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Updated status of the PSB impedance model   

Updated status of the PSB impedance model   . C. Zannini and G. Rumolo Thanks to: E. Benedetto, N. Biancacci, E. Métral , B. Mikulec , N. Mounet, T. Rijoff , B. Salvant , W. Weterings. Overview. Introduction Present PSB impedance model Indirect space charge

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Updated status of the PSB impedance model   

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  1. Updated status of the PSB impedance model    C. Zannini and G. Rumolo Thanks to: E. Benedetto, N. Biancacci, E. Métral, B. Mikulec, N. Mounet, T. Rijoff, B. Salvant, W. Weterings

  2. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  3. Impedance calculations for b < 1 Analytical calculation (applies only to simple structures) 3D EM simulation (CST Particle Studio) In the LHC, SPS, PS CST EM simulation are performed in the ultra-relativistic approximation (b = 1) The use of 3D EM simulations for b < 1 is not straightforward at all

  4. 3D CST EM simulation for b < 1 Depend only on the source contribution due to the interaction of beam and external surroundings • To single out the impedance contribution the direct space charge must be removed

  5. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  6. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account Beam pipe

  7. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) Beam pipe Kickers

  8. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) • Indirect space charge impedance Beam pipe Kickers Indirect space charge impedance

  9. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) • Indirect space charge impedance Beam pipe Kickers Indirect space charge impedance

  10. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) • Indirect space charge impedance Beam pipe Kickers Indirect space charge impedance

  11. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) • Indirect space charge impedance Beam pipe Kickers Indirect space charge impedance

  12. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) • Indirect space charge impedance • Broadband impedance of step transitions Beam pipe Kickers Indirect space charge impedance Step transitions

  13. Present PSB transverse impedance model • Elements included in the database: • Analytical calculation of the resistive wall impedance that takes into account the different PSB vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account • Extraction kicker • impedance due to the ferrite loaded structure • impedance due to the coupling to the external circuits(analytical calculation) • Indirect space charge impedance • Broadband impedance of step transitions • KSW magnets Beam pipe Extraction Kicker KSW Indirect space charge impedance Step transitions

  14. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  15. Indirect space charge Analytical calculation based on the PSB aperture model (provided by O. Berrig) [a, b, L, βx , βy , Apertype]i Rectangular pipe Circular pipe K. Y. Ng, Space charge impedances of beams with non-uniform transverse distributions Elliptic pipe

  16. PSB: indirect space charge impedance

  17. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  18. Indirect space charge: refinement of the calculation Using numerical form factors

  19. Indirect space charge: refinement of the calculation Using numerical form factors

  20. PSB: indirect space charge impedance

  21. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  22. Resistive wall impedance Analytical calculation based on the PSB aperture model (provided by O. Berrig) [a, b, L, βx , βy , Apertype]i Calculation performed with the TLwall code

  23. Resistive wall impedance Analytical calculation based on the PSB aperture model (provided by O. Berrig) Vertical [a, b, L, βx , βy , Apertype]i Calculation performed with the TLwall code

  24. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  25. A theoretical calculation for the C-Magnet model is the impedance calculated using the Tsutsui formalism Constant horizontal impedance

  26. PSB extraction kicker: impedance due to the ferrite loaded structure ZM Vertical

  27. PSB extraction kicker: impedance due to the coupling to the external circuits ZTEM Horizontal Cables in the open-short configuration

  28. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  29. Broadband impedance of a step transition • Based on the results of 3D EM simulations, the broadband impedance contribution due to an abrupt transition is independent of the relativistic beta. Therefore, based on the aperture model, the generalized broadband impedance of the PSB transitions has been calculated as: C. Zannini, Electromagnetic simulations of CERN accelerator components and experimental applications. PhD thesis, Lausanne, EPFL, 2013. CERN-THESIS-2013-076.

  30. Broadband impedance of step transitions L Weak dependence on the relativistic beta and L

  31. Overview • Introduction • Present PSB impedance model • Indirect space charge • Numerical form factor for ISC computation • Resistive wall • Extraction kicker • Broadband impedance of step transitions • KSW • Global PSB impedance model • Comparison with tune shift measurements • Summary and future plans • Other devices studied • Shielding of pumping ports • Insulated flanges

  32. 3D model of the KSW kicker

  33. Coating of the ceramic chamber

  34. Coating of the ceramic chamber

  35. Analytical model: axially symmetric multilayer structure Assuminguniformity of the coatingthickness Resistance of the coating The beamcouplingimpedancestronglydepends on the resistance of the coating

  36. Effect of the ceramic chamber on the KSW longitudinal impedance Titaniumcoating The shielding (coatedceramicchamber) stronglyreduces the longitudinal impedance

  37. Effect of the ceramic chamber on the KSW longitudinal impedance Real part of the longitudinal impedance

  38. Effect of the ceramic chamber on the KSW longitudinal impedance Real part of the longitudinal impedance Titaniumcoating Minimum R defined by the required kicker rise time

  39. Effect of the ceramic chamber on the KSW longitudinal impedance Real part of the longitudinal impedance Increasing the coatingresistance the impedanceshould converge to the case withoutcoating

  40. Effect of the ceramic chamber on the KSW transverse impedance

  41. Effect of the ceramic chamber on the KSW transverse impedance Increase of the impedance due to the smaller aperture

  42. Effect of the ceramic chamber on the KSW transverse impedance The coating shifts the impedancespectrum to lowerfrequencies

  43. Effect of the ceramic chamber on the KSW transverse impedance The frequency shift isproportional to the coatingresistance

  44. Effect of the ceramic chamber on the KSW transverse impedance Real part of the transverse impedance fr The frequency shift isproportional to the coatingresistance

  45. Effect of the ceramic chamber on the KSW transverse impedance

  46. KSW: transverse impedance optimization Shift the KSW impedancespectrum out of the PSB frequency range of interest Frequency range of interest First possible unstable betatron line Maximum frequency excited by the beam

  47. KSW: transverse impedance optimization Shift the KSW impedancespectrum out of the PSB frequency range of interest Frequency range of interest First possible unstable betatron line Maximum frequency excited by the beam Worst case at extraction (smallest bunch length)

  48. Determination of fbeamfor a generic element of impedance Z Normalizedbeam power spectrum

  49. Determination of fbeam: example for the KSW transverse impedance

  50. KSW: transverse impedance optimization Frequency range of interest Shift of the KSW impedancespectrumsignificantly out of the PSB frequency range of interest

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