Simulation of dipolar and quadrupolarwakes with CST Particle Studio

C. ZanniniIn collaboration with E. Métral, G. Rumolo, B. Salvant, and the CERN impedance team

http://sps-impedance.web.cern.ch/sps-impedance/

Overview

• Introduction and motivations

• Separation of dipolar and quadrupolar wakes– resistive wall

– kickers

• Conclusions

Introduction and motivations• In accelerator physics, impedances (and wake fields) play a key role

because they usually limit the performance of existing accelerators and need to be taken into account in the design of new machines

• The effect of impedances becomes significant when the beam intensity inside an accelerator is pushed beyond a certain threshold. Impedances are usually responsible for:– Tune shift and spread– Instabilities, emittance growth, beam loss

• To predict tune shift and instability thresholds we need to know the total impedance of a machine– Electromagnetic simulations are necessary to calculate the contribution to the

total impedance of single accelerator components– Time domain simulations are very important because the wake fields they

provide can be fed directly into macroparticle simulations in order to quantify their effects on the beam in realistic conditions

• Machine experience as well as simulations with simplified impedance models have proved that, for a correct modeling and understanding, we need to consider not only the “classical” dipolar wake fields, but also the quadrupolar components

z

y

x

z

2q 1q

s

)y,x( 11 Define the transverse position of the source particle

)y,x( 22 Define the transverse position of the test particle

1q

2q

Definition of wake potential

21 x)z(wx)z(w)z(W quaddipx

dgeneralizex −=

21 y)z(wy)z(w)z(W quaddipy

dgeneralizey +=

Why do we want to separate the dipolar and quadrupolar contribution?

The generalized wake has an impact on the coherent betatron tune shift with beam intensity

The driving wake has an impact on the dipole transverse instability threshold

21 x)z(wx)z(w)z(W quaddipx

dgeneralizex −=

21 y)z(wy)z(w)z(W quaddipy

dgeneralizey +=

First LHC tune shift measurements, courtesy B. Goddard

Overview

• Introduction and motivations

• Separation of dipolar and quadrupolar wakes– resistive wall

– kickers

• Conclusions

Separating dipolar and quadrupolar wake using CST Particle studio

21 x)z(wx)z(w)z(W quaddipx

dgeneralizex −=

21 y)z(wy)z(w)z(W quaddipy

dgeneralizey +=

Overview

• Introduction and motivations

• Separation of dipolar and quadrupolar wakes– resistive wall

– kickers

• Conclusions

2 b

2 a

babaq

+−

=Aspect ratio q:

First example of application: the resistive beam pipe

b= 1mma=3mmL=10mm

Vacuum

Conductive material

Analytical form factors of the wake functions for rectangular pipes

The values are normalized by those of the round pipe with radius b.

L

K. Yokoya. Resistive Wall Impedance of Beam Pipes of General Cross Section. Number 41. Part. Acc., 1993.

q=0.5

In the horizontal plane, Wgeneral=0, and Wdipolar=- Wquadrupolar

10 In the vertical plane, Wgeneral=3*Wquadrupolar, and Wdipolar= 2* Wquadrupolar

2 b

2 a

First example of application: the resistive beam pipe

σ

Gaussian bunch adopted as excitation signal

First example of application: the resistive beam pipe

Comparing theoretical and simulation results

First example of application: the resistive beam pipe

Comparing theoretical and simulated wake form factors

Overview

• Introduction and motivations

• Separation of dipolar and quadrupolar wakes– resistive wall

– kickers

• Conclusions

Second example of application: Simplified kicker model

Courtesy T. Kroyer

Courtesy M. Barnes

Example: Total horizontal impedance from all the SPS kickers

The theoretical predictions and simulations show similar behaviour

Example: Total vertical impedance for all the SPS kickers

The theoretical predictions and simulations show similar behavior up to 2 GHz

Overview

• Introduction and motivations

• Separation of dipolar and quadrupolar wakes– resistive wall

– kickers

• Conclusions

Conclusion and outlook• CST has proved to be reliable to disentangle dipolar and quadrupolar

component of the wake (or impedance). We are confident to use the wakefields calculated with CST as an input for beam dynamics simulationstudies.

• Results for a rectangular resistive chamber and a simplified kicker modelare in excellent agreement with theory

• Recently the results shown for the kickers have been used as inputs ofbeam dynamics simulation for SPS (HEADTAIL code). It turns out that thelarge simulated quadrupolar contributions of these kickers could explainboth the negative total (dipolar+quadrupolar) horizontal impedanceobserved in bench measurements and the positive horizontal tune shiftmeasured with the SPS beam.

• This method is being applied to more complicated accelerator structures(like cavities, equipment, instrumentation, more realistic kicker models)and will be the basis of a systematic approach to study and classifyaccelerator impedances

Status of the impedance model• Elements included in the database:

– 6.911 km beam pipe (Zotter/Metral analytical calculations for a round pipe including indirect space charge, transformed with Yokoya factor)

– 20 kickers (situation during 2006 run, analytical calculations with Tsutsui model)

– 106 BPHs (CST 3D simulations)

– 96 BPVs (CST 3D simulations)

– 2 TW 200 MHz cavities (4 sections of 11 cells) without couplers (CST 3D simulations)

– 2 TW 200 MHz cavities (5 sections of 11 cells) without couplers (CST 3D simulations)

• Some of the assumptions we need to make:– Ideal electromagnetic material properties (copper, ferrite)

– Transverse kick is linear with transverse displacement

– Simplified geometries:

kickerBeam pipeBPH

BPV

TW 200 MHz

SPS Pumping port

LHC beam screenSPS electrostatic septum

SPS Pumping port shielding and RF antenna

Other devices we are studying

Thank you for your attention!

22

Bibliography• [1]. C. Zannini, E. Métral, G. Rumolo, B. Salvant. Electromagnetic simulations of simple

models of ferrite loaded kickers. CERN-BE-Note-2010-006, 2010.

• [2]. C. Zannini, E. Métral, G. Rumolo, B. Salvant. Using CST Particle Studio simulations to obtain wake fields and impedances of accelerator structures. CERN BE-Note, to be published 2010.

• [3] B. Salvant. Impedance Model of the CERN SPS and Aspects of LHC Single-Bunch Stability. Phd thesis, EPFL, Lausanne, Switzerland, 2009.

• [4] K. Yokoya. Resistive Wall Impedance of Beam Pipes of General Cross Section. Number 41. Part. Acc., 1993.

• [5] H. Tsutsui. Some Simplified Models of Ferrite Kicker Magnet for Calculation of Longitudinal Coupling Impedance. CERN-SL-2000-004 AP, 2000.

• [6] H. Tsutsui. Transverse Coupling Impedance of a Simplified Ferrite Kicker Magnet Model. LHC Project Note 234, 2000.

• [7] L. Palumbo, V.G. Vaccaro, M. Zobov. Wake fields and impedance. LNF-94/041(P), 1994.

• [8] T. Weiland and R. Wanzenberg. Wake Fields and Impedances. DESY, M-91-06 May 1991.