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 εl

• Slow instability for intermediate intensity and low εl

o Excellent qualitative agreement with HEADTAIL simulations • Slightly lower threshold in simulation (amplitude detuning or space charge?)

LIU SPS-BD, 12. December 2013 8

measurements HEADTAIL simulations

4.5x1011 p/b @ 0.35 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 2013 9

measurements HEADTAIL 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 2013 10

measurements HEADTAIL 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, 2013. CERN-THESIS-2013-076.

Transverse Impedance

Broadband impedance of step transitions

Weak dependence on L

L

i

N

i

istransition nZZ

1

ImIm

1Im Z

1Im2Im

ZZ

1Im Z

22

11

bdZ i

Broadband impedance of step transitions

Weak dependence on L2

L2

1Im2Im

ZZ

1Im Z

1Im Z

22

11

bdZ i

i

N

i

istransition nZZ

1

ImIm

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

0 fZZ eff

mz 25.0

Courtesy of Jose E. Varela

Broadband impedance of step transitionsFlange Type Enamel Bellow Num. of

elementsResistor

BPV-QD Yes Yes 90 No

BPH-QF Yes Yes 39 Long

QF-MBA Yes Yes 83 Short

MBA-MBA Yes Yes 14 Short

QF-QF No Yes 26 Short

QD-QD Yes No 99 No

QF-QF No No 20 No

BPH-QF Yes Yes 39 Long

QD-QD No No 75 No

QD-QD Yes No 99 No

Vertical coherent tune shift

100 %

20 %

40 %

60 %

80 %

Step transitions seem to explain almost the totality of the missed tune shift

SPS Pumping portSPS Pumping port shielding

Pumping ports

effeff yy ZZ 20012000 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 [ Zy(f=0) ]= 11.8 MΩ/m

effeff yy ZZ 20012000

Measured 13.1

Expected (only from transitions in the magnets)

11.8

mM /

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)

KickersWall impedance

Longitudinal wall impedance

Calculation performed with ImpedanceWake2D

Longitudinal impedance

28

SPS impedance in total

LIU-SPS BD Meeting, 24th October 2013

fr (GHz) Rsh (MOhm) Q R/Q (kOhm)

0.629 0.388 500 0.78

0.885 0.0146 482 0.030

0.892 0.0198 493 0.040

1.052 0.1597 773 0.207

1.062 0.1903 773 0.246

1.069 0.0454 654 0.069

1.092 0.0570 667 0.085

1.185 0.0116 610 0.019

1.215 0.0012 624 0.002

1.598 0.0426 672 0.063

1.613 0.5975 686 0.871

1.859 0.2951 896 0.329

1.960 0.0721 1993 0.036

0.550 0.2275 1000 0.228

1.050 0.2275 1250 0.182

1.41 1.871 210 8.91

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 MHzfinger

effeff

Lm.f

c4780

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