Parameter Study and Coupled S-Parameter Calculations of Superconducting RF Cavities Tomasz Galek, Thomas Flisgen, Korinna Brackebusch, Kai Papke and Ursula van Rienen CST European User Conference 24.05.2012, Mannheim, Germany
Outline Introduction Motivation Simulation approach Parameter studies on HOM geometrical dependencies Geometrical Perturbation of Cavities Methods for computation of beam excited HOM port signals Acknowledgments 2
Introduction RF-Cavities, HOMs and Wakefields 3
RF-Fields and Cavities to accelerate Charged Particles Superconducting TESLA 1.3 GHz 9-cell cavity.* Input coupler to excite pimode in cavity Electric field of resonant pi mode of 3.9 GHz cavity (phase shift of π from cell to cell). *R. Wanzenberg: Monopole, Dipole and Quadrupole Passbands of the TESLA 9-cell Cavity, TESLA-Report 2001-33 4
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 5
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 6
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 7
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 8
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 9
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 10
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 11
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 12
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 13
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 14
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 15
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 16
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 17
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 18
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 19
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 20
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 21
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 22
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 23
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 24
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 25
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 26
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 27
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 28
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 29
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 30
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 31
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 32
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 33
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 34
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 35
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 36
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 37
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 38
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 39
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 40
Flip Book: Interaction Pi mode and Charged Particle* Negative test charge sees a force in longitudinal (+z) - direction due to and gains energy. *qualitative consideration 41
Total Energy gained by Charged Particle passing Cavity, where is the energy gained by particle, is the charge of particle and the electric field, seen by particle. 42
Modes of Cavity Beside π mode the cavity has an infinite set of other resonant Higher Order Modes: of arbritary chosen HOMs Charged particles travelling through cavity are able to excite Higher Order Modes! 43
Beam Excited Fields or Wakefields and HOMs Bunch of charged particles exciting wakefields (abs. value of E-Field): It is possible to decompose the wakefields as HOMs*, where is the wakefield distribution, a time dependent weighting factor and E-field distribution of HOM. *T. Weiland, R. Wanzenberg, "Wakefields and Impedances", Proceedings of the CAT-CERN Accelerator School (CCAS), pp. 140-180, 1993. 44
How long do the Fields stay in Resonator? Once the charged particle(s) have left the structure, the HOMs decay exponentially:, with for, where is time particles need to pass cavity, a constant amplitude, a constant phase shift, resonant frequency of mode and the quality factor of mode. Due to small losses in cavity, Q-factor is large and HOMs decay slowly. HOMs interact with following particles passing structure and need to be damped. 45
