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## Updated status of the PSB impedance model

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**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 • 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**Impedance calculations for b < 1**Analytical calculation (applies only to simple structures) 3D EM simulations (CST Particle Studio) In the LHC, SPS, PS CST EM simulations are performed in the ultra-relativistic approximation (b = 1) The use of 3D EM simulations for b < 1 is not straightforward at all**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 C. Zannini et al. Electromagnetic Simulations for Non-ultrarelativistic Beams and Application to the CERN Low Energy Machines, IPAC14, to be published**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**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**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**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**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**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**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**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**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**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**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**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**Indirect space charge: refinement of the calculation**Using numerical form factors**Indirect space charge: refinement of the calculation**Using numerical form factors**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**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**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**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**A theoretical calculation for the C-Magnet model**is the impedance calculated using the Tsutsui formalism Constant horizontal impedance**PSB extraction kicker: impedance due to the ferrite loaded**structure ZM Vertical**PSB extraction kicker: impedance due to the coupling to the**external circuits ZTEM Horizontal Cables in the open-short configuration**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**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.**Broadband impedance of step transitions**L Weak dependence on the relativistic beta and L**Broadband impedance of step transitions**L Weak dependence on the relativistic beta and L**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**Analytical model: axially symmetric multilayer structure**Assuminguniformity of the coatingthickness Resistance of the coating The beamcouplingimpedancestronglydepends on the resistance of the coating**KSW magnets**R=8 Ω Vertical**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**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 (analytical calculation) • Broadband impedance of step transitions • KSW magnets Beam pipe Extraction Kicker KSW Indirect space charge impedance Step transitions**Total horizontal driving impedance of the PSB**E E Contributions of the extraction kicker due to the coupling with external circuits**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**Measurement data**D. Quatraro, Collective effects for the LHC injectors: non-ultrarelativisticapproaches. PhD thesis, Bologna, University of Bologna, 2011. CERN-THESIS-2011-103.**Effective impedance of the PSB**Measurements at different energies are consistent with a missing ~2 MΩ/m**Comparison between measurements and model of the vertical**coherent tune shifts at different energies**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**Summary and future plans**• Measurements at different energies are consistent with a missing ~2 MΩ/m of the PSB impedance model • Measurements of the coherent horizontal and vertical tune shift • Update of the model according to new understandings and identification of significant impedance sources • Using the PSB impedance model for beam dynamics studies**Additional impedance studies not discussed here**• Impedance model of the new H- injection region • Comparison between Inconel undulated chamber and titanium coated ceramic chamber • Pumping ports • Foil section • Finemet cavities • The longitudinal impedance does not depend on the relativistic beta • Impedance of insulated flanges with and without RF bypass**Resistive wall impedance: impact of the iron**Resistive wall vertical generalized impedance of the PSB