, magnet design, RF cavity tuning, and collective effects. It provides valuable insights for students and researchers in accelerator physics.

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COURSE SUMMARY A Design Study of a Compressor ring for A Neutrino Factory MT 2009

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

  2. Putting “it” together • The SPS Design Committee get down to business (1971)

  3. SPL

  4. SPL Output Parameters – for the neutrino factory

  5. Neutrino Factory Demands Specifications (from R. Palmer’s conclusion at ISS meeting in RAL on Thursday 27, April 2006)

  6. Accumulate and Compress Scenario

  7. Space charge Q shift • Radial force • equals rate of change of momentum

  8. Smooth approx. - choosing No. of periods

  9. Period geometry • Everything must add up for the ring

  10. 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

  11. Basic Cell of the C0mpressor

  12. Insertion for 3 Bunch Compressor

  13. Compressor Lattice • Your Christmas Present!

  14. 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

  15. Parameters of the Magnets of the Compressor

  16. Magnet design

  17. 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

  18. 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)

  19. 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 :

  20. 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 • But check synchrotron wave number < 0.1

  21. Synchrotron motion (continued) • This is a biased rigid pendulum • For small amplitudes • Synchrotron frequency • Synchrotron “tune”

  22. The bunch and bucket at start of rotation

  23. 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!

  24. Instability • Keil Schnell stability criterion:

  25. Some parameters of accumulator and compressor Table 6: Main parameters of the accumulator and compressor for a neutrino factory

  26. LHC parameters

  27. 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/p55.pdf 2. Choose a lattice http://doc.cern.ch/yellowrep/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/setlink?base=cernrep&categ=Yellow_Report&id=95-06_v1 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.cern.ch/cgi-bin/setlink?base=cernrep&categ=Yellow_Report&id=92-05 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/2005/2005-003/2005-003.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

  28. THE “MOMENT OF TRUTH” • Adams, waiting for the first beam in the SPS, asks his team if they have remembered everything.

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