1. ICFA Workshop on High Order Modes in Superconducting Cavities Batavia, IL, USA, 14 th – 16 th of July 2014 Thomas Flisgen, Johann Heller and Ursula van Rienen Simulation(s and) Results for Diagnostics in (Arrangements of) 3.9 GHz Cavities

2. 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK2 Introduction, motivation and fundamental terms Challenges in computation of eigenmodes and R/Q parameters and Q ext factors in long cavity chains Actual approach: State-Space Concatenations Analysis of multi-cavity monopole and dipole modes in chains of third harmonic cavities Conclusions and outlook Outline

3. 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK3 Introduction, Motivation and a few Fundamental Terms

4. 415.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK ∏-Mode and other Eigenmodes of a Cavity three arbritarily chosen Higher Order Modes (HOMs) ∏-mode used for particle acceleration

5. 515.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Two Quantities* of Interest for Modal Analysis factor describes the energy loss through ports (Q ext factor should be large for ∏-mode and small for other modes) factor describes the interaction between modes and beam and vice versa (should be large for ∏- mode and small for other modes) *amongst other

6. 615.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Challenges in Computation of Eigenmodes, R/Q Parameters and Q ext and in Long Chains

7. 7 String of Cavities in ACC39 @ FLASH Beamline String of cavities in ACC39 mounted in FLASH* 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK ** *Picture courtesy E. Vogel et al.: "Status of the 3rd harmonic systems for FLASH and XFEL in summer 2008", Proc. LINAC 2008. **I. R. R. Shinton, N. Juntong, R. M. Jones: "Modal Dictionary of Cavity Modes for the Third Harmonic XFEL/FLASH Cavities", DESY note: DESY 12-053. Cutoff frequencies of beam pipes : 1. TE11Pol. 1f co = 4.3920 GHz 2. TE11Pol. 2f co = 4.3920 GHz 3. TM01f co = 5.7371 GHz 4. TE21Pol. 1f co = 7.2858 GHz 5. TE21Pol. 2f co = 7.2858 GHz 6. TE01f co = 9.1412 GHz 7. TM11Pol. 1f co = 9.1412 GHz 8. TM11Pol. 2f co = 9.1412 GHz 9. TE31Pol. 1f co = 10.022 GHz 10.TE31Pol. 2f co = 10.022 GHz

8. 8 C1C2 C3 C4 f / Hz Simulation (by means of S-Parameter concatenation) Previous Results: Transmission via ACC39 String computed by means of S-Matrix Concatenations (CSC) 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK H.-W. Glock, K. Rothemund, U. van Rienen: "CSC - A System for Coupled S-Parameter Calculations", TESLA-Report 2001-25 T. Flisgen, H.-W. Glock, P. Zhang, I. R. R. Shinton, N. Baboi, R. M. Jones, and U. van Rienen: "Scattering parameters of the 3.9 GHz accelerating module in a free- electron laser linac: A rigorous comparison between simulations and measurements ", Phys. Rev. ST Accel. Beams, 17:022003, February 2014 Measurement

9. 9 Eigenmodes of Cavities String in ACC39 String of cavities in ACC39 mounted in FLASH* Cutoff frequencies of beam pipes : 1. TE11Pol. 1f co = 4.3920 GHz 2. TE11Pol. 2f co = 4.3920 GHz 3. TM01f co = 5.7371 GHz 4. TE21Pol. 1f co = 7.2858 GHz 5. TE21Pol. 2f co = 7.2858 GHz 6. TE01f co = 9.1412 GHz 7. TM11Pol. 1f co = 9.1412 GHz 8. TM11Pol. 2f co = 9.1412 GHz 9. TE31Pol. 1f co = 10.022 GHz 10.TE31Pol. 2f co = 10.022 GHz ** Eigenmodes are determined by entire string Computation of eigenmodes is expensive 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK *Picture courtesy E. Vogel et al.: "Status of the 3rd harmonic systems for FLASH and XFEL in summer 2008", Proc. LINAC 2008. **I. R. R. Shinton, N. Juntong, R. M. Jones: "Modal Dictionary of Cavity Modes for the Third Harmonic XFEL/FLASH Cavities", DESY note: DESY 12-053.

