chromaticity dependence of the vertical effective impedance in the ps chromaticity dependence of the...

Chromaticity dependence of the vertical effective impedance in the PS

S. Persichelli

N. Biancacci, M. Migliorati, B. Salvant, G. Sterbini, S. Gilardoni, E. Metral, N. Wang

MSWG meeting19-06-2015

Agenda

Overview of the PS impedance model

How to measure the effective impedance in the PS

Tune shift measurement in 2012 at 1.4 and 25 GeV

Tune shift measurement in 2014 at 25 GeV

Impedance vs chromaticity measurement in 2014

Tune shift measurement in 2014-2015 at 2 GeV

Impedance model validation with measurement

Conclusions

PS impedance model

Includes contribution of: Indirect space charge Resistive wall Kickers Cavities Vacuum (flanges, valves, pumps, bellows) Wire scanner Elements installed in LS1 (dummy septum, longitudinal damper, stripline pickup)

All the impedances are weighted by the β function of the PS lattice

Impedance model computed at different energies (1.4, 2, 7, 13, 25 GeV) (Nicolo’)

Access at /afs/cern.ch/project/impedance/PS_impedance_database

PS Impedance webpage: http://impedance.web.cern.ch/impedance/

5

Total impedance model (2 GeV)At injection energy (2 GeV): Calculated 5.4 MΩ/m

Effective transverse impedance is defined as the impedance weighted by the transverse bunch power spectrum!

6

Total impedance model (25 GeV)At extraction energy (25 GeV): Calculated 2.2 MΩ/m

7

Agenda








Conclusions

How do we measure the transverse impedance

For a Gaussian bunch with rms bunch length , the tune shift is proportional to the imaginary part of the transverse effective impedance by:

∆𝑄=−𝛽𝑒 𝐼 0

4𝜎𝑧 √𝜋𝜔02𝑄0𝛾𝑚0

𝐼𝑚 {𝑍𝑇𝑒𝑓𝑓 }

𝑍𝑇𝑒𝑓𝑓=

∑𝑝

𝑍 𝑡 (𝜔 ′ )h(𝜔′−𝜔ξ)

∑𝑝

h(𝜔′−𝜔ξ)

The effective transverse impedance is defined as the impedance weighted by the transverse bunch power spectrum (Gaussian) centered at the chromatic frequency :

h (𝜔 )=𝑒−( 𝜔𝜎 𝑧

𝑐 )2

𝐼 0=𝑒𝑁𝑏

𝑇0

The impedance is always considered total!

9

Tune measurements in the PS

Coherent betatron tune: the number of

betatron oscillations per turn of the bunch center of mass

𝑄0=𝜔𝛽

𝜔0

Chirp signal is used to kick the beam

(single bunch)

The transverse position of the bunch centroid is acquired every turn by a

BPM

A diode detector converts the modulation of the BPM pulses,

related to beam oscillations, into a signal (AF range).

FFT

10

Agenda








Conclusions

Kinetic energy [] [ns]

1.4 GeV25 GeV

Measurements of the transverse impedance (2012)

∆𝑄∝− 𝐼𝑚 {𝑍 𝑇𝑒𝑓𝑓 }Aim of 2012 tune shift measurement: assess the effective impedance

budget at injection and extraction energy

12

Agenda








Conclusions

Tune shift measurements revealed an decrease of vertical impedance of 2 MΩ/m from 2012

No major changing for the impedance budget after LS1

We run few tests to try to repoduce this measurement

Change of excitation (chirp, kick)

Variation of bunch length

Orbit correction Last test: try to measure the tune

shift with different vertical chromaticity set on the machine working point

Tune shift measurements at 25 GeV (2014) 2/9/2014

3/9/2014

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟐 .𝟗±0 .02 ) 𝑀𝛺

𝑚

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟐 .𝟔±0 .04 ) 𝑀𝛺

𝑚

14

Agenda








Conclusions

Working point and chromaticity in the PS

A vertical chromaticity value was initially set using the PS working point application.

Vertical and horizontal tunes and horizontal chromaticity are kept to fixed value, figure-of-eight loop is kept to zero.

