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Stabilizing E-Lens for FCC-hh

Stabilizing E-Lens for FCC-hh. Alexey Burov Fermilab. Oct 19, 2017. AB. AB. by Sergey Arsenyev. Transverse Impedances. On top of that: CC HOM (the most dangerous) f=1.3GHz, Q=2.3 ×10 4 , R s = 3.7 / 65 MOhm/m. AB. Beam Parameters.

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Stabilizing E-Lens for FCC-hh

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  1. Stabilizing E-Lens for FCC-hh Alexey Burov Fermilab Oct 19, 2017 AB

  2. AB

  3. by Sergey Arsenyev Transverse Impedances On top of that: CC HOM (the most dangerous) f=1.3GHz, Q=2.3 ×104 , Rs= 3.7 / 65 MOhm/m AB

  4. Beam Parameters https://impedance.web.cern.ch/impedance/fcchbeam_dynamics_parameters.html AB

  5. How strong should be the instabilities? Growth times, rough numbers CB = coupled-bunch, SB = single-bunch AB

  6. How strong should be the instabilities? Growth times, rough numbers CB = coupled-bunch, SB = single-bunch AB

  7. How strong should be the instabilities? Growth times, rough numbers CB = coupled-bunch, SB = single-bunch AB

  8. How strong should be the instabilities? Growth times, rough numbers CB = coupled-bunch, SB = single-bunch AB

  9. How many octupoles? at 50 TeV FCC LHC AB

  10. What makes octupoles unsuitable Octupoles provide too little non-linearity where it is needed and too high where it is detrimental • Too many are needed • Unreliable: tail-sensitive • Vaccaro diagram reduction problem • Cannot vary from bunch to bunch • Dynamic aperture problems AB

  11. RF Quads ? RF Quads (A. Grudiev et al.) are novel interesting Landau elements. Their effectiveness is sensitive to predictability and reproducibility of the longitudinal tails of the bunches. DA reduction due to the synchro-betatron coupling? AB

  12. E-Lens as a Landau Element E-Lens can deliver nonlinearity just where it is needed: AB

  13. Vaccaro Stability Diagram, weak head-tail, No SC Stability diagram (VD) is defined as a map of real axes on the complex plane : To be stable, the coherent tune shift has to be below the SD. AB

  14. E-Lens Vaccaro Diagrams, round beam SDs for various lens sizes with the same max current density AB

  15. Vaccaro Diagrams for non-round beam VDs for non-round beams AB

  16. Possible e-lens parameters E-Lens parameters for the proton emittance 2.2 microns, at 50 TeV At the injection, the same tune shift is achieved at lower e-current. AB

  17. E-Lens Summary A standard, few meters long e-lens would do the job of 20 000 LHC-type octupoles for the LHC or FCC. E-lens SD is core-based, so it is robust E-Lens can vary along the train A problem of VD reduction can be fully excluded. AB

  18. Many thanks! AB

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