1. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Scattering Parameter Calculation for the 2x7 Superstructure TESLA Collaboration Meeting INFN Frascati May 26-28, 2003 Karsten Rothemund, Dirk Hecht, Ulla van Rienen

2. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics 2x7-Superstructure 7 Cell TESLA Cavity HOM-Coupler Input-Coupler Images: I.Ibendorf Radius Adapter

3. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics 2x7-Superstructure Images: I.Ibendorf Rotation (couplers) Shift of reference planes (MAFIA simulation has tubes on both sides)

4. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Radius Adaptor 57 mm 39 mm f = 1.5 – 3.0 GHz: TTF beam pipe superstructure TE 11 (deg.) TM 01 TE 21 (deg.)

5. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics HOM-Input-Coupler antenna cone shape as in 9 cell HOM coupler (no data available in drawing) Geometry data taken from drawing „Formteil F“ (3 99 9177/D.001),[1] [1] coutesy DESY

6. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics HOM-Coupler (HOM 2 + HOM 3) HOM 2 HOM 3HOM 1 Input rotate HOM 3 shift planes 27.4 mm

7. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics 7 Cell TESLA Cavity f=1.5-3.0 GHz TE11 TM01 TE21 Plot: MWS, simulation: MAFIA, 2D, time domain f/GHz |S..|/dB f/GHz |S..|/dB

8. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Analytical Sections Rotation between HOM-Couplers Rotate reference frame of dipole and quadrupole modes length of section is 0 Wave Guide (neg. and pos.) shift reference plane of cavity shift HOM 3 to correct position

9. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Subsections SubsectionPort-Modes# of this type HOM-Input-coupler 5 + 5 + 1+1 1 HOM coupler 2 + 3 5 + 5 + 1 2 TESLA cavity5 + 5 2 Plane shift cavity5 + 54 Shift of HOM 35 + 52 Rotation5 + 54 Radius adaptor5 + 52 Total number of subsections:17 Total number of modes = S-matrix dimension:174 (to be computed for each frequency point)

10. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics CSC-Computation Calculation of overall S-matrix open ports: beam pipe, 3x HOM-, 1x Input-coupler 1500 values computed in 1.5-3 GHz frequency range shown here:2.46-2.58 GHz (3 rd dipole passband) 481 frequency-points + interpolation S-values of 7-cell cavity f/GHz |S..|/dB

11. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Results Coupling between HOM1 and HOM2 to beam pipe modes HOM1 HOM2 downstream beam pipe upstream beam pipe f/GHz |S..|/dB f/GHz |S..|/dB

12. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Results Coupling between HOM couplers Coupling between Input-coupler and beam pipe modes f/GHz |S..|/dB f/GHz |S..|/dB

13. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Timing S-Parameter CST-MicrowaveStudio TM (2.4 GHz Pentium 4, 4GB RAM): HOM-Input-Coupler: 316,160 mesh points (20 lines/lambda), 5 beam pipe modes + 2 koaxial modes Total computation time: 100 h (12 runs) HOM-Coupler: 178,920 mesh points (20 lines/lambda), 5 beampipe modes + 1 koaxial mode Total computation time: 24 h (11 runs) MAFIA (SUN Enterprise, 400 MHz, 4GB RAM): TESLA 7 cell cavity: 2D-geometry (rz) 31,158 mesh points Total computation time: 2h + 6.5h + 6.75h

14. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Timing CSC CSC: platform: Mathematica 4.1 17 subsections 5 modes in structure dimension of matrix: 174 481 frequency points, 2.46 – 2.58 GHz 430 s on Pentium 3 (1 GHz, 512 MB RAM)

15. Ursula van Rienen, Universität Rostock, FB Elektrotechnik und Informationstechnik, AG Computational Electrodynamics Summary S-parameter of 2x7 TESLA-Superstructure have been calculated (an open structure) with CSC 5 modes have been considered in the structure S-parameter of subsections were computed with CST-MicrowaveStudio TM (coupler sections, 3D) MAFIA (TESLA cavity, 2D-rz-geometry) analytically (shifting planes, rotation) some exemplary coupling parameters have been presented computation times for S-parameters of subsections in order of days additional computation times whole structure then in the order of minutes parameter tuning (e.g. rotation angles, distances) possible