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  • Simulation of dipolar and quadrupolar wakes with CST Particle Studio

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

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

    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 quaddip

    x dgeneralize

    x −=

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

    y dgeneralize

    y +=

  • 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 quaddip

    x dgeneralize

    x −=

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

    y dgeneralize

    y +=

    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 quaddip

    x dgeneralize

    x −=

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

    y dgeneralize

    y +=

  • Overview

    • Introduction and motivations

    • Separation of dipolar and quadrupolar wakes – resistive wall – kickers

    • Conclusions

  • 2 b

    2 a

    ba baq

    + −

    =Aspect ratio q:

    First example of application: the resistive beam pipe

    b= 1mm a=3mm L=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 wake fields calculated with CST as an input for beam dynamics simulation studies.

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

    • Recently the results shown for the kickers have been used as inputs of beam dynamics simulation for SPS (HEADTAIL code). It turns out that the large simulated quadrupolar contributions of these kickers could explain both the negative total (dipolar+quadrupolar) horizontal impedance observed in bench measurements and the positive horizontal tune shift measured 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 classify accelerator 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 pipe BPH

    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.

    Simulation of dipolar and quadrupolar wakes with CST Particle Studio Overview Introduction and motivations Definition of wake potential Slide Number 5 Overview Separating dipolar and quadrupolar wake using CST Particle studio Overview Slide Number 9 First example of application: the resistive beam pipe First example of application: the resistive beam pipe Slide Number 12 Overview Slide Number 14 Slide Number 15 Example: Total horizontal impedance from all the SPS kickers Example: Total vertical impedance for all the SPS kickers Overview Conclusion and outlook Status of the impedance model Slide Number 21 Thank you for your attention! Bibliography

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