10. 1015.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Concatenation Approach with Field Distributions: State-Space Concatenations* *T. Flisgen, H.-W. Glock, and U. van Rienen: "Compact Time-Domain Models of Complex RF Structures Based on the Real Eigenmodes of Segments", IEEE Transactions on Microwave Theory and Techniques, 61(6), June 2013..

11. 11 Workflow State Space Concatenations (SSC*) SSC Topology Information 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Some advantages of SSC: treatment of the individual sections is less computationally demanding identical sections need to be treated only once ** Eigenmode based Model Order Reduction Compact models of individual segments Compact model of full structure **Picture courtesy E. Vogel et al.: "Status of the 3rd harmonic systems for FLASH and XFEL in summer 2008", Proc. LINAC 2008. *T. Flisgen, H.-W. Glock, and U. van Rienen: "Compact Time-Domain Models of Complex RF Structures Based on the Real Eigenmodes of Segments", IEEE Transactions on Microwave Theory and Techniques, 61(6), June 2013.

12. 12 Secondary Quantities of Full Structure Readily Available by Compact (Reduced Order) Model 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Compact model of full structure Impedance Parameters Scattering Parameters Eigenmodes Transient Beam Excitations* *J. Heller, T. Flisgen, and U. van Rienen. Computation of wakefields and HOM port signals by means of reduced order models. In Proceedings of the 16th International Conference on RF Superconductivity 2013 (SRF 2013), pages 361 - 363, Paris, France, 2013.

13. 13 Secondary Quantities of Full Structure Readily Available by Compact (Reduced Order) Model 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Compact model of full structure Impedance Parameters Scattering Parameters Eigenmodes Entire approach is very flexible Transient Beam Excitations

14. 14 SSC in Comparison with other Coupling Methods 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK SSC[1]CSC[2]GSM[3]Mode Matching[4]Spice[5]HPC[6]... Time Domain  Frequency Domain Model Order Reduction  Arbritrary Structures and Topologies  3D Field Information  [1] T. Flisgen et al.,"Compact Time-Domain Models of Complex RF Structures Based on the Real Eigenmodes of Segments", IEEE MTT, 61(6), June 2013. [2] H.-W. Glock et al., "CSC - A procedure for coupled S-parameter calculations", IEEE Trans. Magn., 38(2), March 2002. [3] I. Shinton et al., "Large Scale Linac Simulations using a Globalised Scattering Matrix Approach ", Proc. EPAC08, Italy, 2008. [4] W. Wessel et al., "Mode-matching analysis of general waveguide multiport junctions", IEEE MTT-S Int. Microw. Symp. Dig., June 1999, vol. 3. [5] T. Wittig, et al. "Model order reduction for large systems in computational electromagnetics", LinAlgApp, vol. 415, no. 2–3, June 2006. [6] e.g. F. Yaman et al., "Comparison of Eigenvalue Solvers for Large Sparse Matrix Pencils", Proc. 11th Int. Comput. Accelerator Phys. Conf., Germany, August 2012.

15. 15 Analysis of Multi-Cavity TM 01 and TE 11 Modes in a Simplified Concatenated Arrangement of Third Harmonic Cavities with Bellows 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Simplified FLASH Chain Simplified X-FEL Chain

16. 1615.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Segments of 3 rd Harmonic Cavity Chain Computations performed on an Intel Core i5-2400 CPU @ 3.10 GHz machine equipped with 8 GB RAM meshcells = 44,436 (all symmetry planes used) meshcells = 16,758 (all symmetry planes used) Model Order Reduction (T ≈ 30 min) Model Order Reduction (T ≈ 2 min) meshcells = 1,100 (all symmetry planes used) Model Order Reduction (T < 1 min)

17. 17 Validation of State-Space Concatenations 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK

18. 1815.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Validation using R/Q Parameter for TM 01 Modes Comparison of R/Q (T ≈ 33 min) Constructing field distributions based on segment‘s eigenmodes and weighting factors (T << 1s) Computation of 136 eigenmodes of full structure with CST MWS® EM JDM Solver employing all three symmetry planes (T = 29 h) CST Template Based Post Processing Computations performed on an Intel Core i5-2400 CPU @ 3.10 GHz machine equipped with 8 GB RAM

