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Limits on Chromaticity Correction

This workshop explores the limitations of chromaticity correction in the upgrade of the CERN and GSI Accelerator Complex, and discusses possible solutions such as local and global linear and nonlinear chromaticity correction techniques.

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Limits on Chromaticity Correction

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  1. LHC LUMI 2006 CARE-HHH-APD Workshop on Towards a Roadmap for the Upgrade of the CERN & GSI Accelerator Complex Limits on Chromaticity Correction A. Faus-Golfe, R de Maria and R. Tomás García LHC LUMI 06

  2. Linear Chromaticity Correction the limitation comes from the limit of the sextupole strength directly related to bmax Limits on Chromaticity Correction Problems when: bmax < 20 km Q’ < -275 LHC LUMI 06

  3. Limits on Chromaticity Correction LHC LUMI 06

  4. Linear Chromaticity Correction Limits on Chromaticity Correction LHC LUMI 06

  5. Linear Chromaticity Correction Possible solutions: Limits on Chromaticity Correction Local Chromaticity Correction Global Nonlinear Chromaticity Correction LHC LUMI 06

  6. Local Chromaticity Correction Final Focus Limits on Chromaticity Correction but energy spread introduces chromaticity, which must be corrected with sextupoles If there would be no energy spread in the beam, a telescope could serve as final focus In a thin section of a quadrupole of infinitesimal length the particle receives an angular kick: chromaticity LHC LUMI 06

  7. Local Chromaticity Correction Limits on Chromaticity Correction Kick for off-momentum particles in the sextupole: if 2nd order chromaticity aberrations Correction of the chromaticity introduces geometric aberrations LHC LUMI 06

  8. Local Chromatic Correction • Chromaticityis cancelledlocallyby two sextupolesinterleaved with FD, a bend upstream generates dispersion across FD • Geometric aberrationsof the FD sextupoles are cancelled by two more sextupoles placed in phase with them and upstream of the bend Limits on Chromaticity Correction LHC LUMI 06

  9. Local Chromaticity Correction Problems with: • Anti-symmetriy of the insertions • Non vanishing Dxin the insertions • No space Limits on Chromaticity Correction Difficult solution if it is not designed from the beginning (as ILC or CLIC) LHC LUMI 06

  10. Global Nonlinear Chromaticity Correction Limits on Chromaticity Correction octupoles, decapoles… sextupole families individually powered LHC LUMI 06

  11. Note: DA studies for identifying the most dangerous multipole components in the triplet/doublet quadrupoles (b6, b10) and first dipoles (b3,b5) could be very useful for doing a multipole compensation scheme to ameliorate the DA Limits on Chromaticity Correction LHC LUMI 06

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