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COURSE SUMMARY HT 2011 E. J. N. Wilson

LECTURE 33. COURSE SUMMARY HT 2011 E. J. N. Wilson. Putting “it” together. The SPS Design Committee get down to business (1971). The LHeC Conceptual Design. Physics Case. LHC parameters. Beam Parameters. Space charge Q shift. Radial force equals rate of change of momentum.

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COURSE SUMMARY HT 2011 E. J. N. Wilson

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  1. LECTURE 33 COURSE SUMMARY HT 2011 E. J. N. Wilson

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

  3. The LHeC Conceptual Design

  4. Physics Case

  5. LHC parameters

  6. Beam Parameters

  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. Insertion

  12. 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

  13. Parameters of the Magnets

  14. Magnet design

  15. 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

  16. 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)

  17. 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 :

  18. 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

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

  20. Synchrotron radiation Total instantaneous power radiated by one electron Energy Loss per turn (per electron) Power radiated by a beam of average current Ib

  21. 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!

  22. Radiation integrals Energy loss per turn Damping times Emittance and Partition

  23. Instability • Keil Schnell stability criterion:

  24. 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

  25. 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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