The setting is then remotely sent to the PFW in the ring.

Chromaticities in the PS can be measured by acquiring the tune shift while varying . Introducing a radial offset, we obtain a variation of the revolution frequency of the beam that generates a momentum offset.

Measurement of the vertical chromaticity are performed after each change in the working point to asses the effective value.

16

Measurements of the transverse impedance (2014)at different energies with chromaticity

3 energies considered For each energy, the impedance

corresponding to different chromaticities is computed from tune shift measurement.

The impedance is increasing with chromaticity!

17

Measurements of the transverse impedance (2014) at zero chromaticity

∆𝑄∝− 𝐼𝑚 {𝑍 𝑇𝑒𝑓𝑓 }

Kinetic energy [GeV] [] [ns]713 5525

25 GeV

7 GeV 13 GeV

18

Agenda








Conclusions

Tune shift measurement at 2GeV (2014)

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟖 .𝟏𝟗± 0 .18 ) 𝑀𝛺

𝑚

𝝃 𝒚 𝟎𝝃 𝒚 −𝟏

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟏𝟎 .𝟖𝟐±0 .35 ) 𝑀𝛺

𝑚

Measurement at 2 GeV revealed the same increasing trend with chromaticity

The tune measurement has not a good quality has for the other energies considered

The zero chromaticity value does not correspond to the value predicted by the model!

Need to repeat the measurement in 2015!20

Measurement at 2 GeV starting from March 2015. Large spread between tunes acquired at the same intensity. Machine strongly coupled on the two planes. Tune signal not symmetric respect with the direction of chirp excitation:

the impedance calculated from tune shift is different if we excite the tune in the range 0.2-0.3 or 0.7-0.8.

The impedance vs chromaticity trend of 2014 can’t be reproduced. Impedance calculated from tune shift at different chromaticities are

different every day.

Issues with tune shift measurement at 2 GeV (2015)

The measurement at 2 GeV is affected by the contribution of an “hidden player” of the machine that does not allow to measure the right tune!

21

Chirp excitation range

Chirprange [] [ns]0.2-0.30.7-0.8 111

𝝃 𝒚 −𝟏

Tune signal not symmetric respect with the direction of chirp excitation.

The impedance calculated from tune shift is different if we excite the tune in the range 0.2-0.3 or 0.7-0.8

22

Couple the PS beam with an LHC INDIV beam in the PSB, instead than a TOF

Shorter intensity range from 15-35 1010 More “ideal” beam with small emittance Harmonic tune signal, very peaked Smaller

Average on 100 tune points on the flat plateau reduction of spread between tunes at the same intensity

Change the current in the skew quadrupoles Coupling reduction Monitor instabilities!

Improvements of the tune shift measurement technique at 2GeV (2015)

TOF LHC INDIV

23

Effect on machine linear coupling

Current set on the skeq quadrupoles: +0.35 A – 0.35 A

Current set on the skeq quadrupoles(optimum): +0.39 A – 0.39 A

Fully coupled machine:-0.30 A + 0.30 A

24

Tune shift measurement at 2GeV (2015) with LCH_INDIV beam and no coupling

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟓 .𝟔±0 .22 ) 𝑀 𝛺

𝑚

𝝃 𝒚 𝟎

Measurement at 2 GeV revealed the increasing trend with chromaticity

The tune measurement has a good quality!

The zero chromaticity impedance correspond to the value predicted by the model for the 4 energies considered!

25

Agenda








Conclusions

25 GeV

7 GeV

13 GeV

2 GeV

Summary at zero chromaticity

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟓 .𝟔±0 .22 ) 𝑀 𝛺

𝑚𝐼𝑚 {𝑍 𝑦

𝑒𝑓𝑓 }=(𝟑 .𝟓±0 .13 ) 𝑀𝛺𝑚

𝐼𝑚 {𝑍 𝑦𝑒𝑓𝑓 }=(𝟑 .𝟎±0 .1 ) 𝑀 𝛺

𝑚𝐼𝑚 {𝑍 𝑦

𝑒𝑓𝑓 }=(𝟐 .𝟐±0 .1 ) 𝑀𝛺𝑚 27

Comparison between impedance model and effective impedance at zero chromaticity

Measurement Simulation2 5.6 ± 0.18 5.4 807.25 3.51 ± 0.13 2.54 5513.09 3.06 ±0.12 2.29 5525.48 2.23 ±0.05 2.20 45

Measurement and simulation are in excellent agreements (almost 100%) at 2 and 25 GeV!

