11 Update of the SPS impedance model G. Arduini, O. Berrig, F. Caspers, A. Grudiev, E. Métral, G....

11

Update of the SPS impedance model

G. Arduini, O. Berrig, F. Caspers, A. Grudiev, E. Métral, G. Rumolo, B. Salvant, E. Shaposhnikova, B. Spataro (INFN), C. Zannini, B. Zotter.

Acknowledgments:M. Barnes, C. Boccard, T. Bohl, R. Calaga, J. Evans, H. Damerau, E. Jensen, G.

Papotti,R. Tomas, R. Steinhagen, OP teams,

M. Balk (CST AG),

L. Haenichen, W. Mueller (TU Darmstadt)

Machine Studies Working Group - January 15th, 2009

2

Update of the SPS impedance model

• Context

– LHC intensity upgrade scheme requires 4 or 5 1011 protons per bunch (p/b)

– For instance, fast transverse instability limits bunch intensity to less than 2 1011 p/b (with nominal parameters)

SPS transverse impedance will be one of the bottlenecks to produce 4 1011 p/b

– Ongoing work to identify the major SPS impedance contributors propose possible SPS hardware modifications (such as the large campaign to shield the vacuum pumping ports in 99/01 or

the MKE kicker shielding campaign from 2006).

• Objectives of this talk(Focus has been mainly on transverse impedance)

– Stress the importance of separating the dipolar and quadrupolar impedance contributions

– Use new tools to obtain the impedance and wakes of SPS components (theory and simulations) Example of the SPS kickers, BPMs and beam pipe

– Status of the current transverse impedance model and comparison with measurements

– Next steps

3

Agenda

• Separating the dipolar and quadrupolar impedance contributions.

• Use new tools to obtain the impedance and wakes of SPS components

• Status of the current transverse impedance model and comparison with beam measurements

• Next steps

4

Separating the dipolar and quadrupolar impedance contributions

• Dipolar and quadrupolar contributions (resp. driving and detuning contributions)linearization of the wake dependence with the source (1) and witness (2) transverse locations

y

sz

2

1

Accelerator element

y2

y1

In general, we assume we can expand the wake anywhere in a transverse cross section with powers of x and y

Total vertical wake:

n

lkji

lkjilkjitoty xyxyzAzyxyxW

0,,,2211,,,2211, )(),,,,(

Then we classically: (1) assume top/down and bottom/left symmetries (2) linearize for small displacements(3) assume no coupling between the horizontal and vertical plane

n

lkji

lkjilkjitoty xyxyzAzyxyxW

1,,,2211,,,2211, )(),,,,((1) with i,j,k,l odd numbers

22112211, )()()()(),,,,( yzDxzCyzBxzAzyxyxW toty (2)

(3) 212211, )()(),,,,( yzDyzBzyxyxW toty

2,1,21, )()(),,( yzWyzWzyyW quadydipytoty

Dipolar wake Quadrupolar wakeTotal wake

5

Why is it important to separate the dipolar and quadrupolar impedance contributions?

• dipolar wake leads to coherent oscillations of all particles in the bunch dipolar wake drives coherent instabilities

• quadrupolar wake leads to oscillations that depends on the individual particle’s amplitude quadrupolar wakes leads to incoherent effects (damping and emittance growth)

y

sz

2

1

Accelerator element

y2

y1



Very different impact on beam dynamics!

Vertical coherent motion Vertical beam size

Example:HEADTAILsimulation of abunch interactingwith- only dipolar- dip + quad

Quadrupolar Damping Quadrupolar emittance growth

6

Agenda


• Use new tools to obtain the impedance and wakes of SPS components– General framework to obtain an SPS impedance model

– Example of the impedance of the SPS ferrite kickers


• Next steps

77

General framework to obtain the impedance model of a machineOverview for the case of the SPS

Measured observables(Tune shift, Instability threshold…)

Analytical Calculations

ElectromagneticSimulations

BenchMeasurements

Impedance of a single SPS element

Wake potential of asingle SPS element

Impedance of a single SPS element

Wake function of a single SPS element



iDFT iDFTdeconvolution

“Total” SPS Wake function

SPS machine measurements

Sum for all available SPS elements

Headtail macroparticle simulations

Simulated observables(tune shift, instability threshold…)

How much of the measured transverse impedance is accounted for in the model? Which are the main transverse impedance contributors?

?

Accounting for the respective beta functions

MADXHEADTAIL simulates the dynamics of a bunch of macroparticles interacting with an impedance model

8

Agenda


• Use new tools to obtain the impedance and wakes of SPS components– General framework to obtain an SPS impedance model

– Example of the impedance of the SPS ferrite kickers


• Next steps

9

• Context:– SPS beam based measurements over the years

SPS ferrite kickers suspected to be major contributors to the transverse SPS impedance.

– Method to obtain the impedance of the SPS kickers: 1. Compute impedance for a cylindrical ferrite beam pipe with Zotter/Métral model 2. Multiply it by constant form factors to obtain the dipolar and quadrupolar impedance contributions for a flat chamber beam pipe.

