Status of the SPS impedance model C. Zannini, G. Rumolo, B. Salvant Acknowledgments: H. Bartosik, O.Berrig, G. Iadarola, E. Métral, N. Mounet, V.G. Vaccaro, Jose E. Varela

Overview Present SPS transverse impedance model Broadband impedance of step transitions Future update of the model SPS Longitudinal impedance model Summary

Present SPS transverse impedance model Elements included in the database: – Realistic model that takes into account the different SPS vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account – 19 kickers (CST 3D simulation) – 106 BPHs (CST 3D simulations) – 96 BPVs (CST 3D simulations) – 200 MHz cavities without couplers (CST 3D simulations) – 800 MHz cavities without couplers (CST 3D simulations) – Enamel flanges (CST 3D simulations) KickersBeam pipe BPH BPV TW 200MHz and 800MHz Enamel flanges

Evolution of the extraction kickers in the SPS

SPS vertical impedance model 5

SPS horizontal impedance model 6

Vertical coherent tune shift 100 % 20 % 40 % 60 % 80 % Present SPS impedance model reproduces about 70% of the vertical tune measured in the Q20 Present impedance model reproduces the instability behavior (H. Bartosik, Talk at the SPSU, 12 December 2013) Measurements performed in September 2012

Stability diagram: Q20 o Two regimes of instability in measurements Fast instability threshold with linear dependence on ε l Slow instability for intermediate intensity and low ε l o Excellent qualitative agreement with HEADTAIL simulations Slightly lower threshold in simulation (amplitude detuning or space charge?) LIU SPS-BD, 12. December measurementsHEADTAIL simulations 4.5x eVs nominal Island of slow instability H. Bartosik

Intra-bunch motion: Q20 (I) o Example for slow instability Clear indication for mode 1 in measurement Good agreement with HEADTAIL simulation LIU SPS-BD, 12. December measurementsHEADTAIL simulations H. Bartosik

Intra-bunch motion: Q20 (II) o Example for fast TMC instability Excellent agreement between measurements and simulation Travelling wave pattern clearly visible LIU SPS-BD, 12. December measurementsHEADTAIL simulations H. Bartosik

Horizontal coherent tune shift The kicker impedance model predicts a negative horizontal effective impedance (positive slope of the coherent tune shift) in agreement with the measurements Measurements performed in February 2013

Overview Present SPS transverse impedance model Broadband impedance of step transitions Future update of the model SPS Longitudinal impedance model Summary

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, CERN-THESIS Transverse Impedance

Broadband impedance of step transitions Weak dependence on L L

Broadband impedance of step transitions Weak dependence on L2 L2

Broadband impedance of step transitions L2 mm The imaginary part of the transverse impedance is weakly dependent on the cavity length below 1 GHz For all the SPS cavity like structures the first resonating mode is well above 1 GHz (r<80 mm)

Broadband impedance of step transitions L2

Courtesy of Jose E. Varela Broadband impedance of step transitions Flange Type EnamelBellow N um. of elements Resistor BPV-QDYes 90No BPH-QFYes 39Long QF-MBAYes 83Short MBA-MBAYes 14Short QF-QFNoYes26Short QD-QDYesNo99No QF-QFNo 20No BPH-QFYes 39Long QD-QDNo 75No QD-QDYesNo99No

Vertical coherent tune shift 100 % 20 % 40 % 60 % 80 % Step transitions seem to explain almost the totality of the missed tune shift

SPS Pumping port SPS Pumping port shielding Pumping ports 2000 Impedance reduction campaign: shielding of the pumping ports, lepton cavities etc.)

Estimation of the broadband impedance of unshielded transitions between bending magnets and straight sections 744 step transitions: – 377 MBA-Straight A – 377 MBB-Straight B Imag [ Z y (f=0) ]= 11.8 MΩ/m Measured13.1 Expected (only from transitions in the magnets) 11.8

Overview Present SPS transverse impedance model Broadband impedance of step transitions Future update of the model SPS Longitudinal impedance model Summary

New elements to be added in the model Simulations are ongoing or must be finalized – Septa – Wire scanner – Non standard elements (special transitions, valves) Update due to future installations – New wire scanner – New kicker for high bandwidth feedback system – New MSI-V septum

Overview Present SPS transverse impedance model Broadband impedance of step transitions Future update of the model SPS Longitudinal impedance model Summary

Status of the SPS longitudinal impedance model Elements included in the database: – Realistic model that takes into account the different SPS vacuum chambers weighted by the respective length and beta function. Also the iron in the magnet is taken into account – 19 kickers (CST 3D simulation) Kickers Wall impedance

Longitudinal wall impedance Calculation performed with ImpedanceWake2D

Longitudinal impedance

SPS impedance in total LIU-SPS BD Meeting, 24th October f r (GHz)R sh (MOhm)QR/Q (kOhm) BPMs Zs (?) 200 MHz HOM Flanges + cavity & kicker impedance Courtesy H. Timko

Overview Present SPS transverse impedance model Broadband impedance of step transitions Future update of the model SPS Longitudinal impedance model Summary

Summary and next steps The SPS impedance model (kicker, wall, cavities, BPMs) explains about 70% of the measured vertical coherent tune shift Transition pieces seem to be able to explain the remaining 30% More realistic model of transition pieces Update of the model including septa and wire scanner Continuously update of the model according to new installations and modifications

Thank you for your attention

F. Caspers, T. Kroyer, M. Barnes, E. Gaxiola et al. 32 Serigraphy Seven out of eight SPS extraction kickers have been serigraphed Realistic models: SPS extraction kicker (MKE-L)

Realistic models: MKE kicker with serigraphy

f=44 MHz Comparing MKE with and without serigraphy

The peak observed in the MKE with serigraphy is a quarter-wavelength resonance on the finger length Comparing MKE with and without serigraphy

The trend of the vertical effective impedance along the last 10 years is in good agreement with the expected changing of the kicker impedance model Kickers play a major role in the SPS total impedance Evolution of the extraction kickers in the SPS: vertical tune shift

The trend of the horizontal effective impedance along the last 10 years is in good agreement with the expected changing of the kicker impedance model Kickers play a major role in the SPS total impedance Evolution of the extraction kickers in the SPS: horizontal tune shift