Couplers to damp HOMs HOM couplers power coupler HOM couplers dissipate energy of HOMs (in fact they lower Q-factor of HOMs). HOM couplers connected to matched loads on high temperature level. Ideally they do not couple to π mode. 46
Motivation 47
Motivation: Parasitical use of HOM couplers: Diagnostic System based on HOM port signals* of ACC39 mounted in FLASH String of cavities in ACC39** Information about e.g.: EDP Transversal momentum and offset of bunch Perturbances of cavity Total charge of bunch *Principle according to S. Molloy et al.: High precision superconducting cavity diagnostics with higher order mode measurements", Phys. Rev. Spec. Top. Accel. Beams 9 (2006) 112802, 2006. **Picture taken from: E. Vogel et al.: Status of the 3rd harmonic systems for FLASH and XFEL in summer 2008, Proc. LINAC 2008. 48
Motivation: Parasitical use of HOM couplers: Diagnostic System based on HOM port signals* of ACC39 mounted in FLASH String of cavities in ACC39** Information about e.g.: Beside of measurements simulations are needed for a Transversal momentum and offset of bunch better understanding of the beam excited HOM port signals EDP Perturbances of cavity Total charge of bunch *Principle according to S. Molloy et al.: High precision superconducting cavity diagnostics with higher order mode measurements", Phys. Rev. Spec. Top. Accel. Beams 9 (2006) 112802, 2006. **Picture taken from: E. Vogel et al.: Status of the 3rd harmonic systems for FLASH and XFEL in summer 2008, Proc. LINAC 2008. 49
Simulation Approach 50
Numerical Treatment of RF Structure Structure * Elements of Structure Numerical Treatment of Elements Concatenation Some advantages of decomposition: Numerical treatment of sections is less demanding than treatment of entire structure. Identical sections need to be treated only once. Efficient to simulate influence of pertubation of a segment on full structure. *Picture taken from: E. Vogel et al.: Status of the 3rd harmonic systems for FLASH and XFEL in summer 2008, Proc. LINAC 2008. 51
20 log S12(ω) Sampled S-matrices Topology information Example Coupled S-Parameter Calculation* Calculation of Segment s S-matrices using CST MWS Direct Computation CSC CSC frequency / GHz *H.-W. Glock, K. Rothemund, U. van Rienen: "CSC - A System for Coupled S-Parameter Calculations", TESLA-Report 2001-250 52
Model Validation ACC39 C1 C2 C3 C4 Measurement Simulation frequency / Hz Need to consider the whole string instead of individual cavities since HOMs can propagate through entire string 53
Parameter Studies on HOM Geometrical Dependencies using CSC 54
Third Harmonic Cavity composed of Single Cells midcell inverse length endcell Endcell Midcell 3,090,528 hexahedral cells 8 modes excited on port P1 20 modes excited on port P2 computing time*: 3h 5 min 3,130,608 hexahedral cells 20 modes excited on both ports computing time*: 6h 18 min *using CST MWS FR solver 55
S21(TE11) / db Comparison: Direct vs. Coupling Direct computation with N=8,12 Mio hexahedral mesh cells, computing time FR solver: T=11h CSC coupling of mid- and end cell elements (only TE11 mode is considered), computing time CSC: couple of seconds Parasitarical TM01 passband of direct computation frequency / Hz 56
Perturbation of a Single Cell in the Resonator Length of mid cup is 18.2167 mm instead of 19.2167 mm! 30.05.2011 Source: T. Khabibouline et al.: Higher Order Modes of a 3rd Harmonic Cavity with an Increased End-cup Iris. TESLA-FEL 2003-01, May 2003 57
S21(TE11) / db Influence of Pertubed Cell Position on HOM (1/4) perturbed cell frequency / Hz 58
S21(TE11) / db Influence of Pertubed Cell Position on HOM (2/4) perturbed cell frequency / Hz 59
S21(TE11) / db Influence of Pertubed Cell Position on HOM (3/4) perturbed cell frequency / Hz 60
S21(TE11) / db Influence of Pertubed Cell Position on HOM (4/4) perturbed cell frequency / Hz 61
S21(TE11) / db Influence of Pertubed Cell Position on HOM (4/4) perturbed cell No straight forward determinism to allocate perturbed cell in the chain based on HOM spectrum Strong dependency of second dipole passband on position of perturbed cell frequency / Hz 62