– Analytical dipolar impedance agrees with bench measurements of SPS kickers…

– …However, 1. Form factors can only be applied if the field penetration in the material is smaller than the aperture,

which is not the case for the dielectrics and ferrites.2. negative total horizontal impedance measured on PS kickers on a bench

negative total horizontal impedance measured with beam in the SPS Quadrupolar impedance of the kickers suspected to be underestimated

– Tsutsui formalism also exists, but only dipolar impedance is available

• New tools:– new theoretical formulae for the quadrupolar impedance in the frame of Tsutsui formalism– New 3D simulations of the dipolar and quadrupolar impedance of kickers

Transverse impedance of simple models of kickersContext and objectives

Transverse dipolar impedance: theory (Zotter/Metral) and 2 wire-measurement (Caspers, Gaxiola, Kroyer)

SPS impedance, Metral et al., BEAM 07

1010

Transverse impedance of simple models of kickersNew quadrupolar contribution

• New quadrupolar impedance was derived from the electromagnetic fields derived by Tsutsui for the longitudinal impedance (same source charge distribution)

Analytical impedance for 1 MKE kicker

not possible to apply constant factors to relate the dipolar and quadrupolar contributions Which theory is valid? benchmark with 3D bench measurements

Re(Z) is thickIm(Z) is dashed

1111

Transverse impedance of simple models of kickersCST Particle Studio 3D simulations

Strategy to obtain dipolar and quadrupolar wake potentials from time domain CST simulations

y

x

Wy dipolar

Wake integrationBeam

y

x

Wy quadrupolar

CST Particle Studio is a commercial code that simulates the wake potentials from 3D models

3D kicker model Kicker structure



1212


1.7 million mesh cellsSimulated Rms Bunch length 2 cm

Vertical electric field

1313


DFT

1.7 million mesh cellsSimulated Rms Bunch length 2 cm

Let’s compare with the theory…

1414

Transverse impedance of simple models of kickersComparison between theory (with new quadrupolar) and new simulations

(1) Good agreement between Tsutsui’s dipolar and the new quadrupolar impedance theories with impedance obtained from 3D simulations

(2) This confirms that we should not use the constant form factors for kickers(3) Gives more confidence in the new theory and in the CST simulations(4) |Im(Zx quad)| > Im(Zx dip) as predicted by previous measurements

15

Comparison between Tsutsui, Zotter/Metral and 2 wire measurements

Tsutsui

Tsutsui formula much lower than both 2 wire measurements and Zotter/Metral formula we still need to understand this difference refine the simple kicker model (cells, external circuits, gaps) redo experiments with a focus on getting both the dip and quad impedance

16

Agenda




• Next steps

17

Wake function for the updated impedance model

0 0.5 1 1.5 2 2.5 3-10

0

10

20

30

40

Time delay behind the source charge (in ns)

Wak

e fu

nctio

n in

V/(

pC.m

m)

Vertical quadrupolar wake function

Kickers (Tsutsui model)Kickers + BPMsKickers + BPMs + beam pipe

0 0.5 1 1.5 2 2.5 3-10

0

10

20

30

40


Wak

e fu

nctio

n in

V/(

pC.m

m)

Horizontal dipolar wake function


0 0.5 1 1.5 2 2.5 3-40

-30

-20

-10

0

10


Wak

e fu

nctio

n in

V/(

pC.m

m)

Horizontal quadrupolar wake function


0 0.5 1 1.5 2 2.5 3-10

0

10

20

30

40


Wak

e fu

nctio

n in

V/(

pC.m

m)

Vertical dipolar wake function


horizontal

Vertical

dipolar quadrupolar

Kickers is the largest single bunch contribution BPMs leads to significant oscillations beam pipe mostly affects the very short range and the multibunch

SPS bunch length (4)

into HEADTAIL

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0 5 . 1 0 10 1 . 1 0 11 1 .5 1 0 11 2 . 1 0 11 2 .5 1 0 11 0 .0 0 1

0 .0 0 0

0 .0 0 1

0 .0 0 2

0 .0 0 3

0 .0 0 4

0 .0 0 5

N b 1 0 9 pbG

row

thR

ate1turns

N b 0 1 8 4 pb0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

0 .0 0 4

0 .0 0 2

0 .0 0 0

0 .0 0 2

0 .0 0 4

N u m b e r o f T u rn s

y

N b 0 1 7 8 pb0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

0 .0 0 4

0 .0 0 2

0 .0 0 0

0 .0 0 2

0 .0 0 4


y

N b 0 1 4 pb0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

0 .0 0 4

0 .0 0 2

0 .0 0 0

0 .0 0 2

0 .0 0 4


y

N b 0 7 4 pb0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

0 .0 0 4

0 .0 0 2

0 .0 0 0

0 .0 0 2

0 .0 0 4


y

Simulated growth rate Vs bunch populationfor all kickers

Horizontal

Vertical

Coherent position <y>

Exponential fit

Vertical coherent motion <y> for selected bunch populations

N b 0 1 5 8 pb0 2 0 0 0 4 0 0 0 6 0 0 0 8 0 0 0

0 .0 0 4

0 .0 0 2

0 .0 0 0

0 .0 0 2

0 .0 0 4


y

HEADTAIL simulations with all the kickers (2006 situation)