19. 1915.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK R/Q Parameter Validation for TM 01 Modes SSC CST EM Solver

20. 2015.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Validation of External Q ext for TM 01 Modes Comparison of external Q‘s (T < 1 s) S-Parameter computation of full structure using CST MWS® FR Solver with two symmetry planes (T = 22 min) Pole Fitter** on S-Parameters (T = 2 min) (T ≈ 33 min) Concatenation of Matching Models* *T. Flisgen, J. Heller, and U. van Rienen: "Time-Domain Absorbing Boundary Terminations for Waveguide Ports Based on State-Space Models ", IEEE Transactions on Magnetics, 50(2), February 2014. **B. Gustavsen et al.: "Rational approximation of frequency domain responses by vector fitting", IEEE Trans. Power Delivery, vol. 14, no. 3, July 1999.

21. 2115.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Q ext Validation of SSC (2 nd TM01 Band) + SSC Direct approach

22. 2215.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Validation of Z-Parameter for TE 11 Modes Comparison of Impedance Parameter (T < 1 s) Z-Parameter computation of Full structure using CST MWS® FR Solver with two symmetry planes (T = 22 min) (T ≈ 33 min)

23. 2315.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Validation of Z-Parameter for TE 11 Modes Comparison of Impedance Parameter (T < 1 s) Z-Parameter computation of full structure using CST MWS® FR Solver with two symmetry planes (T = 22 min) (T ≈ 33 min) Impedance is available in terms of an analytical function in the complex angular frequency s=jω!

24. 2415.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Impedance Parameter Validation (TE 11 Modes) + SSC Direct

25. 2515.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Comparison of Modal Properties in Three Different Symmetric Arrangements employing SSC

26. 2615.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Q ext Factor Comparison (2 nd TM 01 Band)

27. 2715.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK R/Q Parameter Comparison (TM 01 Bands) First TM monopole bandSecond TM monopole band

28. 2815.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK R/Q Parameter Comparison (TM 01 Bands) First TM monopole bandSecond TM monopole band Modes in between the bands arise which have a significant R/Q

29. 2915.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK First TM monopole bandSecond TM monopole band R/Q Parameter Comparison (TM 01 Bands)

30. 3015.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Longitudinal Field Profile

31. 3115.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Longitudinal Field Profile For this mode, the generated model is used beyond its validity region, because Higher Order Mode (HOM) couplers are not considered so far.

32. 3215.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Q ext Factor Comparison (TE 11 Bands) First TE dipole bandSecond TE dipole band Third TE dipole band

33. 3315.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Q ext Factor Comparison (TE 11 Bands) First TE dipole bandSecond TE dipole band Third TE dipole band

34. 3415.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Longitudinal Field Profile (TE 11 Mode)

35. 3515.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Longitudinal Field Profile (TE 11 Mode) Mode has a resonant frequency larger than the corresponding TE 11 cutoff frequency (f co ≈ 4.39 GHz), but it is still trapped in the chain!

36. 3615.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK For this mode, the generated model is used beyond its validity region, because Higher Order Mode (HOM) couplers are not considered so far. Next step: improving the model by accounting for HOM couplers. Longitudinal Field Profile (TE 11 Mode)

37. 3715.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Z-Parameter Validation with HOM Couplers Comparison of Impedance Parameter Z-Parameter computation of full structure using CST MWS® FR Solver (T = 2 h 43 min) (T ≈ 51 min)

38. 3815.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Impedance Parameter Validation + SSC Direct Preliminary Result

39. 39 Conclusions and Outlook 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK

40. 40 Summary, Conclusions, and Outlook 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK The State-Space Concatenation approach allows for eigenmode computation of long cavity chains using workstation computers Scheme delivers (amongst others) eigenmodes, Q ext ‘s and R/Q‘s Scheme is successfully validated by means of straightforward computations Need for computation of multi-cavity modes is justified Further studies based on SSC are in preparation which account for rotational symmetry breaking HOM couplers are in preparation

41. 41 Acknowledgement 15.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK

42. 4215.07.2014T. Flisgen, J. Heller and U. van Rienen UNIVERSITÄT ROSTOCK Relative Error in R/Q Parameter (TM 01 Band) SSC CST EM Solver