20 log S12(ω) Influence Input Coupler Reflection on HOM Spectrum Complex Reflection Factor at Input Coupler Im Transmission from left to right HOM coupler Re Reference Sweep frequency / Hz 63
20 log S12(ω) Influence Input Coupler Reflection on HOM Spectrum Complex Reflection Factor at Input Coupler Im Transmission from left to right HOM coupler Re Strong dependency of second dipole passband on reflection factor at input coupler Reference Sweep frequency / Hz 64
Cornell Design HOM damping design for BERLINPRO HOM waveguide couplers Input coupler 65
BERLINPRO : Design of the waveguide HOM couplers Identifying of HOMs propagating in 3 cavities chains HOMs Q loaded estimation using pole fitting * * H.-W. Glock, T. Galek, G. Pöplau, U. van Rienen, HOM Spectrum and Q-Factor estimations of the High-Beta CERN-SPL-Cavities, Proceedings of 1st International Particle Accelerator Con-ference (IPAC 2010), Kyoto, Japan, May 23 28, 2010 (2010): pp. 2905-2907. 66
Geometrical Perturbation of Cavities 67
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Development of Methods to Compute Beam Excited HOM Port Signals at ACC39 71
Beam Excited Fields in ACC39 For computation of HOM port signals of ACC39 the entire chain of cavities needs to be considered. Costly to discretize entire structure, but ACC39 is made of identical sub-structures (at least in ideal case). Efficient to compute (HOM) port signal contributions of substructures and concatenate those. Additional feature: sections with constant cross section can be described analytically (if lossless). Generalized CSC: Coupled Time Domain Computations* *T. Flisgen, H.-W. Glock and U. van Rienen: A Concatenation Scheme for the Computation of Beam Excited Higher Order Mode Port Signals, Proceedings of IPAC2011, San Sebastián, Spain 72
Decomposition of Structure and Concatenation Direct computation of transient beam excited port signals* using CST Particle Studio Elementwise computation of transient beam excited port signals* using CST Particle Studio Obj. 1 Obj. 2? CTC *scattered in TM01 mode 73
CTC - Proof of Principle Direct computation CTC (S-parameter computed in an interval f = 1GHz...8GHz) Direct computation * *signals filtered with low pass filter fc = 10 GHz Bunch properties: 74
CTC - Proof of Principle Direct computation CTC (S-parameter computed in an interval f = 1GHz...8GHz) Direct computation * Good agreement between direct computation and element-wise computation *signals filtered with low pass filter fc = 10 GHz Bunch properties: 75
Topology information Workflow for State Space Coupling* Solve real eigenproblem for each segment Coupling Scattering formulation of full structure in time domain* Impedance formulation of full structure in time domain *transient response available using Ordinary Differential Equations (ODE) Solver *Bachelor project of Johann Heller 76
Validation Example for State Space Coupling* Section I and III: Beampipe with antenna tip 50 3-D eigenmodes computed for modal expansion Section II: Simplified third harmonic cavity with three cells 50 3-D eigenmodes computed for modal expansion *Bachelor project of Johann Heller 77
Comparison Direct vs. State Space Coupling* *Plot courtesy of Johann Heller Considered pipe modes for expansion: 1. TE11 Pol. 1 fco = 4.3920 GHz 2. TE11 Pol. 2 fco = 4.3920 GHz 3. TM01 fco = 5.7371 GHz 4. TE21 Pol. 1 fco = 7.2858 GHz 5. TE21 Pol. 2 fco = 7.2858 GHz 6. TE01 fco = 9.1412 GHz 7. TM11 Pol. 1 fco = 9.1412 GHz 8. TM11 Pol. 2 fco = 9.1412 GHz frequency / GHz 78
Comparison Direct vs. State Space Coupling* frequency / GHz Considered pipe modes for expansion: 1. TE11 Pol. 1 fco = 4.3920 GHz 2. TE11 Pol. 2 fco = 4.3920 GHz 3. TM01 fco = 5.7371 GHz 4. TE21 Pol. 1 fco = 7.2858 GHz 5. TE21 Pol. 2 fco = 7.2858 GHz 6. TE01 fco = 9.1412 GHz 7. TM11 Pol. 1 fco = 9.1412 GHz 8. TM11 Pol. 2 fco = 9.1412 GHz Good agreement between direct computation and element-wise computation *Plot courtesy of Johann Heller 79
Acknowledgments EuCARD : European Coordination for Accelerator Research & Development, EU FP7 Research Infrastructure Grant No. 227579 DoHRo: Dortmund-HZB-Rostock Innovative Technologien und Komponenten zukünftiger Teilchenbeschleuniger in Strahlungsquellen, funding approved by German Federal Ministry of Research & Education, Project: 05K10HRC 80