Nb=74 109 p/b

Nb=14 109 p/b

Nb=158 109 p/b

Nb=178 109 p/b

Nb=184 109 p/b

1919

HEADTAIL simulation with the current SPS impedance model

positive horizontal tune shift, as observed in SPS beam measurements since many years! observed vertical tune is carried by several coherent modes until the instability

All SPS kickers in 2006 (Tsutsui model)

0 5 . 1 0 10 1 . 1 0 11 1 .5 1 0 11 2 . 1 0 11 2 .5 1 0 11 0 .0 0 1

0 .0 0 0

0 .0 0 1

0 .0 0 2

0 .0 0 3

0 .0 0 4

0 .0 0 5

N b 1 0 9 pbG

row

thR

ate1turns

Simulated growth rate Vs bunch populationfor all kickers

Horizontal

Verticalsmall couplingbetween

modes 0 and -1

medium coupling?between

modes -2 and ?

large coupling?between

modes -3 and ?

2020

HEADTAIL simulation with the current SPS impedance model

positive horizontal tune shift, as observed in SPS beam measurements since many years! observed vertical tune is carried by several coherent modes until the instability

BPMs + beam pipe+ kickers (Tsutsui model for the kickers)

2121

Mode spectrum of the vertical coherent motion as a function of bunch current

Measured with an SPS single bunch

Measured spectral linesMax spectral line2nd max spectral line

..

Fast transverse instability in the SPS Measurements (2007) and HEADTAIL simulations: mode spectra

Vertical tune shift with intensity strong sidebands even at low currents (most likely non zero chromaticity) complicated behaviour of the main mode and the second mode. Indication that the mode that leads to the instability is not mode 0

Also see APC 24/10/2008

22

History of the transverse impedance of kickers over the years: theory, simulations and measurements for the whole machine

Im(Zeff) [M/m]

Tune shift Measurement

Theory kickers

(Sacherer)

Simulation

Kickers

(Tsutsui)

Simulation

Kickers+BPMs+beam pipe

(Tsutsui)

2001 19.1 3.5 3.6 7.2

2003 22.2 6.4

2006 23.6 8.7 9.0 12.8

2007 22

2008 22

+5MKE

+4MKE

From HEADTAIL simulations, improved SPS impedance model accounts for:- 55% of the measured vertical SPS tune shift and main instability threshold- 90% of the measured horizontal SPS tune shift

Need to include serigraphed kickers

dipolar=2/3 total dipolar<1/2 total dipolar<1/2 total

Tune shift is “proportional” to the total impedance, but proportion of dip and quad impedance?

+4.5 +5.2 +5.4 +5.6

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Agenda




• Conclusions and next steps

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Conclusions

• It is important to separate the dipolar and quadrupolar impedance contributions. The dipolar impedance drives coherent instabilities The quadrupolar impedance damps coherent motion and leads to emittance growth.

• New tools: example of kickers– New theoretical formulae for the quadrupolar impedance in the frame of Tsutsui formalism– New 3D simulations of the dipolar and quadrupolar impedance of simple models of kickers– Good agreement between theory and simulations!– Method with constant form factors is valid for good conductors but should not be applied for

kickers

• From HEADTAIL simulations, improved SPS impedance model accounts for: 55% of the measured vertical SPS tune shift and main instability threshold 90% of the measured horizontal SPS tune shift

• Complicated wake function leads to complicated mode spectrum. Monitoring the tune shift only gives information on the total impedance, when

the main objective is reducing instabilities i.e. minimizing the dipolar impedance.

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Ongoing work and next steps

• Refine current impedance models for the kickers (cells, serigraphy, external circuits,etc.) Carlo Zannini, Hugo Day et al

• Dipolar and quadrupolar simulations and/or measurements of other potential sources of impedance (pumping ports, RF cavities)

Olav Berrig, Bruno Spataro et al

• Include new theories and simulations to improve the longitudinal impedance model together with BE/RF-BR.

• Implement this framework to obtain the LHC impedance model Nicolas Mounet et al

• Continue to follow the changes of hardware to trace the impedance sources

• Use localization of impedance technique to identify impedance contributors. Rama Calaga et al

• Implement the effect of the wake in front of the bunch in HEADTAIL.

2626

Thank you very much for your attention!

27

Tsutsui

28

Wake functions from theory and wake potentials from simulations for all SPS kickers (2006 situation)

Simulated rms bunch length: 2 cm

Important to use short bunch lengths! Wake with bunch length of 2 cm is close enough to theory

Simulated rms bunch length: 10 cm

Theory gives an impedance, simulations gives a wake potential.For HEADTAIL simulations, we need the wake function….

11 Update of the SPS impedance model G. Arduini, O. Berrig, F. Caspers, A. Grudiev, E. Métral, G....

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