At 7 and 13 GeV measurement and simulation are in very good agreement (70-80%)

Coupling is decreasing with the beam energy: measurement at 7 GeV were probably affected!

The transverse impedance model of the PS is fully validated by simulation and beam based measurement!

28

The indirect space charge contribution

2 GeV 7 GeV 13 GeV 25 GeV

𝑍𝑆𝐶𝑥 ,𝑦∝−

1

𝛾2

Measurement Simulation2 5.6 ± 0.18 5.4 3.37.25 3.51 ± 0.13 2.54 0.5913.09 3.06 ±0.12 2.29 0.3325.48 2.23 ±0.05 2.20 0.22

Tota

l mea

sure

d im

peda

nce

29

Agenda








Conclusions

Conclusions

The imaginary part of the vertical effective impedance of the PS has been

computed measuring the tune shift with intensity at different energies and zero

chromaticity.

The transverse impedance model of the PS has been validated at four different

energies with simulations and analytical methods.

The computed and the measured impedance model are in excellent agreement.

Tune shift measurement revealed that the impedance increases with

chromaticity for all the energies considered.

The tune measurement is very sensitive to machine coupling, especially at low

energies.

Tune measurements are reproducible working with a not coupled machine and a

LHC INDIV beam from the PSB

PublicationsJournals and proceedings : M. Migliorati, S. Persichelli et al., Beam-wall interaction in the CERN Proton

Synchrotron for the LHC upgrade, Phys. Rev. ST Accel. Beams 16, 031001, 2013. S. Persichelli, Trapped modes in a dummy extraction septum for CERN Proton

Synchrotron, Il Nuovo Cimento Vol. 37 C, N. 4, July 2014. N. Biancacci, S. Persichelli et al., Beam Coupling Impedance Localizing Technique

Validation and Measurements in CERN Machines, Proc. of IPAC13, 2013. S. Persichelli et al., The Proton Synchrotron Transverse impedance model, Proc. of

IPAC14, 2014. S. Persichelli et al., Impedance Studies of the Dummy Septum for CERN PS Multi-

turn Extraction, Proc. of IPAC14, 2014. S. Persichelli, M. Migliorati et al, Impedance Studies for the PS Finemet Loaded

Longitudinal Damper, Proc. of IPAC14, 2014. S. Persichelli, M. Migliorati, Beam coupling impedance simulation and RF

measurements of a passive extraction septum for particle absorbing in the CERN proton synchrotron, Atti della XX RiNEm 2014.

S. Persichelli, N. Biancacci et al., Chromaticity Dependence of the Transverse Effectivie Impedance in the CERN Proton Synchrotron , Proc. of IPAC15, 2015.

H. Damerau, M. Migliorati, S. Persichelli et al., Evaluation of the broadband longitudinal impedance of the CERN PS, CERN-ATS-Note-2012-064 MD, 2012.

S. Persichelli, M. Paoluzzi et al., Finemet cavity impedance studies, CERN-ACC-NOTE-2013-0033, 2013.

Thank you for your attention

How to build an impedance model

Get to know the machine elements:• Shape of the beam pipe• Cavities for acceleration• Magnets• Beam instrumentations…

Perform beam based measurements of the

global machine impedance

Perform simulations/ calculation/

measurements of the impedance contributors

Sum of the contributions to obtain the total

impedance

The impedance model is built

YES NOAre they in agreement?

!

Total impedance model (2 GeV)


At injection energy (2 GeV): Calculated} 5.4 MΩ/m Measured} (6 MΩ/m


At extraction energy (25 GeV): Calculated 2.2 MΩ/m Measured } (2 MΩ/m

chromaticity dependence of the vertical effective impedance in the ps chromaticity dependence of the...

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