CERN – TUD – GSI Webmeeting Impedance of the SIS100 Beampipe 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 1 10 November 2018 | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Prof. Dr.-Ing. Thomas Weiland

Easy geometry to compare analytical and numerical results Thin wall A Benchmark Example Easy geometry to compare analytical and numerical results Thin wall Longitudinally homogeneous structure Inner radius b=40 mm Wall thickness d=0.3 mm Length l=1 m Conductivity κ=1.4•106 Ω-1m-1 (stainless steel) Not to scale! 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 2

Analytical Results for Longitudinal Imp. Wall thickness = skindepth Al-Khateeb’s results are identical to ReWall Ohmic resistance of pipe with equivalent wall thickness Zotter Gluckstern: F: Radius of PEC boundary cylinder Source: PRSTAB 4, 024402 (2001) 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 3

Numerical Longitudinal Impedance Power Loss Calculation by CST EM STUDIO® MQS Frequency-Domain 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 4

Numerical Results for Longitudinal Imp. Solid lines: Analytical results as shown before but semilogarithmic Skindepth not resolved 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 5

Numerical Results for Longitudinal Imp. Extremely small dependence on outside domain but no saturation; saturation value is Ohmic resistance Large outside domain, easier to mesh with HEX 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 6

Transverse Impedance Restriction to v=c Restriction to dipolar impedance Longitudinally homogeneous pipe Harmonic steady state fields in Time Domain (fixed freq.) Dipolar differential (cosφ – distributed) current Thick wall approximation: Source: L. Vos, The trans. imp. of a cyl. pipe with arbit. surface imp. 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 7

Analytical Results for Transverse Imp. Wrong long. imp. due to finite outside domain ωc/2π Wall thickness = skindepth 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 8

Numerical Results for Transverse Imp. No visible influence of outside domain because dipolar fields decrease one order faster! 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 9

Finite Wire Spacing Comparison between 2 mm and 20 mm wire spacing Influence of wire spacing only for very low freq. Comparison between 2 mm and 20 mm wire spacing Relative deviation in transverse impedance result vs. freq. 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 10

Current Work (1) Design of Beampipe not yet decided! Source: Detailed Specifications for SIS 100 dipole chamber with supplementary cooling tubes / contact cooling Design of Beampipe not yet decided! 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 11

Current Work (2) Monopole: No Influence of Cooling Tubes above 90kHz Impedance Results in the Range of Ohmic Resistance / Thick Wall 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 12

Current Work (3) Dipole: Small Influence of Cooling Tubes Strange Impedance Results Currently Under Investigation 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 13

Thank you very much for your kind attention Acknowledgements Thank you very much for your kind attention Any questions or suggestions? 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 14

10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 15

Monopole Transmission Coefficient 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 16

Dipole Transmission Coefficient (Numerical) 10 November 2018 | TU Darmstadt | Fachbereich 18 | Institut Theorie Elektromagnetischer Felder | Uwe Niedermayer | 17